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On Monday, August 22, 2005 8:20 AM Martin Rubey wrote:

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.

)abbrev domain UNITS Units
Units(R: Field): Exports == Implementation where
U == Fraction Polynomial Integer
Exports == with
"*": (%,%) -> %
"+": (%,%) -> %
coerce: % -> OutputForm
withUnits: (R, U)  -> %
setUnitSystem!: String -> String
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)$U spad  Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/884360936492130004-25px001.spad using old system compiler. UNITS abbreviates domain Units ------------------------------------------------------------------------ initializing NRLIB UNITS for Units compiling into NRLIB UNITS compiling exported setUnitSystem! : String -> String Time: 0.02 SEC. compiling local transform : Fraction Polynomial Integer -> Record(scalar: R,units: Fraction Polynomial Integer) Time: 0.05 SEC. compiling exported withUnits : (R,Fraction Polynomial Integer) ->$
UNITS;withUnits;RF$;3 is replaced by CONS Time: 0 SEC. compiling exported * : ($,$) ->$
Time: 0.01 SEC.
compiling exported + : ($,$) -> $Time: 0 SEC. compiling exported coerce :$ -> OutputForm
Time: 0 SEC.
(time taken in buildFunctor:  0)
;;;     ***       |Units| REDEFINED
;;;     ***       |Units| REDEFINED
Time: 0 SEC.
Warnings:
[1] *:  expr has no value
[2] *:  units has no value
[3] +:  units has no value
[4] +:  expr has no value
[5] +:  scalar has no value
[6] coerce:  expr has no value
[7] coerce:  units has no value
Cumulative Statistics for Constructor Units
Time: 0.08 seconds
finalizing NRLIB UNITS
Processing Units for Browser database:
--->-->Units(constructor): Not documented!!!!
--->-->Units((* (% % %))): Not documented!!!!
--->-->Units((+ (% % %))): Not documented!!!!
--->-->Units((coerce ((OutputForm) %))): Not documented!!!!
--->-->Units((withUnits (% R (Fraction (Polynomial (Integer)))))): Not documented!!!!
--->-->Units((setUnitSystem! ((String) (String)))): Not documented!!!!
--->-->Units(): Missing Description
; compiling file "/var/aw/var/LatexWiki/UNITS.NRLIB/UNITS.lsp" (written 04 APR 2022 05:50:09 PM):
; /var/aw/var/LatexWiki/UNITS.NRLIB/UNITS.fasl written
; compilation finished in 0:00:00.036
------------------------------------------------------------------------
Units is now explicitly exposed in frame initial
Units will be automatically loaded when needed from
/var/aw/var/LatexWiki/UNITS.NRLIB/UNITS

For example:

fricas
x:=withUnits(2.1,m)
 (1)
Type: Units(Float)
fricas
y:=withUnits(3.2,s)
 (2)
Type: Units(Float)
fricas
x*y
 (3)
Type: Units(Float)
fricas
z:=withUnits(z::Polynomial Float,kg)
 (4)
Type: Units(Fraction(Polynomial(Float)))
fricas
z*z
 (5)
Type: Units(Fraction(Polynomial(Float)))

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