From 69e9c61fc39d40e17de1939e935881a6ff9ea508 Mon Sep 17 00:00:00 2001 From: fredrikr79 Date: Fri, 7 Nov 2025 13:38:01 +0100 Subject: [PATCH] ex11: init --- exercise11/lib.typ | 74 ++++++++++++++++++++++++++++++++++++++++ exercise11/main.typ | 38 +++++++++++++++++++++ exercise11/problem1.typ | 4 +++ exercise11/problems.pdf | Bin 0 -> 236588 bytes 4 files changed, 116 insertions(+) create mode 100644 exercise11/lib.typ create mode 100644 exercise11/main.typ create mode 100644 exercise11/problem1.typ create mode 100644 exercise11/problems.pdf diff --git a/exercise11/lib.typ b/exercise11/lib.typ new file mode 100644 index 0000000..1cbd8ec --- /dev/null +++ b/exercise11/lib.typ @@ -0,0 +1,74 @@ +#let title(cont, size: 18pt) = align(center)[ + #text(size: size * 2, weight: "bold")[#underline[#cont]] +] + +// writes a butcher tableau using the minimum required amount of numbers. +#let butcher(s, nums) = { + let nums = nums.map(x => if type(x) == float or type(x) == int { + $#x$ + } else { x }) + table( + stroke: (x, y) => if x == 0 and y == s { + (right: 0.7pt + black, top: 0.7pt + black) + } else if x == 0 { + (right: 0.7pt + black) + } else if y == s { + (top: 0.7pt + black) + }, + align: (x, y) => ( + if x > 0 { center } else { left } + ), + columns: s + 1, + $0$, ..range(s).map(x => none), // first row + ..range(2, s + 1) + .map(i => { + let p(i) = calc.floor(i * i / 2 + i / 2 - 1) + ( + nums.slice(p(i - 1), p(i - 1) + i), + range(i, s + 1).map(x => none), + ).flatten() + }) + .flatten(), + none, ..nums.rev().slice(0, s).rev() // last row + ) +} + +// automatically adds aligned "if" and "otherwise" strings to a case block. +// +// example: +// ``` +// $ccases(x, x > 0, -x, x <= 0)$ +// // is the same as +// $cases(x & quad "if" space x > 0, -x & quad "if" space x <= 0$ +// +// $ccases(x, x > 0, -x)$ +// // is the same as +// $cases(x & quad "if" space x > 0, -x & quad "otherwise"$ +// ``` +#let ccases(..args) = { + let parsed = args.pos().map(x => if type(x) == content { x } else { $#x$ }) + let result_array = parsed + .windows(2) + .enumerate() + .filter(x => calc.rem-euclid(x.first(), 2) == 0) + .map(array.last) + .map(x => x.intersperse($& quad "if" space$).join()) + if calc.rem-euclid(parsed.len(), 2) != 0 { + result_array.push($#parsed.last() & quad "otherwise"$) + } + math.cases(..result_array) +}; + +// write fourier series faster +#let fourier( + x: $x$, + N: $oo$, + a_0: $a_0$, + a_n: $a_n$, + b_n: $b_n$, +) = { + $ + #a_0/2 + sum_(n=1)^#N #a_n cos(n #x) + + sum_(n=1)^#N #b_n sin(n #x) + $ +} diff --git a/exercise11/main.typ b/exercise11/main.typ new file mode 100644 index 0000000..91b85d1 --- /dev/null +++ b/exercise11/main.typ @@ -0,0 +1,38 @@ +#import "lib.typ" + +#let FONT_SIZE = 18pt; + +#set page(paper: "a4", margin: (x: 2.6cm, y: 2.8cm), numbering: "1 : 1") +#set par(justify: true, leading: 0.52em) + +#set text(font: "FreeSerif", size: FONT_SIZE, lang: "us") +#show math.equation: set text( + font: "Euler Math", + size: (FONT_SIZE * 1.0), + lang: "en", +) + +#set heading(numbering: none) +#show heading.where(level: 1): it => { + rect(inset: FONT_SIZE / 2)[#it] +} + +#show ref: it => if it.element.func() != heading { it } else { + link(it.target, it.element.body) +} + +#lib.title(size: FONT_SIZE)[exercise 11] + +these are my solutions to the eleventh exercise set of TMA4135. + +this document was created using +#link("https://typst.app/")[#text(blue.darken(5%))[typst]]. + +\ + +#outline(title: none) + +#pagebreak() + +#include "problem1.typ" + diff --git a/exercise11/problem1.typ b/exercise11/problem1.typ new file mode 100644 index 0000000..446a378 --- /dev/null +++ b/exercise11/problem1.typ @@ -0,0 +1,4 @@ +#import "@preview/physica:0.9.6": * +#import "lib.typ": ccases + += problem 1 diff --git a/exercise11/problems.pdf b/exercise11/problems.pdf new file mode 100644 index 0000000000000000000000000000000000000000..03cb99b7ef9188731876a057e0fabf3c1988dee6 GIT binary patch literal 236588 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