Re: [Axiom-developer] Unit package question

[Martin Rubey]

Dear Ralf, CY,

in fact, I like this idea even better than mine. In private communication, we
developed the domain below, but your idea is conceptually better, I think. The
full blown thing would then be a category Units, that has as domains Mass,
Time, Length, ... I suppose.

Martin

)abb domain UNITS Units
Units(R: Field): Exports == Implementation where
  U == Fraction Polynomial Integer

  Exports == with

    "*": (%,%) -> %

    "+": (%,%) -> %

    coerce: % -> OutputForm

    withUnits: (R, U)  -> %

    setUnitSystem!: String -> String

  Implementation == add
    Rep := Record(expr: R, units: U) 

    system: String := "MKS"
    setUnitSystem! s == 
      t := system
      system := s
      t

    transform: U -> Record(scalar: R, units: U)

    transform u ==
      m := 'm::Symbol::Polynomial(Integer)::U
      v := u
      if system = "MKS"
      then v := eval(u, ['cm,        'dm], _
                        [m*1/100::U, m*1/10::U])$RationalFunction(Integer)

      s: Fraction Integer := leadingCoefficient(numer(v)) _
                           / leadingCoefficient(denom(v))
      r: U := leadingMonomial(numer(v))::U _
            / leadingMonomial(denom(v))::U _
            / s ::U
      [s::R, r]

    withUnits(e, u) == [e, u]::Rep

    x * y  == [(x::Rep).expr * (y::Rep).expr, (x::Rep).units * (y::Rep).units]

    x + y  == 
      ux := transform((x::Rep).units)
      uy := transform((y::Rep).units)
      if ux.units = uy.units
      then [(x::Rep).expr*ux.scalar + (y::Rep).expr*uy.scalar, ux.units]
      else error "+: Units have to match"

    coerce x == coerce((x::Rep).expr)$R * coerce((x::Rep).units)$U