See also the page named to Units and Dimensions.
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.
spad
)abbrev 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
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/UNITSFor example:
fricas
x:=withUnits(2.1,m)
Type: Units(Float)
fricas
y:=withUnits(3.2,s)
Type: Units(Float)
fricas
x*y
Type: Units(Float)
fricas
z:=withUnits(z::Polynomial Float,kg)
Type: Units(Fraction(Polynomial(Float)))
fricas
z*z
Type: Units(Fraction(Polynomial(Float)))
