From 6d0903be082b05c0d60b46b0539e1b721779b067 Mon Sep 17 00:00:00 2001 From: Leedehai Date: Sat, 9 Dec 2023 17:23:37 -0500 Subject: [PATCH] Add taylorterm(), the n-th term in Taylor series Also, correct innerproduct to the more usual form . --- README.md | 4 +-- physica-manual.pdf | Bin 368667 -> 315365 bytes physica-manual.typ | 73 ++++++++++++++++++++++++++++++++++----------- physica.typ | 33 +++++++++++++++----- 4 files changed, 83 insertions(+), 27 deletions(-) diff --git a/README.md b/README.md index aba0f29..bbadfad 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,6 @@ :green_book: The [manual](https://github.com/Leedehai/typst-physics/blob/master/physica-manual.pdf).

-logo +logo

# The physica package for Typst @@ -21,7 +21,7 @@ natural sciences, including: * Dirac braket notations, * Common math functions, * Differentials and derivatives, including partial derivatives of mixed orders with automatic order summation, -* Familiar "h-bar", tensor abstract index notations, isotopes, +* Familiar "h-bar", tensor abstract index notations, isotopes, Taylor series term, * Signal sequences i.e. digital timing diagrams. :warning: [Typst](https://typst.app) is in beta and evolving, and this package diff --git a/physica-manual.pdf b/physica-manual.pdf index 90ae372d29589db6aef9677f83d4c4a854c46c95..6493a4dfa609fafa664b4a8c5ebf4dda3a8b5407 100644 GIT binary patch delta 234119 zcmV(=K-s^Wz!v476Oc&;PDMgTR#=fwp$1MxLPu6uvGzCtvpoWM1O`q;LPu6ule-4z z0y8(WL0ka>leV)vli&&Ov)u|t1OhiQm+?^rCX-7K5CO@PTn`|B7*0ylG$arL4TLnL zoRpJ>G^HFR1WI{RptR+*l*6IimZroBF?~=*s_ zI;{1=7YH%^8qf282i7iK_3L~005wk`M7pqa@rJdyFcLBi*F;*na?8Ls-`n(KTssJ9 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`f`, `(f+g)`, +- _x_: the variable name e.g. `x`, +- _x0_: the variable value at the expansion point e.g. `x_0`, `(1+a)`, +- _idx_: the index of the term, e.g. `0`, `1`, `2`, `n`, `(n+1)`. +If _x0_ or _idx_ is in a parenthesis e.g. `(1+k)`, then the function +automatically removes the outer parenthesis where appropriate. + +#align(center, [*Examples*]) + +#grid( + columns: (50%, 50%), + row-gutter: 1em, + column-gutter: 2em, + [ + *(1)* #hl(`taylorterm(f,x,x_0,0)`) \ + $ taylorterm(f,x,x_0,0) $ + ], + [ + *(2)* #hl(`taylorterm(f,x,x_0,1)`) \ + $ taylorterm(f,x,x_0,1) $ + ], + [ + *(3)* #hl(`taylorterm(f,x,(1+a),2)`) \ + $ taylorterm(f,x,(1+a),2) $ + ], + [ + *(4)* #hl(`taylorterm(f,x,x_0,n)`) \ + $ taylorterm(f,x,x_0,n) $ + ], + [ + *(5)* #hl(`taylorterm(F,x^nu,x^nu_0,n)`) \ + $ taylorterm(F,x^nu,x^nu_0,n) $ + ], + [ + *(6)* #hl(`taylorterm(f_p,x,x_0,(n+1))`) \ + $ taylorterm(f_p,x,x_0,(n+1)) $ + ], +) + + === Signal sequences (digital timing diagrams) In engineering, people often need to draw digital timing diagrams for signals, like $signals("1|0|1|0")$. diff --git a/physica.typ b/physica.typ index b4a8271..e895592 100644 --- a/physica.typ +++ b/physica.typ @@ -206,6 +206,11 @@ #let crossproduct = $times$ #let cprod = crossproduct +#let innerproduct(u, v) = { + $lr(angle.l #u, #v angle.r)$ +} +#let iprod = innerproduct + // == Matrices #let matrixdet(..sink) = { @@ -288,8 +293,8 @@ #let jmat = jacobianmatrix #let hessianmatrix(fs, xs, delim:"(") = { - assert(type(fs) == array, message: "expecting a one-element array") - assert(fs.len() == 1, message: "expecting only one function name") + assert(type(fs) == array, message: "usage: hessianmatrix(f; x, y...)") + assert(fs.len() == 1, message: "usage: hessianmatrix(f; x, y...)") let f = fs.at(0) assert(type(xs) == array, message: "expecting an array of variable names") let row_arrays = () // array of arrays @@ -364,11 +369,6 @@ $ lr(bar.v ket#h(0pt)mid(angle.r#h(0pt)angle.l)#h(0pt)bra bar.v) $ }) -#let innerproduct = braket -#let iprod = innerproduct -#let outerproduct = ketbra -#let oprod = outerproduct - #let matrixelement(n, M, m) = style(styles => { $ lr(angle.l #n#h(0pt)mid(bar.v)#h(0pt)#M#h(0pt)mid(bar.v)#h(0pt)#m angle.r) $ }) @@ -663,6 +663,25 @@ math.attach((T,hphantom(sym.zwj)).join(), t: uppers.join(), b: lowers.join()) } +#let taylorterm(fn, xv, x0, idx) = { + let noparen(expr) = { + if type(expr) == content and expr.func() == math.lr { + let children = expr.at("body").at("children") + children.slice(1, children.len() - 1).join() + } else { + expr + } + } + + if idx == [0] or idx == 0 { + $fn (noparen(x0))$ + } else if idx == [1] or idx == 1 { + $fn^((1)) (noparen(x0))(xv - x0)$ + } else { + $frac(fn^((noparen(idx))) (noparen(x0)), idx !)(xv - x0)^noparen(idx)$ + } +} + #let isotope(element, /*atomic mass*/a: none, /*atomic number*/z: none) = { $attach(upright(element), tl: #a, bl: #z)$ }