#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)
};