ex11: init

exercise11/lib.typ

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+#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)
+  $
+}

exercise11/main.typ

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+#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"
+

exercise11/problem1.typ

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+#import "@preview/physica:0.9.6": *
+#import "lib.typ": ccases
+
+= problem 1