2x2 Matrix implementation in Slang

gistfile1.scala

val class Mat2 Double⁴ {
  // instead of Double⁴ we could also write ⟨a: Double, b: Double, c: Double, d: Double⟩
  // then we'd have access to the elements with a, b, c, d instead of A₀, A₁, A₂, A₃

  private alias A = data // `data` is alias for `this`, but with type ⟨Double,Double,Double,Double⟩ or Double⁴
  def subscript(i: Int) = Aᵢ // a vector Double⁴ already has a subscript method, we expose it

  def +(M: Mat2) = Mat2[A + M] // expose Double⁴.+, with the right type (PS there's implicit Mat2 -> Double⁴)
  def -(M: Mat2) = Mat2[A - M] // expose Double⁴.-, with the right type
  def *(x: Double) = Mat2[A * ⟨x,x,x,x⟩]
  def /(x: Double) = Mat2[A / ⟨x,x,x,x⟩]

  def *(v: Vec2) = Vec2⟨Vec2⟨A₀, A₁⟩ ∙ v,
                        Vec2⟨A₂, A₃⟩ ∙ v⟩

  def *(M: Mat2) = Mat2⟨A₀ * M₀ + A₁ * M₂, A₀ * M₁ + A₁ * M₃,
                        A₂ * M₀ + A₃ * M₂, A₂ * M₁ + A₃ * M₃⟩

  def transpose() = Mat2⟨A₀, A₂,
                         A₁, A₃⟩
  alias …ᵀ = transpose // Capital superscript letters can be postfix operators
  alias …´ = transpose // so can "accute accent"

  def determinant() = A₀ * A₃ - A₁ * A₂
  alias |…| = determinant // closed operator

  def inverse() = Mat2⟨ A₃, -A₁,
                       -A₂,  A₀⟩ / |this|
  // we can't write `|A|` instead of `|this|` because |…| is not defined for Double⁴

  def superscript(i: Int) = if i == -1 then inverse() else throw Exception("superscript is only defined for -1");
  // this should ideally be compile time e.g.
  // def superscript(-1) = inverse or
  // alias superscript(-1) = inverse

}