75 lines
1.9 KiB
Typst
75 lines
1.9 KiB
Typst
#let title(cont, size: 18pt) = align(center)[
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#text(size: size * 2, weight: "bold")[#underline[#cont]]
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]
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// writes a butcher tableau using the minimum required amount of numbers.
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#let butcher(s, nums) = {
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let nums = nums.map(x => if type(x) == float or type(x) == int {
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$#x$
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} else { x })
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table(
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stroke: (x, y) => if x == 0 and y == s {
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(right: 0.7pt + black, top: 0.7pt + black)
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} else if x == 0 {
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(right: 0.7pt + black)
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} else if y == s {
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(top: 0.7pt + black)
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},
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align: (x, y) => (
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if x > 0 { center } else { left }
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),
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columns: s + 1,
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$0$, ..range(s).map(x => none), // first row
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..range(2, s + 1)
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.map(i => {
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let p(i) = calc.floor(i * i / 2 + i / 2 - 1)
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(
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nums.slice(p(i - 1), p(i - 1) + i),
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range(i, s + 1).map(x => none),
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).flatten()
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})
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.flatten(),
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none, ..nums.rev().slice(0, s).rev() // last row
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)
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}
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// automatically adds aligned "if" and "otherwise" strings to a case block.
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//
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// example:
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// ```
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// $ccases(x, x > 0, -x, x <= 0)$
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// // is the same as
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// $cases(x & quad "if" space x > 0, -x & quad "if" space x <= 0$
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//
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// $ccases(x, x > 0, -x)$
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// // is the same as
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// $cases(x & quad "if" space x > 0, -x & quad "otherwise"$
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// ```
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#let ccases(..args) = {
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let parsed = args.pos().map(x => if type(x) == content { x } else { $#x$ })
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let result_array = parsed
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.windows(2)
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.enumerate()
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.filter(x => calc.rem-euclid(x.first(), 2) == 0)
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.map(array.last)
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.map(x => x.intersperse($& quad "if" space$).join())
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if calc.rem-euclid(parsed.len(), 2) != 0 {
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result_array.push($#parsed.last() & quad "otherwise"$)
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}
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math.cases(..result_array)
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};
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// write fourier series faster
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#let fourier(
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x: $x$,
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N: $oo$,
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a_0: $a_0$,
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a_n: $a_n$,
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b_n: $b_n$,
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) = {
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$
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#a_0/2 + sum_(n=1)^#N #a_n cos(n #x)
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+ sum_(n=1)^#N #b_n sin(n #x)
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$
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}
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