Add "sign" method

M2/Macaulay2/d/actors4.d

@@ -99,13 +99,24 @@ setupfun("setGroupID",setpgidfun);
 absfun(e:Expr):Expr := (
      when e
      is i:ZZcell do toExpr(abs(i.v))
-     is x:RRcell do toExpr(if sign(x.v) then -x.v else x.v)
+     is x:RRcell do toExpr(if signbit(x.v) then -x.v else x.v)
      is x:RRicell do toExpr(abs(x.v))
      is x:CCcell do toExpr(abs(x.v))
      is r:QQcell do toExpr(abs(r.v))
      else WrongArg("a number, real or complex"));
 setupfun("abs0",absfun);
 
+sign(e:Expr):Expr := (
+    when e
+    is x:ZZcell do toExpr(sign(x.v))
+    is x:QQcell do toExpr(sign(x.v))
+    is x:RRcell do toExpr(sign(x.v))
+    is x:CCcell do (
+	if isZero(x.v) then toExpr(toCC(0, 0, precision(x.v)))
+	else toExpr(x.v / abs(x.v)))
+    else WrongArg("a number, real or complex"));
+setupfun("sign0", sign);
+
 select(a:Sequence,f:Expr):Expr := (
      b := new array(bool) len length(a) do provide false;
      found := 0;

M2/Macaulay2/d/gmp.d

@@ -92,11 +92,10 @@ export min(x:ulong,y:ulong):ulong := if x<y then x else y;
 
 export max(x:ulong,y:ulong):ulong := if x<y then y else x;
 
-
-
-isPositive0(x:ZZ) ::=  1 == Ccode(int, "mpz_sgn(", x, ")");
-isZero0    (x:ZZ) ::=  0 == Ccode(int, "mpz_sgn(", x, ")");
-isNegative0(x:ZZ) ::= -1 == Ccode(int, "mpz_sgn(", x, ")");
+export sign(x:ZZ):int := Ccode(int, "mpz_sgn(", x, ")");
+isPositive0(x:ZZ) ::=  1 == sign(x);
+isZero0    (x:ZZ) ::=  0 == sign(x);
+isNegative0(x:ZZ) ::= -1 == sign(x);
 
 export isPositive(x:ZZ):bool := isPositive0(x);
 
@@ -645,8 +644,9 @@ export denominatorRef(x:QQmutable) ::= Ccode( ZZmutable, "mpq_denref(",  x, ")")
 
 export hash(x:QQ):hash_t := hash(numeratorRef(x))+1299841*hash(denominatorRef(x));
 
-isZero0    (x:QQ):bool :=  0 == Ccode(int, "mpq_sgn(",x,")");
-isNegative0(x:QQ):bool := -1 == Ccode(int, "mpq_sgn(",x,")");
+export sign(x:QQ):int := Ccode(int, "mpq_sgn(",x,")");
+isZero0    (x:QQ):bool :=  0 == sign(x);
+isNegative0(x:QQ):bool := -1 == sign(x);
 
 export isZero    (x:QQ):bool := isZero0(x);
 export isNegative(x:QQ):bool := isNegative0(x);
@@ -856,10 +856,11 @@ export realPart(z:CC):RR := z.re;
 export imaginaryPart(z:CC):RR := z.im;
 
 -- warning: these routines just check the sign bit, and don't verify finiteness!
-isPositive0(x:RR) ::=  1 == Ccode(int, "mpfr_sgn(", x, ")");
-isNegative0(x:RR) ::= -1 == Ccode(int, "mpfr_sgn(", x, ")");
-isZero0    (x:RR) ::=  0 == Ccode(int, "mpfr_sgn(", x, ")");
-
+export sign(x:RR):int := Ccode(int, "mpfr_sgn(", x, ")");
+isPositive0(x:RR) ::=  1 == sign(x);
+isNegative0(x:RR) ::= -1 == sign(x);
+isZero0    (x:RR) ::=  0 == sign(x);
+
 isPositive0(x:RRi) ::=  0 < Ccode(int, "mpfi_is_strictly_pos(", x, ")");
 isNegative0(x:RRi) ::=  0 < Ccode(int, "mpfi_is_strictly_neg(", x, ")");
 isZero0    (x:RRi) ::=  0 < Ccode(int, "mpfi_is_zero(", x, ")");
@@ -2576,9 +2577,7 @@ export yn(n:long,x:RR):RR := (
      Ccode( void, "mpfr_yn(", z, ",",n,",", x, ", MPFR_RNDN)" );
      moveToRRandclear(z));
 
-export sign(x:RR):bool := 0 != Ccode(int,"mpfr_signbit(",x,")");
-
-export sign(x:RRi):bool := 0 != Ccode(int,"mpfi_is_neg(",x,")");
+export signbit(x:RR):bool := 0 != Ccode(int,"mpfr_signbit(",x,")");
 
 -- complex transcendental functions
 

M2/Macaulay2/d/gmp1.d

@@ -70,7 +70,7 @@ export format(
      sep:string,		     -- separator between mantissa and exponent
      x:RR						-- the number to format
      ) : array(string) := (	   -- return: ("-","132.456") or ("","123.456")
-     ng := sign(x);
+     ng := signbit(x);
      if isinf(x) then return array(string)(if ng then "-" else "","infinity");
      if isnan(x) then return array(string)(if ng then "-" else "","NotANumber");
      meaningful := int(floor(precision(x) / log2ten)) + 1;
@@ -171,9 +171,9 @@ tostringRRipointer = tostringRRi;
 
 
 export toExternalString(x:RR):string := (
-     if isinf(x) then return if x < 0 then "-infinity" else "infinity";
-     if isnan(x) then return if sign(x) then "-NotANumber" else "NotANumber";
-     ng := sign(x);
+     ng := signbit(x);
+     if isinf(x) then return if ng then "-infinity" else "infinity";
+     if isnan(x) then return if ng then "-NotANumber" else "NotANumber";
      if ng then x = -x;
      ex := long(0);
      s := getstr(ex, base, 0, x);

M2/Macaulay2/m2/exports.m2

@@ -1137,6 +1137,7 @@ export {
 	"showStructure",
 	"showTex",
 	"showUserStructure",
+	"sign",
 	"sin",
 	"singularLocus",
 	"sinh",

M2/Macaulay2/m2/integers.m2

@@ -57,6 +57,10 @@ abs = method()
 abs ZZ := abs RR := abs RRi := abs CC := abs QQ := abs0
 abs Constant := abs @@ numeric
 
+sign = method()
+sign Number := sign0
+sign Constant := sign @@ numeric
+
 lcm = method(Binary => true)
 installMethod(lcm, () -> 1)
 lcm(ZZ,ZZ) := (f,g) -> (

M2/Macaulay2/packages/BettiCharacters.m2

@@ -1120,9 +1120,9 @@ Node
 	the sign character just constructed: the result is the
 	same as the character of the resolution.
     Example
-    	sign = character(R,15,hashTable {(0,{7}) =>
+    	sgn = character(R,15,hashTable {(0,{7}) =>
 		matrix{{1,-1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1}}})
-	dual(c,id_QQ)[-5] ** sign === c
+	dual(c,id_QQ)[-5] ** sgn === c
     Text
     	The second argument in the @TT "dual"@ command is the
 	restriction of complex conjugation to the field of
@@ -2840,8 +2840,8 @@ Node
 	    observed by tensoring with the character of the
 	    sign representation concentrated in degree 3.
     	Example
-	    sign = character(R,3, hashTable { (0,{3}) => matrix{{1,-1,1}} })
-	    dual(a,{1,2,3}) ** sign === a
+	    sgn = character(R,3, hashTable { (0,{3}) => matrix{{1,-1,1}} })
+	    dual(a,{1,2,3}) ** sgn === a
 
 ///
 
@@ -3062,10 +3062,10 @@ K = freeResolution ideal vars R
 S4 = symmetricGroupActors(R)
 A = action(K,S4)
 c = character A
-sign = character(R,5, hashTable { (-4,{-4}) => matrix{{-1,1,1,-1,1}} })
+sgn = character(R,5, hashTable { (-4,{-4}) => matrix{{-1,1,1,-1,1}} })
 -- check duality of representations in Koszul complex
 -- which is true up to a twist by a sign representation
-assert(dual(c,id_QQ) == c ** sign)
+assert(dual(c,id_QQ) == c ** sgn)
 ///
 
 end

M2/Macaulay2/packages/GradedLieAlgebras.m2

@@ -72,7 +72,6 @@ export {
     "mbRing",
     "minimalModel",
     "normalForm",
-    "sign",
     "Signs",
     "weight",    
     "VectorSpace",
@@ -2464,8 +2463,6 @@ isignlocal(BasicList,LieAlgebra):=(x,L)->
 -- the sign of an element 
 -- in the Ext-algebra
 
-
-sign=method()
 sign(LieElement) := (x)->(
     L:=class x;
    -- xx:=normalForm(x);

M2/Macaulay2/packages/GradedLieAlgebras/doc.m2

@@ -53,7 +53,7 @@ doc ///
 			{\mathbb Z}^n\times {\mathbb Z}/2{\mathbb Z}$, 
 			where the first 
 			component is called the @TO degree@, and the last component
-			is called the @TO sign@, which is 0 or 1 and have effect 
+			is called the @TO2{(sign, LieElement), "sign"}@, which is 0 or 1 and have effect 
 			on the axioms, see below. The list of components of the
 			grading except the sign 
 			is called the @TO weight@, and the last component of the 
@@ -72,7 +72,7 @@ doc ///
    			which are specified by @TO [lieAlgebra,Signs]@. 
    			The sign of a homogeneous element can be 
 			obtained by the function 
-   			@TO sign@. In the axioms
+   			@TO (sign, LieElement)@. In the axioms
    			below the sign of an element $a$ is written sign($a$).
 
 
@@ -249,7 +249,7 @@ doc ///
 	SeeAlso
 		lieDerivation
 		"isWellDefined(ZZ,LieDerivation)"
-		sign		
+		(sign, LieDerivation)
 		"Homomorphisms and derivations"  
 ///
 
@@ -717,7 +717,7 @@ Outputs
   L: LieAlgebra 
 SeeAlso
    lieAlgebra
-   sign
+   (sign, LieElement)
    "Second Lie algebra tutorial"
 Description
   Text
@@ -727,7 +727,7 @@ Description
     then all generators will be odd. The default value is that
     all generators are even. The signs affect the axioms of a Lie 
     superalgebra, see @TO LieAlgebra@. 
-    Use @TO sign@ to 
+    Use @TO (sign, LieElement)@ to 
     compute the sign of an arbitrary homogeneous Lie expression. 
 
   Example
@@ -743,7 +743,7 @@ Headline
   name for an optional argument for lieAlgebra
 SeeAlso
   lieAlgebra
-  sign
+  (sign, LieElement)
   "Second Lie algebra tutorial"
 Description
   Text
@@ -2171,7 +2171,7 @@ Description
       (ext_1+2 ext_0) ext_2 
 SeeAlso
       ExtAlgebra
-      sign
+      (sign, ExtElement)
       weight
 
 ///

M2/Macaulay2/packages/GradedLieAlgebras/doc2.m2

@@ -392,7 +392,7 @@ Headline =>
      be thought of as arbitrary.
      The weight of a derivation $d$ is the weight of $d$ as a graded map
      and may also be obtained as ", TT "d#weight.", 
-SeeAlso => {"firstDegree(LieElement)","sign","degreeLength"},
+SeeAlso => {"firstDegree(LieElement)",(sign, LieElement),"degreeLength"},
 SYNOPSIS {  
     Usage =>
       "w=weight(x)",   
@@ -983,7 +983,6 @@ document {
      }
 document {
 Key => {
-         sign,
        (sign,LieElement),
        (sign,ExtElement),
        (sign,LieDerivation)

M2/Macaulay2/packages/GradedLieAlgebras/tut2.m2

@@ -82,7 +82,7 @@ doc ///
 			defines the signs of all the generators to be 1.  
 			The signs affect the axioms of a Lie superalgebra, 
 			see @TO LieAlgebra@. 
-			Use @TO sign@ to 
+			Use @TO (sign, LieElement)@ to 
 			compute the sign of an arbitrary homogeneous Lie expression.
 
 

M2/Macaulay2/packages/Macaulay2Doc/functions.m2

@@ -247,6 +247,7 @@ load "./functions/setRandomSeed-doc.m2"
 load "./functions/setupLift-doc.m2"
 load "./functions/setupPromote-doc.m2"
 load "./functions/show-doc.m2"
+load "./functions/sign-doc.m2"
 load "./functions/sin-doc.m2"
 load "./functions/sinh-doc.m2"
 load "./functions/smithNormalForm-doc.m2"

M2/Macaulay2/packages/Macaulay2Doc/functions/sign-doc.m2

@@ -0,0 +1,29 @@
+doc ///
+  Key
+    sign
+    (sign, Number)
+    (sign, Constant)
+  Headline
+    sign (signum) function
+  Usage
+    sign x
+  Inputs
+    x:Number
+  Outputs
+    :{ZZ,CC}
+  Description
+    Text
+      When @VAR "x"@ is real, then this returns 1 if it is positive, -1 if it
+      is negative, and 0 if it is zero.
+    Example
+      sign 5
+      sign (-3)
+      sign 0
+    Text
+      If @VAR "x"@ is complex and nonzero, then this returns $x/|x|$.
+    Example
+      sign(-7*ii)
+  SeeAlso
+    "GradedLieAlgebras::sign(LieElement)"
+    "Permutations::sign(Permutation)"
+///

M2/Macaulay2/packages/Macaulay2Doc/ov_analytic_functions.m2

@@ -20,6 +20,7 @@ Node
     :Special functions
       integrate
       abs
+      sign
       floor
       (floor, Number)
       ceiling

M2/Macaulay2/packages/Parametrization.m2

@@ -702,16 +702,6 @@ return(rslt);
 --p=rtpt(1180943,-14640196896);
 --p_(0,0)^2+1180943*p_(0,1)^2-14640196896*p_(0,2)^2
 
-sign=method()
-sign(ZZ):=(n)->(
-if n>0 then return(1);
-if n<0 then return(-1);
-0)
-sign(QQ):=(n)->(
-if n>0 then return(1);
-if n<0 then return(-1);
-0)
-
 -- Jval(ZZ,ZZ,ZZ)
 -- computes the index of the argument
 

M2/Macaulay2/packages/Permanents.m2

@@ -50,7 +50,7 @@ ryser Matrix := (M) -> (
       for i from 1 to n-1 do(del = append(del,0););--delta is of length n
 
       --take the initial product corresponding to delta all +1's
-      sign:=1;
+      sgn:=1;
       prod:=1;
       for i from 0 to n-1 do(
 	  prod=prod*s#i;
@@ -60,7 +60,7 @@ ryser Matrix := (M) -> (
       curIndex:=0;--which position in the gray code changed
       curVal:=0;--what is the new value in the changed position of the gray code
       for count from 2 to 2^n do(--start at 2 because we already took the initial product corresponding to delta consisting of all 1's
-	  sign=(-1)*sign;
+	  sgn=(-1)*sgn;
 	  --increment delta
 	  flag:=1;
 	  for k from 0 to n-1 when flag==1 do(
@@ -79,7 +79,7 @@ ryser Matrix := (M) -> (
 	  	  prod=prod*s#i;
 	      );
 
-	  permanent = permanent+sign*prod;
+	  permanent = permanent+sgn*prod;
 	  );
 
       permanent
@@ -117,7 +117,7 @@ glynn Matrix := (M) -> (
       for i from 1 to n-2 do(del = append(del,0););--delta is of length n-1 because first position is always positive, so we don't consider it in the gray code
 
       --take the initial product corresponding to delta all +1's
-      sign:=1;
+      sgn:=1;
       prod:=1;
       for i from 0 to n-1 do(
 	  prod=prod*s#i;
@@ -127,7 +127,7 @@ glynn Matrix := (M) -> (
       curIndex:=0;--which position in the gray code changed
       curVal:=0;--what is the new value in the changed position of the gray code
       for count from 2 to 2^(n-1) do(--start at 2 because we already took the initial product corresponding to delta consisting of all 1's
-	  sign=(-1)*sign;
+	  sgn=(-1)*sgn;
 	  --increment delta
 	  flag:=1;
 	  for k from 0 to n-2 when flag==1 do(
@@ -146,7 +146,7 @@ glynn Matrix := (M) -> (
 	  	  prod=prod*s#i;
 	      );
 
-	  perm = perm+sign*prod;
+	  perm = perm+sgn*prod;
 	  );
 
       --need to divide in Glynn's formula