From 2c5f23e8821da460df5a57b752183891aaedfa93 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 --- physica-manual.pdf | Bin 368667 -> 315556 bytes physica-manual.typ | 45 +++++++++++++++++++++++++++++++++++++++++++++ physica.typ | 23 +++++++++++++++++++++-- 3 files changed, 66 insertions(+), 2 deletions(-) diff --git a/physica-manual.pdf b/physica-manual.pdf index 90ae372d29589db6aef9677f83d4c4a854c46c95..6f0ba24dcca020d00c0c95d6191eefe5b1c171fd 100644 GIT binary patch delta 207471 zcmZ^}byOU|yDj=72_!)S1RLDlXV3siaJLy;g3BPmoesf0cyM-q{Sjyl z2s9MW_hy4goMfA74@t8Oj%IZYq9mDzJb6 z2S1-6gf|I|9EA&ukBXm@Lw~2Fb5x(Ag@5u5;=1-|NQmY$ry_(mXOZ$rL2&z<)d$bWwME#ppx)9x6wdsOUU`hIXrU@ziAT6A<|J^hb2HNYPqqi~b^MSuaa47BGC{|Ty3CO2)US~0$<;jg->YB%nkt2rz@6toj=2w(W~l;#!q z5D#PkF@Ht=%5E3dzt;^aADK2q3{4v$7F`2v3y-)LMr|t>maCuUu0z?`dP2i?iCDX> zt2Fc&IEWfT_``#{bJxY!-=5(*K#l1?0TZ&JYSpH(YWdF0;&}9kczWhoO_rE8+NY16 zGD6HE>>`Y 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zuX;!b`oEL{{)ci1211yS|87h$4FYjNpfm<4je`8U9*kgB#9tU1BTbNnEFSdoFk+Ao;rh$JM?xS0_BV$9iy0&g0{_>D3CbX0P~`vX1NiS%KmcKozm$Q&;eTTY z^xpze7v~W{9!C12Nsw^J1$h8L8#okwak(JjFxcN1;-4k-&+Gpy4M!5L2wlWb=!>R9 z!ZClD4v8Sl^@kT5BcOjRH6#N5*Lo&k$iL`EApXXXC**4T?o!IhQM$QXy1IM2TH8>ios9kX8q diff --git a/physica-manual.typ b/physica-manual.typ index 0be2ee7..efeb21b 100644 --- a/physica-manual.typ +++ b/physica-manual.typ @@ -852,6 +852,51 @@ $ isotope("Bi",a:211,z:83) --> isotope("Tl",a:207,z:81) + isotope("He",a:4,z:2) *(4)* #hl(`isotope("Tl",a:207,z:81) --> isotope("Pb",a:207,z:82) + isotope(e,a:0,z:-1)`) $ isotope("Tl",a:207,z:81) --> isotope("Pb",a:207,z:82) + isotope(e,a:0,z:-1) $ +=== The n-th term in Taylor series + +#v(1em) + +Function: `taylorterm(`_func_, _x_, _x0_, _idx_`)`. +- _func_: the function e.g. `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..9b742a6 100644 --- a/physica.typ +++ b/physica.typ @@ -288,8 +288,8 @@ #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 @@ -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) = { $attach(upright(element), tl: #a, bl: #z)$ }

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