From c4bb53ccf771e4741c7652eee830f35b2fad3c44 Mon Sep 17 00:00:00 2001 From: LordBaryhobal Date: Tue, 25 Jun 2024 18:50:29 +0200 Subject: [PATCH] added polynomials --- gallery/example3.pdf | Bin 160062 -> 160062 bytes gallery/example4.pdf | Bin 0 -> 169907 bytes gallery/example4.typ | 34 +++++++ src/lib.typ | 1 + src/poly.typ | 233 +++++++++++++++++++++++++++++++++++++++++++ 5 files changed, 268 insertions(+) create mode 100644 gallery/example4.pdf create mode 100644 gallery/example4.typ create mode 100644 src/poly.typ diff --git a/gallery/example3.pdf b/gallery/example3.pdf index 78f7120e7e89ae4a7abf1025dd2a5f895e20cc63..ab2412c0f83d9e7ec5a044694f33ac89504a1abf 100644 GIT binary patch delta 165 zcmdn@h;!c~&W0AoElkl_ET#qqM$_Z7n54n1?R8m90Zgo>23A1P%Q;L2P$ow%(`wP8 z;=o*|6vs5n++g=CH#5Uhzn}oW=_hiTG_Xr;XU$`J#bkh0o1?9*rh*1msp;~CO!5HB C8Z&AD delta 165 zcmdn@h;!c~&W0AoElkl_EC%L=2GirSn54n1?R8m90Zgn0=2k$_%Q;L2P$ow%(`r#4 z|EP>C|I}iyY_q6g7kE_^_va5iA)DQxMvWkLqk={j0s0k2432m*22#A1mkls5< 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zEWfX7-2g)_0Y_!HE}>EO=P%%Z280I!G9xX0Hly2*517jS)a3`x#r%^e z0EYf%ixbKiI0*xsXE-}rrf%thK=%^RziLP%FmwL;UkB&e87$xg(a$xkoFqv1_J4~{ c7SMlBI-7feAVoQy`2-j$zyskwKSA*S06~cwRR910 literal 0 HcmV?d00001 diff --git a/gallery/example4.typ b/gallery/example4.typ new file mode 100644 index 0000000..a671a61 --- /dev/null +++ b/gallery/example4.typ @@ -0,0 +1,34 @@ +#import "/src/lib.typ": * + +#let p = poly.poly(0,1,2,3,4) +#let q = poly.poly(5,6,7) + +#let a = poly.add(p, q) +#let b = poly.sub(p, q) + +$ + p = #poly.display(p) quad q = #poly.display(q)\ + p + q = #poly.display(a)\ + p - q = #poly.display(b)\ +$ + +#let P = poly.poly(7, -3, -3, 1, 1) +#let Q = poly.poly(-2, 1, 1) + +$ + P = #poly.display(P) quad Q = #poly.display(Q)\ + P / Q = #poly.display(P) / #poly.display(Q) +$ + +#let div = poly.div(P, Q) +#align(center, grid( + columns: 2, + align: left, + column-gutter: 2em, + row-gutter: 1em, + [dividend: #poly.display(div.dividend)], + grid.cell(rowspan: 4, (div.display)()), + [divisor: #poly.display(div.divisor)], + [quotient: #poly.display(div.quotient)], + [rest: #poly.display(div.rest)], +)) diff --git a/src/lib.typ b/src/lib.typ index f90a91b..5b20562 100644 --- a/src/lib.typ +++ b/src/lib.typ @@ -1,4 +1,5 @@ #import "mat.typ" +#import "poly.typ" #import "vec.typ" #import "gauss.typ" \ No newline at end of file diff --git a/src/poly.typ b/src/poly.typ new file mode 100644 index 0000000..21c23d3 --- /dev/null +++ b/src/poly.typ @@ -0,0 +1,233 @@ +#let is-poly(poly) = { + if type(poly) != dictionary {return false} + if poly.at("type", default: none) != "polynomial" {return false} + return true +} + +#let _check(poly) = { + if not is-poly(poly) { + panic("Argument is not a polynomial") + } +} + +#let poly(..args, trim-zeros: true) = { + let coefs = args.pos() + + if trim-zeros { + let last-i = coefs.rev().position(c => c != 0) + if last-i == none { + last-i = -1 + } + + coefs = coefs.slice(0, calc.min(coefs.len(), coefs.len() - last-i)) + } + + if coefs.len() == 0 { + coefs.push(0) + } + + return ( + type: "polynomial", + coefs: coefs, + deg: coefs.len() - 1 + ) +} + +#let copy(original) = { + _check(original) + return poly(..original.coefs) +} + +#let display(poly) = { + _check(poly) + + let fractions = (2, 3, 4, 5, 6) + let beautify-frac(value) = { + if calc.round(value) == value { + return str(value) + } + for den in fractions { + for num in range(1, 2 * den) { + if value == num / den { + return str(num) + "/" + str(den) + } + } + } + return str(value) + } + + let res = "" + for (i, coef) in poly.coefs.rev().enumerate() { + if coef == 0 and poly.deg > 0 { + continue + } + if i != 0 { + res += " " + if coef < 0 { res += "-" } + else { res += "+" } + } else if coef < 0 { + res += "-" + } + + if calc.abs(coef) != 1 or poly.deg - i == 0 { + res += str(beautify-frac(calc.abs(coef))) + } + if poly.deg - i > 0 { + res += "x" + } + if poly.deg - i > 1 { + res += "^" + str(poly.deg - i) + } + } + return eval("$" + res + "$") +} + +#let pad(poly1, deg) = { + let coefs = poly1.coefs + coefs += (0,) * calc.max(0, (deg - poly1.deg)) + return poly(..coefs, trim-zeros: false) +} + +#let shift(poly1, deg) = { + let coefs = (0,) * calc.max(0, (deg - poly1.deg)) + coefs += poly1.coefs + return poly(..coefs) +} + +#let add(poly1, poly2) = { + let deg = calc.max(poly1.deg, poly2.deg) + let poly1 = pad(poly1, deg) + let poly2 = pad(poly2, deg) + + let coefs = poly1.coefs.zip(poly2.coefs).map(p => p.sum()) + + return poly(..coefs) +} + +#let sub(poly1, poly2) = { + let deg = calc.max(poly1.deg, poly2.deg) + let poly1 = pad(poly1, deg) + let poly2 = pad(poly2, deg) + + let coefs = poly1.coefs.zip(poly2.coefs).map(p => p.at(0) - p.at(1)) + + return poly(..coefs) +} + +#let mul(poly1, f) = { + let coefs = poly1.coefs.map(c => c * f) + return poly(..coefs) +} + +#let to-cells(poly) = { + let cells = () + let first = true + for (i, coef) in poly.coefs.rev().enumerate() { + if coef == 0 and poly.deg > 0 { + cells.push("") + continue + } + let cell = "" + if i != 0 { + if coef < 0 { cell += "-" } + else if not first { cell += "+" } + } else if coef < 0 { + cell += "-" + } + + if calc.abs(coef) != 1 or poly.deg - i == 0 { + cell += str(calc.abs(coef)) + } + if poly.deg - i > 0 { + cell += "x" + } + if poly.deg - i > 1 { + cell += "^" + str(poly.deg - i) + } + cells.push(eval("$" + cell + "$")) + first = false + } + if poly.coefs.position(c => c != 0) == none { + cells.last() = "0" + } + return cells +} + +#let div( + poly1, + poly2, + max-steps: 10 +) = { + let P = poly1 + let Q = poly2 + let p = P + let rows = () + let steps = () + let D = poly() + let count = 0 + + while p.deg >= Q.deg and p.coefs.position(c => c != 0) != none { + let f = p.coefs.at(p.deg) / Q.coefs.at(Q.deg) + let sub = shift(mul(Q, -f), p.deg) + let rem = add(p, sub) + let d = shift(poly(f), p.deg - Q.deg) + steps.push(( + p: p, + sub: sub, + rem: rem, + f: f, + d: d + )) + + D = add(D, d) + p = rem + if count >= max-steps { + panic("Exceeded maximum number of steps") + break + } + count += 1 + } + + let make-table( + vpad: 5pt, + hpad: 5pt, + stroke: black + 1pt, + debug-grid: false + ) = { + let cells = () + cells += to-cells(P) + cells.push(table.vline(stroke: stroke)) + cells.push(display(Q)) + cells.push(table.hline(start: P.deg + 1, stroke: stroke)) + + for (i, step) in steps.enumerate() { + cells += to-cells(pad(step.sub, P.deg)) + if i == 0 { + cells.push(display(D)) + } else { + cells.push("") + } + cells.push(table.hline(start: P.deg - step.sub.deg, end: P.deg - step.sub.deg + Q.deg + 1, stroke: stroke)) + cells += to-cells(pad(step.rem, P.deg)) + cells.push("") + } + + table( + columns: P.deg + 2, + stroke: if debug-grid {gray + 1pt} else {none}, + fill: none, + align: (x, _) => if x == P.deg + 1 {left} else {right}, + inset: (left: hpad, right: hpad, top: vpad, bottom: vpad), + ..cells + ) + } + + return ( + dividend: P, + divisor: Q, + quotient: D, + rest: p, + steps: steps, + display: make-table + ) +} \ No newline at end of file