From a90055a036c98e2a86a8bb835e1fbf8bd7378d65 Mon Sep 17 00:00:00 2001 From: euwbah Date: Fri, 31 Oct 2025 22:33:26 +0800 Subject: [PATCH 1/2] autodiv:0.1.0 --- packages/preview/auto-div/0.1.0/LICENSE | 21 ++ packages/preview/auto-div/0.1.0/README.md | 65 ++++++ packages/preview/auto-div/0.1.0/auto-div.typ | 188 ++++++++++++++++++ packages/preview/auto-div/0.1.0/example.pdf | Bin 0 -> 47969 bytes packages/preview/auto-div/0.1.0/example.typ | 20 ++ .../preview/auto-div/0.1.0/imgs/example.png | Bin 0 -> 45854 bytes packages/preview/auto-div/0.1.0/lib.pdf | Bin 0 -> 2306 bytes packages/preview/auto-div/0.1.0/lib.typ | 1 + packages/preview/auto-div/0.1.0/typst.toml | 13 ++ 9 files changed, 308 insertions(+) create mode 100644 packages/preview/auto-div/0.1.0/LICENSE create mode 100644 packages/preview/auto-div/0.1.0/README.md create mode 100644 packages/preview/auto-div/0.1.0/auto-div.typ create mode 100644 packages/preview/auto-div/0.1.0/example.pdf create mode 100644 packages/preview/auto-div/0.1.0/example.typ create mode 100644 packages/preview/auto-div/0.1.0/imgs/example.png create mode 100644 packages/preview/auto-div/0.1.0/lib.pdf create mode 100644 packages/preview/auto-div/0.1.0/lib.typ create mode 100644 packages/preview/auto-div/0.1.0/typst.toml diff --git a/packages/preview/auto-div/0.1.0/LICENSE b/packages/preview/auto-div/0.1.0/LICENSE new file mode 100644 index 0000000000..9b5add1eb9 --- /dev/null +++ b/packages/preview/auto-div/0.1.0/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2025 euwbah + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. \ No newline at end of file diff --git a/packages/preview/auto-div/0.1.0/README.md b/packages/preview/auto-div/0.1.0/README.md new file mode 100644 index 0000000000..68aa006d99 --- /dev/null +++ b/packages/preview/auto-div/0.1.0/README.md @@ -0,0 +1,65 @@ +# auto-div + +For automatic polynomial division. + +Currently, only integer and fractional coefficients are supported. More number systems planned for future releases. + +## Quick start + +For example, to evaluate $x^4 + 3x^3 + \frac{5}{2} x + 6$ divided by $x + 2$, specify the coefficients `(1, 3, 0, "5/2", 6)` and `(1, 2)` respectively. + +```typst +#import "@preview/auto-div:0.1.0": poly-div, poly-div-working + +Just the working itself (works both inside and outside math mode): + +$ #poly-div-working((1, 3, 0, "5/2", 6), (1, 2)) $ + +Obtaining parts of the polynomial division as math: + +#let result = poly-div((1, 3, 0, "5/2", 6), (1, 2)) +$ + result.dividend = (result.quotient) (result.divisor) + (result.remainder) +$ + +Obtaining quotient and remainder as an array of polynomial coefficients: + +Quotient: #result.quot-coeff + +Remainder: #result.rem-coeff +``` + +![Example image](imgs/example.png) + +> 💡 To do calculations with the returned coefficients' fraction strings, use [`fractus`](https://typst.app/universe/package/fractus/). + +## Methods + +### `poly-div` + +Polynomial long division. + +If only displaying the working of a polynomial long division without needing results in an array of numbers, use +`poly-div-working` instead. + +#### Parameters + +- `dividend` (`array`, positional): Coefficients of the dividend. Last element is x^0. For fractional coefficients, specify as strings e.g. "15/4", otherwise use integers. +- `divisor` (`array`, positional): Coefficients of divisor. Last element is for x^0. For fractional coefficients, specify as strings e.g. "15/4", otherwise use integers. +- `var` (`content`, named): The variable of the polynomial. Default is $x$. + +#### Returns + +Returns a dict: `(working:, quotient:, remainder:, quot-coeff:, rem-coeff:)`: + +- `working` (`content`): displayable content showing the working (as a table) +- `dividend` (`math.equation`): the dividend as a math equation object +- `divisor` (`math.equation`): the divisor as a math equation object +- `quotient` (`math.equation`): the quotient as a math equation object +- `remainder` (`math.equation`): the remainder as a math equation object +- `quot-coeff` (`array`): the coefficients of the quotient polynomial as an array of fraction strings +- `rem-coeff` (`array`): the coefficients of the remainder polynomial as an array of fraction strings + +### `poly-div-working` + +Same as `poly-div`, but returns only the `working`. \ No newline at end of file diff --git a/packages/preview/auto-div/0.1.0/auto-div.typ b/packages/preview/auto-div/0.1.0/auto-div.typ new file mode 100644 index 0000000000..6efb5f6c18 --- /dev/null +++ b/packages/preview/auto-div/0.1.0/auto-div.typ @@ -0,0 +1,188 @@ +#import "@preview/fractus:0.1.0" as fr + +/// Polynomial long division. +/// +/// If only displaying the working of a polynomial long division without needing results in an array of numbers, use +/// `poly-div-working` instead. +/// +/// == Returns +/// +/// Returns a dict: `(working:, dividend:, divisor:, quotient:, remainder:, quot-coeff:, rem-coeff:)` +/// +/// - `working` (`content`): displayable content showing the working (as a table) +/// - `dividend` (`math.equation`): the dividend as a math equation object +/// - `divisor` (`math.equation`): the divisor as a math equation object +/// - `quotient` (`math.equation`): the quotient as a math equation object +/// - `remainder` (`math.equation`): the remainder as a math equation object +/// - `quot-coeff` (`array`): the coefficients of the quotient polynomial as an array of fraction strings +/// - `rem-coeff` (`array`): the coefficients of the remainder polynomial as an array of fraction strings +/// +/// +/// - dividend (array): Coefficients of the dividend. Last element is x^0. For fractional coefficients, specify as strings e.g. "15/4". +/// - divisor (array): Coefficients of divisor. Last element is for x^0. For fractional coefficients, specify as strings e.g. "15/4". +/// - var (content): The variable of the polynomial. Default is `$x$`. +/// -> (working:, dividend:, divisor:, quotient:, remainder:, quot-coeff:, rem-coeff:) +#let poly-div( + dividend, + divisor, + var: $x$ +) = { + + let paren-space = 0.4em + + /// Use this function to construct fractus fraction objects. + /// + /// In fractus, fractions are represented as "n/d" strings, and operations operate on strings. + let simplify = fr.simplify + + /// Use this to display a fraction string of the form `"n/d"` as a math mode fraction. + let as-math(frc) = { + if frc == none { + return none + } + let (n, d) = frc.replace("-", "−").split("/") + if d != "1" { + $#n/#d$ + } else { + $#n$ + } + } + + let dividend = dividend.map(simplify) + let remainder = dividend.map(x => x) // shallow copy + let divisor = divisor.map(simplify) + let max-quotient-deg = dividend.len() - divisor.len() + let quotient = (simplify(0),) * (max-quotient-deg + 1) + + // List of table cells for the columns below the dividend, excludes + // the divisor, quotient, and dividend itself. + // + // One element per table row. + let working-table-rows = () + + // List of start positions of table horizontal lines + // for denoting subtractions + let subtraction-underline-pos = () + + /// Express polynomial coefficients as list of table cells + /// (left padding not included, right padding included) + let expr-cells(poly) = { + let cells = () + for (idx, coeff) in poly.enumerate() { + if fr.float(coeff) != 0 { + if idx != poly.len() - 1 { + // non-constant term, no need to specify 1 or -1, just use + or - + if idx != 0 and fr.float(coeff) > 0 { + // prepend explicit + for subsequent terms + coeff = if fr.float(coeff) == 1 {$+$} else {$+ #as-math(coeff)$} + } else if fr.float(coeff) == 1 { + // if leading term and positive 1 coeficient, no need coefficient. + coeff = $$ + } else if fr.float(coeff) == -1 { + coeff = $-$ + } else if fr.float(coeff) >= 0 { + coeff = as-math(coeff) + } else { + coeff = $-#as-math(fr.opposite(coeff))$ + } + } else { + if idx != 0 and fr.float(coeff) > 0 { + coeff = $+#as-math(coeff)$ + } else if fr.float(coeff) >= 0 { + coeff = as-math(coeff) + } else { + coeff = $-#as-math(fr.opposite(coeff))$ + } + } + let deg = poly.len() - 1 - idx + if deg > 1 { + cells.push([$#coeff#var^#deg$]) + } else if deg == 1 { + cells.push([#coeff#var]) + } else { + cells.push([#coeff]) + } + } else { + if idx != 0 { + cells.push([]) // empty cell for 0 coefficient + } else { + cells.push($0$) + } + } + } + return cells + } + + while remainder.len() >= divisor.len() { + let quotient-degree = remainder.len() - divisor.len() + let quotient-coeff = fr.division(remainder.first(), divisor.first()) + let subtract = divisor.map(x => fr.product(x, quotient-coeff)) + (simplify(0),) * quotient-degree + let rem = remainder.zip(subtract).map(((x, s)) => fr.difference(x, s)) + if fr.float(rem.first()) != 0 { + panic("Failed to eliminate top degree coefficient") + } + quotient.at(quotient.len() - quotient-degree - 1) = quotient-coeff + remainder = rem + while remainder.len() >= 1 and fr.float(remainder.first()) == 0 { + remainder = remainder.slice(1) + } + if quotient-coeff != 0 { + let sub-cells = expr-cells(subtract) + sub-cells.first() = $- ($ + sub-cells.first() + sub-cells.last() = sub-cells.last() + $)$ + working-table-rows.push(sub-cells) + let remainder-cells = expr-cells(remainder) + if remainder-cells.len() != 0 { + remainder-cells.last() = remainder-cells.last() + $#h(paren-space)$ + } + working-table-rows.push(remainder-cells) + subtraction-underline-pos.push(1 + dividend.len() - divisor.len() - quotient-degree) + } + } + + let columns = 1 + dividend.len() + let cells = () + // quotient row + let quot-cells = expr-cells(quotient) + quot-cells.last() = quot-cells.last() + $#h(paren-space)$ + cells += ([],) * (columns - quotient.len()) + quot-cells + // divisor & dividend row + let div-cells = expr-cells(dividend) + div-cells.last() = div-cells.last() + $#h(paren-space)$ + cells += (expr-cells(divisor).reduce((acc, x) => acc + x), ) + div-cells + // working rows + for row-cells in working-table-rows { + cells += ([],) * (columns - row-cells.len()) + row-cells + } + let content = table( + align: right, + inset: (x: 0pt, y: 5pt), + column-gutter: 2pt, + columns: columns, + stroke: none, + table.vline(x: 1, start: 1, end: 2, stroke: 0.7pt), + table.hline(y: 1, start: 1, stroke: 0.7pt), + ..subtraction-underline-pos.enumerate().map(((idx, start)) => table.hline(y: 3 + idx * 2, start: start, stroke: 0.7pt)), + ..cells + ) + ( + working: content, + dividend: expr-cells(dividend).reduce((acc, x) => acc + x), + divisor: expr-cells(divisor).reduce((acc, x) => acc + x), + quotient: expr-cells(quotient).reduce((acc, x) => acc + x), + remainder: expr-cells(remainder).reduce((acc, x) => acc + x), + quot-coeff: quotient, + rem-coeff: remainder + ) +} + +/// Use this to directly show the working for a polynomial long division. +/// +/// - dividend (array): Coefficients of the dividend. 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