3dso8.xact.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 8.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[    845358,      22613]
NotebookOptionsPosition[    832205,      22207]
NotebookOutlinePosition[    833474,      22245]
CellTagsIndexPosition[    833431,      22242]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["3d SO(8) Gauged Sugra", "Title",
 CellChangeTimes->{{3.61881732451235*^9, 3.618817333139786*^9}}],

Cell["Repeating some calculations by Deger et al using Mathematica", \
"Subtitle",
 CellChangeTimes->{{3.618817337777649*^9, 3.618817351502112*^9}}],

Cell[CellGroupData[{

Cell["Tensor Definitions", "Section",
 CellChangeTimes->{{3.617950884251278*^9, 3.617950895313588*^9}, {
  3.617951307457595*^9, 3.617951312580701*^9}}],

Cell[CellGroupData[{

Cell["Initialization", "Subsection",
 CellChangeTimes->{{3.61881282100416*^9, 3.618812824189906*^9}}],

Cell["xVect and GMFormats are packages written by GM.", "Text",
 CellChangeTimes->{{3.618113394643775*^9, 3.618113415256179*^9}, {
   3.618405934385282*^9, 3.618405942963093*^9}, 3.618550723340671*^9, {
   3.618551395829957*^9, 3.618551408965*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"<<", "GMFormats`GMFormats`"}], "\n", 
 RowBox[{
  RowBox[{"<<", "xVect`xVect`"}], ";"}]}], "Input",
 CellChangeTimes->{{3.6179478637007008`*^9, 3.6179478637021008`*^9}, {
   3.617949676990096*^9, 3.617949785824709*^9}, {3.617950412178196*^9, 
   3.617950424277273*^9}, {3.6179504949730597`*^9, 3.6179505381488523`*^9}, {
   3.6179505803030157`*^9, 3.6179505815854673`*^9}, {3.617950645562292*^9, 
   3.617950647536458*^9}, {3.6179700174364223`*^9, 3.617970019345439*^9}, {
   3.6179709236974993`*^9, 3.617970927445716*^9}, {3.6180338855628967`*^9, 
   3.618033931522093*^9}, {3.6183312679181757`*^9, 3.618331269058234*^9}, {
   3.61833179084207*^9, 3.618331808322322*^9}, {3.618332228805633*^9, 
   3.618332242240726*^9}, {3.618332461551607*^9, 3.618332480629224*^9}, {
   3.618333030394886*^9, 3.618333046130457*^9}, {3.618333171240963*^9, 
   3.618333193807788*^9}, {3.618335816145172*^9, 3.618335848340054*^9}, {
   3.618375289261096*^9, 3.618375306211822*^9}, {3.618550697370542*^9, 
   3.6185506984459343`*^9}, {3.61855141479998*^9, 3.618551416498076*^9}, {
   3.618551482820792*^9, 3.618551511015135*^9}, {3.6192687490079737`*^9, 
   3.6192687722931557`*^9}, {3.6193304815683393`*^9, 3.6193304961287813`*^9}, 
   3.620541523482638*^9, 3.620669104111685*^9, 3.620836682929792*^9, {
   3.620840359447002*^9, 3.6208403618482943`*^9}}],

Cell[CellGroupData[{

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894625132*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Package xAct`xPerm`  version \"\>", 
   "\[InvisibleSpace]", "\<\"1.2.1\"\>", "\[InvisibleSpace]", "\<\", \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"{", 
    RowBox[{"2014", ",", "2", ",", "15"}], "}"}]}],
  SequenceForm["Package xAct`xPerm`  version ", "1.2.1", ", ", {2014, 2, 15}],
  
  Editable->False]], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894644126*^9}],

Cell[BoxData["\<\"CopyRight (C) 2003-2014, Jose M. Martin-Garcia, under the \
General Public License.\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894649292*^9}],

Cell[BoxData["\<\"Connecting to external linux executable...\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894702112*^9}],

Cell[BoxData["\<\"Connection established.\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894756487*^9}],

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894758861*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Package xAct`xTensor`  version \"\>", 
   "\[InvisibleSpace]", "\<\"1.1.0\"\>", "\[InvisibleSpace]", "\<\", \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"{", 
    RowBox[{"2014", ",", "2", ",", "23"}], "}"}]}],
  SequenceForm[
  "Package xAct`xTensor`  version ", "1.1.0", ", ", {2014, 2, 23}],
  Editable->False]], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894760833*^9}],

Cell[BoxData["\<\"CopyRight (C) 2002-2014, Jose M. Martin-Garcia, under the \
General Public License.\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894762533*^9}],

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894764141*^9}],

Cell[BoxData["\<\"These packages come with ABSOLUTELY NO WARRANTY; for \
details type Disclaimer[]. This is free software, and you are welcome to \
redistribute it under certain conditions. See the General Public License for \
details.\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894766111*^9}],

Cell[BoxData["\<\"------------------------------------------------------------\
\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848894770689*^9}],

Cell[BoxData["\<\"xVect, George Moutsopoulos 2014, under GPL, personal \
version\"\>"], "Print",
 CellChangeTimes->{{3.620818691702899*^9, 3.620818720382772*^9}, 
   3.620834811132854*^9, {3.620835187935155*^9, 3.620835230408592*^9}, 
   3.6208353230823593`*^9, 3.620835742007414*^9, 3.620835834209531*^9, 
   3.620836540892741*^9, 3.62083668527566*^9, 3.620836759024602*^9, 
   3.620836902334928*^9, {3.620837003837886*^9, 3.620837015379931*^9}, 
   3.620837239880226*^9, 3.620837316792136*^9, 3.62083836691953*^9, 
   3.620838631512847*^9, 3.6208403807292633`*^9, 3.620840782832368*^9, 
   3.6208439420000362`*^9, {3.6208443546321487`*^9, 3.620844368914732*^9}, 
   3.6208446515518723`*^9, 3.620844716825259*^9, 3.620848555528328*^9, {
   3.6208488098506107`*^9, 3.6208488268321953`*^9}, 3.620848895157732*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Structures and ",
 Cell[BoxData[
  FormBox["tensors", TraditionalForm]]]
}], "Subsection",
 CellChangeTimes->{{3.6180273369209223`*^9, 3.6180273379847*^9}, {
  3.618331201515151*^9, 3.6183312070273943`*^9}, {3.618496615583426*^9, 
  3.618496619118457*^9}, {3.618551575763918*^9, 3.618551577942913*^9}}],

Cell["Mostly minus signature metric", "Text",
 CellChangeTimes->{{3.6164971435705757`*^9, 3.6164971519839067`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefManifold", "[", 
   RowBox[{"M3", ",", "3", ",", 
    RowBox[{"{", 
     RowBox[{
     "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Tau]"}], 
     "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DefMetric", "[", 
   RowBox[{"1", ",", 
    RowBox[{"g", "[", 
     RowBox[{
      RowBox[{"-", "\[Mu]"}], ",", 
      RowBox[{"-", "\[Nu]"}]}], "]"}], ",", "CD", ",", 
    RowBox[{"{", 
     RowBox[{"\"\<;\>\"", ",", "\"\<\[Del]\>\""}], "}"}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DefOrthoFrame", "[", 
   RowBox[{"viel", ",", "g"}], "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.615791842056237*^9, 3.615791882501789*^9}, 
   3.61667123785043*^9, {3.6179366687969923`*^9, 3.617936672755658*^9}, {
   3.617950454990654*^9, 3.617950478474267*^9}, {3.617950547286731*^9, 
   3.617950547422667*^9}, {3.61795058906503*^9, 3.617950589234241*^9}, 
   3.618812519665779*^9, {3.620835258985984*^9, 3.620835264228095*^9}, {
   3.6208353073889923`*^9, 3.620835308341545*^9}, {3.620837019096837*^9, 
   3.620837020870591*^9}, {3.620838650056347*^9, 3.620838652407449*^9}, {
   3.620852527034276*^9, 3.620852530622374*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefManifold", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"manifold \"\>", "\[InvisibleSpace]", "M3", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefManifold, ": Defining ", 
   "manifold ", $CellContext`M3, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895395183*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefVBundle", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vbundle \"\>", "\[InvisibleSpace]", "TangentM3", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefVBundle, ": Defining ", 
   "vbundle ", $CellContext`TangentM3, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.6208488954060383`*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"symmetric metric tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"g", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric metric tensor ", 
   xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895411343*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"antisymmetric tensor \"\>", "\[InvisibleSpace]", 
   
   RowBox[{"epsilong", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "antisymmetric tensor ", 
   $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895415303*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefCovD", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"covariant derivative \"\>", "\[InvisibleSpace]", 
   
   RowBox[{"CD", "[", 
    RowBox[{"-", "\[Mu]"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefCovD, ": Defining ", "covariant derivative ", 
   $CellContext`CD[-$CellContext`\[Mu]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895423065*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vanishing torsion tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"TorsionCD", "[", 
    RowBox[{"\[Mu]", ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "vanishing torsion tensor ", 
   $CellContext`TorsionCD[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895429675*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"symmetric Christoffel tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"ChristoffelCD", "[", 
    RowBox[{"\[Mu]", ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", 
   "symmetric Christoffel tensor ", 
   $CellContext`ChristoffelCD[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895436983*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"Riemann tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"RiemannCD", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}], ",", 
     RowBox[{"-", "\[Sigma]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "Riemann tensor ", 
   $CellContext`RiemannCD[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho], -$CellContext`\[Sigma]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895442848*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"symmetric Ricci tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"RicciCD", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric Ricci tensor ", 
   $CellContext`RicciCD[-$CellContext`\[Mu], -$CellContext`\[Nu]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895449813*^9}],

Cell[BoxData["\<\"** DefCovD:  Contractions of Riemann automatically replaced \
by Ricci.\"\>"], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.62084889576775*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"Ricci scalar \"\>", "\[InvisibleSpace]", 
   RowBox[{"RicciScalarCD", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "Ricci scalar ", 
   $CellContext`RicciScalarCD[], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895782782*^9}],

Cell[BoxData["\<\"** DefCovD:  Contractions of Ricci automatically replaced \
by RicciScalar.\"\>"], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895785881*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"symmetric Einstein tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"EinsteinCD", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", 
   "symmetric Einstein tensor ", 
   $CellContext`EinsteinCD[-$CellContext`\[Mu], -$CellContext`\[Nu]], ". ", 
   ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895795918*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vanishing Weyl tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"WeylCD", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}], ",", 
     RowBox[{"-", "\[Sigma]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "vanishing Weyl tensor ", 
   $CellContext`WeylCD[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho], -$CellContext`\[Sigma]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895802984*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"symmetric TFRicci tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"TFRicciCD", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "symmetric TFRicci tensor ", 
   $CellContext`TFRicciCD[-$CellContext`\[Mu], -$CellContext`\[Nu]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895810207*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"Kretschmann scalar \"\>", "\[InvisibleSpace]", 
   RowBox[{"KretschmannCD", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "Kretschmann scalar ", 
   $CellContext`KretschmannCD[], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895820737*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** DefCovD:  Computing RiemannToWeylRules for dim \"\>", 
   "\[InvisibleSpace]", "3"}],
  SequenceForm["** DefCovD:  Computing RiemannToWeylRules for dim ", 3],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895824841*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** DefCovD:  Computing RicciToTFRicci for dim \"\>", 
   "\[InvisibleSpace]", "3"}],
  SequenceForm["** DefCovD:  Computing RicciToTFRicci for dim ", 3],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895834847*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** DefCovD:  Computing RicciToEinsteinRules for dim \"\>", 
   "\[InvisibleSpace]", "3"}],
  SequenceForm["** DefCovD:  Computing RicciToEinsteinRules for dim ", 3],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.6208488958382587`*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"weight +2 density \"\>", "\[InvisibleSpace]", 
   RowBox[{"Detg", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"Determinant.\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "weight +2 density ", 
   $CellContext`Detg[], ". ", "Determinant."],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848827597542*^9, 3.620848895908579*^9}]
}, Open  ]]
}, Open  ]],

Cell[TextData[{
 "We define the bundle ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["V", "8"], TraditionalForm]]],
 " and its decomposition ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["V", "8"], "=", 
    RowBox[{
     SubscriptBox["V", "2"], "+", 
     SubscriptBox["V", "6"]}]}], TraditionalForm]]],
 " ",
 " (see TraceProductDummy)",
 "."
}], "Text",
 CellChangeTimes->{{3.61684760764454*^9, 3.616847662784623*^9}, {
  3.618113719469118*^9, 3.618113732224835*^9}, {3.618375822837411*^9, 
  3.6183758233882647`*^9}, {3.618551617912819*^9, 3.618551626357009*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefVBundle", "[", 
   RowBox[{"SO8V", ",", "M3", ",", "8", ",", 
    RowBox[{"{", 
     RowBox[{
     "A", ",", "B", ",", "A1", ",", "A2", ",", "A3", ",", "A4", ",", "A5", 
      ",", "A6"}], "}"}]}], "]"}], ";"}], "\n", 
 RowBox[{
  RowBox[{"DefVBundle", "[", 
   RowBox[{"SO2V", ",", "M3", ",", "2", ",", 
    RowBox[{"{", 
     RowBox[{
     "a", ",", "b", ",", "c", ",", "d", ",", "a1", ",", "a2", ",", "a3", ",", 
      "a4"}], "}"}]}], "]"}], ";"}], "\n", 
 RowBox[{
  RowBox[{"DefVBundle", "[", 
   RowBox[{"SO6V", ",", "M3", ",", "6", ",", 
    RowBox[{"{", 
     RowBox[{
     "ac", ",", "bc", ",", "dc", ",", "ec", ",", "ac1", ",", "ac2", ",", 
      "ac3", ",", "ac4"}], "}"}]}], "]"}], ";"}], "\n", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellEpilog->None,
 CellChangeTimes->{{3.616497243792274*^9, 3.6164972546555233`*^9}, {
  3.616671279012453*^9, 3.61667130013039*^9}, {3.616764848592278*^9, 
  3.616764851708679*^9}, {3.617950487081767*^9, 3.617950490603972*^9}, {
  3.617950569384286*^9, 3.617950569578141*^9}, {3.617950608064886*^9, 
  3.6179506082166767`*^9}, {3.618048813894384*^9, 3.618048836088798*^9}, {
  3.61811731198422*^9, 3.618117325643784*^9}, {3.619449632898448*^9, 
  3.619449633057473*^9}, {3.619449837513136*^9, 3.6194498386817427`*^9}, {
  3.620835276528304*^9, 3.6208353027572727`*^9}, {3.6208353764022093`*^9, 
  3.6208353859758987`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefVBundle", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vbundle \"\>", "\[InvisibleSpace]", "SO8V", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefVBundle, ": Defining ", 
   "vbundle ", $CellContext`SO8V, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.6208488282910013`*^9, 3.620848896125711*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefVBundle", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vbundle \"\>", "\[InvisibleSpace]", "SO2V", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefVBundle, ": Defining ", 
   "vbundle ", $CellContext`SO2V, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.6208488282910013`*^9, 3.620848896135179*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefVBundle", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vbundle \"\>", "\[InvisibleSpace]", "SO6V", 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefVBundle, ": Defining ", 
   "vbundle ", $CellContext`SO6V, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.6208488282910013`*^9, 3.620848896182869*^9}]
}, Open  ]]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"PrintAs", "[", "A1", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(A\), \(1\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "A2", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(A\), \(2\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "A3", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(A\), \(3\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "A4", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(A\), \(4\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "a1", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(1\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "a2", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(2\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "a3", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(3\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "a4", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(4\)]\)\>\""}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"PrintAs", "[", "ac", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(c\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "bc", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(b\), \(c\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "dc", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(d\), \(c\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "ec", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(e\), \(c\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "ac1", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(c1\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "ac2", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(c2\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "ac2", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(c2\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "ac3", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(c3\)]\)\>\""}], ";", 
  RowBox[{
   RowBox[{"PrintAs", "[", "ac4", "]"}], "^=", 
   "\"\<\!\(\*SubscriptBox[\(a\), \(c4\)]\)\>\""}], ";"}]}], "Input",
 CellChangeTimes->{{3.6194220920193644`*^9, 3.619422158879977*^9}, {
  3.619449636646833*^9, 3.619449823651597*^9}}],

Cell["We use an inner product on SO8V.", "Text",
 CellChangeTimes->{{3.618113743323332*^9, 3.618113772467392*^9}, 
   3.6185516450380917`*^9}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"delta8", "[", 
     RowBox[{
      RowBox[{"-", "A"}], ",", 
      RowBox[{"-", "B"}]}], "]"}], ",", "M3", ",", 
    RowBox[{"Symmetric", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "A"}], ",", 
       RowBox[{"-", "B"}]}], "}"}], "]"}], ",", 
    RowBox[{"PrintAs", "\[Rule]", "\"\<\[Delta]\>\""}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.616851757740706*^9, 3.61685178334496*^9}, {
   3.616851829094285*^9, 3.6168518850254*^9}, {3.6168542568469343`*^9, 
   3.616854297253009*^9}, {3.616854490332086*^9, 3.616854508486704*^9}, {
   3.616855413833912*^9, 3.616855417294372*^9}, {3.6168556749045258`*^9, 
   3.616855760341605*^9}, {3.616855934751199*^9, 3.616856014820135*^9}, {
   3.616856045645829*^9, 3.6168560481085587`*^9}, {3.616857713804235*^9, 
   3.616857837395315*^9}, 3.6168584080474052`*^9, {3.616858955172153*^9, 
   3.6168589783201447`*^9}, {3.616859033202591*^9, 3.6168590615221367`*^9}, {
   3.616859094151016*^9, 3.616859097033023*^9}, {3.616859794496254*^9, 
   3.616859798969941*^9}, 3.616865087359292*^9, {3.617944017958605*^9, 
   3.61794402955672*^9}, {3.617949175923657*^9, 3.6179491763881483`*^9}, {
   3.617950698395021*^9, 3.6179507009597683`*^9}, {3.6179718838196783`*^9, 
   3.617971893445822*^9}, {3.617971960302884*^9, 3.6179719635115643`*^9}, 
   3.61797217206644*^9, {3.617972217252124*^9, 3.617972218910068*^9}, {
   3.618064771523262*^9, 3.6180648018266563`*^9}, {3.6180653259883337`*^9, 
   3.6180653289509487`*^9}, {3.6181401935386677`*^9, 3.618140298241043*^9}, {
   3.618140347882921*^9, 3.618140367589426*^9}, {3.618140413489112*^9, 
   3.618140471573813*^9}, {3.618140514603198*^9, 3.618140530890938*^9}, {
   3.618140633091195*^9, 3.618140640475336*^9}, {3.618140689986212*^9, 
   3.6181407028096743`*^9}, {3.618140807601231*^9, 3.6181408109311867`*^9}, {
   3.618316589959816*^9, 3.618316598910903*^9}, {3.618318052985879*^9, 
   3.61831806228153*^9}, 3.6183311200881777`*^9, 3.618375848712472*^9, 
   3.618376320240664*^9, {3.6185536514265614`*^9, 3.618553655415545*^9}, {
   3.6185553806053057`*^9, 3.618555395083037*^9}, {3.618562580759345*^9, 
   3.618562587340597*^9}, {3.6185634532281237`*^9, 3.6185634564072638`*^9}, {
   3.618733748150239*^9, 3.618733766120987*^9}, 3.618733912596313*^9, {
   3.619422082292592*^9, 3.619422083353971*^9}, {3.620137838529427*^9, 
   3.62013785722677*^9}, {3.6201572979623213`*^9, 3.620157326686304*^9}, 
   3.620158138805922*^9, 3.620158302257413*^9, 3.620159173212681*^9, 
   3.6202134846488867`*^9, 3.620213633548386*^9, 3.6202138233638144`*^9, {
   3.620835420074185*^9, 3.6208354313546457`*^9}, {3.620835462083147*^9, 
   3.6208354786395197`*^9}}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"delta8", "[", 
    RowBox[{
     RowBox[{"-", "A"}], ",", 
     RowBox[{"-", "B"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`delta8[-$CellContext`A, -$CellContext`B], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.62084882868458*^9, 3.620848896478302*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{"MakeLinearMetric", "[", 
  RowBox[{"delta8", "[", 
   RowBox[{"A", ",", "B"}], "]"}], "]"}], "\n", 
 RowBox[{"MakeLinearMetric", "[", 
  RowBox[{"delta8", "[", 
   RowBox[{"a", ",", "b"}], "]"}], "]"}], "\n", 
 RowBox[{"MakeLinearMetric", "[", 
  RowBox[{"delta8", "[", 
   RowBox[{"ac", ",", "bc"}], "]"}], "]"}]}], "Input",
 CellChangeTimes->{{3.616851757740706*^9, 3.61685178334496*^9}, {
   3.616851829094285*^9, 3.6168518850254*^9}, {3.6168542568469343`*^9, 
   3.616854297253009*^9}, {3.616854490332086*^9, 3.616854508486704*^9}, {
   3.616855413833912*^9, 3.616855417294372*^9}, {3.6168556749045258`*^9, 
   3.616855760341605*^9}, {3.616855934751199*^9, 3.616856014820135*^9}, {
   3.616856045645829*^9, 3.6168560481085587`*^9}, {3.616857713804235*^9, 
   3.616857837395315*^9}, 3.6168584080474052`*^9, {3.616858955172153*^9, 
   3.6168589783201447`*^9}, {3.616859033202591*^9, 3.6168590615221367`*^9}, {
   3.616859094151016*^9, 3.616859097033023*^9}, {3.616859794496254*^9, 
   3.616859798969941*^9}, 3.616865087359292*^9, {3.617944017958605*^9, 
   3.61794402955672*^9}, {3.617949175923657*^9, 3.6179491763881483`*^9}, {
   3.617950698395021*^9, 3.6179507009597683`*^9}, {3.6179718838196783`*^9, 
   3.617971893445822*^9}, {3.617971960302884*^9, 3.6179719635115643`*^9}, 
   3.61797217206644*^9, {3.617972217252124*^9, 3.617972218910068*^9}, {
   3.618064771523262*^9, 3.6180648018266563`*^9}, {3.6180653259883337`*^9, 
   3.6180653289509487`*^9}, {3.6181401935386677`*^9, 3.618140298241043*^9}, {
   3.618140347882921*^9, 3.618140367589426*^9}, {3.618140413489112*^9, 
   3.618140471573813*^9}, {3.618140514603198*^9, 3.618140530890938*^9}, {
   3.618140633091195*^9, 3.618140640475336*^9}, {3.618140689986212*^9, 
   3.6181407028096743`*^9}, {3.618140807601231*^9, 3.6181408109311867`*^9}, {
   3.618316589959816*^9, 3.618316598910903*^9}, {3.618318052985879*^9, 
   3.61831806228153*^9}, 3.6183311200881777`*^9, 3.618375848712472*^9, 
   3.618376320240664*^9, {3.6185536514265614`*^9, 3.618553655415545*^9}, {
   3.6185553806053057`*^9, 3.618555395083037*^9}, {3.618562580759345*^9, 
   3.618562587340597*^9}, {3.6185634532281237`*^9, 3.6185634564072638`*^9}, {
   3.618733748150239*^9, 3.618733766120987*^9}, 3.618733912596313*^9, {
   3.619422082292592*^9, 3.619422083353971*^9}, {3.620137838529427*^9, 
   3.62013785722677*^9}, {3.6201572979623213`*^9, 3.620157326686304*^9}, 
   3.620158138805922*^9, 3.620158302257413*^9, 3.620159173212681*^9, 
   3.6202134846488867`*^9, 3.620213633548386*^9, 3.6202138233638144`*^9, {
   3.620835420074185*^9, 3.6208354313546457`*^9}, {3.620839063118486*^9, 
   3.6208391097229843`*^9}, {3.62083920009227*^9, 3.620839203302215*^9}}],

Cell["\<\
We define covariant derivatives on the inner space. In particular, we \
decompose the total derivative.\
\>", "Text",
 CellChangeTimes->{{3.618113788998404*^9, 3.6181138198936*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefCovD", "[", 
   RowBox[{
    RowBox[{"SO8D", "[", 
     RowBox[{"-", "\[Mu]"}], "]"}], ",", "SO8V", ",", 
    RowBox[{"{", 
     RowBox[{"\"\</\>\"", ",", "\"\<D\>\""}], "}"}], ",", 
    RowBox[{"ExtendedFrom", "\[Rule]", "CD"}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.61795240467887*^9, 3.617952519791541*^9}, {
   3.617952664624447*^9, 3.6179526804463387`*^9}, {3.617952764014586*^9, 
   3.617952768117158*^9}, 3.618048814008782*^9, {3.6180515058695498`*^9, 
   3.6180515127186604`*^9}, {3.618051543137529*^9, 3.618051550082985*^9}, 
   3.618052102156753*^9, {3.618052294133048*^9, 3.6180523234655943`*^9}, {
   3.618052425997143*^9, 3.618052431318569*^9}, 3.618065128753797*^9, {
   3.618065214721278*^9, 3.6180652743918037`*^9}, 3.6180655581811247`*^9, {
   3.61813796066422*^9, 3.61813796310747*^9}, {3.618496565471356*^9, 
   3.618496579775302*^9}, {3.6206671318606997`*^9, 3.6206671402637653`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefCovD", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"covariant derivative \"\>", "\[InvisibleSpace]", 
   
   RowBox[{"SO8D", "[", 
    RowBox[{"-", "\[Mu]"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefCovD, ": Defining ", "covariant derivative ", 
   $CellContext`SO8D[-$CellContext`\[Mu]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848828936223*^9, 3.620848896680977*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vanishing tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"ChristoffelCDSO8D", "[", 
    RowBox[{"\[Mu]", ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "vanishing tensor ", 
   $CellContext`ChristoffelCDSO8D[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848828936223*^9, 3.620848896683975*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"nonsymmetric AChristoffel tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"AChristoffelSO8D", "[", 
    RowBox[{"A", ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "A2"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", 
   "nonsymmetric AChristoffel tensor ", 
   $CellContext`AChristoffelSO8D[$CellContext`A, -$CellContext`\[Nu], \
-$CellContext`A2], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848828936223*^9, 3.620848896686791*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"FRiemann tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"FRiemannSO8D", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "A2"}], ",", "A3"}], "]"}], 
   "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"Antisymmetric only in the first pair.\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "FRiemann tensor ", 
   $CellContext`FRiemannSO8D[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`A2, $CellContext`A3], ". ", 
   "Antisymmetric only in the first pair."],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848828936223*^9, 3.620848896688983*^9}]
}, Open  ]]
}, Open  ]],

Cell["We define the tensors", "Text",
 CellChangeTimes->{{3.6168476707829638`*^9, 3.616847674861*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"V", "[", 
     RowBox[{
      RowBox[{"-", "\[Mu]"}], ",", "A", ",", "B"}], "]"}], ",", "M3", ",", 
    RowBox[{"Symmetric", "[", 
     RowBox[{"{", 
      RowBox[{"A", ",", "B"}], "}"}], "]"}]}], "]"}], ";"}], "\n", 
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"F", "[", 
     RowBox[{"A", ",", "B"}], "]"}], ",", "M3", ",", 
    RowBox[{"Antisymmetric", "[", 
     RowBox[{"{", 
      RowBox[{"A", ",", "B"}], "}"}], "]"}]}], "]"}], ";", 
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"f", "[", "]"}], ",", "M3"}], "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.615793705860653*^9, 3.615793759814927*^9}, {
   3.615794000891244*^9, 3.615794003442029*^9}, {3.616764900223632*^9, 
   3.616764903066671*^9}, {3.61676499303293*^9, 3.6167650308411207`*^9}, {
   3.617950501151054*^9, 3.617950509818241*^9}, {3.6179505739065237`*^9, 
   3.617950574065168*^9}, {3.6179506119948797`*^9, 3.6179506121488523`*^9}, 
   3.618051402599306*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"V", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", "A", ",", "B"}], "]"}], 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`V[-$CellContext`\[Mu], $CellContext`A, $CellContext`B], ". ", 
   ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848829084436*^9, 3.620848896823127*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"F", "[", 
    RowBox[{"A", ",", "B"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`F[$CellContext`A, $CellContext`B], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848829084436*^9, 3.6208488968319273`*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"f", "[", "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   xAct`xVect`f[], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848829084436*^9, 3.620848896834268*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Reducing SO(8)->SO(2)SO(6)", "Subsection",
 CellChangeTimes->{{3.6205470158467903`*^9, 3.620547017340981*^9}, {
  3.620669085364979*^9, 3.6206690934663353`*^9}}],

Cell["Some helper functions", "Text",
 CellChangeTimes->{{3.619422220733163*^9, 3.619422224997794*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"zerocomponents", "=", 
   RowBox[{
    RowBox[{"MakeZeroRuleMO", "[", 
     RowBox[{"\[Mu]", "\[Rule]", "g"}], "]"}], "[", 
    RowBox[{
     RowBox[{"V", "[", 
      RowBox[{"\[Mu]", ",", "a", ",", "ac"}], "]"}], ",", 
     RowBox[{"V", "[", 
      RowBox[{"\[Mu]", ",", "ac", ",", "a"}], "]"}], ",", 
     RowBox[{"V", "[", 
      RowBox[{"\[Mu]", ",", "ac", ",", "bc"}], "]"}], ",", 
     RowBox[{"F", "[", 
      RowBox[{"a", ",", "ac"}], "]"}], ",", 
     RowBox[{"F", "[", 
      RowBox[{"ac", ",", "a"}], "]"}], ",", 
     RowBox[{"F", "[", 
      RowBox[{"ac", ",", "bc"}], "]"}], ",", 
     RowBox[{"delta8", "[", 
      RowBox[{
       RowBox[{"-", "a"}], ",", 
       RowBox[{"-", "ac"}]}], "]"}], ",", 
     RowBox[{"delta8", "[", 
      RowBox[{
       RowBox[{"-", "ac"}], ",", 
       RowBox[{"-", "a"}]}], "]"}]}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{
  3.6194222619996862`*^9, {3.619422358786242*^9, 3.619422444427678*^9}, {
   3.620547306709092*^9, 3.620547353732765*^9}, {3.620547477571425*^9, 
   3.620547488824622*^9}, {3.620667405121544*^9, 3.6206674262974157`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"DefVSum", "[", 
   RowBox[{"SO8reduction", ",", 
    RowBox[{"{", 
     RowBox[{"SO8V", ",", 
      RowBox[{"{", 
       RowBox[{"SO2V", ",", "SO6V"}], "}"}]}], "}"}]}], "]"}], ";"}]], "Input",\

 CellChangeTimes->{{3.6206674304186573`*^9, 3.620667456896888*^9}, {
   3.6206686111102047`*^9, 3.620668635071184*^9}, {3.62084044949144*^9, 
   3.620840453037116*^9}, 3.620841240998851*^9}],

Cell[BoxData["\<\"don't forget to manually define the connections to be \
reduced and reduced components of tensors\"\>"], "Print",
 CellChangeTimes->{
  3.620841242418359*^9, 3.620841978132119*^9, 3.6208439441031113`*^9, {
   3.620844355283409*^9, 3.6208443711867657`*^9}, 3.6208446542392797`*^9, 
   3.6208447196238613`*^9, 3.620848558317762*^9, {3.620848810379429*^9, 
   3.620848829315339*^9}, 3.620848897066205*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"DefVSum", "[", 
   RowBox[{"SO8reduction", ",", "SO8D"}], "]"}], ";"}]], "Input",
 CellChangeTimes->{{3.6206674304186573`*^9, 3.620667456896888*^9}, {
  3.6206686111102047`*^9, 3.620668635071184*^9}, {3.62084044949144*^9, 
  3.620840453037116*^9}, {3.620841240998851*^9, 3.620841244647416*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefCovD", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"covariant derivative \"\>", "\[InvisibleSpace]", 
   
   RowBox[{"SO8DSO8reduction", "[", 
    RowBox[{"-", "\[Tau]$709"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefCovD, ": Defining ", "covariant derivative ", 
   $CellContext`SO8DSO8reduction[-$CellContext`\[Tau]$709], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.620848558368091*^9, {3.620848810431884*^9, 3.620848829371501*^9}, 
   3.62084889711662*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"vanishing tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"ChristoffelCDSO8DSO8reduction", "[", 
    RowBox[{"\[Mu]", ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "\[Rho]"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "vanishing tensor ", 
   $CellContext`ChristoffelCDSO8DSO8reduction[$CellContext`\[Mu], \
-$CellContext`\[Nu], -$CellContext`\[Rho]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.620848558368091*^9, {3.620848810431884*^9, 3.620848829371501*^9}, 
   3.6208488971184072`*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"nonsymmetric AChristoffel tensor \"\>", 
   "\[InvisibleSpace]", 
   RowBox[{"AChristoffelSO8DSO8reduction", "[", 
    RowBox[{"A", ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "A2"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", 
   "nonsymmetric AChristoffel tensor ", 
   $CellContext`AChristoffelSO8DSO8reduction[$CellContext`A, -$CellContext`\
\[Nu], -$CellContext`A2], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.620848558368091*^9, {3.620848810431884*^9, 3.620848829371501*^9}, 
   3.620848897122464*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"FRiemann tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"FRiemannSO8DSO8reduction", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}], ",", 
     RowBox[{"-", "A2"}], ",", "A3"}], "]"}], 
   "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"Antisymmetric only in the first pair.\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefTensor, ": Defining ", "FRiemann tensor ", 
   $CellContext`FRiemannSO8DSO8reduction[-$CellContext`\[Mu], -$CellContext`\
\[Nu], -$CellContext`A2, $CellContext`A3], ". ", 
   "Antisymmetric only in the first pair."],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.620848558368091*^9, {3.620848810431884*^9, 3.620848829371501*^9}, 
   3.620848897125208*^9}],

Cell[BoxData[
 RowBox[{"\<\"\\!\\(\\\"D\\\"\\_\\(\\*InterpretationBox[StyleBox[\\\"SO2V\\\",\
 Rule[AutoSpacing, False], Rule[ShowAutoStyles, False]], SO2V, Rule[Editable, \
False]] \[CirclePlus] \\*InterpretationBox[StyleBox[\\\"SO6V\\\", \
Rule[AutoSpacing, False], Rule[ShowAutoStyles, False]], SO6V, Rule[Editable, \
False]]\\)\\)\"\>", " ", "\<\" printed as \"\>", 
  " ", "\<\"we defined the reduced connection \"\>", " ", 
  "SO8DSO8reduction"}]], "Print",
 CellChangeTimes->{
  3.620848558368091*^9, {3.620848810431884*^9, 3.620848829371501*^9}, 
   3.620848897127994*^9}],

Cell[BoxData[
 RowBox[{"\<\"we set the components of the reduced connection one-form to \
match those of \"\>", " ", "SO8D"}]], "Print",
 CellChangeTimes->{
  3.620848558368091*^9, {3.620848810431884*^9, 3.620848829371501*^9}, 
   3.6208488972052813`*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DefVSum", "[", 
  RowBox[{"SO8reduction", ",", "zerocomponents"}], "]"}]], "Input",
 CellChangeTimes->{{3.6206674304186573`*^9, 3.620667456896888*^9}, {
   3.6206686111102047`*^9, 3.620668635071184*^9}, {3.62084044949144*^9, 
   3.620840453037116*^9}, {3.620841240998851*^9, 3.620841244647416*^9}, 
   3.620841757208029*^9}],

Cell[BoxData["\<\"rules added\"\>"], "Print",
 CellChangeTimes->{
  3.620848558546752*^9, {3.62084881047288*^9, 3.620848829437682*^9}, 
   3.6208488972722797`*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["sigma and epsilon", "Subsection",
 CellChangeTimes->{{3.619449907427382*^9, 3.619449907834915*^9}, {
  3.62029654141094*^9, 3.6202965452123613`*^9}, {3.6206690176972427`*^9, 
  3.620669026433029*^9}}],

Cell["\<\
epsilon2: we lower indices on select tensors using the lower right index for \
contraction.\
\>", "Text",
 CellChangeTimes->{{3.6186438782982407`*^9, 3.618643885033238*^9}, {
  3.6201382873973503`*^9, 3.620138386684647*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"epsilon2", "[", 
     RowBox[{
      RowBox[{"-", "a"}], ",", 
      RowBox[{"-", "b"}]}], "]"}], ",", 
    RowBox[{"{", "M3", "}"}], ",", 
    RowBox[{"Antisymmetric", "[", 
     RowBox[{"{", 
      RowBox[{"1", ",", "2"}], "}"}], "]"}], ",", 
    RowBox[{"PrintAs", "\[Rule]", "\"\<\[Epsilon]\>\""}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"$AsymMetricDownLeft", "=", 
   RowBox[{"-", "1"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"MakeLinearMetric", "[", 
   RowBox[{"epsilon2", "[", 
    RowBox[{"a", ",", "b"}], "]"}], "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.61856494389565*^9, 3.618565194839922*^9}, 
   3.618565229559638*^9, {3.6185686551676598`*^9, 3.6185686688401747`*^9}, {
   3.6185688169930162`*^9, 3.618568817348096*^9}, {3.618673511018074*^9, 
   3.618673546959231*^9}, {3.618673701025613*^9, 3.618673705035532*^9}, {
   3.618675512353363*^9, 3.618675518609913*^9}, {3.6187344823501997`*^9, 
   3.618734491048891*^9}, {3.618817808183228*^9, 3.618817810933352*^9}, {
   3.620137809125499*^9, 3.62013781221317*^9}, {3.620138146546693*^9, 
   3.6201381531306067`*^9}, {3.620138251066147*^9, 3.620138256754177*^9}}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"epsilon2", "[", 
    RowBox[{
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`epsilon2[-xAct`xVect`a, -xAct`xVect`b], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848829489579*^9, 3.6208488973199253`*^9}]
}, Open  ]],

Cell["\<\
The vector space SO2V with antisymmetric metric \[Epsilon] is a spinor space \
of Cl(1,2) and Clifford algebra given by the sigma metrices. We use epsilon2 \
for raising/lowering sigma matrix indices.\
\>", "Text",
 CellChangeTimes->{{3.6186773073690033`*^9, 3.6186773665524597`*^9}, {
   3.618677425786311*^9, 3.6186774716965723`*^9}, {3.618677961113337*^9, 
   3.61867804044137*^9}, {3.6186780778134737`*^9, 3.618678089236211*^9}, {
   3.6186781241129436`*^9, 3.61867813544665*^9}, {3.618678228686418*^9, 
   3.618678357579259*^9}, {3.61867839903636*^9, 3.618678403894267*^9}, 
   3.618678655012046*^9, {3.618680100439876*^9, 3.618680109781831*^9}, {
   3.618680337157371*^9, 3.618680343181088*^9}, {3.618681629171382*^9, 
   3.618681765678491*^9}, 3.618735287392207*^9, {3.6187353282409554`*^9, 
   3.618735345388443*^9}, {3.620138417830822*^9, 3.6201384533159723`*^9}, {
   3.620139188306531*^9, 3.620139189063731*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"sigma", "[", 
     RowBox[{"\[Mu]", ",", 
      RowBox[{"-", "a"}], ",", 
      RowBox[{"-", "b"}]}], "]"}], ",", 
    RowBox[{"{", "M3", "}"}], ",", 
    RowBox[{"Symmetric", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "a"}], ",", 
       RowBox[{"-", "b"}]}], "}"}], "]"}], ",", 
    RowBox[{"PrintAs", "\[Rule]", "\"\<\[Sigma]\>\""}]}], "]"}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.618680351416068*^9, 3.618680377367181*^9}, {
   3.618680413762548*^9, 3.618680425708168*^9}, 3.6186804936185303`*^9, {
   3.618681979928125*^9, 3.618681986728057*^9}, {3.6201384598423653`*^9, 
   3.6201384951709223`*^9}, 3.62013917732075*^9, {3.620143210891987*^9, 
   3.6201432364609423`*^9}, {3.6201432777434*^9, 3.620143396685279*^9}, 
   3.620220198792096*^9, {3.620313181921343*^9, 3.620313184812606*^9}, {
   3.620313271625477*^9, 3.620313289278224*^9}, 3.620314809294087*^9, {
   3.62054159974067*^9, 3.620541606021955*^9}}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"sigma", "[", 
    RowBox[{"\[Mu]", ",", 
     RowBox[{"-", "a"}], ",", 
     RowBox[{"-", "b"}]}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`sigma[$CellContext`\[Mu], -xAct`xVect`a, -xAct`xVect`b], ". ",
    ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.6208488297537737`*^9, 3.620848897574073*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{"rule", "=", 
   RowBox[{
    RowBox[{"MakeZeroRuleMO", "[", 
     RowBox[{"\[Mu]", "\[Rule]", "g"}], "]"}], "[", 
    RowBox[{"sigma", "[", 
     RowBox[{
      RowBox[{"-", "\[Mu]"}], ",", "c", ",", 
      RowBox[{"-", "c"}]}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"CliffordRules", "=", 
   RowBox[{
    RowBox[{"MakeVRuleMO", "[", 
     RowBox[{
      RowBox[{"\[Mu]", "\[Rule]", "g"}], ",", 
      RowBox[{"\[Nu]", "\[Rule]", "g"}], ",", 
      RowBox[{"a", "\[Rule]", "epsilon2"}], ",", 
      RowBox[{"b", "\[Rule]", "epsilon2"}]}], "]"}], "[", 
    "\[IndentingNewLine]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       RowBox[{"sigma", "[", 
        RowBox[{"\[Mu]", ",", "a", ",", 
         RowBox[{"-", "c"}]}], "]"}], 
       RowBox[{"sigma", "[", 
        RowBox[{"\[Nu]", ",", "c", ",", 
         RowBox[{"-", "b"}]}], "]"}]}], ",", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{
        RowBox[{"-", 
         RowBox[{"g", "[", 
          RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]}], 
        RowBox[{"IdDelta", "[", 
         RowBox[{"a", ",", 
          RowBox[{"-", "b"}]}], "]"}]}], "-", 
       RowBox[{
        RowBox[{
         RowBox[{"epsilon", "[", "g", "]"}], "[", 
         RowBox[{"\[Mu]", ",", "\[Nu]", ",", 
          RowBox[{"-", "\[Rho]"}]}], "]"}], 
        RowBox[{"sigma", "[", 
         RowBox[{"\[Rho]", ",", "a", ",", 
          RowBox[{"-", "b"}]}], "]"}]}]}]}], "}"}], "\[IndentingNewLine]", 
    "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"SigmaContractWithRules", "=", 
   RowBox[{"ContractTensorRule", "[", 
    RowBox[{
     RowBox[{"sigma", "[", 
      RowBox[{"\[Mu]", ",", "a", ",", "b"}], "]"}], ",", 
     RowBox[{"g", "[", 
      RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], ",", 
     RowBox[{"epsilon2", "[", 
      RowBox[{"a", ",", "b"}], "]"}]}], "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.620314820228253*^9, 3.620314933607226*^9}, {
   3.620315112776767*^9, 3.6203151266073027`*^9}, {3.620315235038856*^9, 
   3.6203152555699472`*^9}, {3.620317101178956*^9, 3.620317105564707*^9}, 
   3.620317150584858*^9, {3.620317502743082*^9, 3.620317505366905*^9}, {
   3.62031757526047*^9, 3.620317641857601*^9}, {3.620317816457984*^9, 
   3.6203178183834476`*^9}, {3.620318021990439*^9, 3.62031803405539*^9}, {
   3.6205441503159657`*^9, 3.620544154703249*^9}, {3.620544332373011*^9, 
   3.62054434234374*^9}, {3.620668699420733*^9, 3.62066876662883*^9}, {
   3.620668806706665*^9, 3.620668844481032*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"AutomaticRules", "[", 
   RowBox[{"sigma", ",", 
    RowBox[{"Join", "[", 
     RowBox[{"rule", ",", "CliffordRules", ",", "SigmaContractWithRules"}], 
     "]"}]}], "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.618680351416068*^9, 3.618680377367181*^9}, {
   3.618680413762548*^9, 3.618680425708168*^9}, 3.6186804936185303`*^9, {
   3.618681979928125*^9, 3.618681986728057*^9}, {3.6201384598423653`*^9, 
   3.6201384951709223`*^9}, 3.62013917732075*^9, {3.620143210891987*^9, 
   3.6201432364609423`*^9}, {3.6201432777434*^9, 3.620143396685279*^9}, 
   3.620220198792096*^9, {3.620313181921343*^9, 3.620313184812606*^9}, {
   3.620313271625477*^9, 3.620313289278224*^9}, {3.620314809294087*^9, 
   3.6203148134869137`*^9}, {3.620315280074974*^9, 3.620315284399785*^9}, {
   3.620317823612542*^9, 3.620317824888523*^9}, {3.620668849057136*^9, 
   3.620668876934284*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"   Rules \"\>", "\[InvisibleSpace]", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], 
   "\[InvisibleSpace]", "\<\" have been declared as DownValues for \"\>", 
   "\[InvisibleSpace]", "sigma", "\[InvisibleSpace]", "\<\".\"\>"}],
  SequenceForm["   Rules ", 
   Shallow[{1, 2, 3, 4}], 
   " have been declared as DownValues for ", $CellContext`sigma, "."],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848830595244*^9, 3.620848898417242*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"   Rules \"\>", "\[InvisibleSpace]", 
   RowBox[{"{", 
    RowBox[{
    "5", ",", "6", ",", "7", ",", "8", ",", "9", ",", "10", ",", "11", ",", 
     "12", ",", "13", ",", "14", ",", 
     RowBox[{"\[LeftSkeleton]", "102", "\[RightSkeleton]"}]}], "}"}], 
   "\[InvisibleSpace]", "\<\" have been declared as UpValues for \"\>", 
   "\[InvisibleSpace]", "sigma", "\[InvisibleSpace]", "\<\".\"\>"}],
  SequenceForm["   Rules ", 
   Shallow[{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
     23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 
    41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 
    59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 
    77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 
    95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110,
     111, 112, 113, 114, 115, 116}], 
   " have been declared as UpValues for ", $CellContext`sigma, "."],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848830595244*^9, 3.6208488987307167`*^9}]
}, Open  ]]
}, Open  ]],

Cell["\<\
The tensor F can be replaced with epsilon\
\>", "Text",
 CellChangeTimes->{{3.618811894188443*^9, 3.6188119039934072`*^9}, {
  3.620544491957213*^9, 3.620544493933114*^9}}],

Cell[BoxData[
 RowBox[{"RepF", ":=", 
  RowBox[{"Rep", "[", 
   RowBox[{
    RowBox[{"F", "[", 
     RowBox[{"a", ",", "b"}], "]"}], ",", 
    RowBox[{
     RowBox[{"f", "[", "]"}], 
     RowBox[{"epsilon2", "[", 
      RowBox[{"a", ",", "b"}], "]"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.6188119066773767`*^9, 3.618811934895339*^9}, 
   3.618811998705824*^9}],

Cell["\<\
We define Vt[-\[Mu],\[Nu]] as the preimage of V[-\[Mu],-a,-b] in Clifford.\
\>", "Text",
 CellChangeTimes->{{3.6187356657891703`*^9, 3.618735732515232*^9}, {
   3.618735878992239*^9, 3.618735879319849*^9}, {3.61873591923207*^9, 
   3.618735921910099*^9}, 3.618736294789526*^9}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"Vt", "[", 
     RowBox[{
      RowBox[{"-", "\[Mu]"}], ",", "\[Nu]"}], "]"}], ",", 
    RowBox[{"{", "M3", "}"}], ",", 
    RowBox[{"PrintAs", "\[Rule]", "\"\<V\>\""}]}], "]"}], ";"}], "\n", 
 RowBox[{
  RowBox[{"VabRules", "=", 
   RowBox[{
    RowBox[{"MakeVRuleMO", "[", 
     RowBox[{"\[Mu]", "\[Rule]", "g"}], "]"}], "[", "\[IndentingNewLine]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"V", "[", 
       RowBox[{"\[Mu]", ",", "a", ",", "b"}], "]"}], ",", 
      RowBox[{
       RowBox[{"1", "/", "2"}], 
       RowBox[{"Vt", "[", 
        RowBox[{"\[Mu]", ",", 
         RowBox[{"-", "\[Nu]"}]}], "]"}], 
       RowBox[{"sigma", "[", 
        RowBox[{"\[Nu]", ",", "a", ",", "b"}], "]"}]}]}], "}"}], 
    "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"RepVab", "[", "exp_", "]"}], ":=", 
   RowBox[{"exp", "/.", "VabRules"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.618664751582011*^9, 3.618664778680085*^9}, {
   3.620310684043717*^9, 3.620310693098773*^9}, {3.6203110475549383`*^9, 
   3.6203112423338213`*^9}, {3.620311295185143*^9, 3.6203113070166397`*^9}, {
   3.620311359269834*^9, 3.620311384880261*^9}, 3.620311486480467*^9, {
   3.6203192502758303`*^9, 3.6203192904449873`*^9}, {3.62031976542353*^9, 
   3.620319811890809*^9}, {3.620542573186838*^9, 3.6205426255107737`*^9}, 
   3.620544502366416*^9, 3.6206689634826612`*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"Vt", "[", 
    RowBox[{
     RowBox[{"-", "\[Mu]"}], ",", "\[Nu]"}], "]"}], 
   "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`Vt[-$CellContext`\[Mu], $CellContext`\[Nu]], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620848831295319*^9, 3.620848899213187*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Dump", "Section",
 CellChangeTimes->{{3.620669066570363*^9, 3.620669067229437*^9}}],

Cell[CellGroupData[{

Cell["Dump", "Subsection",
 CellChangeTimes->{{3.619449898549787*^9, 3.6194498998004513`*^9}, {
  3.620669037078741*^9, 3.620669037815564*^9}}],

Cell["\<\
We define replacement function for \[Epsilon] \[Epsilon] = \[Delta]\[Delta]-\
\[Delta]\[Delta].\
\>", "Text",
 CellChangeTimes->{{3.618675537260757*^9, 3.618675649082664*^9}, {
  3.618678510020149*^9, 3.6186785548224154`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"RepBiEps", "[", "exp_", "]"}], ":=", 
   RowBox[{"Rep", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"epsilon2", "[", 
       RowBox[{"a", ",", "b"}], "]"}], 
      RowBox[{"epsilon2", "[", 
       RowBox[{"c", ",", "d"}], "]"}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"delta8", "[", 
        RowBox[{"a", ",", "c"}], "]"}], 
       RowBox[{"delta8", "[", 
        RowBox[{"b", ",", "d"}], "]"}]}], "-", 
      RowBox[{
       RowBox[{"delta8", "[", 
        RowBox[{"a", ",", "d"}], "]"}], 
       RowBox[{"delta8", "[", 
        RowBox[{"b", ",", "c"}], "]"}]}]}]}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.61856494389565*^9, 3.618565194839922*^9}, 
   3.618565229559638*^9, {3.6185686551676598`*^9, 3.6185686688401747`*^9}, {
   3.6185688169930162`*^9, 3.618568817348096*^9}, {3.618673511018074*^9, 
   3.618673546959231*^9}, {3.618673701025613*^9, 3.618673705035532*^9}, {
   3.618675512353363*^9, 3.6186755339396763`*^9}, {3.618675809156486*^9, 
   3.6186758176643963`*^9}, {3.61867585702844*^9, 3.618675910674739*^9}, {
   3.6186759776027603`*^9, 3.618675979867075*^9}, {3.61867602388172*^9, 
   3.6186760659883738`*^9}, 3.6186784962112503`*^9, 3.618681304331748*^9, {
   3.618682657714089*^9, 3.618682705257325*^9}, 3.618735529744198*^9, {
   3.618817843404875*^9, 3.618817863451932*^9}}],

Cell["\<\
We define a function for substituting an antisymmetric expression with \
\[Epsilon] (we should avoid the latter due to the metric ambiguacy)\
\>", "Text",
 CellChangeTimes->{{3.618678561721439*^9, 3.61867857315032*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"RepAsymSO2", "[", "exp_", "]"}], ":=", 
     RowBox[{"exp", "/.", 
      RowBox[{
       RowBox[{
        RowBox[{
         RowBox[{"tens1_", "[", 
          RowBox[{"ind11___", ",", "a_", ",", "ind12___"}], "]"}], "*", 
         "tens3___", "  ", 
         RowBox[{"tens2_", "[", 
          RowBox[{"ind21___", ",", "b_", ",", "ind22___"}], "]"}]}], "-", 
        RowBox[{
         RowBox[{"tens1_", "[", 
          RowBox[{"ind11___", ",", "b_", ",", "ind12___"}], "]"}], " ", "*", 
         "tens3___", "*", 
         RowBox[{"tens2_", "[", 
          RowBox[{"ind21___", ",", "a_", ",", "ind22___"}], "]"}]}]}], ":>", 
       RowBox[{"Module", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"a1", "=", 
            RowBox[{"DummyIn", "[", "SO2V", "]"}]}], ",", 
           RowBox[{"a2", "=", 
            RowBox[{"DummyIn", "[", "SO2V", "]"}]}]}], "}"}], ",", 
         "\[IndentingNewLine]", " ", 
         RowBox[{
          RowBox[{"epsilon2", "[", 
           RowBox[{"a", ",", "b"}], "]"}], 
          RowBox[{"epsilon2", "[", 
           RowBox[{"a1", ",", "a2"}], "]"}], 
          RowBox[{"tens1", "[", 
           RowBox[{"ind11", ",", 
            RowBox[{"-", "a1"}], ",", "ind12"}], "]"}], 
          RowBox[{"tens2", "[", 
           RowBox[{"ind21", ",", 
            RowBox[{"-", "a2"}], ",", "ind22"}], "]"}], "tens3"}]}], 
        "\[IndentingNewLine]", "]"}]}]}]}], ";"}], "/;", " ", 
   RowBox[{
    RowBox[{"SO2V`Q", "[", "a", "]"}], "&&", 
    RowBox[{"SO2V`Q", "[", "b", "]"}]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.61856494389565*^9, 3.618565194839922*^9}, 
   3.618565229559638*^9, {3.6185686551676598`*^9, 3.6185686688401747`*^9}, {
   3.6185688169930162`*^9, 3.618568817348096*^9}, {3.618673511018074*^9, 
   3.618673546959231*^9}, {3.618673701025613*^9, 3.618673705035532*^9}, {
   3.618675512353363*^9, 3.6186755339396763`*^9}, {3.618675809156486*^9, 
   3.6186758176643963`*^9}, {3.61867585702844*^9, 3.618675910674739*^9}, {
   3.6186759776027603`*^9, 3.618675979867075*^9}, {3.61867602388172*^9, 
   3.6186760659883738`*^9}, 3.6186784962112503`*^9, {3.6186822123328543`*^9, 
   3.618682212955237*^9}, 3.6187355353540792`*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell["Clifford(1,2) test conventions", "Subsection",
 CellChangeTimes->{{3.618563042907981*^9, 3.618563060364201*^9}, {
   3.6186763489981527`*^9, 3.618676354838663*^9}, {3.6186772652094507`*^9, 
   3.6186772715904503`*^9}, {3.6187444436682053`*^9, 3.6187444542204943`*^9}, 
   3.6188177990299683`*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"mmdd", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "0"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "0"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"0", ",", 
         RowBox[{"-", "1"}]}], "}"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", "1"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"1", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"epsdd", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"0", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"epsuu", "=", "epsdd"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mmud", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"Sum", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"mmdd", "[", 
         RowBox[{"[", 
          RowBox[{"m", ",", "i", ",", "j"}], "]"}], "]"}], 
        RowBox[{"epsuu", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "k"}], "]"}], "]"}]}], ",", 
       RowBox[{"{", 
        RowBox[{"i", ",", "2"}], "}"}]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"m", ",", "3"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k", ",", "2"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mmdu", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"mmud", "[", 
      RowBox[{"[", 
       RowBox[{"m", ",", "i", ",", "j"}], "]"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"m", ",", "3"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "2"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"mmuu", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"Sum", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"mmud", "[", 
         RowBox[{"[", 
          RowBox[{"m", ",", "j", ",", "i"}], "]"}], "]"}], 
        RowBox[{"epsuu", "[", 
         RowBox[{"[", 
          RowBox[{"i", ",", "k"}], "]"}], "]"}]}], ",", 
       RowBox[{"{", 
        RowBox[{"i", ",", "2"}], "}"}]}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"m", ",", "3"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "2"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"k", ",", "2"}], "}"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"met3d", "=", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", 
      RowBox[{"-", "1"}], ",", 
      RowBox[{"-", "1"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Id2", "=", 
   RowBox[{"IdentityMatrix", "[", "2", "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.618743240471506*^9, 3.618743291266879*^9}, {
   3.618743349383348*^9, 3.618743387109417*^9}, {3.618743501165695*^9, 
   3.618743568107019*^9}, {3.6187436625544767`*^9, 3.618743706695394*^9}, {
   3.618743751259884*^9, 3.6187437542135563`*^9}, {3.618743802066573*^9, 
   3.61874380329956*^9}, {3.618743838484723*^9, 3.6187438668611*^9}, {
   3.6187438990881557`*^9, 3.618744111257427*^9}, {3.6187441440773163`*^9, 
   3.618744159415856*^9}, 3.6187442181536827`*^9, {3.618744288044959*^9, 
   3.61874430079062*^9}, 3.618744390280981*^9, {3.61881126044026*^9, 
   3.618811266008965*^9}, {3.618811632192973*^9, 3.618811635993771*^9}}],

Cell["Clifford Cl(1,2) mostly minus {s,s}=-2g", "Text",
 CellChangeTimes->{{3.6188113440517473`*^9, 3.618811361171379*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"Sum", "[", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"mmud", "[", 
         RowBox[{"[", 
          RowBox[{"m", ",", "i", ",", "k"}], "]"}], "]"}], 
        RowBox[{"mmud", "[", 
         RowBox[{"[", 
          RowBox[{"n", ",", "k", ",", "j"}], "]"}], "]"}]}], "+", 
       RowBox[{
        RowBox[{"mmud", "[", 
         RowBox[{"[", 
          RowBox[{"n", ",", "i", ",", "k"}], "]"}], "]"}], 
        RowBox[{"mmud", "[", 
         RowBox[{"[", 
          RowBox[{"m", ",", "k", ",", "j"}], "]"}], "]"}]}]}], ",", 
      RowBox[{"{", 
       RowBox[{"k", ",", "2"}], "}"}]}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"m", ",", "3"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"n", ",", "3"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"i", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", "2"}], "}"}]}], "]"}], "==", 
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "2"}], 
     RowBox[{"met3d", "[", 
      RowBox[{"[", 
       RowBox[{"m", ",", "n"}], "]"}], "]"}], 
     RowBox[{"Id2", "[", 
      RowBox[{"[", 
       RowBox[{"i", ",", "j"}], "]"}], "]"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"m", ",", "3"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"n", ",", "3"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"i", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", "2"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.618811363902583*^9, 3.6188115474207573`*^9}}],

Cell["Tracing two sigma matrices over spacetime indices", "Text",
 CellChangeTimes->{{3.618811298130835*^9, 3.618811333303587*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"Sum", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"mmuu", "[", 
        RowBox[{"[", 
         RowBox[{"m", ",", "i", ",", "j"}], "]"}], "]"}], 
       RowBox[{"met3d", "[", 
        RowBox[{"[", 
         RowBox[{"m", ",", "n"}], "]"}], "]"}], 
       RowBox[{"mmdd", "[", 
        RowBox[{"[", 
         RowBox[{"n", ",", "k", ",", "l"}], "]"}], "]"}]}], ",", 
      RowBox[{"{", 
       RowBox[{"m", ",", "3"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"n", ",", "3"}], "}"}]}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"i", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"k", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"l", ",", "2"}], "}"}]}], "]"}], "\[Equal]", 
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"Id2", "[", 
       RowBox[{"[", 
        RowBox[{"i", ",", "k"}], "]"}], "]"}], 
      RowBox[{"Id2", "[", 
       RowBox[{"[", 
        RowBox[{"j", ",", "l"}], "]"}], "]"}]}], "+", 
     RowBox[{
      RowBox[{"Id2", "[", 
       RowBox[{"[", 
        RowBox[{"j", ",", "k"}], "]"}], "]"}], 
      RowBox[{"Id2", "[", 
       RowBox[{"[", 
        RowBox[{"i", ",", "l"}], "]"}], "]"}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"i", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"k", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"l", ",", "2"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.618743240471506*^9, 3.618743291266879*^9}, {
   3.618743349383348*^9, 3.618743387109417*^9}, {3.618743501165695*^9, 
   3.618743568107019*^9}, {3.6187436625544767`*^9, 3.618743706695394*^9}, {
   3.618743751259884*^9, 3.6187437542135563`*^9}, {3.618743802066573*^9, 
   3.61874380329956*^9}, {3.618743838484723*^9, 3.6187438668611*^9}, {
   3.6187438990881557`*^9, 3.618744126933021*^9}, {3.6187441647093477`*^9, 
   3.618744207191476*^9}, {3.618744282125504*^9, 3.618744413308238*^9}, {
   3.618811275372711*^9, 3.618811291879287*^9}, 3.618811555672542*^9}],

Cell["The module is the one where dvol=1", "Text",
 CellChangeTimes->{{3.618811565223983*^9, 3.6188115734275923`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"mmud", "[", 
    RowBox[{"[", "1", "]"}], "]"}], ".", 
   RowBox[{"mmud", "[", 
    RowBox[{"[", "2", "]"}], "]"}], ".", 
   RowBox[{"mmud", "[", 
    RowBox[{"[", "3", "]"}], "]"}]}], "\[Equal]", "Id2"}]], "Input",
 CellChangeTimes->{{3.61881158229536*^9, 3.6188116517683496`*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell["Bases", "Subsection",
 CellChangeTimes->{{3.6180273218324137`*^9, 3.618027322839445*^9}}],

Cell["We define special bases and how they are related (xCoba)", "Text",
 CellChangeTimes->{{3.616847678867434*^9, 3.616847691448086*^9}, {
  3.617951249072321*^9, 3.617951261476204*^9}, {3.617970069305285*^9, 
  3.6179700717041807`*^9}, {3.618138803593478*^9, 3.618138806335883*^9}}],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"DefBasis", "[", 
    RowBox[{"SO8Basis", ",", "SO8V", ",", 
     RowBox[{"{", 
      RowBox[{
      "1", ",", "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", 
       "8"}], "}"}], ",", 
     RowBox[{"BasisColor", "\[Rule]", 
      RowBox[{"RGBColor", "[", 
       RowBox[{"1", ",", "0", ",", "0"}], "]"}]}]}], "]"}], ";", 
   "\[IndentingNewLine]", 
   RowBox[{"DefBasis", "[", 
    RowBox[{"SO6Basis", ",", "SO6V", ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8"}], "}"}], 
     ",", 
     RowBox[{"BasisColor", "\[Rule]", 
      RowBox[{"RGBColor", "[", 
       RowBox[{"1", ",", "0", ",", "0"}], "]"}]}]}], "]"}], ";", 
   "\[IndentingNewLine]", 
   RowBox[{"DefBasis", "[", 
    RowBox[{"SO2Basis", ",", "SO2V", ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "2"}], "}"}], ",", 
     RowBox[{"BasisColor", "\[Rule]", 
      RowBox[{"RGBColor", "[", 
       RowBox[{"1", ",", "0", ",", "0"}], "]"}]}]}], "]"}], ";", 
   "\[IndentingNewLine]", 
   RowBox[{"SplitBasis", "[", 
    RowBox[{"SO8Basis", ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"SO2Basis", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"1", ",", "2"}], "}"}]}], ",", 
       RowBox[{"SO6Basis", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8"}], 
         "}"}]}]}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", 
   RowBox[{"FoldOut", "[", "]"}]}], "*)"}]], "Input",
 CellChangeTimes->{{3.61579494024067*^9, 3.6157950596301937`*^9}, 
   3.615796897049755*^9, {3.615796968209466*^9, 3.615796968358891*^9}, {
   3.6166713891167803`*^9, 3.61667142029456*^9}, {3.6167650510677557`*^9, 
   3.616765105537636*^9}, {3.6167656070705013`*^9, 3.61676562903412*^9}, {
   3.616765666770958*^9, 3.616765690816639*^9}, {3.616772970826983*^9, 
   3.616772971299087*^9}, {3.617943181211637*^9, 3.6179431855461073`*^9}, {
   3.61795061657666*^9, 3.617950620061874*^9}, {3.6180488140340843`*^9, 
   3.618048836016233*^9}, {3.618138808694563*^9, 3.6181388141296988`*^9}}],

Cell["not sure, how to set values for subbasis", "Text",
 CellChangeTimes->{{3.61676529267754*^9, 3.6167653044891157`*^9}}],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{
   RowBox[{"ComponentValue", "[", 
    RowBox[{
     RowBox[{"ComponentArray", "[", 
      RowBox[{"F", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"a", ",", "SO2Basis"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"b", ",", "SO2Basis"}], "}"}]}], "]"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"0", ",", 
         RowBox[{"f", "[", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"f", "[", "]"}]}], ",", "0"}], "}"}]}], "}"}]}], "]"}], ";",
    "\[IndentingNewLine]", 
   RowBox[{"ComponentValue", "[", 
    RowBox[{
     RowBox[{"ComponentArray", "[", 
      RowBox[{"F", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"A", ",", "SO8Basis"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"bc", ",", "SO6Basis"}], "}"}]}], "]"}], "]"}], ",", 
     RowBox[{"Table", "[", 
      RowBox[{"0", ",", 
       RowBox[{"{", "8", "}"}], ",", 
       RowBox[{"{", "6", "}"}]}], "]"}]}], "]"}], ";", 
   RowBox[{"ComponentValue", "[", 
    RowBox[{
     RowBox[{"ComponentArray", "[", 
      RowBox[{"F", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"A", ",", "SO8Basis"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"B", ",", "SO8Basis"}], "}"}]}], "]"}], "]"}], ",", 
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"If", "[", 
        RowBox[{
         RowBox[{
          RowBox[{"i", "<", "3"}], "&&", 
          RowBox[{"j", "<", "3"}]}], ",", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", 
              RowBox[{"f", "[", "]"}]}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"f", "[", "]"}]}], ",", "0"}], "}"}]}], "}"}], "[", 
          RowBox[{"[", 
           RowBox[{"i", ",", "j"}], "]"}], "]"}], ",", "0"}], "]"}], ",", 
       RowBox[{"{", 
        RowBox[{"i", ",", "8"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"j", ",", "8"}], "}"}]}], "]"}]}], "]"}], ";"}], 
  "*)"}]], "Input",
 CellChangeTimes->{{3.6157968324706793`*^9, 3.615796951915662*^9}, 
   3.615797061527446*^9, {3.6158029738026333`*^9, 3.615802976720374*^9}, {
   3.6166714347959347`*^9, 3.6166714407551117`*^9}, {3.6167651353945093`*^9, 
   3.6167651662982283`*^9}, {3.6167652151110067`*^9, 3.616765256207797*^9}, 
   3.616765289043643*^9, {3.616777392715151*^9, 3.616777451239752*^9}, {
   3.6181388164897327`*^9, 3.61813881995362*^9}}],

Cell["ortho is an orthonormal basis", "Text",
 CellChangeTimes->{{3.618643861420764*^9, 3.618643867384495*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefBasis", "[", 
   RowBox[{"ortho", ",", "TangentM3", ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", "1", ",", "2"}], "}"}], ",", 
    RowBox[{"BasisColor", "\[Rule]", 
     RowBox[{"RGBColor", "[", 
      RowBox[{"1", ",", "0", ",", "0"}], "]"}]}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"SignatureOfMetric", "[", "g", "]"}], "^=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "0"}], "}"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"MetricInBasis", "[", 
   RowBox[{"g", ",", "ortho", ",", "\"\<Orthonormal\>\""}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"spinconn", "[", 
     RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ",", "M3", ",", 
    RowBox[{"Antisymmetric", "[", 
     RowBox[{"{", 
      RowBox[{"\[Nu]", ",", "\[Rho]"}], "}"}], "]"}], ",", 
    RowBox[{"PrintAs", "\[Rule]", "\"\<\[Omega]\>\""}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"RepOmega", "[", "ortho_", "]"}], "[", "exp_", "]"}], ":=", 
  RowBox[{"ReplaceAll", "[", 
   RowBox[{
    RowBox[{"BreakChristoffel", "[", 
     RowBox[{"exp", ",", 
      RowBox[{"(*", 
       RowBox[{
        RowBox[{
         RowBox[{"Head", "@", 
          RowBox[{
           RowBox[{"Christoffel", "[", 
            RowBox[{"PDOfBasis", "[", "ortho", "]"}], "]"}], "[", 
           RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}]}], ",", 
         "CD"}], "]"}], "*)"}], "\[IndentingNewLine]", 
      RowBox[{"GiveSymbol", "[", 
       RowBox[{"Christoffel", ",", 
        RowBox[{"PDOfBasis", "[", "ortho", "]"}]}], "]"}], ",", 
      RowBox[{"CovDOfMetric", "[", 
       RowBox[{"First", "[", "$Metrics", "]"}], "]"}]}], "]"}], ",", 
    RowBox[{
     RowBox[{
      RowBox[{"RicciRotation", "[", 
       RowBox[{
        RowBox[{"CovDOfMetric", "[", 
         RowBox[{"First", "[", "$Metrics", "]"}], "]"}], ",", "ortho"}], 
       "]"}], "[", 
      RowBox[{"\[Mu]_", ",", "\[Nu]_", ",", "\[Rho]_"}], "]"}], "\[Rule]", 
     RowBox[{"-", 
      RowBox[{"spinconn", "[", 
       RowBox[{"\[Nu]", ",", "\[Rho]", ",", "\[Mu]"}], "]"}]}]}]}], 
   "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.615808732999278*^9, 3.61580882615129*^9}, {
   3.615809011353425*^9, 3.615809012840169*^9}, {3.61676674135292*^9, 
   3.6167667749674273`*^9}, {3.6167668238141403`*^9, 3.616766854904992*^9}, {
   3.616766923892455*^9, 3.6167669392393703`*^9}, {3.616767106999011*^9, 
   3.61676722024615*^9}, {3.61676729392063*^9, 3.616767303922678*^9}, {
   3.6167673594708433`*^9, 3.616767365017312*^9}, {3.616767509725546*^9, 
   3.6167675111283007`*^9}, 3.616773081258287*^9, {3.616775636130682*^9, 
   3.616775651521689*^9}, {3.618564562388303*^9, 3.618564566537241*^9}, {
   3.619364827173915*^9, 3.6193648579925528`*^9}, 3.619365242192502*^9, {
   3.619365646301016*^9, 3.6193656559895573`*^9}, {3.619365726561389*^9, 
   3.619365780128627*^9}, {3.6193658778256187`*^9, 3.61936588465698*^9}, {
   3.619365933683111*^9, 3.619365935892556*^9}, {3.6193665208160257`*^9, 
   3.619366583563414*^9}, {3.619366624368394*^9, 3.619366650128758*^9}}]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Fierz Identities", "Section",
 CellChangeTimes->{{3.615804522522813*^9, 3.615804526792944*^9}}],

Cell[CellGroupData[{

Cell["Master Fierz Formula", "Subsection",
 CellChangeTimes->{{3.618750446130396*^9, 3.6187504497752542`*^9}, {
  3.6187505993781013`*^9, 3.6187506011278667`*^9}}],

Cell[TextData[Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["\[Epsilon]", "A"], 
    SuperscriptBox[
     OverscriptBox["\[Epsilon]", "_"], "B"]}], "=", 
   RowBox[{
    RowBox[{
     RowBox[{"1", "/", "2"}], " ", 
     SuperscriptBox["F", "BA"]}], "-", 
    RowBox[{
     RowBox[{"1", "/", "2"}], 
     SuperscriptBox["V", "\[Mu]AB"], 
     SubscriptBox["\[Gamma]", "\[Mu]"]}]}]}], TraditionalForm]]]], "Text",
 CellChangeTimes->{{3.6187504670268*^9, 3.618750577176496*^9}, {
  3.6188205598925753`*^9, 3.6188205802760277`*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell["First Fierz", "Subsection",
 CellChangeTimes->{{3.61580453088864*^9, 3.615804540774296*^9}}],

Cell["There is an antisymmetric and a symmetric projection", "Text",
 CellChangeTimes->{{3.618565297408105*^9, 3.618565310588965*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz1", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"F", "[", 
     RowBox[{"a", ",", "b"}], "]"}], 
    RowBox[{"F", "[", 
     RowBox[{"c", ",", "d"}], "]"}]}], "\[Equal]", 
   RowBox[{
    RowBox[{
     RowBox[{"1", "/", "2"}], 
     RowBox[{"F", "[", 
      RowBox[{"c", ",", "b"}], "]"}], 
     RowBox[{"F", "[", 
      RowBox[{"a", ",", "d"}], "]"}]}], "-", 
    RowBox[{
     RowBox[{"1", "/", "2"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Mu]", ",", "b", ",", "c"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", "a", ",", "d"}], "]"}]}]}]}]}]], "Input",
 CellChangeTimes->{{3.615801643323414*^9, 3.615801669775097*^9}, {
   3.615801738468585*^9, 3.6158017742486763`*^9}, {3.615801855231353*^9, 
   3.6158018828255787`*^9}, {3.615801968692749*^9, 3.615801975347904*^9}, {
   3.61580205175875*^9, 3.61580206306643*^9}, {3.615802116955782*^9, 
   3.615802187466185*^9}, {3.6158022271564302`*^9, 3.615802227720873*^9}, {
   3.615803030381114*^9, 3.615803030770978*^9}, {3.61580315790915*^9, 
   3.615803161227187*^9}, {3.615803428033462*^9, 3.6158034511241083`*^9}, 
   3.6158084455666313`*^9, {3.615808709924346*^9, 3.61580871874463*^9}, {
   3.616671477504517*^9, 3.616671478636732*^9}, {3.6167664086903477`*^9, 
   3.6167664093050127`*^9}, 3.618562955157777*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`F[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"c", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`F[xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`c, xAct`xVect`b],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{3.6202964918705187`*^9, 3.620310748545986*^9, 
  3.620319333320014*^9, 3.6205426379905043`*^9, 3.620669144830244*^9, 
  3.6208440192754374`*^9}]
}, Closed]],

Cell["The antisymmetric is trivial", "Text",
 CellChangeTimes->{{3.618565453518258*^9, 3.618565458837723*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz1", "//", "RepF"}]], "Input",
 CellChangeTimes->{{3.6185652897823067`*^9, 3.6185654407469*^9}, 
   3.618735655570798*^9, 3.618811944079879*^9, 3.618811979226515*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {"c", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[xAct`xVect`c, $CellContext`d],
    Editable->False], " ", 
   SuperscriptBox[
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], "2"]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{3.620296560322525*^9, 3.620310750281724*^9, 
  3.6203193357806797`*^9, 3.6206691548046093`*^9, 3.620844021134713*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"%", "//", 
   RowBox[{"EqTimes", "[", 
    RowBox[{"epsilon2", "[", 
     RowBox[{
      RowBox[{"-", "b"}], ",", 
      RowBox[{"-", "c"}]}], "]"}], " ", "]"}]}], "//", 
  "Simplification"}]], "Input",
 CellChangeTimes->{{3.6185652897823067`*^9, 3.6185654407469*^9}, 
   3.618735655570798*^9, 3.618811944079879*^9, 3.618811979226515*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.6202965627674026`*^9, 3.620310752489238*^9, 
  3.620319337910582*^9, 3.620669164640624*^9, 3.6208440243506413`*^9}]
}, Closed]],

Cell["The symmetric one gives orthonormality", "Text",
 CellChangeTimes->{{3.6185655007209053`*^9, 3.6185655094572773`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Fierz1", "//", "RepF"}], "\n", 
 RowBox[{"%", "//", 
  RowBox[{"EqTimes", "[", 
   RowBox[{
    RowBox[{"sigma", "[", 
     RowBox[{"\[Nu]", ",", 
      RowBox[{"-", "a"}], ",", 
      RowBox[{"-", "d"}]}], "]"}], 
    RowBox[{"sigma", "[", 
     RowBox[{"\[Sigma]", ",", 
      RowBox[{"-", "b"}], ",", 
      RowBox[{"-", "c"}]}], "]"}]}], "]"}]}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"%", "/.", "VabRules"}], "//", "Expand"}], "//", 
   "Simplification"}], "//", "ContractMetric"}]}], "Input",
 CellChangeTimes->{{3.6185654967969007`*^9, 3.618565619098237*^9}, {
   3.618565660111812*^9, 3.618565676815374*^9}, {3.618565774905571*^9, 
   3.618565802194355*^9}, {3.618565877853251*^9, 3.618565909443178*^9}, {
   3.618565993770607*^9, 3.6185660367488937`*^9}, {3.618566134264607*^9, 
   3.61856622864345*^9}, {3.618568909845284*^9, 3.618568910563472*^9}, {
   3.618568956365734*^9, 3.618568969559485*^9}, 3.618569332897909*^9, {
   3.618569388956047*^9, 3.618569419767338*^9}, 3.618569548923423*^9, {
   3.6185700008500843`*^9, 3.618570009206993*^9}, {3.61857043231866*^9, 
   3.618570433820737*^9}, {3.618664561252486*^9, 3.618664573472765*^9}, {
   3.618673875718514*^9, 3.618673894718368*^9}, {3.618673992581077*^9, 
   3.618674016221532*^9}, {3.61867404884424*^9, 3.6186742207990093`*^9}, {
   3.618674254810321*^9, 3.618674287844429*^9}, {3.618674370764353*^9, 
   3.618674381958561*^9}, {3.618682755897094*^9, 3.618682802660556*^9}, 
   3.618727417668743*^9, 3.618742204735332*^9, 3.618812155099001*^9, 
   3.620310834606298*^9, {3.62031090676258*^9, 3.620310936881522*^9}, {
   3.620311410517213*^9, 3.620311414361815*^9}, {3.620311543955021*^9, 
   3.620311544666998*^9}, {3.620311606153101*^9, 3.62031160649964*^9}, {
   3.620311786427199*^9, 3.62031180865567*^9}, {3.620311855337049*^9, 
   3.620311937608753*^9}, {3.620312607265855*^9, 3.620312615040105*^9}, 
   3.620312671181198*^9, {3.620319367029737*^9, 3.620319370001216*^9}, {
   3.620319837481874*^9, 3.620319894725018*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {"c", "d"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[xAct`xVect`c, $CellContext`d],
    Editable->False], " ", 
   SuperscriptBox[
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], "2"]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{
  3.6202965920537577`*^9, {3.620296631340794*^9, 3.620296667300642*^9}, 
   3.620310761533579*^9, {3.620310822366794*^9, 3.6203108362484293`*^9}, {
   3.620310914902645*^9, 3.620310937864242*^9}, 3.620311255432493*^9, {
   3.620311396343717*^9, 3.620311415139593*^9}, {3.62031152984754*^9, 
   3.6203115452648277`*^9}, 3.620311607044023*^9, 3.620311760543828*^9, 
   3.620311810926997*^9, {3.620311847501631*^9, 3.6203118605673437`*^9}, {
   3.620311898168933*^9, 3.620311938087593*^9}, {3.6203126111531763`*^9, 
   3.620312615667746*^9}, 3.620312672058125*^9, 3.620319340144697*^9, 
   3.620319370620791*^9, 3.620319717325108*^9, {3.6203198259442873`*^9, 
   3.620319847625936*^9}, {3.62031988284479*^9, 3.620319895387598*^9}, 
   3.620542649302446*^9, 3.620544526329739*^9, 3.6205445995800056`*^9, 
   3.620669190946398*^9, 3.620844026175598*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", "2"}], " ", 
   SuperscriptBox[
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], "2"], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"\[Sigma]", "\[Nu]"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[$CellContext`\[Sigma], $CellContext`\[Nu]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Nu]", " ", " "},
           {" ", "a", "d"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Nu], -xAct`xVect`a, -$CellContext`d],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Sigma]", " ", " "},
           {" ", "b", "c"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Sigma], -xAct`xVect`b, -xAct`xVect`c],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"a", "d"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"c", "b"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"]}], "-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "a", "d"},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {"\[Mu]", "b", "c"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6202965920537577`*^9, {3.620296631340794*^9, 3.620296667300642*^9}, 
   3.620310761533579*^9, {3.620310822366794*^9, 3.6203108362484293`*^9}, {
   3.620310914902645*^9, 3.620310937864242*^9}, 3.620311255432493*^9, {
   3.620311396343717*^9, 3.620311415139593*^9}, {3.62031152984754*^9, 
   3.6203115452648277`*^9}, 3.620311607044023*^9, 3.620311760543828*^9, 
   3.620311810926997*^9, {3.620311847501631*^9, 3.6203118605673437`*^9}, {
   3.620311898168933*^9, 3.620311938087593*^9}, {3.6203126111531763`*^9, 
   3.620312615667746*^9}, 3.620312672058125*^9, 3.620319340144697*^9, 
   3.620319370620791*^9, 3.620319717325108*^9, {3.6203198259442873`*^9, 
   3.620319847625936*^9}, {3.62031988284479*^9, 3.620319895387598*^9}, 
   3.620542649302446*^9, 3.620544526329739*^9, 3.6205445995800056`*^9, 
   3.620669190946398*^9, 3.620844026209793*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", "2"}], " ", 
   SuperscriptBox[
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], "2"], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"\[Nu]", "\[Sigma]"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[$CellContext`\[Nu], $CellContext`\[Sigma]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{"-", 
    FractionBox["1", "2"]}], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "\[Sigma]"},
           {"\[Mu]", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`Vt[-$CellContext`\[Mu], $CellContext`\[Sigma]],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {"\[Mu]", "\[Nu]"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`Vt[$CellContext`\[Mu], $CellContext`\[Nu]],
    Editable->False]}]}]], "Output",
 CellChangeTimes->{
  3.6202965920537577`*^9, {3.620296631340794*^9, 3.620296667300642*^9}, 
   3.620310761533579*^9, {3.620310822366794*^9, 3.6203108362484293`*^9}, {
   3.620310914902645*^9, 3.620310937864242*^9}, 3.620311255432493*^9, {
   3.620311396343717*^9, 3.620311415139593*^9}, {3.62031152984754*^9, 
   3.6203115452648277`*^9}, 3.620311607044023*^9, 3.620311760543828*^9, 
   3.620311810926997*^9, {3.620311847501631*^9, 3.6203118605673437`*^9}, {
   3.620311898168933*^9, 3.620311938087593*^9}, {3.6203126111531763`*^9, 
   3.620312615667746*^9}, 3.620312672058125*^9, 3.620319340144697*^9, 
   3.620319370620791*^9, 3.620319717325108*^9, {3.6203198259442873`*^9, 
   3.620319847625936*^9}, {3.62031988284479*^9, 3.620319895387598*^9}, 
   3.620542649302446*^9, 3.620544526329739*^9, 3.6205445995800056`*^9, 
   3.620669190946398*^9, 3.6208440262690907`*^9}]
}, Closed]],

Cell["\<\
We have shown that V is a vielbein and (ab) are flat 3d indices (sign \
unknown, but we confirm it later in second fierz)\
\>", "Text",
 CellChangeTimes->{{3.618676188649684*^9, 3.618676218847151*^9}, {
  3.6187610311003437`*^9, 3.618761038484847*^9}, {3.618761190206012*^9, 
  3.6187611983660803`*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell["Defining V as a Vielbein", "Subsection",
 CellChangeTimes->{{3.6188270055899887`*^9, 3.6188270086182747`*^9}, {
  3.618842552780937*^9, 3.618842561826131*^9}}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefConstantSymbol", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"constant symbol \"\>", "\[InvisibleSpace]", 
   "sign", "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefConstantSymbol, ": Defining ", 
   "constant symbol ", $CellContext`sign, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.618812213995977*^9, 3.6188129438307867`*^9, 
  3.618820350671659*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"Vt", "[", 
   RowBox[{"\[Mu]_", ",", "\[Nu]_"}], "]"}], ":=", 
  RowBox[{"2", 
   RowBox[{"f", "[", "]"}], " ", 
   RowBox[{"viel", "[", 
    RowBox[{"\[Nu]", ",", "\[Mu]"}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.6186762244999437`*^9, 3.6186762621673527`*^9}, {
   3.618676295107889*^9, 3.618676325888072*^9}, {3.618727844682177*^9, 
   3.6187278518980427`*^9}, {3.618727897733571*^9, 3.618727928123177*^9}, {
   3.618728077082672*^9, 3.618728080363401*^9}, {3.618728146397217*^9, 
   3.6187281465973673`*^9}, {3.618728179136237*^9, 3.618728198271288*^9}, 
   3.618760508888651*^9, 3.618760634432087*^9, {3.618760710887329*^9, 
   3.618760712200979*^9}, 3.618761027100328*^9, 3.6187611859564857`*^9, {
   3.618763327217497*^9, 3.618763327694648*^9}, {3.618764029213689*^9, 
   3.61876404939869*^9}, 3.618764552130322*^9, 3.618764743053461*^9, {
   3.618812218953734*^9, 3.618812219994547*^9}, 3.618826994605321*^9, {
   3.620852853131896*^9, 3.620852862960644*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Second Fierz", "Subsection",
 CellChangeTimes->{{3.6158084073127623`*^9, 3.615808409960163*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Fierz2", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"F", "[", 
     RowBox[{"a", ",", "b"}], "]"}], 
    RowBox[{"V", "[", 
     RowBox[{"\[Mu]", ",", "c", ",", "d"}], "]"}]}], "\[Equal]", 
   RowBox[{
    RowBox[{
     RowBox[{"1", "/", "2"}], 
     RowBox[{"F", "[", 
      RowBox[{"c", ",", "b"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Mu]", ",", "a", ",", "d"}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"1", "/", "2"}], " ", 
     RowBox[{"V", "[", 
      RowBox[{"\[Mu]", ",", "b", ",", "c"}], "]"}], 
     RowBox[{"F", "[", 
      RowBox[{"a", ",", "d"}], "]"}]}], "-", 
    RowBox[{
     RowBox[{"1", "/", "2"}], " ", 
     RowBox[{"epsilong", "[", 
      RowBox[{"\[Mu]", ",", 
       RowBox[{"-", "\[Nu]"}], ",", 
       RowBox[{"-", "\[Rho]"}]}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Nu]", ",", "b", ",", "c"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Rho]", ",", "a", ",", "d"}], "]"}]}]}]}]}], "\n", 
 RowBox[{"Fierz2", "=", 
  RowBox[{"Fierz2", "//", "RepVab"}]}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"%", "//", "RepF"}], "//", 
   RowBox[{"EqTimes", "[", 
    RowBox[{"1", "/", 
     RowBox[{
      RowBox[{"f", "[", "]"}], "^", "2"}]}], "]"}]}], "//", 
  "Expand"}], "\n", 
 RowBox[{"Fierz2", "=", "%"}], "\n", 
 RowBox[{"Fierz2", "//", "EqIndices"}]}], "Input",
 CellChangeTimes->{{3.6158084604436903`*^9, 3.6158084899799843`*^9}, {
   3.618750631074416*^9, 3.618750633338357*^9}, {3.618751503253003*^9, 
   3.618751505933428*^9}, 3.618751558215239*^9, {3.6187518489957447`*^9, 
   3.61875199491687*^9}, {3.618752073104312*^9, 3.6187520778586617`*^9}, {
   3.6187521154795427`*^9, 3.618752134473711*^9}, {3.618760617066682*^9, 
   3.618760617797234*^9}, {3.61876098906113*^9, 3.618760989805046*^9}, {
   3.61876442818157*^9, 3.618764440101591*^9}, {3.618764603275638*^9, 
   3.618764604853915*^9}, 3.6203119663175077`*^9, 3.6203121400687037`*^9, {
   3.620312217050871*^9, 3.62031222737216*^9}, {3.6203126419128447`*^9, 
   3.620312644650299*^9}, {3.6203126831752977`*^9, 3.620312686613311*^9}, {
   3.620319919263527*^9, 3.620319945986127*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`F[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {"\[Mu]", "c", "d"},
           {" ", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`V[$CellContext`\[Mu], xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Mu]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Mu]", " ", " "},
            {" ", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Nu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Nu], xAct`xVect`b, xAct`xVect`c],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{
  3.620311969123104*^9, 3.620312140912327*^9, 3.62031222875*^9, 
   3.6203126879003*^9, {3.620319923994254*^9, 3.620319946548057*^9}, 
   3.6205446038037987`*^9, 3.620544823618124*^9, {3.6206692093152227`*^9, 
   3.620669225046465*^9}, 3.62066932013881*^9, 3.620844032689629*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`F[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Mu]", "c", "d"},
           {" ", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Mu]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Mu]", " ", " "},
            {" ", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Nu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Nu], xAct`xVect`b, xAct`xVect`c],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{
  3.620311969123104*^9, 3.620312140912327*^9, 3.62031222875*^9, 
   3.6203126879003*^9, {3.620319923994254*^9, 3.620319946548057*^9}, 
   3.6205446038037987`*^9, 3.620544823618124*^9, {3.6206692093152227`*^9, 
   3.620669225046465*^9}, 3.62066932013881*^9, 3.620844032767033*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Mu]", "c", "d"},
           {" ", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Mu]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Mu]", " ", " "},
            {" ", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Nu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Nu], xAct`xVect`b, xAct`xVect`c],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{
  3.620311969123104*^9, 3.620312140912327*^9, 3.62031222875*^9, 
   3.6203126879003*^9, {3.620319923994254*^9, 3.620319946548057*^9}, 
   3.6205446038037987`*^9, 3.620544823618124*^9, {3.6206692093152227`*^9, 
   3.620669225046465*^9}, 3.62066932013881*^9, 3.6208440328187647`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Mu]", "c", "d"},
           {" ", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Mu]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Mu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Mu]", " ", " "},
            {" ", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Nu]", "b", "c"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Nu], xAct`xVect`b, xAct`xVect`c],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{
  3.620311969123104*^9, 3.620312140912327*^9, 3.62031222875*^9, 
   3.6203126879003*^9, {3.620319923994254*^9, 3.620319946548057*^9}, 
   3.6205446038037987`*^9, 3.620544823618124*^9, {3.6206692093152227`*^9, 
   3.620669225046465*^9}, 3.62066932013881*^9, 3.620844032884799*^9}],

Cell[BoxData[
 RowBox[{"HoldFirst", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"a", 
         RowBox[{",", "\[ThinSpace]"}], "b", 
         RowBox[{",", "\[ThinSpace]"}], "c", 
         RowBox[{",", "\[ThinSpace]"}], "d", 
         RowBox[{",", "\[ThinSpace]"}], "\[Mu]"}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[
      xAct`xVect`a, xAct`xVect`b, 
       xAct`xVect`c, $CellContext`d, $CellContext`\[Mu]],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[
       StyleBox[
        RowBox[{"{", "}"}],
        FontColor->RGBColor[0, 0, 1]],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[],
      Editable->False]}], "}"}], "\[Equal]", 
   RowBox[{"{", 
    RowBox[{
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"a", 
         RowBox[{",", "\[ThinSpace]"}], "b", 
         RowBox[{",", "\[ThinSpace]"}], "c", 
         RowBox[{",", "\[ThinSpace]"}], "d", 
         RowBox[{",", "\[ThinSpace]"}], "\[Mu]"}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[
      xAct`xVect`a, xAct`xVect`b, 
       xAct`xVect`c, $CellContext`d, $CellContext`\[Mu]],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"\[Nu]", 
         RowBox[{",", "\[ThinSpace]"}], "\[Rho]"}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[$CellContext`\[Nu], $CellContext`\[Rho]],
      Editable->False]}], "}"}]}], "]"}]], "Output",
 CellChangeTimes->{
  3.620311969123104*^9, 3.620312140912327*^9, 3.62031222875*^9, 
   3.6203126879003*^9, {3.620319923994254*^9, 3.620319946548057*^9}, 
   3.6205446038037987`*^9, 3.620544823618124*^9, {3.6206692093152227`*^9, 
   3.620669225046465*^9}, 3.62066932013881*^9, 3.620844032887108*^9}]
}, Closed]],

Cell["The symxasym part", "Text",
 CellChangeTimes->{{3.6187646913728123`*^9, 3.618764698060542*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz2sa", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"Fierz2", "//", 
     RowBox[{"EqTimes", "[", 
      RowBox[{
       RowBox[{"sigma", "[", 
        RowBox[{"\[Sigma]", ",", 
         RowBox[{"-", "a"}], ",", 
         RowBox[{"-", "b"}]}], "]"}], 
       RowBox[{"epsilon2", "[", 
        RowBox[{
         RowBox[{"-", "c"}], ",", 
         RowBox[{"-", "d"}]}], "]"}]}], "]"}]}], "//", "Expand"}], "//", 
   "Simplification"}]}]], "Input",
 CellChangeTimes->{{3.618752544520602*^9, 3.618752695139032*^9}, {
   3.618752750984404*^9, 3.6187528116160097`*^9}, {3.618755955492424*^9, 
   3.618755968423729*^9}, {3.6187596771934032`*^9, 3.618759690571992*^9}, {
   3.618760201182373*^9, 3.618760208216893*^9}, {3.618760381988593*^9, 
   3.618760424722466*^9}, {3.6188130176335573`*^9, 3.618813068472505*^9}, 
   3.618813262091831*^9, 3.618820384644835*^9, {3.618820420438559*^9, 
   3.6188204222584877`*^9}, {3.620312240964641*^9, 3.620312317513214*^9}, {
   3.620312706759115*^9, 3.620312780194495*^9}, {3.620319957950781*^9, 
   3.620319982702064*^9}, 3.620669771797007*^9, {3.620844059744665*^9, 
   3.620844060800644*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.620312252339877*^9, 3.620312318016109*^9}, 
   3.620312722037508*^9, {3.6203127616368217`*^9, 3.6203127810138197`*^9}, {
   3.6203199672773314`*^9, 3.620319983433622*^9}, 3.620544619728064*^9, 
   3.6205446767247763`*^9, {3.620544832405879*^9, 3.620544848384252*^9}, {
   3.620669217316885*^9, 3.620669220363212*^9}, 3.620669335107132*^9, 
   3.620669792939548*^9, {3.62084403750561*^9, 3.6208440629747887`*^9}}]
}, Closed]],

Cell["\<\
We have thus found the sign (orientation) of V\
\>", "Text",
 CellChangeTimes->{{3.618813310294902*^9, 3.618813328848054*^9}}],

Cell["The other symxasym part", "Text",
 CellChangeTimes->{{3.618813336072981*^9, 3.618813343866375*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Fierz2sa", "=", 
  RowBox[{"Fierz2", "//", 
   RowBox[{"EqTimes", "[", 
    RowBox[{
     RowBox[{"sigma", "[", 
      RowBox[{"\[Sigma]", ",", 
       RowBox[{"-", "c"}], ",", 
       RowBox[{"-", "d"}]}], "]"}], 
     RowBox[{"epsilon2", "[", 
      RowBox[{
       RowBox[{"-", "a"}], ",", 
       RowBox[{"-", "b"}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "Simplification"}]}], "Input",
 CellChangeTimes->{{3.618752544520602*^9, 3.618752695139032*^9}, {
   3.618752750984404*^9, 3.6187528116160097`*^9}, {3.618755955492424*^9, 
   3.618755968423729*^9}, {3.6187596771934032`*^9, 3.618759690571992*^9}, {
   3.618760201182373*^9, 3.618760208216893*^9}, {3.618760381988593*^9, 
   3.618760424722466*^9}, {3.618763942060342*^9, 3.6187639477223988`*^9}, {
   3.618820458297058*^9, 3.6188204598514338`*^9}, 3.6188270302744207`*^9, 
   3.620312327188078*^9, {3.620312787234124*^9, 3.620312838249654*^9}, 
   3.620319989607176*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"4", " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {"\[Sigma]", "\[Mu]"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[$CellContext`\[Sigma], $CellContext`\[Mu]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {" ", " "},
           {"a", "b"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[-xAct`xVect`a, -xAct`xVect`b],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"c", "b"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Mu]", "a", "d"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"a", "d"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Mu]", "b", "c"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Mu], xAct`xVect`b, xAct`xVect`c],
       Editable->False]}], "-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]g", 
           StyleBox[GridBox[{
              {"\[Mu]", " ", " "},
              {" ", "\[Nu]", "\[Rho]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilong[$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Nu]", "b", "c"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Nu], xAct`xVect`b, xAct`xVect`c],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "a", "d"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
       Editable->False]}]}], ")"}], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Sigma]", " ", " "},
           {" ", "c", "d"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Sigma], -xAct`xVect`c, -$CellContext`d],
    
    Editable->False]}]}]], "Output",
 CellChangeTimes->{
  3.620312328376412*^9, {3.6203127960645723`*^9, 3.6203128389839993`*^9}, 
   3.6203199903564997`*^9, 3.620544850687315*^9, 3.6206697963758583`*^9, 
   3.620844067948162*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{
  3.620312328376412*^9, {3.6203127960645723`*^9, 3.6203128389839993`*^9}, 
   3.6203199903564997`*^9, 3.620544850687315*^9, 3.6206697963758583`*^9, 
   3.620844067987048*^9}]
}, Closed]],

Cell["We take the symxsym part", "Text",
 CellChangeTimes->{{3.6188133916287823`*^9, 3.618813397021411*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz2ss", "=", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"Fierz2", "//", 
       RowBox[{"EqTimes", "[", 
        RowBox[{
         RowBox[{"sigma", "[", 
          RowBox[{"\[Sigma]", ",", 
           RowBox[{"-", "c"}], ",", 
           RowBox[{"-", "d"}]}], "]"}], 
         RowBox[{"sigma", "[", 
          RowBox[{"\[Tau]", ",", 
           RowBox[{"-", "a"}], ",", 
           RowBox[{"-", "b"}]}], "]"}]}], "]"}]}], "//", "Expand"}], "//", 
     "Simplification"}], "//", "ContractMetric"}], "//", 
   "Simplification"}]}]], "Input",
 CellChangeTimes->{{3.618763365599947*^9, 3.618763375792598*^9}, 
   3.618763445385129*^9, {3.618763496647911*^9, 3.618763522835834*^9}, 
   3.618763608341317*^9, {3.6187636392745447`*^9, 3.618763655697351*^9}, {
   3.618763785558229*^9, 3.6187638344201927`*^9}, {3.618763888658628*^9, 
   3.618763890579175*^9}, {3.618763971017541*^9, 3.618763974881344*^9}, 
   3.618764235096534*^9, {3.6203128475762777`*^9, 3.620312851311754*^9}, {
   3.6203200084293337`*^9, 3.620320047727786*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{
  3.6203128633091173`*^9, {3.6203129031177063`*^9, 3.6203129710299673`*^9}, 
   3.6203130217208767`*^9, {3.620320003278425*^9, 3.620320049136634*^9}, 
   3.62054485617304*^9, 3.620669813898584*^9, 3.6208440810695467`*^9}]
}, Closed]],

Cell["Finally the SymxSym part.", "Text",
 CellChangeTimes->{{3.618764356572074*^9, 3.618764367189519*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz2aa", "=", 
  RowBox[{
   RowBox[{"Fierz2", "//", 
    RowBox[{"EqTimes", "[", 
     RowBox[{
      RowBox[{"epsilon2", "[", 
       RowBox[{
        RowBox[{"-", "c"}], ",", 
        RowBox[{"-", "d"}]}], "]"}], 
      RowBox[{"epsilon2", "[", 
       RowBox[{
        RowBox[{"-", "a"}], ",", 
        RowBox[{"-", "b"}]}], "]"}]}], "]"}]}], "//", 
   "Simplification"}]}]], "Input",
 CellChangeTimes->{{3.618763390174439*^9, 3.61876339799328*^9}, {
  3.618763456545864*^9, 3.618763462829948*^9}, {3.620313035424118*^9, 
  3.62031305585361*^9}, {3.620320065783774*^9, 3.6203200669982033`*^9}}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.620313037403297*^9, 3.6203130569083443`*^9}, {
   3.620320062357635*^9, 3.6203200677045527`*^9}, 3.62054485877299*^9, 
   3.620669816218292*^9, 3.6208440833187027`*^9}]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Third Fierz", "Subsection",
 CellChangeTimes->{{3.615808415786491*^9, 3.615808417937469*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz3", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"V", "[", 
     RowBox[{
      RowBox[{"-", "\[Mu]"}], ",", "a", ",", "b"}], "]"}], 
    RowBox[{"V", "[", 
     RowBox[{
      RowBox[{"-", "\[Nu]"}], ",", "c", ",", "d"}], "]"}]}], "\[Equal]", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"-", "1"}], "/", "2"}], "  ", 
     RowBox[{
      RowBox[{"epsilon", "[", "g", "]"}], "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", 
       RowBox[{"-", "\[Nu]"}], ",", 
       RowBox[{"-", "\[Rho]"}]}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Rho]", ",", "a", ",", "d"}], "]"}], 
     RowBox[{"F", "[", 
      RowBox[{"c", ",", "b"}], "]"}]}], "-", 
    RowBox[{
     RowBox[{"1", "/", "2"}], "  ", 
     RowBox[{"g", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", 
       RowBox[{"-", "\[Nu]"}]}], "]"}], 
     RowBox[{"F", "[", 
      RowBox[{"a", ",", "d"}], "]"}], 
     RowBox[{"F", "[", 
      RowBox[{"c", ",", "b"}], "]"}]}], "-", 
    RowBox[{
     RowBox[{"1", "/", "2"}], "  ", 
     RowBox[{"g", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", 
       RowBox[{"-", "\[Nu]"}]}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Rho]", ",", "a", ",", "d"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{
       RowBox[{"-", "\[Rho]"}], ",", "c", ",", "b"}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"1", "/", "2"}], " ", 
     RowBox[{"V", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", "a", ",", "d"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{
       RowBox[{"-", "\[Nu]"}], ",", "c", ",", "b"}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"1", "/", "2"}], " ", 
     RowBox[{"V", "[", 
      RowBox[{
       RowBox[{"-", "\[Nu]"}], ",", "a", ",", "d"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", "c", ",", "b"}], "]"}]}], "+", 
    RowBox[{
     RowBox[{"1", "/", "2"}], "  ", 
     RowBox[{"epsilong", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", 
       RowBox[{"-", "\[Nu]"}], ",", 
       RowBox[{"-", "\[Rho]"}]}], "]"}], 
     RowBox[{"F", "[", 
      RowBox[{"a", ",", "d"}], "]"}], 
     RowBox[{"V", "[", 
      RowBox[{"\[Rho]", ",", "c", ",", "b"}], "]"}]}]}]}]}]], "Input",
 CellChangeTimes->{{3.615798359528105*^9, 3.615798367638307*^9}, {
   3.615801927295969*^9, 3.615801940121978*^9}, {3.615801981174584*^9, 
   3.615801984388797*^9}, {3.616767949367488*^9, 3.616767954644781*^9}, {
   3.616768009845117*^9, 3.616768087817346*^9}, {3.616768228623145*^9, 
   3.61676823085887*^9}, {3.6167683071493587`*^9, 3.6167683118089523`*^9}, {
   3.616768407325027*^9, 3.616768435900002*^9}, {3.616768474792666*^9, 
   3.616768602754382*^9}, {3.616768692264449*^9, 3.61676871456316*^9}, {
   3.616768764018116*^9, 3.616768894231081*^9}, 3.6167689431997957`*^9, 
   3.616769130675185*^9, 3.618764783674013*^9, {3.6188138384556932`*^9, 
   3.618813838651515*^9}, {3.6188139928045807`*^9, 3.618814019434392*^9}, {
   3.6188141021955547`*^9, 3.618814118993888*^9}, {3.6188180908367033`*^9, 
   3.6188181065214157`*^9}, {3.6188188074992647`*^9, 3.618818811364175*^9}, {
   3.618819414334029*^9, 3.618819457358526*^9}, {3.618819494422719*^9, 
   3.618819494859441*^9}, {3.618821179336616*^9, 3.618821229038081*^9}, {
   3.618821490404517*^9, 3.6188215027029667`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "a", "b"},
           {"\[Mu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "c", "d"},
           {"\[Nu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`V[-$CellContext`\[Nu], xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "c", "b"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Mu], xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "c", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`c, xAct`xVect`b],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "c", "b"},
            {"\[Rho]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"F", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`F[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {"\[Rho]", "c", "b"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{3.620313062386427*^9, 3.620320071191886*^9, 
  3.6205448607068872`*^9, 3.6206698213914948`*^9, 3.620844085834359*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Fierz3", "=", 
  RowBox[{
   RowBox[{"Fierz3", "//", "RepF"}], "//", "RepVab"}]}]], "Input",
 CellChangeTimes->{{3.615798359528105*^9, 3.615798367638307*^9}, {
   3.615801927295969*^9, 3.615801940121978*^9}, {3.615801981174584*^9, 
   3.615801984388797*^9}, {3.616767949367488*^9, 3.616767954644781*^9}, {
   3.616768009845117*^9, 3.616768087817346*^9}, {3.616768228623145*^9, 
   3.61676823085887*^9}, {3.6167683071493587`*^9, 3.6167683118089523`*^9}, {
   3.616768407325027*^9, 3.616768435900002*^9}, {3.616768474792666*^9, 
   3.616768602754382*^9}, {3.616768692264449*^9, 3.61676871456316*^9}, {
   3.616768764018116*^9, 3.616768894231081*^9}, 3.6167689431997957`*^9, 
   3.616769130675185*^9, 3.618764783674013*^9, {3.61881434903979*^9, 
   3.618814366673049*^9}, {3.6188144000051517`*^9, 3.618814402092794*^9}, 
   3.620313065915941*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SuperscriptBox[
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], "2"], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {" ", "a", "b"},
           {"\[Mu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`a, xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {" ", "c", "d"},
           {"\[Nu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`c, $CellContext`d],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "c", "b"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", "d"},
            {"\[Mu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "c", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`c, xAct`xVect`b],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"c", "b"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "c", "b"},
            {"\[Rho]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", "d"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
     Editable->False]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", "d"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "c", "b"},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{3.620313066594376*^9, 3.620320073672867*^9, 
  3.620544863449151*^9, 3.620669826209189*^9, 3.6208440890867853`*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Fierz3aa", "=", 
  RowBox[{"Fierz3", "//", 
   RowBox[{"EqTimes", "[", 
    RowBox[{
     RowBox[{"epsilon2", "[", 
      RowBox[{
       RowBox[{"-", "a"}], ",", 
       RowBox[{"-", "b"}]}], "]"}], 
     RowBox[{"epsilon2", "[", 
      RowBox[{
       RowBox[{"-", "c"}], ",", 
       RowBox[{"-", "d"}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "Simplification"}]}], "Input",
 CellChangeTimes->{{3.618814494567791*^9, 3.618814546823015*^9}, {
   3.6188182422598543`*^9, 3.618818294653769*^9}, {3.618818325331287*^9, 
   3.618818359981021*^9}, {3.6188189981842747`*^9, 3.618819000294868*^9}, 
   3.618819071703003*^9, {3.6188195893414783`*^9, 3.618819615474454*^9}, {
   3.618820712022986*^9, 3.61882071876108*^9}, {3.618820802075615*^9, 
   3.618820831423643*^9}, {3.620313076238682*^9, 3.620313082333755*^9}, {
   3.6203132062142153`*^9, 3.6203132113227654`*^9}, 3.6205448714725237`*^9}],

Cell[BoxData[
 RowBox[{"0", "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {" ", " "},
           {"a", "b"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[-xAct`xVect`a, -xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {" ", " "},
           {"c", "d"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[-xAct`xVect`c, -$CellContext`d],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FractionBox["1", "2"]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"a", "d"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"c", "b"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"g", 
           StyleBox[GridBox[{
              {" ", " "},
              {"\[Mu]", "\[Nu]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "c", "b"},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "d"},
              {"\[Nu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "d"},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "c", "b"},
              {"\[Nu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`c, xAct`xVect`b],
       Editable->False]}], "-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"c", "b"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]g", 
           StyleBox[GridBox[{
              {" ", " ", " "},
              {"\[Mu]", "\[Nu]", "\[Rho]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "a", "d"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"g", 
           StyleBox[GridBox[{
              {" ", " "},
              {"\[Mu]", "\[Nu]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "c", "b"},
              {"\[Rho]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "a", "d"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"a", "d"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]g", 
           StyleBox[GridBox[{
              {" ", " ", " "},
              {"\[Mu]", "\[Nu]", "\[Rho]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "c", "b"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6203130830008383`*^9, {3.62031319689439*^9, 3.620313211891635*^9}, 
   3.620313299516923*^9, 3.620320083451693*^9, {3.6205448654572783`*^9, 
   3.620544872437037*^9}, 3.620669834088703*^9, 3.620844091026667*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{
  3.6203130830008383`*^9, {3.62031319689439*^9, 3.620313211891635*^9}, 
   3.620313299516923*^9, 3.620320083451693*^9, {3.6205448654572783`*^9, 
   3.620544872437037*^9}, 3.620669834088703*^9, 3.620844091059977*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   RowBox[{"Fierz3as", "=", 
    RowBox[{"Fierz3", "//", 
     RowBox[{"EqTimes", "[", 
      RowBox[{
       RowBox[{"epsilon2", "[", 
        RowBox[{
         RowBox[{"-", "a"}], ",", 
         RowBox[{"-", "b"}]}], "]"}], 
       RowBox[{"sigma", "[", 
        RowBox[{"\[Sigma]", ",", 
         RowBox[{"-", "c"}], ",", 
         RowBox[{"-", "d"}]}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"%", "//", "Simplification"}], "//", "ToCanonical"}]}]}]], "Input",\

 CellChangeTimes->{
  3.618821287697701*^9, {3.618821519306415*^9, 3.618821572132066*^9}, {
   3.618821603281888*^9, 3.6188216787772827`*^9}, {3.6203133083461523`*^9, 
   3.620313352819106*^9}, {3.620320090399932*^9, 3.620320102156722*^9}}],

Cell[BoxData[
 RowBox[{"0", "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Epsilon]", 
        StyleBox[GridBox[{
           {" ", " "},
           {"a", "b"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`epsilon2[-xAct`xVect`a, -xAct`xVect`b],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FractionBox["1", "2"]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"a", "d"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"c", "b"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"g", 
           StyleBox[GridBox[{
              {" ", " "},
              {"\[Mu]", "\[Nu]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "c", "b"},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "d"},
              {"\[Nu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "d"},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "c", "b"},
              {"\[Nu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`c, xAct`xVect`b],
       Editable->False]}], "-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"c", "b"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]g", 
           StyleBox[GridBox[{
              {" ", " ", " "},
              {"\[Mu]", "\[Nu]", "\[Rho]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "a", "d"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "-", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"g", 
           StyleBox[GridBox[{
              {" ", " "},
              {"\[Mu]", "\[Nu]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "c", "b"},
              {"\[Rho]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "a", "d"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`d],
       Editable->False]}], "+", 
     RowBox[{
      FractionBox["1", "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]", 
           StyleBox[GridBox[{
              {"a", "d"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilon2[xAct`xVect`a, $CellContext`d],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Epsilon]g", 
           StyleBox[GridBox[{
              {" ", " ", " "},
              {"\[Mu]", "\[Nu]", "\[Rho]"}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
       Editable->False], " ", 
      SuperscriptBox[
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False], "2"], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {"\[Rho]", "c", "b"},
              {" ", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`c, xAct`xVect`b],
       Editable->False]}]}], ")"}], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {"\[Sigma]", " ", " "},
           {" ", "c", "d"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[$CellContext`\[Sigma], -xAct`xVect`c, -$CellContext`d],
    
    Editable->False]}]}]], "Output",
 CellChangeTimes->{{3.6203133171335783`*^9, 3.620313354926805*^9}, {
   3.620320086942058*^9, 3.620320102727682*^9}, 3.620544876847466*^9, 
   3.620669836799911*^9, 3.620844093273744*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.6203133171335783`*^9, 3.620313354926805*^9}, {
   3.620320086942058*^9, 3.620320102727682*^9}, 3.620544876847466*^9, 
   3.620669836799911*^9, 3.6208440933685102`*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   RowBox[{"Fierz3sa", "=", 
    RowBox[{
     RowBox[{"Fierz3", "//", 
      RowBox[{"EqTimes", "[", 
       RowBox[{
        RowBox[{"epsilon2", "[", 
         RowBox[{
          RowBox[{"-", "c"}], ",", 
          RowBox[{"-", "d"}]}], "]"}], 
        RowBox[{"sigma", "[", 
         RowBox[{"\[Sigma]", ",", 
          RowBox[{"-", "a"}], ",", 
          RowBox[{"-", "b"}]}], "]"}]}], "]"}]}], "//", "Expand"}]}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"%", "//", "Simplification"}], "//", 
    "Simplification"}]}]}]], "Input",
 CellChangeTimes->{{3.618821689278737*^9, 3.618821703009098*^9}, {
  3.62031336046745*^9, 3.620313397279337*^9}, {3.620320108693596*^9, 
  3.6203201294434433`*^9}}],

Cell[BoxData[
 RowBox[{"0", "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Sigma]", "\[Rho]", " "},
            {" ", " ", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Sigma], $CellContext`\[Rho], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Sigma]", "\[Rho]", " "},
            {" ", " ", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Sigma], $CellContext`\[Rho], \
-$CellContext`\[Nu]],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Rho]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {"\[Sigma]", "\[Rho]", " "},
            {" ", " ", "\[Mu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[$CellContext`\[Sigma], $CellContext`\[Rho], \
-$CellContext`\[Mu]],
     Editable->False], " ", 
    SuperscriptBox[
     InterpretationBox[
      StyleBox["f",
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xVect`f[],
      Editable->False], "2"], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{{3.620313364013019*^9, 3.620313398410191*^9}, {
   3.620320111081815*^9, 3.620320130099897*^9}, 3.6205448810004387`*^9, 
   3.6206698394499607`*^9, 3.620844095754068*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.620313364013019*^9, 3.620313398410191*^9}, {
   3.620320111081815*^9, 3.620320130099897*^9}, 3.6205448810004387`*^9, 
   3.6206698394499607`*^9, 3.620844095804963*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{"Fierz3ss", "=", 
   RowBox[{
    RowBox[{"Fierz3", "//", 
     RowBox[{"EqTimes", "[", 
      RowBox[{
       RowBox[{"sigma", "[", 
        RowBox[{"\[Tau]", ",", 
         RowBox[{"-", "a"}], ",", 
         RowBox[{"-", "b"}]}], "]"}], 
       RowBox[{"sigma", "[", 
        RowBox[{"\[Sigma]", ",", 
         RowBox[{"-", "c"}], ",", 
         RowBox[{"-", "d"}]}], "]"}]}], "]"}]}], "//", 
    "Simplification"}]}]}]], "Input",
 CellChangeTimes->{{3.618821711326262*^9, 3.618821789714016*^9}, {
   3.6203134083146*^9, 3.6203134392348623`*^9}, 3.6203201358582277`*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{{3.620313418897818*^9, 3.620313440514204*^9}, 
   3.620320136702252*^9, 3.620544882916061*^9, 3.62066984207417*^9, 
   3.6208440994866657`*^9}]
}, Closed]],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Fierz*\>\"", "]"}]], "Input",
 CellChangeTimes->{{3.6205449055067883`*^9, 3.620544921070527*^9}, {
  3.6205449981742487`*^9, 3.620545006144752*^9}}]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Derivatives from the article", "Section",
 CellChangeTimes->{{3.6167731495262957`*^9, 3.616773154843355*^9}, {
  3.61806403341989*^9, 3.618064035189516*^9}}],

Cell[CellGroupData[{

Cell["Definitions", "Subsection",
 CellChangeTimes->{{3.618842588691321*^9, 3.6188425904595013`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"DefTensor", "[", 
   RowBox[{
    RowBox[{"At1", "[", 
     RowBox[{"A", ",", "B"}], "]"}], ",", "M3", ",", 
    RowBox[{"Symmetric", "[", 
     RowBox[{"{", 
      RowBox[{"A", ",", "B"}], "}"}], "]"}], ",", 
    RowBox[{
    "PrintAs", "\[Rule]", "\"\<\!\(\*SubscriptBox[\(A\), \(1\)]\)\>\""}]}], 
   "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"DefConstantSymbol", "[", 
   RowBox[{"gc", ",", 
    RowBox[{"PrintAs", "\[Rule]", "\"\<g\>\""}]}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"FoldOut", "[", "]"}]}], "Input",
 CellChangeTimes->{{3.6167733377700033`*^9, 3.616773349900907*^9}, {
  3.617951382668187*^9, 3.617951398511978*^9}, {3.6180640374091187`*^9, 
  3.6180640490868473`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefTensor", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"tensor \"\>", "\[InvisibleSpace]", 
   RowBox[{"At1", "[", 
    RowBox[{"A", ",", "B"}], "]"}], "\[InvisibleSpace]", "\<\". \"\>", 
   "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm["** ", xAct`xTensor`DefTensor, ": Defining ", "tensor ", 
   $CellContext`At1[$CellContext`A, $CellContext`B], ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620313455430675*^9, 3.620320141689735*^9, 
  3.620545017482031*^9, 3.620669848330628*^9, 3.620844182494293*^9, 
  3.620844398422226*^9, 3.6208446613359547`*^9, 3.620844725797385*^9, 
  3.6208485786537647`*^9, 3.6208489070696487`*^9}],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"** \"\>", "\[InvisibleSpace]", "DefConstantSymbol", 
   "\[InvisibleSpace]", "\<\": Defining \"\>", 
   "\[InvisibleSpace]", "\<\"constant symbol \"\>", "\[InvisibleSpace]", "gc",
    "\[InvisibleSpace]", "\<\". \"\>", "\[InvisibleSpace]", "\<\"\"\>"}],
  SequenceForm[
  "** ", xAct`xTensor`DefConstantSymbol, ": Defining ", 
   "constant symbol ", $CellContext`gc, ". ", ""],
  Editable->False]], "Print",
 CellChangeTimes->{3.620313455430675*^9, 3.620320141689735*^9, 
  3.620545017482031*^9, 3.620669848330628*^9, 3.620844182494293*^9, 
  3.620844398422226*^9, 3.6208446613359547`*^9, 3.620844725797385*^9, 
  3.6208485786537647`*^9, 3.620848907091498*^9}]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Derivatives on F", "Subsection",
 CellChangeTimes->{{3.6185628546157913`*^9, 3.618562861288216*^9}, {
  3.618562940719219*^9, 3.618562940913361*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"KY1", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"SO8D", "[", 
     RowBox[{"-", "\[Mu]"}], "]"}], "[", 
    RowBox[{"F", "[", 
     RowBox[{"A", ",", "B"}], "]"}], "]"}], "\[Equal]", 
   RowBox[{"2", " ", "gc", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"At1", "[", 
        RowBox[{"A1", ",", "A"}], "]"}], 
       RowBox[{"delta8", "[", 
        RowBox[{
         RowBox[{"-", "A1"}], ",", 
         RowBox[{"-", "A2"}]}], "]"}], 
       RowBox[{"V", "[", 
        RowBox[{
         RowBox[{"-", "\[Mu]"}], ",", "B", ",", "A2"}], "]"}]}], "//", 
      RowBox[{
       RowBox[{"Antisymmetrize", "[", 
        RowBox[{"#", ",", 
         RowBox[{"{", 
          RowBox[{"A", ",", "B"}], "}"}]}], "]"}], "&"}]}], 
     ")"}]}]}]}]], "Input",
 CellChangeTimes->{{3.616773194831949*^9, 3.616773295872069*^9}, {
   3.616773579521852*^9, 3.616773664195822*^9}, {3.616773769999928*^9, 
   3.616773772214054*^9}, {3.616773859682061*^9, 3.61677387546533*^9}, {
   3.616774111556981*^9, 3.6167741339827957`*^9}, 3.616774202575118*^9, {
   3.61677445435426*^9, 3.616774458784362*^9}, {3.617952778753957*^9, 
   3.6179527826159267`*^9}, {3.617954817517467*^9, 3.617954835295236*^9}, 
   3.6180521022193527`*^9, {3.618558118369326*^9, 3.618558123814917*^9}}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"A", "B"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`F[$CellContext`A, $CellContext`B]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "B"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`B],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "A", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`A, $CellContext`A2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["A", "1"], "A"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`A1, $CellContext`A],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "B", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`B, $CellContext`A2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.620313461141225*^9, 3.620320144010182*^9, 
  3.6205450281514893`*^9, 3.620669852174283*^9, 3.620844188464674*^9, 
  3.6208444080848103`*^9, 3.620844664267448*^9, 3.620844727929538*^9}]
}, Closed]],

Cell["Project the derivative onto the a,b components", "Text",
 CellChangeTimes->{{3.6187469154798517`*^9, 3.618746936380905*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"SymbolOfCovD", "[", "SO8DSO8reduction", "]"}], "^=", 
   RowBox[{"{", 
    RowBox[{"\"\<;\>\"", ",", "\"\<\!\(\*OverscriptBox[\(D\), \(_\)]\)\>\""}],
     "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.620845868411605*^9, 3.6208459280960283`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{"KY1", "\[IndentingNewLine]", 
 RowBox[{"%", "//", 
  RowBox[{"ProjectOnto", "[", 
   RowBox[{"a", ",", "b", ",", 
    RowBox[{"-", "\[Mu]"}]}], "]"}]}], "\n", 
 RowBox[{"%", "//", 
  RowBox[{"ReduceVSum", "[", "SO8reduction", "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "Simplification"}]}], "Input",
 CellChangeTimes->{{3.6179528839407387`*^9, 3.617952921720765*^9}, {
   3.6179704660049343`*^9, 3.617970467670409*^9}, {3.6179711209666357`*^9, 
   3.617971166938566*^9}, 3.6179713474859123`*^9, {3.6179719003011217`*^9, 
   3.617971902703549*^9}, 3.6179720507781878`*^9, {3.617973108051244*^9, 
   3.617973138070627*^9}, 3.618064069235207*^9, {3.6180641051152153`*^9, 
   3.618064169565419*^9}, {3.618064206849267*^9, 3.618064209438506*^9}, {
   3.618064353510453*^9, 3.618064385368384*^9}, {3.61811423596185*^9, 
   3.618114236122693*^9}, {3.618496717218082*^9, 3.618496728998426*^9}, {
   3.618507065629209*^9, 3.61850706589675*^9}, {3.618556726525444*^9, 
   3.618556733966185*^9}, 3.6185568517599497`*^9, {3.618557329862462*^9, 
   3.6185573353772917`*^9}, {3.6185576931947107`*^9, 3.618557720375886*^9}, {
   3.618557831898925*^9, 3.618557832700282*^9}, 3.6185582443314953`*^9, {
   3.6185610248276243`*^9, 3.618561025756817*^9}, 3.618561523842331*^9, 
   3.61856228123214*^9, {3.618821897919565*^9, 3.618821907077544*^9}, {
   3.6188219727540607`*^9, 3.6188219789091253`*^9}, {3.620313502415881*^9, 
   3.620313505945163*^9}, {3.620313557007325*^9, 3.6203135603112497`*^9}, {
   3.620320202244157*^9, 3.620320206038219*^9}, {3.6203208644979553`*^9, 
   3.620320882927762*^9}, {3.620669873028417*^9, 3.6206698828320847`*^9}}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"A", "B"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`F[$CellContext`A, $CellContext`B]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "B"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`B],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "A", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`A, $CellContext`A2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["A", "1"], "A"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`A1, $CellContext`A],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "B", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`B, $CellContext`A2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6203135065067368`*^9, 3.620313561426044*^9, {3.62032014702547*^9, 
   3.620320155017576*^9}, 3.62032020659256*^9, 3.620320287528537*^9, 
   3.620320455745315*^9, 3.620320522448255*^9, 3.620320723476712*^9, {
   3.620320875678895*^9, 3.62032088370227*^9}, 3.620320999060814*^9, 
   3.620545032034656*^9, 3.620669892424621*^9, 3.62067013345475*^9, 
   3.6206702272828007`*^9, 3.620670330639904*^9, {3.620670367994573*^9, 
   3.620670387711961*^9}, {3.620670836650985*^9, 3.620670874043096*^9}, 
   3.620670943979474*^9, 3.620671016254586*^9, 3.620671436559187*^9, 
   3.620671931190825*^9, 3.6208441928380613`*^9, 3.620844411161745*^9, 
   3.620844665949182*^9, 3.620844730041011*^9, 3.620844822180378*^9, 
   3.620845930988525*^9}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`F[xAct`xVect`a, xAct`xVect`b]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, xAct`xVect`b],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`A2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["A", "1"], "a"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`A1, xAct`xVect`a],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`b, $CellContext`A2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6203135065067368`*^9, 3.620313561426044*^9, {3.62032014702547*^9, 
   3.620320155017576*^9}, 3.62032020659256*^9, 3.620320287528537*^9, 
   3.620320455745315*^9, 3.620320522448255*^9, 3.620320723476712*^9, {
   3.620320875678895*^9, 3.62032088370227*^9}, 3.620320999060814*^9, 
   3.620545032034656*^9, 3.620669892424621*^9, 3.62067013345475*^9, 
   3.6206702272828007`*^9, 3.620670330639904*^9, {3.620670367994573*^9, 
   3.620670387711961*^9}, {3.620670836650985*^9, 3.620670874043096*^9}, 
   3.620670943979474*^9, 3.620671016254586*^9, 3.620671436559187*^9, 
   3.620671931190825*^9, 3.6208441928380613`*^9, 3.620844411161745*^9, 
   3.620844665949182*^9, 3.620844730041011*^9, 3.620844822180378*^9, 
   3.6208459310352907`*^9}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox[
      OverscriptBox["D", "_"], "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8DSO8reduction[-$CellContext`\[Mu]][
    $CellContext`F[xAct`xVect`a, xAct`xVect`b]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["a", "1"], 
               SubscriptBox["a", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`a2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["a", "3"], "a"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`a3, xAct`xVect`a],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["a", "3"], 
               SubscriptBox["a", "4"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`a3, -$CellContext`a4],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "4"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`b, $CellContext`a4],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6203135065067368`*^9, 3.620313561426044*^9, {3.62032014702547*^9, 
   3.620320155017576*^9}, 3.62032020659256*^9, 3.620320287528537*^9, 
   3.620320455745315*^9, 3.620320522448255*^9, 3.620320723476712*^9, {
   3.620320875678895*^9, 3.62032088370227*^9}, 3.620320999060814*^9, 
   3.620545032034656*^9, 3.620669892424621*^9, 3.62067013345475*^9, 
   3.6206702272828007`*^9, 3.620670330639904*^9, {3.620670367994573*^9, 
   3.620670387711961*^9}, {3.620670836650985*^9, 3.620670874043096*^9}, 
   3.620670943979474*^9, 3.620671016254586*^9, 3.620671436559187*^9, 
   3.620671931190825*^9, 3.6208441928380613`*^9, 3.620844411161745*^9, 
   3.620844665949182*^9, 3.620844730041011*^9, 3.620844822180378*^9, 
   3.62084593109404*^9}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox[
      OverscriptBox["D", "_"], "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", "b"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8DSO8reduction[-$CellContext`\[Mu]][
    $CellContext`F[xAct`xVect`a, xAct`xVect`b]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {"b", 
                SubscriptBox["a", "1"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[xAct`xVect`b, $CellContext`a1],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`a2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`b, $CellContext`a2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6203135065067368`*^9, 3.620313561426044*^9, {3.62032014702547*^9, 
   3.620320155017576*^9}, 3.62032020659256*^9, 3.620320287528537*^9, 
   3.620320455745315*^9, 3.620320522448255*^9, 3.620320723476712*^9, {
   3.620320875678895*^9, 3.62032088370227*^9}, 3.620320999060814*^9, 
   3.620545032034656*^9, 3.620669892424621*^9, 3.62067013345475*^9, 
   3.6206702272828007`*^9, 3.620670330639904*^9, {3.620670367994573*^9, 
   3.620670387711961*^9}, {3.620670836650985*^9, 3.620670874043096*^9}, 
   3.620670943979474*^9, 3.620671016254586*^9, 3.620671436559187*^9, 
   3.620671931190825*^9, 3.6208441928380613`*^9, 3.620844411161745*^9, 
   3.620844665949182*^9, 3.620844730041011*^9, 3.620844822180378*^9, 
   3.620845931179186*^9}]
}, Closed]],

Cell["Project KY1 onto the [a,ac] components", "Text",
 CellChangeTimes->{{3.618746945445614*^9, 3.618746959582821*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{"KY1", "\[IndentingNewLine]", 
 RowBox[{"%", "//", 
  RowBox[{"ProjectOnto", "[", 
   RowBox[{"a", ",", "ac", ",", 
    RowBox[{"-", "\[Mu]"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", 
   RowBox[{"ReduceVSum", "[", "SO8reduction", "]"}]}], "//", 
  "Simplification"}]}], "Input",
 CellChangeTimes->{{3.618065392341864*^9, 3.618065415044347*^9}, {
   3.618065450292544*^9, 3.618065491458956*^9}, {3.618114374493655*^9, 
   3.618114385424119*^9}, {3.6181161023576527`*^9, 3.618116102586618*^9}, {
   3.618138838578027*^9, 3.6181388394583273`*^9}, {3.6185591743809137`*^9, 
   3.618559213929615*^9}, {3.618559250040058*^9, 3.6185595178823338`*^9}, {
   3.618559582684367*^9, 3.618559591198316*^9}, {3.618561303493285*^9, 
   3.6185613898883743`*^9}, {3.6185614934762077`*^9, 3.618561497920966*^9}, {
   3.6185622618649683`*^9, 3.618562270114654*^9}, {3.61856268481217*^9, 
   3.618562686701949*^9}, 3.618562758195293*^9, {3.618746970156999*^9, 
   3.618746970398334*^9}, {3.6188219910276117`*^9, 3.61882200021594*^9}, {
   3.620313565920916*^9, 3.620313567094721*^9}, {3.6206719933064327`*^9, 
   3.620671995760769*^9}}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"A", "B"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`F[$CellContext`A, $CellContext`B]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "B"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`B],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "A", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`A, $CellContext`A2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["A", "1"], "A"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`A1, $CellContext`A],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "B", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`B, $CellContext`A2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.620313567900181*^9, 3.62032100317971*^9, 
  3.620545041783358*^9, 3.6206719996403627`*^9, 3.620845943910797*^9}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", 
            SubscriptBox["a", "c"]},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`F[xAct`xVect`a, $CellContext`ac]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], 
                SubscriptBox["a", "c"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`ac],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`A2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["A", "1"], "a"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`A1, xAct`xVect`a],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", 
               SubscriptBox["a", "c"], 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`ac, $CellContext`A2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.620313567900181*^9, 3.62032100317971*^9, 
  3.620545041783358*^9, 3.6206719996403627`*^9, 3.620845943971162*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {
        RowBox[{"A", "[", "D", "]"}], 
        StyleBox[GridBox[{
           {
            SubscriptBox["a", "c"], " ", " "},
           {" ", "\[Mu]", 
            SubscriptBox["a", "1"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AChristoffelSO8D[$CellContext`ac, -$CellContext`\[Mu], \
-$CellContext`a1],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {"a", 
            SubscriptBox["a", "1"]},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`F[xAct`xVect`a, $CellContext`a1],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{"-", 
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False]}], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {
        SubscriptBox["A", "1"], 
        StyleBox[GridBox[{
           {
            SubscriptBox["a", "c"], 
            SubscriptBox["a", "1"]},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`At1[$CellContext`ac, $CellContext`a1],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "a", 
            SubscriptBox["a", "2"]},
           {"\[Mu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`V[-$CellContext`\[Mu], xAct`xVect`a, $CellContext`a2],
    Editable->False]}]}]], "Output",
 CellChangeTimes->{3.620313567900181*^9, 3.62032100317971*^9, 
  3.620545041783358*^9, 3.6206719996403627`*^9, 3.620845944049445*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"%", "//", "RepF"}], "//", "RepVab"}], "//", 
   RowBox[{"EqTimes", "[", 
    RowBox[{"epsilon2", "[", 
     RowBox[{
      RowBox[{"-", "a"}], ",", 
      RowBox[{"-", "b"}]}], "]"}], "]"}]}], "//", "Simplification"}]], "Input",\

 CellChangeTimes->{{3.618747011395122*^9, 3.618747016902589*^9}, {
  3.6187470479605007`*^9, 3.618747101067565*^9}, {3.6188220221244087`*^9, 
  3.618822071392703*^9}, {3.618824801774509*^9, 3.6188248036104383`*^9}, {
  3.618824905914207*^9, 3.6188249462649*^9}, {3.620313584236643*^9, 
  3.6203135961071863`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {
        RowBox[{"A", "[", "D", "]"}], 
        StyleBox[GridBox[{
           {
            SubscriptBox["a", "c"], " ", " "},
           {" ", "\[Mu]", "b"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`AChristoffelSO8D[$CellContext`ac, -$CellContext`\[Mu], -
     xAct`xVect`b],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   FractionBox["1", "2"], " ", 
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {
        SubscriptBox["A", "1"], 
        StyleBox[GridBox[{
           {
            SubscriptBox["a", "c"], "a"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`At1[$CellContext`ac, xAct`xVect`a],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {"a", 
            SubscriptBox["a", "1"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-xAct`xVect`a, -$CellContext`a1],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Mu]", "\[Nu]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Sigma]", 
        StyleBox[GridBox[{
           {" ", " ", 
            SubscriptBox["a", "1"]},
           {"\[Rho]", "b", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`sigma[-$CellContext`\[Rho], -xAct`xVect`b, $CellContext`a1],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {"\[Nu]", "\[Rho]"},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`Vt[$CellContext`\[Nu], $CellContext`\[Rho]],
    Editable->False]}]}]], "Output",
 CellChangeTimes->{3.620313597130597*^9, 3.620321006221745*^9, 
  3.620545055231893*^9, 3.620672008946109*^9, 3.620845967521202*^9}]
}, Closed]],

Cell["Finally we project onto [ac,bc]", "Text",
 CellChangeTimes->{{3.61874887822394*^9, 3.61874888914678*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"KY1", "//", 
  RowBox[{"ProjectOnto", "[", 
   RowBox[{"ac", ",", "bc", ",", 
    RowBox[{"-", "\[Mu]"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", 
   RowBox[{"ReduceVSum", "[", "SO8reduction", "]"}]}], "//", 
  "Simplification"}]}], "Input",
 CellChangeTimes->{{3.6180657059702578`*^9, 3.618065811826291*^9}, {
   3.618562744090692*^9, 3.618562744894874*^9}, 3.618562828104478*^9, {
   3.6188271496273193`*^9, 3.618827158475896*^9}, {3.620313613256414*^9, 
   3.6203136140861*^9}, {3.620672019055505*^9, 3.620672021732932*^9}}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"F", 
        StyleBox[GridBox[{
           {
            SubscriptBox["a", "c"], 
            SubscriptBox["b", "c"]},
           {" ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`F[$CellContext`ac, $CellContext`bc]],
   Editable->False], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], 
                SubscriptBox["b", "c"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`bc],
        Editable->False]}], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", 
               SubscriptBox["a", "c"], 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`ac, $CellContext`A2],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["a", "c"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[$CellContext`A1, $CellContext`ac],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Delta]", 
           StyleBox[GridBox[{
              {" ", " "},
              {
               SubscriptBox["A", "1"], 
               SubscriptBox["A", "2"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"V", 
           StyleBox[GridBox[{
              {" ", 
               SubscriptBox["b", "c"], 
               SubscriptBox["A", "2"]},
              {"\[Mu]", " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`V[-$CellContext`\[Mu], $CellContext`bc, $CellContext`A2],
       Editable->False]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.6203136145165577`*^9, 3.620321009172879*^9, 
  3.6205450601806707`*^9, 3.62067202283578*^9, 3.6208459710865583`*^9}],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.6203136145165577`*^9, 3.620321009172879*^9, 
  3.6205450601806707`*^9, 3.62067202283578*^9, 3.620845971088901*^9}]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Derivatives on V", "Subsection",
 CellChangeTimes->{{3.618562931525527*^9, 3.6185629370878563`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"KY2", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"SO8D", "[", 
     RowBox[{"-", "\[Mu]"}], "]"}], "[", 
    RowBox[{"V", "[", 
     RowBox[{
      RowBox[{"-", "\[Nu]"}], ",", "A", ",", "B"}], "]"}], "]"}], "\[Equal]", 
   
   RowBox[{
    RowBox[{"2", " ", "gc", " ", 
     RowBox[{"g", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", 
       RowBox[{"-", "\[Nu]"}]}], "]"}], 
     RowBox[{"delta8", "[", 
      RowBox[{
       RowBox[{"-", "A1"}], ",", 
       RowBox[{"-", "A2"}]}], "]"}], 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"At1", "[", 
          RowBox[{"A1", ",", "A"}], "]"}], 
         RowBox[{"F", "[", 
          RowBox[{"B", ",", "A2"}], "]"}]}], "+", 
        RowBox[{
         RowBox[{"At1", "[", 
          RowBox[{"A1", ",", "B"}], "]"}], 
         RowBox[{"F", "[", 
          RowBox[{"A", ",", "A2"}], "]"}]}]}], ")"}], "/", "2"}]}], "+", 
    RowBox[{"2", " ", "gc", " ", 
     RowBox[{"epsilong", "[", 
      RowBox[{
       RowBox[{"-", "\[Mu]"}], ",", 
       RowBox[{"-", "\[Nu]"}], ",", 
       RowBox[{"-", "\[Rho]"}]}], "]"}], 
     RowBox[{"delta8", "[", 
      RowBox[{
       RowBox[{"-", "A1"}], ",", 
       RowBox[{"-", "A2"}]}], "]"}], 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"At1", "[", 
          RowBox[{"A1", ",", "A"}], "]"}], 
         RowBox[{"V", "[", 
          RowBox[{"\[Rho]", ",", "B", ",", "A2"}], "]"}]}], "+", 
        RowBox[{
         RowBox[{"At1", "[", 
          RowBox[{"A1", " ", ",", "B"}], "]"}], 
         RowBox[{"V", "[", 
          RowBox[{"\[Rho]", ",", "A", ",", "A2"}], "]"}]}]}], ")"}], "/", 
      "2"}]}]}]}]}]], "Input",
 CellChangeTimes->{{3.6188271655671062`*^9, 3.6188271682488213`*^9}, {
  3.6188426291131067`*^9, 3.618842697828826*^9}, {3.618843102521994*^9, 
  3.618843105125106*^9}}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "A", "B"},
           {"\[Nu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`V[-$CellContext`\[Nu], $CellContext`A, $CellContext`B]],
   Editable->False], "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["A", "1"], 
             SubscriptBox["A", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "B"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`B],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"F", 
            StyleBox[GridBox[{
               {"A", 
                SubscriptBox["A", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`F[$CellContext`A, $CellContext`A2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "A"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`A],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"F", 
            StyleBox[GridBox[{
               {"B", 
                SubscriptBox["A", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`F[$CellContext`B, $CellContext`A2],
        Editable->False]}]}], ")"}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["A", "1"], 
             SubscriptBox["A", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "B"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`B],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "A", 
                SubscriptBox["A", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], $CellContext`A, $CellContext`A2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "A"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, $CellContext`A],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "B", 
                SubscriptBox["A", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], $CellContext`B, $CellContext`A2],
        Editable->False]}]}], ")"}]}]}]}]], "Output",
 CellChangeTimes->{3.620313631124919*^9, 3.620581173781551*^9, 
  3.620672033263844*^9, 3.620672198778282*^9, 3.620846007905438*^9, 
  3.6208485895932817`*^9, 3.620848846303862*^9, 3.620848911059855*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"EqIndices", "[", "KY2", "]"}]], "Input",
 CellChangeTimes->{{3.618843119820449*^9, 3.618843127335039*^9}}],

Cell[BoxData[
 RowBox[{"HoldFirst", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"A", 
         RowBox[{",", "\[ThinSpace]"}], "B", 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Mu]"}], 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Nu]"}]}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[$CellContext`A, $CellContext`B, -$CellContext`\
\[Mu], -$CellContext`\[Nu]],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[
       StyleBox[
        RowBox[{"{", "}"}],
        FontColor->RGBColor[0, 0, 1]],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[],
      Editable->False]}], "}"}], "\[Equal]", 
   RowBox[{"{", 
    RowBox[{
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"A", 
         RowBox[{",", "\[ThinSpace]"}], "B", 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Mu]"}], 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Nu]"}]}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[$CellContext`A, $CellContext`B, -$CellContext`\
\[Mu], -$CellContext`\[Nu]],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"A1", 
         RowBox[{",", "\[ThinSpace]"}], "A2", 
         RowBox[{",", "\[ThinSpace]"}], "\[Rho]"}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[$CellContext`A1, $CellContext`A2, $CellContext`\
\[Rho]],
      Editable->False]}], "}"}]}], "]"}]], "Output",
 CellChangeTimes->{3.620672202695898*^9, 3.620846011930942*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"KY2ab", "=", 
  RowBox[{"KY2", "//", 
   RowBox[{"ProjectOnto", "[", 
    RowBox[{"a", ",", "b", ",", 
     RowBox[{"-", "\[Mu]"}], ",", 
     RowBox[{"-", "\[Nu]"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", 
   RowBox[{"ReduceVSum", "[", "SO8reduction", "]"}]}], "//", "RepF"}], "\n", 
 RowBox[{"%", "//", 
  RowBox[{
   RowBox[{"ChangeCovD", "[", 
    RowBox[{"#", ",", "SO8DSO8reduction", ",", "CD"}], "]"}], 
   "&"}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", "TraceProductDummy"}], "\[IndentingNewLine]", 
 RowBox[{"last", "=", 
  RowBox[{
   RowBox[{"%", "//", 
    RowBox[{"Rep", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"AChristoffel", "[", 
        RowBox[{"CD", ",", "SO8DSO8reduction"}], "]"}], "[", 
       RowBox[{"A", ",", 
        RowBox[{"-", "\[Mu]"}], ",", 
        RowBox[{"-", "B"}]}], "]"}], ",", 
      RowBox[{"-", 
       RowBox[{
        RowBox[{"AChristoffel", "[", "SO8DSO8reduction", "]"}], "[", 
        RowBox[{"A", ",", 
         RowBox[{"-", "\[Mu]"}], ",", 
         RowBox[{"-", "B"}]}], "]"}]}]}], "]"}]}], "//", 
   "Simplification"}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", 
  RowBox[{"ReduceVSum", "[", "SO8reduction", "]"}]}]}], "Input",
 CellChangeTimes->{{3.618843203199917*^9, 3.6188432487656813`*^9}, {
   3.619325840484496*^9, 3.6193258435205603`*^9}, {3.6193275035298777`*^9, 
   3.619327552045624*^9}, {3.619327684601954*^9, 3.61932769085357*^9}, {
   3.619327942068202*^9, 3.61932796490307*^9}, {3.6193280219456778`*^9, 
   3.619328022313109*^9}, {3.6193282712790327`*^9, 3.619328356326717*^9}, {
   3.619328445686675*^9, 3.6193284886405087`*^9}, {3.619328968825897*^9, 
   3.6193290654936543`*^9}, {3.61932924230786*^9, 3.619329258702209*^9}, {
   3.619329353476727*^9, 3.619329384451872*^9}, {3.619329523546008*^9, 
   3.619329544675456*^9}, {3.61932960613862*^9, 3.619329630802696*^9}, {
   3.6193300765820837`*^9, 3.619330131796698*^9}, {3.619330186498693*^9, 
   3.619330186869178*^9}, {3.6193302202598248`*^9, 3.6193303148880177`*^9}, {
   3.6193305318241043`*^9, 3.619330620944868*^9}, {3.619331392653006*^9, 
   3.619331424656801*^9}, {3.619331782688088*^9, 3.619331816781782*^9}, {
   3.6193672296333714`*^9, 3.619367267730467*^9}, {3.620313638389676*^9, 
   3.620313646604321*^9}, {3.6205820504471416`*^9, 3.620582052233768*^9}, {
   3.620672264880048*^9, 3.6206723545800457`*^9}, {3.6206724578004847`*^9, 
   3.620672458337614*^9}, 3.620673484281242*^9, {3.6208460209966784`*^9, 
   3.62084608072147*^9}, {3.6208462418879013`*^9, 3.620846285762805*^9}, {
   3.6208463392814207`*^9, 3.6208463496971617`*^9}, {3.620846583806035*^9, 
   3.620846599607909*^9}, {3.620846666341168*^9, 3.620846668027125*^9}, {
   3.620848984742322*^9, 3.6208490166580143`*^9}}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox["D", "\[Mu]"], GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "a", "b"},
           {"\[Nu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8D[-$CellContext`\[Mu]][
    $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
   Editable->False], "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["A", "1"], 
             SubscriptBox["A", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"F", 
            StyleBox[GridBox[{
               {"a", 
                SubscriptBox["A", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`F[xAct`xVect`a, $CellContext`A2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"F", 
            StyleBox[GridBox[{
               {"b", 
                SubscriptBox["A", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`F[xAct`xVect`b, $CellContext`A2],
        Editable->False]}]}], ")"}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["A", "1"], 
             SubscriptBox["A", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`A1, -$CellContext`A2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "a", 
                SubscriptBox["A", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`A2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["A", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`A1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "b", 
                SubscriptBox["A", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`A2],
        Editable->False]}]}], ")"}]}]}]}]], "Output",
 CellChangeTimes->{
  3.6206734873876333`*^9, {3.6208460467316027`*^9, 3.6208460494988947`*^9}, 
   3.6208460819843607`*^9, 3.620846164225469*^9, 3.620846286585787*^9, 
   3.620846350226019*^9, 3.620846601204218*^9, 3.620846669897698*^9, 
   3.620848592574194*^9, {3.6208489140841503`*^9, 3.620848919186434*^9}, {
   3.620849002181505*^9, 3.620849017334484*^9}, 3.6208509143953342`*^9, 
   3.620852879908146*^9, 3.620852919642428*^9}],

Cell[BoxData[
 RowBox[{
  InterpretationBox[
   StyleBox[
    RowBox[{
     SubscriptBox[
      SubscriptBox["\<\"D\"\>", 
       RowBox[{
        InterpretationBox[
         StyleBox["SO2V",
          ShowAutoStyles->False,
          AutoSpacing->False],
         SO2V,
         Editable->False], " ", "\[CirclePlus]", " ", 
        InterpretationBox[
         StyleBox["SO6V",
          ShowAutoStyles->False,
          AutoSpacing->False],
         SO6V,
         Editable->False]}]], "\[Mu]"], GridBox[{
       {"V", 
        StyleBox[GridBox[{
           {" ", "a", "b"},
           {"\[Nu]", " ", " "}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}]}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   $CellContext`SO8DSO8reduction[-$CellContext`\[Mu]][
    $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
   Editable->False], "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Epsilon]", 
            StyleBox[GridBox[{
               {"a", 
                SubscriptBox["a", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Epsilon]", 
            StyleBox[GridBox[{
               {"b", 
                SubscriptBox["a", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False]}]}], ")"}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "a", 
                SubscriptBox["a", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "b", 
                SubscriptBox["a", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
        Editable->False]}]}], ")"}]}]}]}]], "Output",
 CellChangeTimes->{
  3.6206734873876333`*^9, {3.6208460467316027`*^9, 3.6208460494988947`*^9}, 
   3.6208460819843607`*^9, 3.620846164225469*^9, 3.620846286585787*^9, 
   3.620846350226019*^9, 3.620846601204218*^9, 3.620846669897698*^9, 
   3.620848592574194*^9, {3.6208489140841503`*^9, 3.620848919186434*^9}, {
   3.620849002181505*^9, 3.620849017334484*^9}, 3.6208509143953342`*^9, 
   3.620852879908146*^9, 3.620852919722375*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     InterpretationBox[
      StyleBox[GridBox[{
         {
          RowBox[{"A", "[", 
           RowBox[{"\[Del]", 
            RowBox[{",", 
             SubscriptBox["\<\"D\"\>", 
              RowBox[{
               InterpretationBox[
                StyleBox["SO2V",
                 ShowAutoStyles->False,
                 AutoSpacing->False],
                SO2V,
                Editable->False], " ", "\[CirclePlus]", " ", 
               InterpretationBox[
                StyleBox["SO6V",
                 ShowAutoStyles->False,
                 AutoSpacing->False],
                SO6V,
                Editable->False]}]]}]}], "]"}], 
          StyleBox[GridBox[{
             {"b", " ", " "},
             {" ", "\[Mu]", "A"}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->9]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AChristoffelCDSO8DSO8reduction[
      xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`A],
      Editable->False]}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "A"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`A],
     Editable->False]}], "-", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          RowBox[{"\[Del]", 
           RowBox[{",", 
            SubscriptBox["\<\"D\"\>", 
             RowBox[{
              InterpretationBox[
               StyleBox["SO2V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO2V,
               Editable->False], " ", "\[CirclePlus]", " ", 
              InterpretationBox[
               StyleBox["SO6V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO6V,
               Editable->False]}]]}]}], "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", "A"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelCDSO8DSO8reduction[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`A],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "A", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], $CellContext`A, xAct`xVect`b],
     Editable->False]}], "+", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`CD[-$CellContext`\[Mu]][
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Epsilon]", 
            StyleBox[GridBox[{
               {"a", 
                SubscriptBox["a", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Epsilon]", 
            StyleBox[GridBox[{
               {"b", 
                SubscriptBox["a", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False]}]}], ")"}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "a", 
                SubscriptBox["a", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "b", 
                SubscriptBox["a", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
        Editable->False]}]}], ")"}]}]}]}]], "Output",
 CellChangeTimes->{
  3.6206734873876333`*^9, {3.6208460467316027`*^9, 3.6208460494988947`*^9}, 
   3.6208460819843607`*^9, 3.620846164225469*^9, 3.620846286585787*^9, 
   3.620846350226019*^9, 3.620846601204218*^9, 3.620846669897698*^9, 
   3.620848592574194*^9, {3.6208489140841503`*^9, 3.620848919186434*^9}, {
   3.620849002181505*^9, 3.620849017334484*^9}, 3.6208509143953342`*^9, 
   3.620852879908146*^9, 3.6208529197882023`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     InterpretationBox[
      StyleBox[GridBox[{
         {
          RowBox[{"A", "[", 
           RowBox[{"\[Del]", 
            RowBox[{",", 
             SubscriptBox["\<\"D\"\>", 
              RowBox[{
               InterpretationBox[
                StyleBox["SO2V",
                 ShowAutoStyles->False,
                 AutoSpacing->False],
                SO2V,
                Editable->False], " ", "\[CirclePlus]", " ", 
               InterpretationBox[
                StyleBox["SO6V",
                 ShowAutoStyles->False,
                 AutoSpacing->False],
                SO6V,
                Editable->False]}]]}]}], "]"}], 
          StyleBox[GridBox[{
             {"b", " ", " "},
             {" ", "\[Mu]", 
              SubscriptBox["a", "1"]}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->9]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      $CellContext`AChristoffelCDSO8DSO8reduction[
      xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
      Editable->False]}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`a1],
     Editable->False]}], "-", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          RowBox[{"\[Del]", 
           RowBox[{",", 
            SubscriptBox["\<\"D\"\>", 
             RowBox[{
              InterpretationBox[
               StyleBox["SO2V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO2V,
               Editable->False], " ", "\[CirclePlus]", " ", 
              InterpretationBox[
               StyleBox["SO6V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO6V,
               Editable->False]}]]}]}], "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "c"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelCDSO8DSO8reduction[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`ac],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "c"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`ac],
     Editable->False]}], "-", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          RowBox[{"\[Del]", 
           RowBox[{",", 
            SubscriptBox["\<\"D\"\>", 
             RowBox[{
              InterpretationBox[
               StyleBox["SO2V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO2V,
               Editable->False], " ", "\[CirclePlus]", " ", 
              InterpretationBox[
               StyleBox["SO6V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO6V,
               Editable->False]}]]}]}], "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelCDSO8DSO8reduction[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", 
             SubscriptBox["a", "1"], "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], $CellContext`a1, xAct`xVect`b],
     Editable->False]}], "-", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          RowBox[{"\[Del]", 
           RowBox[{",", 
            SubscriptBox["\<\"D\"\>", 
             RowBox[{
              InterpretationBox[
               StyleBox["SO2V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO2V,
               Editable->False], " ", "\[CirclePlus]", " ", 
              InterpretationBox[
               StyleBox["SO6V",
                ShowAutoStyles->False,
                AutoSpacing->False],
               SO6V,
               Editable->False]}]]}]}], "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "c"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelCDSO8DSO8reduction[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`ac],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", 
             SubscriptBox["a", "c"], "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], $CellContext`ac, xAct`xVect`b],
     Editable->False]}], "+", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`CD[-$CellContext`\[Mu]][
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Epsilon]", 
            StyleBox[GridBox[{
               {"a", 
                SubscriptBox["a", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Epsilon]", 
            StyleBox[GridBox[{
               {"b", 
                SubscriptBox["a", "2"]},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox["f",
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`f[],
        Editable->False]}]}], ")"}], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "b"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "a", 
                SubscriptBox["a", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {
            SubscriptBox["A", "1"], 
            StyleBox[GridBox[{
               {
                SubscriptBox["a", "1"], "a"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`At1[$CellContext`a1, xAct`xVect`a],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[GridBox[{
           {"V", 
            StyleBox[GridBox[{
               {"\[Rho]", "b", 
                SubscriptBox["a", "2"]},
               {" ", " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
        Editable->False]}]}], ")"}]}]}]}]], "Output",
 CellChangeTimes->{
  3.6206734873876333`*^9, {3.6208460467316027`*^9, 3.6208460494988947`*^9}, 
   3.6208460819843607`*^9, 3.620846164225469*^9, 3.620846286585787*^9, 
   3.620846350226019*^9, 3.620846601204218*^9, 3.620846669897698*^9, 
   3.620848592574194*^9, {3.6208489140841503`*^9, 3.620848919186434*^9}, {
   3.620849002181505*^9, 3.620849017334484*^9}, 3.6208509143953342`*^9, 
   3.620852879908146*^9, 3.620852919873602*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          SubscriptBox["\<\"D\"\>", 
           RowBox[{
            InterpretationBox[
             StyleBox["SO2V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO2V,
             Editable->False], " ", "\[CirclePlus]", " ", 
            InterpretationBox[
             StyleBox["SO6V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO6V,
             Editable->False]}]], "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8DSO8reduction[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          SubscriptBox["\<\"D\"\>", 
           RowBox[{
            InterpretationBox[
             StyleBox["SO2V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO2V,
             Editable->False], " ", "\[CirclePlus]", " ", 
            InterpretationBox[
             StyleBox["SO6V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO6V,
             Editable->False]}]], "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "c"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8DSO8reduction[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`ac],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "c"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`ac],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          SubscriptBox["\<\"D\"\>", 
           RowBox[{
            InterpretationBox[
             StyleBox["SO2V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO2V,
             Editable->False], " ", "\[CirclePlus]", " ", 
            InterpretationBox[
             StyleBox["SO6V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO6V,
             Editable->False]}]], "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8DSO8reduction[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "b", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`b, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          SubscriptBox["\<\"D\"\>", 
           RowBox[{
            InterpretationBox[
             StyleBox["SO2V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO2V,
             Editable->False], " ", "\[CirclePlus]", " ", 
            InterpretationBox[
             StyleBox["SO6V",
              ShowAutoStyles->False,
              AutoSpacing->False],
             SO6V,
             Editable->False]}]], "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "c"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8DSO8reduction[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`ac],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "b", 
             SubscriptBox["a", "c"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`b, $CellContext`ac],
     Editable->False]}], "+", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`CD[-$CellContext`\[Mu]][
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"V", 
              StyleBox[GridBox[{
                 {"\[Rho]", "a", 
                  SubscriptBox["a", "2"]},
                 {" ", " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"V", 
              StyleBox[GridBox[{
                 {"\[Rho]", "b", 
                  SubscriptBox["a", "2"]},
                 {" ", " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6206734873876333`*^9, {3.6208460467316027`*^9, 3.6208460494988947`*^9}, 
   3.6208460819843607`*^9, 3.620846164225469*^9, 3.620846286585787*^9, 
   3.620846350226019*^9, 3.620846601204218*^9, 3.620846669897698*^9, 
   3.620848592574194*^9, {3.6208489140841503`*^9, 3.620848919186434*^9}, {
   3.620849002181505*^9, 3.620849017334484*^9}, 3.6208509143953342`*^9, 
   3.620852879908146*^9, 3.6208529199897947`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "b", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`b, $CellContext`a1],
     Editable->False]}], "+", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`CD[-$CellContext`\[Mu]][
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"V", 
              StyleBox[GridBox[{
                 {"\[Rho]", "a", 
                  SubscriptBox["a", "2"]},
                 {" ", " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"V", 
              StyleBox[GridBox[{
                 {"\[Rho]", "b", 
                  SubscriptBox["a", "2"]},
                 {" ", " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.6206734873876333`*^9, {3.6208460467316027`*^9, 3.6208460494988947`*^9}, 
   3.6208460819843607`*^9, 3.620846164225469*^9, 3.620846286585787*^9, 
   3.620846350226019*^9, 3.620846601204218*^9, 3.620846669897698*^9, 
   3.620848592574194*^9, {3.6208489140841503`*^9, 3.620848919186434*^9}, {
   3.620849002181505*^9, 3.620849017334484*^9}, 3.6208509143953342`*^9, 
   3.620852879908146*^9, 3.620852920057551*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"last", "=", "%"}]], "Input",
 CellChangeTimes->{{3.6208490326286917`*^9, 3.6208490350181837`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "b", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`b, $CellContext`a1],
     Editable->False]}], "+", 
   InterpretationBox[
    StyleBox[
     RowBox[{
      SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
        {"V", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}]}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`CD[-$CellContext`\[Mu]][
     $CellContext`V[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b]],
    Editable->False]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"V", 
              StyleBox[GridBox[{
                 {"\[Rho]", "a", 
                  SubscriptBox["a", "2"]},
                 {" ", " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`V[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"V", 
              StyleBox[GridBox[{
                 {"\[Rho]", "b", 
                  SubscriptBox["a", "2"]},
                 {" ", " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`V[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.62084903625815*^9, 3.620850918679936*^9, 
  3.620852884793447*^9, 3.620852935856803*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Vt", "[", 
  RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input",
 CellChangeTimes->{{3.620853027913329*^9, 3.620853039127438*^9}}],

Cell[BoxData[
 RowBox[{"2", " ", 
  InterpretationBox[
   StyleBox["f",
    ShowAutoStyles->False,
    AutoSpacing->False],
   xAct`xVect`f[],
   Editable->False], " ", 
  InterpretationBox[
   StyleBox[GridBox[{
      {"e", 
       StyleBox[GridBox[{
          {"\[Nu]", "\[Mu]"},
          {" ", " "}
         },
         GridBoxSpacings->{"Columns" -> {
             Offset[0.], {
              Offset[0.034999999999999996`]}, 
             Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
              Offset[0.]}}, "RowsIndexed" -> {}}],
        FontSize->9]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.034999999999999996`]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    ShowAutoStyles->False,
    AutoSpacing->False],
   xAct`xVect`viel[$CellContext`\[Nu], $CellContext`\[Mu]],
   Editable->False]}]], "Output",
 CellChangeTimes->{3.620853039576908*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"VabRules", "=", 
   RowBox[{
    RowBox[{"MakeVRuleMO", "[", 
     RowBox[{"\[Mu]", "\[Rule]", "g"}], "]"}], "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"V", "[", 
       RowBox[{"\[Mu]", ",", "a", ",", "b"}], "]"}], ",", 
      RowBox[{
       RowBox[{"f", "[", "]"}], 
       RowBox[{"viel", "[", 
        RowBox[{"ortho\[Mu]", ",", "\[Mu]"}], "]"}], 
       RowBox[{"sigma", "[", 
        RowBox[{
         RowBox[{"-", "ortho\[Mu]"}], ",", "a", ",", "b"}], "]"}]}]}], "}"}], 
    "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.620852981090394*^9, 3.6208530123442297`*^9}, {
  3.6208530598559713`*^9, 3.620853097652912*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"last", "/.", "VabRules"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"%", "//", 
   RowBox[{"MakeZero", "[", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
         {"\[Sigma]", 
          StyleBox[GridBox[{
             {" ", "a", "b"},
             {
              OverscriptBox["\[Mu]", "_"], " ", " "}
            },
            GridBoxSpacings->{"Columns" -> {
                Offset[0.], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                 Offset[0.]}}, "RowsIndexed" -> {}}],
           FontSize->9]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Center}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.034999999999999996`]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}]}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`CD[-$CellContext`\[Mu]][
      $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
       xAct`xVect`b]],
     Editable->False], 
    StyleBox["]",
     ShowAutoStyles->False,
     AutoSpacing->False]}]}], 
  StyleBox["//",
   ShowAutoStyles->False,
   AutoSpacing->False], 
  StyleBox["Simplification",
   ShowAutoStyles->False,
   AutoSpacing->False]}], "\[IndentingNewLine]", 
 RowBox[{"%", "//", 
  RowBox[{
   RowBox[{"ChangeCovD", "[", 
    RowBox[{"#", ",", "CD", ",", "orthoCD"}], "]"}], 
   "&"}]}], "\[IndentingNewLine]", 
 RowBox[{"%", "/.", 
  RowBox[{
  "AChristoffelCDorthoCD", "\[Rule]", 
   "AChristoffelorthoCD"}]}], "\[IndentingNewLine]", 
 RowBox[{"last2", "=", 
  RowBox[{"%", "//", "BreakChristoffel"}]}]}], "Input",
 CellChangeTimes->{{3.618843203199917*^9, 3.6188432487656813`*^9}, {
   3.619325840484496*^9, 3.6193258435205603`*^9}, {3.6193275035298777`*^9, 
   3.619327552045624*^9}, {3.619327684601954*^9, 3.61932769085357*^9}, {
   3.619327942068202*^9, 3.61932796490307*^9}, {3.6193280219456778`*^9, 
   3.619328022313109*^9}, {3.6193282712790327`*^9, 3.619328356326717*^9}, {
   3.619328445686675*^9, 3.6193284886405087`*^9}, {3.619328968825897*^9, 
   3.6193290654936543`*^9}, {3.61932924230786*^9, 3.619329258702209*^9}, {
   3.619329353476727*^9, 3.619329384451872*^9}, {3.619329523546008*^9, 
   3.619329544675456*^9}, {3.61932960613862*^9, 3.619329630802696*^9}, {
   3.6193300765820837`*^9, 3.619330131796698*^9}, {3.619330186498693*^9, 
   3.619330186869178*^9}, {3.6193302202598248`*^9, 3.6193303148880177`*^9}, {
   3.6193305318241043`*^9, 3.619330620944868*^9}, {3.619331392653006*^9, 
   3.619331424656801*^9}, {3.619331782688088*^9, 3.619331816781782*^9}, {
   3.6193672296333714`*^9, 3.619367267730467*^9}, {3.620313638389676*^9, 
   3.620313646604321*^9}, {3.6205820504471416`*^9, 3.620582052233768*^9}, {
   3.620672264880048*^9, 3.6206723545800457`*^9}, {3.6206724578004847`*^9, 
   3.620672458337614*^9}, 3.620673484281242*^9, {3.62084663314672*^9, 
   3.620846637652134*^9}, {3.6208490969986343`*^9, 3.62084912812425*^9}, {
   3.620849710521975*^9, 3.620849740385478*^9}, {3.6208497707420387`*^9, 
   3.620849810496317*^9}, {3.620849869401197*^9, 3.620849913781128*^9}, {
   3.6208499781116667`*^9, 3.620850087855019*^9}, {3.620850359558351*^9, 
   3.620850434241743*^9}, {3.620850669030755*^9, 3.6208506694501677`*^9}, {
   3.620850773563233*^9, 3.620850824856571*^9}, {3.6208508595782623`*^9, 
   3.6208508751570063`*^9}, {3.6208509248460712`*^9, 
   3.6208509580795527`*^9}, {3.6208509933659*^9, 3.620851119917219*^9}, {
   3.620851154020426*^9, 3.6208511596855097`*^9}, {3.620852428900701*^9, 
   3.6208524314624662`*^9}, {3.620852966541733*^9, 3.62085297372812*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "1"]},
            {
             OverscriptBox["\[Mu]", "_"], " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`ortho\[Mu], 
      xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"e", 
         StyleBox[GridBox[{
            {
             OverscriptBox["\[Mu]", "_"], "\[Rho]"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "b", 
             SubscriptBox["a", "1"]},
            {
             OverscriptBox["\[Mu]", "_"], " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`ortho\[Mu], 
      xAct`xVect`b, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"e", 
         StyleBox[GridBox[{
            {
             OverscriptBox["\[Mu]", "_"], "\[Rho]"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {
             OverscriptBox["\[Mu]", "_"], " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, xAct`xVect`b],
     
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"e", 
         StyleBox[GridBox[{
            {
             OverscriptBox["\[Mu]", "_"], "\[Rho]"},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       SubscriptBox["\[Del]", "\[Mu]"], "f"}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`CD[-$CellContext`\[Mu]][
      xAct`xVect`f[]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
     Editable->False], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"e", 
            StyleBox[GridBox[{
               {
                OverscriptBox["\[Mu]", "_"], "\[Rho]"},
               {" ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[
         RowBox[{
          SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
            {"\[Sigma]", 
             StyleBox[GridBox[{
                {" ", "a", "b"},
                {
                 OverscriptBox["\[Mu]", "_"], " ", " "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->9]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}]}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`CD[-$CellContext`\[Mu]][
         $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
          xAct`xVect`b]],
        Editable->False]}], "+", 
      RowBox[{
       InterpretationBox[
        StyleBox[GridBox[{
           {"\[Sigma]", 
            StyleBox[GridBox[{
               {" ", "a", "b"},
               {
                OverscriptBox["\[Mu]", "_"], " ", " "}
              },
              GridBoxSpacings->{"Columns" -> {
                  Offset[0.], {
                   Offset[0.034999999999999996`]}, 
                  Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                   Offset[0.]}}, "RowsIndexed" -> {}}],
             FontSize->9]}
          },
          
          GridBoxAlignment->{
           "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
            "Rows" -> {{Center}}, "RowsIndexed" -> {}},
          GridBoxSpacings->{"Columns" -> {
              Offset[0.27999999999999997`], {
               Offset[0.034999999999999996`]}, 
              Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
              Offset[0.2], {
               Offset[0.4]}, 
              Offset[0.2]}, "RowsIndexed" -> {}}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
         xAct`xVect`b],
        Editable->False], " ", 
       InterpretationBox[
        StyleBox[
         RowBox[{
          SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
            {"e", 
             StyleBox[GridBox[{
                {
                 OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                {" ", " "}
               },
               GridBoxSpacings->{"Columns" -> {
                   Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                   Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
              FontSize->9]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Center}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.034999999999999996`]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}]}],
         ShowAutoStyles->False,
         AutoSpacing->False],
        $CellContext`CD[-$CellContext`\[Mu]][
         xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]]],
        Editable->False]}]}], ")"}]}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Nu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Nu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Nu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Nu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.6203136601690807`*^9, 3.6203136654831257`*^9}, {
   3.6205811883640213`*^9, 3.620581193718054*^9}, 3.620581591338416*^9, 
   3.620581625077613*^9, 3.620582053055242*^9, 3.6206723552333097`*^9, 
   3.620672459605282*^9, 3.620849133647088*^9, 3.620849242200865*^9, 
   3.6208492746757708`*^9, 3.6208496116645737`*^9, 3.620849742015387*^9, 
   3.6208497732285013`*^9, 3.6208498116766233`*^9, 3.6208499153837233`*^9, {
   3.6208499823180428`*^9, 3.6208500887933064`*^9}, 3.6208502845323677`*^9, {
   3.6208504285785093`*^9, 3.6208504349567623`*^9}, 3.620850594714541*^9, 
   3.620850672267049*^9, 3.620850963883483*^9, {3.620850997148963*^9, 
   3.620851036397546*^9}, 3.620851066678542*^9, {3.6208511303632927`*^9, 
   3.6208511609611998`*^9}, 3.6208524327423077`*^9, 3.620852893284272*^9, 
   3.6208531021915092`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Nu]", "\[Rho]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"b", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"a", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "b"},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
        xAct`xVect`b],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[
           RowBox[{
            SubscriptBox["\[Del]", "\[Mu]"], "f"}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`CD[-$CellContext`\[Mu]][
           xAct`xVect`f[]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[
           RowBox[{
            SubscriptBox["\[Del]", "\[Mu]"], GridBox[{
              {"e", 
               StyleBox[GridBox[{
                  {
                   OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                  {" ", " "}
                 },
                 GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
                FontSize->9]}
             },
             
             GridBoxAlignment->{
              "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
               "Rows" -> {{Center}}, "RowsIndexed" -> {}},
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.27999999999999997`], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
               "Rows" -> {
                 Offset[0.2], {
                  Offset[0.4]}, 
                 Offset[0.2]}, "RowsIndexed" -> {}}]}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`CD[-$CellContext`\[Mu]][
           xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]]],
          Editable->False]}]}], ")"}]}]}], ")"}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.6203136601690807`*^9, 3.6203136654831257`*^9}, {
   3.6205811883640213`*^9, 3.620581193718054*^9}, 3.620581591338416*^9, 
   3.620581625077613*^9, 3.620582053055242*^9, 3.6206723552333097`*^9, 
   3.620672459605282*^9, 3.620849133647088*^9, 3.620849242200865*^9, 
   3.6208492746757708`*^9, 3.6208496116645737`*^9, 3.620849742015387*^9, 
   3.6208497732285013`*^9, 3.6208498116766233`*^9, 3.6208499153837233`*^9, {
   3.6208499823180428`*^9, 3.6208500887933064`*^9}, 3.6208502845323677`*^9, {
   3.6208504285785093`*^9, 3.6208504349567623`*^9}, 3.620850594714541*^9, 
   3.620850672267049*^9, 3.620850963883483*^9, {3.620850997148963*^9, 
   3.620851036397546*^9}, 3.620851066678542*^9, {3.6208511303632927`*^9, 
   3.6208511609611998`*^9}, 3.6208524327423077`*^9, 3.620852893284272*^9, 
   3.620853102421495*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Nu]", "\[Rho]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"b", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"a", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "b"},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
        xAct`xVect`b],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {
              RowBox[{"A", "[", 
               RowBox[{"\[Del]", 
                RowBox[{",", 
                 SuperscriptBox["\[Del]", "\[Omega]"]}]}], "]"}], 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "},
                 {" ", "\[Mu]", 
                  OverscriptBox["\[Nu]", "_"]}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AChristoffelCDorthoCD[$CellContext`ortho\[Mu], \
-$CellContext`\[Mu], -$CellContext`ortho\[Nu]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Nu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Nu], $CellContext`\[Rho]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         RowBox[{"(", 
          InterpretationBox[
           StyleBox[
            RowBox[{
             SubscriptBox[
              SuperscriptBox["\[Del]", "\[Omega]"], "\[Mu]"], "f"}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`orthoCD[-$CellContext`\[Mu]][
            xAct`xVect`f[]],
           Editable->False], ")"}]}]}], ")"}]}]}], ")"}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.6203136601690807`*^9, 3.6203136654831257`*^9}, {
   3.6205811883640213`*^9, 3.620581193718054*^9}, 3.620581591338416*^9, 
   3.620581625077613*^9, 3.620582053055242*^9, 3.6206723552333097`*^9, 
   3.620672459605282*^9, 3.620849133647088*^9, 3.620849242200865*^9, 
   3.6208492746757708`*^9, 3.6208496116645737`*^9, 3.620849742015387*^9, 
   3.6208497732285013`*^9, 3.6208498116766233`*^9, 3.6208499153837233`*^9, {
   3.6208499823180428`*^9, 3.6208500887933064`*^9}, 3.6208502845323677`*^9, {
   3.6208504285785093`*^9, 3.6208504349567623`*^9}, 3.620850594714541*^9, 
   3.620850672267049*^9, 3.620850963883483*^9, {3.620850997148963*^9, 
   3.620851036397546*^9}, 3.620851066678542*^9, {3.6208511303632927`*^9, 
   3.6208511609611998`*^9}, 3.6208524327423077`*^9, 3.620852893284272*^9, 
   3.6208531025047483`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Nu]", "\[Rho]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"b", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"a", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "b"},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
        xAct`xVect`b],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {
              RowBox[{"A", "[", 
               SuperscriptBox["\[Del]", "\[Omega]"], "]"}], 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "},
                 {" ", "\[Mu]", 
                  OverscriptBox["\[Nu]", "_"]}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AChristoffelorthoCD[$CellContext`ortho\[Mu], \
-$CellContext`\[Mu], -$CellContext`ortho\[Nu]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Nu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Nu], $CellContext`\[Rho]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         RowBox[{"(", 
          InterpretationBox[
           StyleBox[
            RowBox[{
             SubscriptBox[
              SuperscriptBox["\[Del]", "\[Omega]"], "\[Mu]"], "f"}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`orthoCD[-$CellContext`\[Mu]][
            xAct`xVect`f[]],
           Editable->False], ")"}]}]}], ")"}]}]}], ")"}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.6203136601690807`*^9, 3.6203136654831257`*^9}, {
   3.6205811883640213`*^9, 3.620581193718054*^9}, 3.620581591338416*^9, 
   3.620581625077613*^9, 3.620582053055242*^9, 3.6206723552333097`*^9, 
   3.620672459605282*^9, 3.620849133647088*^9, 3.620849242200865*^9, 
   3.6208492746757708`*^9, 3.6208496116645737`*^9, 3.620849742015387*^9, 
   3.6208497732285013`*^9, 3.6208498116766233`*^9, 3.6208499153837233`*^9, {
   3.6208499823180428`*^9, 3.6208500887933064`*^9}, 3.6208502845323677`*^9, {
   3.6208504285785093`*^9, 3.6208504349567623`*^9}, 3.620850594714541*^9, 
   3.620850672267049*^9, 3.620850963883483*^9, {3.620850997148963*^9, 
   3.620851036397546*^9}, 3.620851066678542*^9, {3.6208511303632927`*^9, 
   3.6208511609611998`*^9}, 3.6208524327423077`*^9, 3.620852893284272*^9, 
   3.620853102596116*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Nu]", "\[Rho]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"b", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"a", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "b"},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
        xAct`xVect`b],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {
              RowBox[{"A", "[", 
               SuperscriptBox["\[Del]", "\[Omega]"], "]"}], 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "},
                 {" ", "\[Mu]", 
                  OverscriptBox["\[Nu]", "_"]}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AChristoffelorthoCD[$CellContext`ortho\[Mu], \
-$CellContext`\[Mu], -$CellContext`ortho\[Nu]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Nu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Nu], $CellContext`\[Rho]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         RowBox[{"(", 
          InterpretationBox[
           StyleBox[
            RowBox[{
             SubscriptBox[
              SuperscriptBox["\[Del]", "\[Omega]"], "\[Mu]"], "f"}],
            ShowAutoStyles->False,
            AutoSpacing->False],
           $CellContext`orthoCD[-$CellContext`\[Mu]][
            xAct`xVect`f[]],
           Editable->False], ")"}]}]}], ")"}]}]}], ")"}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{{3.6203136601690807`*^9, 3.6203136654831257`*^9}, {
   3.6205811883640213`*^9, 3.620581193718054*^9}, 3.620581591338416*^9, 
   3.620581625077613*^9, 3.620582053055242*^9, 3.6206723552333097`*^9, 
   3.620672459605282*^9, 3.620849133647088*^9, 3.620849242200865*^9, 
   3.6208492746757708`*^9, 3.6208496116645737`*^9, 3.620849742015387*^9, 
   3.6208497732285013`*^9, 3.6208498116766233`*^9, 3.6208499153837233`*^9, {
   3.6208499823180428`*^9, 3.6208500887933064`*^9}, 3.6208502845323677`*^9, {
   3.6208504285785093`*^9, 3.6208504349567623`*^9}, 3.620850594714541*^9, 
   3.620850672267049*^9, 3.620850963883483*^9, {3.620850997148963*^9, 
   3.620851036397546*^9}, 3.620851066678542*^9, {3.6208511303632927`*^9, 
   3.6208511609611998`*^9}, 3.6208524327423077`*^9, 3.620852893284272*^9, 
   3.6208531026776247`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"last2", "//", "ChangeCovD"}], "\[IndentingNewLine]", 
 RowBox[{"%", "/.", 
  RowBox[{"viel", "\[Rule]", "g"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"%", "//", 
     RowBox[{
      RowBox[{"ReplaceIndex", "[", 
       RowBox[{"#", ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"ortho\[Mu]", "\[Rule]", "\[Sigma]"}], ",", 
          RowBox[{
           RowBox[{"-", "ortho\[Mu]"}], "\[Rule]", 
           RowBox[{"-", "\[Sigma]"}]}], ",", 
          RowBox[{"ortho\[Nu]", "\[Rule]", "\[Tau]"}], ",", 
          RowBox[{
           RowBox[{"-", "ortho\[Nu]"}], "\[Rule]", 
           RowBox[{"-", "\[Tau]"}]}]}], "}"}]}], "]"}], "&"}]}], "//", 
    "Simplification"}], "//", "ToCanonical"}], "//", 
  "ContractMetric"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"last3", "=", "%"}], ";"}]}], "Input",
 CellChangeTimes->{{3.620851227038109*^9, 3.620851241651915*^9}, {
  3.6208512976101418`*^9, 3.6208513066757317`*^9}, {3.6208514225813627`*^9, 
  3.620851460589899*^9}, {3.6208514962445087`*^9, 3.620851648894513*^9}, {
  3.6208531781228943`*^9, 3.6208532913381557`*^9}, {3.620853344645216*^9, 
  3.620853387334268*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Nu]", "\[Rho]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"b", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"a", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"e", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "b"},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
        xAct`xVect`b],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {
              RowBox[{"A", "[", 
               SuperscriptBox["\[Del]", "\[Omega]"], "]"}], 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "},
                 {" ", "\[Mu]", 
                  OverscriptBox["\[Nu]", "_"]}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AChristoffelorthoCD[$CellContext`ortho\[Mu], \
-$CellContext`\[Mu], -$CellContext`ortho\[Nu]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Nu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Nu], $CellContext`\[Rho]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[
           RowBox[{
            SubscriptBox["\[PartialD]", "\[Mu]"], "f"}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xTensor`PD[-$CellContext`\[Mu]][
           xAct`xVect`f[]],
          Editable->False]}]}], ")"}]}]}], ")"}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"e", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`viel[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.620851242976762*^9, 3.6208513074002113`*^9, 3.620851452943514*^9, {
   3.620851514873064*^9, 3.6208515279182997`*^9}, {3.620851608766679*^9, 
   3.620851649858315*^9}, 3.620852440374743*^9, {3.620853196881497*^9, 
   3.6208532167106133`*^9}, {3.62085326435391*^9, 3.6208532924656887`*^9}, 
   3.6208533455673647`*^9, 3.620853388011692*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   InterpretationBox[
    StyleBox[GridBox[{
       {"g", 
        StyleBox[GridBox[{
           {" ", " "},
           {"\[Nu]", "\[Rho]"}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Rho]],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"b", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"g", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`g[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`a, $CellContext`a1],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           RowBox[{"A", "[", "D", "]"}], 
           StyleBox[GridBox[{
              {"a", " ", " "},
              {" ", "\[Mu]", 
               SubscriptBox["a", "1"]}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`AChristoffelSO8D[
       xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox["f",
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`f[],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"g", 
           StyleBox[GridBox[{
              {
               OverscriptBox["\[Mu]", "_"], "\[Rho]"},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       xAct`xVect`g[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
       Editable->False], " ", 
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "b", 
               SubscriptBox["a", "1"]},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], 
        xAct`xVect`b, $CellContext`a1],
       Editable->False]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {"\[Sigma]", 
           StyleBox[GridBox[{
              {" ", "a", "b"},
              {
               OverscriptBox["\[Mu]", "_"], " ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`sigma[-$CellContext`ortho\[Mu], xAct`xVect`a, 
        xAct`xVect`b],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {
              RowBox[{"A", "[", 
               SuperscriptBox["\[Del]", "\[Omega]"], "]"}], 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "},
                 {" ", "\[Mu]", 
                  OverscriptBox["\[Nu]", "_"]}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`AChristoffelorthoCD[$CellContext`ortho\[Mu], \
-$CellContext`\[Mu], -$CellContext`ortho\[Nu]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox["f",
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`f[],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Nu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[$CellContext`ortho\[Nu], $CellContext`\[Rho]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[
           RowBox[{
            SubscriptBox["\[PartialD]", "\[Mu]"], "f"}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xTensor`PD[-$CellContext`\[Mu]][
           xAct`xVect`f[]],
          Editable->False]}]}], ")"}]}]}], ")"}]}], "\[Equal]", 
  RowBox[{
   InterpretationBox[
    StyleBox["g",
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`gc,
    Editable->False], " ", 
   InterpretationBox[
    StyleBox[GridBox[{
       {"\[Delta]", 
        StyleBox[GridBox[{
           {" ", " "},
           {
            SubscriptBox["a", "1"], 
            SubscriptBox["a", "2"]}
          },
          GridBoxSpacings->{"Columns" -> {
              Offset[0.], {
               Offset[0.034999999999999996`]}, 
              Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
               Offset[0.]}}, "RowsIndexed" -> {}}],
         FontSize->9]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}}, 
        "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.034999999999999996`]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}],
     ShowAutoStyles->False,
     AutoSpacing->False],
    $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
    Editable->False], " ", 
   InterpretationBox[
    StyleBox["f",
     ShowAutoStyles->False,
     AutoSpacing->False],
    xAct`xVect`f[],
    Editable->False], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"b", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`b, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"a", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "a", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`a, $CellContext`a2],
          Editable->False]}]}], ")"}]}], "+", 
     RowBox[{
      InterpretationBox[
       StyleBox[GridBox[{
          {
           SubscriptBox["A", "1"], 
           StyleBox[GridBox[{
              {"a", 
               SubscriptBox["a", "1"]},
              {" ", " "}
             },
             GridBoxSpacings->{"Columns" -> {
                 Offset[0.], {
                  Offset[0.034999999999999996`]}, 
                 Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                  Offset[0.]}}, "RowsIndexed" -> {}}],
            FontSize->9]}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Center}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.034999999999999996`]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        ShowAutoStyles->False,
        AutoSpacing->False],
       $CellContext`At1[xAct`xVect`a, $CellContext`a1],
       Editable->False], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]", 
              StyleBox[GridBox[{
                 {"b", 
                  SubscriptBox["a", "2"]},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {" ", " "},
                 {"\[Mu]", "\[Nu]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
          Editable->False]}], "+", 
        RowBox[{
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Epsilon]g", 
              StyleBox[GridBox[{
                 {" ", " ", " "},
                 {"\[Mu]", "\[Nu]", "\[Rho]"}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"g", 
              StyleBox[GridBox[{
                 {
                  OverscriptBox["\[Mu]", "_"], "\[Rho]"},
                 {" ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          xAct`xVect`g[$CellContext`ortho\[Mu], $CellContext`\[Rho]],
          Editable->False], " ", 
         InterpretationBox[
          StyleBox[GridBox[{
             {"\[Sigma]", 
              StyleBox[GridBox[{
                 {" ", "b", 
                  SubscriptBox["a", "2"]},
                 {
                  OverscriptBox["\[Mu]", "_"], " ", " "}
                },
                GridBoxSpacings->{"Columns" -> {
                    Offset[0.], {
                    Offset[0.034999999999999996`]}, 
                    Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                    Offset[0.]}}, "RowsIndexed" -> {}}],
               FontSize->9]}
            },
            
            GridBoxAlignment->{
             "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
              "Rows" -> {{Center}}, "RowsIndexed" -> {}},
            GridBoxSpacings->{"Columns" -> {
                Offset[0.27999999999999997`], {
                 Offset[0.034999999999999996`]}, 
                Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
                Offset[0.2], {
                 Offset[0.4]}, 
                Offset[0.2]}, "RowsIndexed" -> {}}],
           ShowAutoStyles->False,
           AutoSpacing->False],
          $CellContext`sigma[-$CellContext`ortho\[Mu], 
           xAct`xVect`b, $CellContext`a2],
          Editable->False]}]}], ")"}]}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{
  3.620851242976762*^9, 3.6208513074002113`*^9, 3.620851452943514*^9, {
   3.620851514873064*^9, 3.6208515279182997`*^9}, {3.620851608766679*^9, 
   3.620851649858315*^9}, 3.620852440374743*^9, {3.620853196881497*^9, 
   3.6208532167106133`*^9}, {3.62085326435391*^9, 3.6208532924656887`*^9}, 
   3.6208533455673647`*^9, 3.620853388081498*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"b", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`a, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "b", 
             SubscriptBox["a", "1"]},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`b, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          SuperscriptBox["\[Del]", "\[Omega]"], "]"}], 
         StyleBox[GridBox[{
            {"\[Rho]", " ", " "},
            {" ", "\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelorthoCD[$CellContext`\[Rho], \
-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Rho]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Rho], xAct`xVect`a, xAct`xVect`b],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", "a", "b"},
            {"\[Nu]", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Nu], xAct`xVect`a, xAct`xVect`b],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       SubscriptBox["\[PartialD]", "\[Mu]"], "f"}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xTensor`PD[-$CellContext`\[Mu]][
      xAct`xVect`f[]],
     Editable->False]}]}], "\[Equal]", 
  RowBox[{
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"b", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`b, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "2"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`a, $CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]", 
         StyleBox[GridBox[{
            {"b", 
             SubscriptBox["a", "2"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilon2[xAct`xVect`b, $CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"b", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`b, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "a", 
             SubscriptBox["a", "2"]},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`a, $CellContext`a2],
     Editable->False]}], "+", 
   RowBox[{
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {
             SubscriptBox["a", "1"], 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-$CellContext`a1, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Rho]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Rho]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Rho]", "b", 
             SubscriptBox["a", "2"]},
            {" ", " ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Rho], xAct`xVect`b, $CellContext`a2],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{
  3.620851242976762*^9, 3.6208513074002113`*^9, 3.620851452943514*^9, {
   3.620851514873064*^9, 3.6208515279182997`*^9}, {3.620851608766679*^9, 
   3.620851649858315*^9}, 3.620852440374743*^9, {3.620853196881497*^9, 
   3.6208532167106133`*^9}, {3.62085326435391*^9, 3.6208532924656887`*^9}, 
   3.6208533455673647`*^9, 3.620853388297367*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"last3", "//", "EqIndices"}]], "Input",
 CellChangeTimes->{{3.6208534199965143`*^9, 3.620853507194482*^9}}],

Cell[BoxData[
 RowBox[{"HoldFirst", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"a", 
         RowBox[{",", "\[ThinSpace]"}], "b", 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Mu]"}], 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Nu]"}]}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[
      xAct`xVect`a, xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`\[Nu]],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"a1", 
         RowBox[{",", "\[ThinSpace]"}], "\[Rho]"}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[$CellContext`a1, $CellContext`\[Rho]],
      Editable->False]}], "}"}], "\[Equal]", 
   RowBox[{"{", 
    RowBox[{
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"a", 
         RowBox[{",", "\[ThinSpace]"}], "b", 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Mu]"}], 
         RowBox[{",", "\[ThinSpace]"}], 
         RowBox[{"-", "\[Nu]"}]}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[
      xAct`xVect`a, xAct`xVect`b, -$CellContext`\[Mu], -$CellContext`\[Nu]],
      Editable->False], ",", 
     InterpretationBox[
      StyleBox[
       RowBox[{
        StyleBox["{",
         FontColor->RGBColor[0, 0, 1]], 
        RowBox[{"a1", 
         RowBox[{",", "\[ThinSpace]"}], "a2", 
         RowBox[{",", "\[ThinSpace]"}], "\[Rho]"}], 
        StyleBox["}",
         FontColor->RGBColor[0, 0, 1]]}],
       ShowAutoStyles->False,
       AutoSpacing->False],
      xAct`xTensor`IndexList[$CellContext`a1, $CellContext`a2, $CellContext`\
\[Rho]],
      Editable->False]}], "}"}]}], "]"}]], "Output",
 CellChangeTimes->{{3.6208534248274927`*^9, 3.620853468830508*^9}, 
   3.6208535074941883`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"last4", "=", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"last3", "//", 
      RowBox[{"EqTimes", "[", 
       RowBox[{"sigma", "[", 
        RowBox[{
         RowBox[{"-", "\[Sigma]"}], ",", 
         RowBox[{"-", "a"}], ",", 
         RowBox[{"-", "b"}]}], "]"}], "]"}]}], "//", "Expand"}], "//", 
    "Simplification"}], "//", "ContractMetric"}]}]], "Input",
 CellChangeTimes->{{3.620853402369157*^9, 3.620853413090364*^9}, {
  3.6208535235018578`*^9, 3.620853568424014*^9}, {3.620853644807045*^9, 
  3.620853646292642*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", 
          SuperscriptBox["\[Del]", "\[Omega]"], "]"}], 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Sigma]", "\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelorthoCD[-$CellContext`\[Sigma], -$CellContext`\
\[Mu], -$CellContext`\[Nu]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False]}], "+", 
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", "a"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`a, -$CellContext`\[Mu], -xAct`xVect`a],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Sigma]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Sigma]],
     Editable->False]}], "+", 
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         RowBox[{"A", "[", "D", "]"}], 
         StyleBox[GridBox[{
            {"a", " ", " "},
            {" ", "\[Mu]", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`AChristoffelSO8D[
     xAct`xVect`a, -$CellContext`\[Mu], -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Nu]", "\[Sigma]", "\[Tau]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Nu], -$CellContext`\[Sigma], \
-$CellContext`\[Tau]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {"\[Tau]", " ", 
             SubscriptBox["a", "1"]},
            {" ", "a", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[$CellContext`\[Tau], -xAct`xVect`a, $CellContext`a1],
     Editable->False]}], "+", 
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Sigma]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Sigma]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[
      RowBox[{
       SubscriptBox["\[PartialD]", "\[Mu]"], "f"}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xTensor`PD[-$CellContext`\[Mu]][
      xAct`xVect`f[]],
     Editable->False]}]}], "\[Equal]", 
  RowBox[{
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {"a", 
             SubscriptBox["a", "1"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-xAct`xVect`a, -$CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Epsilon]g", 
         StyleBox[GridBox[{
            {" ", " ", " "},
            {"\[Mu]", "\[Nu]", "\[Sigma]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`epsilong[-$CellContext`\[Mu], -$CellContext`\[Nu], \
-$CellContext`\[Sigma]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False]}], "-", 
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {"a", 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-xAct`xVect`a, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Nu]", "\[Sigma]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Nu], -$CellContext`\[Sigma]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", " ", 
             SubscriptBox["a", "2"]},
            {"\[Mu]", 
             SubscriptBox["a", "1"], " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Mu], -$CellContext`a1, \
$CellContext`a2],
     Editable->False]}], "+", 
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {"a", 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-xAct`xVect`a, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Sigma]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Sigma]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", " ", 
             SubscriptBox["a", "2"]},
            {"\[Nu]", 
             SubscriptBox["a", "1"], " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Nu], -$CellContext`a1, \
$CellContext`a2],
     Editable->False]}], "+", 
   RowBox[{"2", " ", 
    InterpretationBox[
     StyleBox["g",
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`gc,
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {
         SubscriptBox["A", "1"], 
         StyleBox[GridBox[{
            {"a", 
             SubscriptBox["a", "1"]},
            {" ", " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`At1[xAct`xVect`a, $CellContext`a1],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Delta]", 
         StyleBox[GridBox[{
            {" ", " "},
            {"a", 
             SubscriptBox["a", "2"]}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`delta8[-xAct`xVect`a, -$CellContext`a2],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox["f",
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`f[],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"g", 
         StyleBox[GridBox[{
            {" ", " "},
            {"\[Mu]", "\[Nu]"}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     xAct`xVect`g[-$CellContext`\[Mu], -$CellContext`\[Nu]],
     Editable->False], " ", 
    InterpretationBox[
     StyleBox[GridBox[{
        {"\[Sigma]", 
         StyleBox[GridBox[{
            {" ", " ", 
             SubscriptBox["a", "2"]},
            {"\[Sigma]", 
             SubscriptBox["a", "1"], " "}
           },
           GridBoxSpacings->{"Columns" -> {
               Offset[0.], {
                Offset[0.034999999999999996`]}, 
               Offset[0.]}, "ColumnsIndexed" -> {}, "Rows" -> {{
                Offset[0.]}}, "RowsIndexed" -> {}}],
          FontSize->9]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Center}},
          "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.034999999999999996`]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}],
      ShowAutoStyles->False,
      AutoSpacing->False],
     $CellContext`sigma[-$CellContext`\[Sigma], -$CellContext`a1, \
$CellContext`a2],
     Editable->False]}]}]}]], "Output",
 CellChangeTimes->{{3.620853542290532*^9, 3.620853569246093*^9}, 
   3.620853647517929*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{681, 741},
WindowMargins->{{Automatic, 0}, {Automatic, 0}},
ShowSelection->True,
ShowCellTags->True,
Magnification->1.25,
FrontEndVersion->"8.0 for Linux x86 (64-bit) (October 10, 2011)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> 
     FrontEnd`FileName[{"Creative"}, "NaturalColor.nb", CharacterEncoding -> 
       "UTF-8"]]], 
   Cell[
    StyleData["Input"], CellMargins -> {{66, 10}, {0, 0}}, FontWeight -> 
    "Plain", FontSlant -> "Plain", FontTracking -> "Plain", 
    FontVariations -> {
     "Masked" -> False, "Outline" -> False, "Shadow" -> False, 
      "StrikeThrough" -> False, "Underline" -> False}], 
   Cell[
    StyleData["Output"], CellMargins -> {{66, 10}, {0, 0}}, FontSize -> 12], 
   Cell[
    StyleData["ContOutput", StyleDefinitions -> StyleData["Output"]], 
    CellChangeTimes -> {3.6185764637654533`*^9}, MenuSortingValue -> 10000], 
   Cell[
    StyleData["CalculationHeading"]]}, Visible -> False, FrontEndVersion -> 
  "8.0 for Linux x86 (64-bit) (October 10, 2011)", StyleDefinitions -> 
  "PrivateStylesheetFormatting.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 103, 1, 85, "Title"],
Cell[685, 25, 148, 2, 30, "Subtitle"],
Cell[CellGroupData[{
Cell[858, 31, 152, 2, 96, "Section"],
Cell[CellGroupData[{
Cell[1035, 37, 101, 1, 47, "Subsection"],
Cell[1139, 40, 248, 3, 37, "Text"],
Cell[CellGroupData[{
Cell[1412, 47, 1362, 20, 64, "Input"],
Cell[CellGroupData[{
Cell[2799, 71, 812, 11, 52, "Print"],
Cell[3614, 84, 1084, 19, 28, "Print"],
Cell[4701, 105, 833, 11, 52, "Print"],
Cell[5537, 118, 792, 10, 28, "Print"],
Cell[6332, 130, 773, 10, 28, "Print"],
Cell[7108, 142, 812, 11, 52, "Print"],
Cell[7923, 155, 1088, 19, 52, "Print"],
Cell[9014, 176, 833, 11, 52, "Print"],
Cell[9850, 189, 812, 11, 52, "Print"],
Cell[10665, 202, 967, 13, 121, "Print"],
Cell[11635, 217, 812, 11, 52, "Print"],
Cell[12450, 230, 812, 11, 52, "Print"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[13323, 248, 326, 7, 47, "Subsection"],
Cell[13652, 257, 115, 1, 37, "Text"],
Cell[CellGroupData[{
Cell[13792, 262, 1268, 29, 110, "Input"],
Cell[CellGroupData[{
Cell[15085, 295, 494, 10, 28, "Print"],
Cell[15582, 307, 506, 10, 28, "Print"],
Cell[16091, 319, 666, 15, 52, "Print"],
Cell[16760, 336, 736, 17, 52, "Print"],
Cell[17499, 355, 588, 13, 52, "Print"],
Cell[18090, 370, 724, 16, 52, "Print"],
Cell[18817, 388, 744, 17, 75, "Print"],
Cell[19564, 407, 784, 17, 52, "Print"],
Cell[20351, 426, 678, 15, 52, "Print"],
Cell[21032, 443, 168, 2, 52, "Print"],
Cell[21203, 447, 546, 11, 52, "Print"],
Cell[21752, 460, 173, 2, 52, "Print"],
Cell[21928, 464, 698, 17, 52, "Print"],
Cell[22629, 483, 792, 17, 52, "Print"],
Cell[23424, 502, 686, 15, 52, "Print"],
Cell[24113, 519, 558, 11, 52, "Print"],
Cell[24674, 532, 304, 6, 52, "Print"],
Cell[24981, 540, 296, 6, 28, "Print"],
Cell[25280, 548, 310, 6, 52, "Print"],
Cell[25593, 556, 562, 11, 52, "Print"]
}, Open  ]]
}, Open  ]],
Cell[26182, 571, 578, 19, 61, "Text"],
Cell[CellGroupData[{
Cell[26785, 594, 1415, 32, 179, "Input"],
Cell[CellGroupData[{
Cell[28225, 630, 496, 10, 28, "Print"],
Cell[28724, 642, 496, 10, 28, "Print"],
Cell[29223, 654, 496, 10, 28, "Print"]
}, Open  ]]
}, Open  ]],
Cell[29746, 668, 2156, 56, 225, "Input"],
Cell[31905, 726, 142, 2, 37, "Text"],
Cell[CellGroupData[{
Cell[32072, 732, 2795, 47, 87, "Input"],
Cell[34870, 781, 620, 13, 28, "Print"]
}, Open  ]],
Cell[35505, 797, 2710, 41, 87, "Input"],
Cell[38218, 840, 191, 4, 61, "Text"],
Cell[CellGroupData[{
Cell[38434, 848, 1013, 19, 87, "Input"],
Cell[CellGroupData[{
Cell[39472, 871, 592, 13, 52, "Print"],
Cell[40067, 886, 720, 15, 52, "Print"],
Cell[40790, 903, 742, 17, 75, "Print"],
Cell[41535, 922, 832, 18, 75, "Print"]
}, Open  ]]
}, Open  ]],
Cell[42394, 944, 102, 1, 37, "Text"],
Cell[CellGroupData[{
Cell[42521, 949, 1093, 27, 110, "Input"],
Cell[CellGroupData[{
Cell[43639, 980, 627, 13, 28, "Print"],
Cell[44269, 995, 569, 11, 28, "Print"],
Cell[44841, 1008, 505, 10, 28, "Print"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[45407, 1025, 167, 2, 47, "Subsection"],
Cell[45577, 1029, 103, 1, 37, "Text"],
Cell[45683, 1032, 1132, 30, 110, "Input"],
Cell[CellGroupData[{
Cell[46840, 1066, 421, 11, 40, "Input"],
Cell[47264, 1079, 420, 6, 52, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[47721, 1090, 329, 6, 40, "Input"],
Cell[CellGroupData[{
Cell[48075, 1100, 678, 15, 52, "Print"],
Cell[48756, 1117, 799, 17, 52, "Print"],
Cell[49558, 1136, 819, 19, 75, "Print"],
Cell[50380, 1157, 909, 20, 75, "Print"],
Cell[51292, 1179, 580, 10, 75, "Print"],
Cell[51875, 1191, 255, 5, 52, "Print"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[52179, 1202, 348, 6, 40, "Input"],
Cell[52530, 1210, 163, 3, 28, "Print"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[52742, 1219, 206, 3, 47, "Subsection"],
Cell[52951, 1224, 234, 5, 61, "Text"],
Cell[CellGroupData[{
Cell[53210, 1233, 1305, 29, 133, "Input"],
Cell[54518, 1264, 623, 13, 28, "Print"]
}, Open  ]],
Cell[55156, 1280, 933, 14, 85, "Text"],
Cell[CellGroupData[{
Cell[56114, 1298, 1014, 23, 64, "Input"],
Cell[57131, 1323, 655, 14, 28, "Print"]
}, Open  ]],
Cell[57801, 1340, 2546, 64, 271, "Input"],
Cell[CellGroupData[{
Cell[60372, 1408, 963, 17, 110, "Input"],
Cell[CellGroupData[{
Cell[61360, 1429, 525, 11, 52, "Print"],
Cell[61888, 1442, 1144, 20, 52, "Print"]
}, Open  ]]
}, Open  ]],
Cell[63059, 1466, 182, 4, 37, "Text"],
Cell[63244, 1472, 368, 11, 40, "Input"],
Cell[63615, 1485, 287, 5, 37, "Text"],
Cell[CellGroupData[{
Cell[63927, 1494, 1475, 36, 133, "Input"],
Cell[65405, 1532, 607, 12, 28, "Print"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[66073, 1551, 89, 1, 96, "Section"],
Cell[CellGroupData[{
Cell[66187, 1556, 143, 2, 47, "Subsection"],
Cell[66333, 1560, 236, 5, 57, "Text"],
Cell[66572, 1567, 1365, 31, 171, "Input"],
Cell[67940, 1600, 229, 4, 95, "Text"],
Cell[68172, 1606, 2276, 53, 495, "Input"]
}, Closed]],
Cell[CellGroupData[{
Cell[70485, 1664, 302, 4, 36, "Subsection"],
Cell[70790, 1670, 3673, 110, 4483, "Input"],
Cell[74466, 1782, 123, 1, 647, "Text"],
Cell[74592, 1785, 1540, 49, 1971, "Input"],
Cell[76135, 1836, 131, 1, 647, "Text"],
Cell[76269, 1839, 2159, 60, 1971, "Input"],
Cell[78431, 1901, 118, 1, 808, "Text"],
Cell[78552, 1904, 329, 9, 883, "Input"]
}, Closed]],
Cell[CellGroupData[{
Cell[78918, 1918, 95, 1, 36, "Subsection"],
Cell[79016, 1921, 284, 3, 137, "Text"],
Cell[79303, 1926, 2104, 49, 853, "Input"],
Cell[81410, 1977, 123, 1, 137, "Text"],
Cell[81536, 1980, 2579, 73, 941, "Input"],
Cell[84118, 2055, 111, 1, 137, "Text"],
Cell[84232, 2058, 3221, 75, 1378, "Input"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[87502, 2139, 101, 1, 58, "Section"],
Cell[CellGroupData[{
Cell[87628, 2144, 163, 2, 47, "Subsection"],
Cell[87794, 2148, 548, 16, 43, "Text"]
}, Closed]],
Cell[CellGroupData[{
Cell[88379, 2169, 98, 1, 36, "Subsection"],
Cell[88480, 2172, 134, 1, 37, "Text"],
Cell[CellGroupData[{
Cell[88639, 2177, 1332, 31, 64, "Input"],
Cell[89974, 2210, 6364, 178, 57, "Output"]
}, Closed]],
Cell[96353, 2391, 110, 1, 32, "Text"],
Cell[CellGroupData[{
Cell[96488, 2396, 194, 3, 40, "Input"],
Cell[96685, 2401, 6754, 191, 57, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[103476, 2597, 373, 10, 40, "Input"],
Cell[103852, 2609, 168, 2, 40, "Output"]
}, Closed]],
Cell[104035, 2614, 124, 1, 32, "Text"],
Cell[CellGroupData[{
Cell[104184, 2619, 2035, 38, 110, "Input"],
Cell[106222, 2659, 7486, 202, 57, "Output"],
Cell[113711, 2863, 8868, 233, 85, "Output"],
Cell[122582, 3098, 4189, 110, 57, "Output"]
}, Closed]],
Cell[126786, 3211, 313, 6, 56, "Text"]
}, Closed]],
Cell[CellGroupData[{
Cell[127136, 3222, 165, 2, 36, "Subsection"],
Cell[127304, 3226, 555, 12, 52, "Print"],
Cell[127862, 3240, 1005, 18, 40, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[128904, 3263, 102, 1, 47, "Subsection"],
Cell[CellGroupData[{
Cell[129031, 3268, 2120, 53, 179, "Input"],
Cell[131154, 3323, 9741, 267, 83, "Output"],
Cell[140898, 3592, 10414, 292, 97, "Output"],
Cell[151315, 3886, 9846, 267, 83, "Output"],
Cell[161164, 4155, 9844, 267, 83, "Output"],
Cell[171011, 4424, 2328, 69, 64, "Output"]
}, Closed]],
Cell[173354, 4496, 101, 1, 32, "Text"],
Cell[CellGroupData[{
Cell[173480, 4501, 1151, 25, 110, "Input"],
Cell[174634, 4528, 466, 6, 40, "Output"]
}, Closed]],
Cell[175115, 4537, 136, 3, 32, "Text"],
Cell[175254, 4542, 105, 1, 37, "Text"],
Cell[CellGroupData[{
Cell[175384, 4547, 980, 21, 110, "Input"],
Cell[176367, 4570, 11207, 297, 113, "Output"],
Cell[187577, 4869, 226, 4, 40, "Output"]
}, Closed]],
Cell[187818, 4876, 108, 1, 32, "Text"],
Cell[CellGroupData[{
Cell[187951, 4881, 1074, 25, 133, "Input"],
Cell[189028, 4908, 273, 4, 40, "Output"]
}, Closed]],
Cell[189316, 4915, 107, 1, 37, "Text"],
Cell[CellGroupData[{
Cell[189448, 4920, 624, 17, 110, "Input"],
Cell[190075, 4939, 222, 3, 40, "Output"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[190346, 4948, 99, 1, 36, "Subsection"],
Cell[CellGroupData[{
Cell[190470, 4953, 3309, 86, 179, "Input"],
Cell[193782, 5041, 19084, 524, 137, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[212903, 5570, 867, 14, 40, "Input"],
Cell[213773, 5586, 20509, 573, 163, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[234319, 6164, 941, 20, 110, "Input"],
Cell[235263, 6186, 21423, 569, 141, "Output"],
Cell[256689, 6757, 267, 4, 40, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[256993, 6766, 775, 21, 110, "Input"],
Cell[257771, 6789, 21415, 569, 181, "Output"],
Cell[279189, 7360, 221, 3, 40, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[279447, 7368, 751, 22, 133, "Input"],
Cell[280201, 7392, 7168, 200, 44, "Output"],
Cell[287372, 7594, 221, 3, 40, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[287630, 7602, 611, 17, 110, "Input"],
Cell[288244, 7621, 194, 3, 40, "Output"]
}, Closed]],
Cell[288453, 7627, 190, 3, 40, "Input"]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[288692, 7636, 163, 2, 96, "Section"],
Cell[CellGroupData[{
Cell[288880, 7642, 101, 1, 47, "Subsection"],
Cell[CellGroupData[{
Cell[289006, 7647, 751, 20, 110, "Input"],
Cell[CellGroupData[{
Cell[289782, 7671, 762, 14, 28, "Print"],
Cell[290547, 7687, 709, 13, 52, "Print"]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[291317, 7707, 155, 2, 47, "Subsection"],
Cell[CellGroupData[{
Cell[291497, 7713, 1294, 33, 87, "Input"],
Cell[292794, 7748, 8437, 226, 71, "Output"]
}, Closed]],
Cell[301246, 7977, 130, 1, 32, "Text"],
Cell[301379, 7980, 295, 7, 44, "Input"],
Cell[CellGroupData[{
Cell[301699, 7991, 1655, 25, 110, "Input"],
Cell[303357, 8018, 8986, 235, 71, "Output"],
Cell[312346, 8255, 8976, 235, 44, "Output"],
Cell[321325, 8492, 9012, 236, 44, "Output"],
Cell[330340, 8730, 7773, 206, 44, "Output"]
}, Closed]],
Cell[338128, 8939, 120, 1, 32, "Text"],
Cell[CellGroupData[{
Cell[338273, 8944, 1157, 20, 87, "Input"],
Cell[339433, 8966, 8365, 225, 71, "Output"],
Cell[347801, 9193, 8465, 228, 71, "Output"],
Cell[356269, 9423, 5691, 163, 47, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[361997, 9591, 604, 15, 64, "Input"],
Cell[362604, 9608, 6736, 193, 57, "Output"]
}, Closed]],
Cell[369355, 9804, 111, 1, 32, "Text"],
Cell[CellGroupData[{
Cell[369491, 9809, 578, 12, 64, "Input"],
Cell[370072, 9823, 8580, 231, 71, "Output"],
Cell[378655, 10056, 167, 2, 40, "Output"]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[378871, 10064, 106, 1, 47, "Subsection"],
Cell[CellGroupData[{
Cell[379002, 10069, 1885, 59, 156, "Input"],
Cell[380890, 10130, 15447, 419, 71, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[396374, 10554, 130, 2, 40, "Input"],
Cell[396507, 10558, 2134, 67, 64, "Output"]
}, Closed]],
Cell[CellGroupData[{
Cell[398678, 10630, 2786, 56, 248, "Input"],
Cell[401467, 10688, 15658, 423, 71, "Output"],
Cell[417128, 11113, 16428, 449, 98, "Output"],
Cell[433559, 11564, 21554, 588, 125, "Output"],
Cell[455116, 12154, 27231, 746, 179, "Output"],
Cell[482350, 12902, 26127, 699, 152, "Output"],
Cell[508480, 13603, 19835, 521, 98, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[528352, 14129, 122, 2, 40, "Input"],
Cell[528477, 14133, 19510, 516, 98, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[548024, 14654, 152, 3, 40, "Input"],
Cell[548179, 14659, 1187, 36, 44, "Output"]
}, Open  ]],
Cell[549381, 14698, 671, 19, 87, "Input"],
Cell[CellGroupData[{
Cell[550077, 14721, 3954, 85, 140, "Input"],
Cell[554034, 14808, 36341, 965, 163, "Output"],
Cell[590378, 15775, 29763, 771, 134, "Output"],
Cell[620144, 16548, 31178, 805, 136, "Output"],
Cell[651325, 17355, 31104, 803, 136, "Output"],
Cell[682432, 18160, 31106, 803, 136, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[713575, 18968, 1197, 29, 179, "Input"],
Cell[714775, 18999, 30550, 795, 136, "Output"],
Cell[745328, 19796, 30532, 795, 136, "Output"],
Cell[775863, 20593, 27268, 769, 152, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[803168, 21367, 130, 2, 40, "Input"],
Cell[803301, 21371, 2339, 72, 64, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[805677, 21448, 557, 15, 87, "Input"],
Cell[806237, 21465, 25916, 736, 156, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)