Ralf,
On Wednesday, November 15, 2006 7:14 AM you wrote:
>
> >> And I cant compile Martin one, maybe I should not assume that
> >> a Field is an INTDOM ...
>
> > No it not necessary to assume that a Field is an INTDOM.
>
> But it is true.
>
> Field(): Category == Join(EuclideanDomain,UniqueFactorizationDomain,
> DivisionRing) with ...
> EuclideanDomain(): Category == PrincipalIdealDomain with ...
> PrincipalIdealDomain(): Category == GcdDomain with ...
> GcdDomain(): Category == IntegralDomain with ...
>
You are right. I was not clear. I meant it is not necessary to
assume it *as an additional assumption* since it is true by
Axiom's definition of Field. But it is irrelevant to this problem.
> > I also don't understand Martin's workaround since Fraction does
> > not export elt with this signature.
>
> But ...
>
> UnivariatePolynomial(x:Symbol, R:Ring):
> UnivariatePolynomialCategory(R) with ...
>
> UnivariatePolynomialCategory(R:Ring): Category ==
> ...
> if R has IntegralDomain then
> Eltable(Fraction %, Fraction %)
> elt : (Fraction %, Fraction %) -> Fraction %
> ++ elt(a,b) evaluates the fraction of univariate
> polynomials \spad{a}
> ++ with the distinguished variable replaced by b.
>
> So Martin's suggestion does not sound so wrong to me.
>
Yes. However as I said, Fraction UnivariatePolynomial(x,F) does
not export elt so the workaround cannot work as it was written.
I tried writing:
test(a:Fraction UnivariatePolynomial(x, F)):Fraction
UnivariatePolynomial(x, F) ==
elt(a,1$Fraction(UnivariatePolynomial(x,
F)))$UnivariatePolynomial(x, F)
but Aldor continues to insist that there is no such elt that
returns Fraction UnivariatePolynomial(x, F). Perhaps it is a
compiler bug?
In any case, isn't it strange that UnivariatePolynomialCategory
should be Eltable(Fraction %, Fraction %)? What is Fraction doing
in that definition of UnivariatePolynomial(x, F)?
Note the presence of
eval : (%,UnivariatePolynomial(x,Fraction
Integer),UnivariatePolynomial(x,Fraction Integer)) -> %
in the example below. This is the eval that I used in my version.
(1) -> F:=FRAC INT
(1) Fraction Integer
Type: Domain
(2) -> F has Field
(2) true
Type: Boolean
(3) -> F has IntegralDomain
(3) true
Type: Boolean
(4) -> UP(x,FRAC INT) has Eltable(FRAC UP(x,FRAC INT),FRAC UP(x,FRAC
INT))
(4) true
Type: Boolean
(5) -> )sh Fraction UnivariatePolynomial(x,FRAC INT)
Fraction UnivariatePolynomial(x,Fraction Integer) is a domain
constructor.
Abbreviation for Fraction is FRAC
This constructor is exposed in this frame.
Issue )edit C:/Program
Files/axiom/mnt/windows/../../src/algebra/FRAC.spad to s
ee algebra source code for FRAC
------------------------------- Operations
--------------------------------
?*? : (Fraction Integer,%) -> % ?*? : (Integer,%) -> %
...
euclideanSize : % -> NonNegativeInteger
eval : (%,Equation UnivariatePolynomial(x,Fraction Integer)) -> %
eval : (%,List Equation UnivariatePolynomial(x,Fraction Integer)) -> %
eval : (%,List Symbol,List UnivariatePolynomial(x,Fraction Integer)) ->
%
eval : (%,List UnivariatePolynomial(x,Fraction Integer),List
UnivariatePolynomial(x,Fraction Integer)) -> %
eval : (%,Symbol,UnivariatePolynomial(x,Fraction Integer)) -> %
eval : (%,UnivariatePolynomial(x,Fraction
Integer),UnivariatePolynomial(x,Fraction Integer)) -> %
expressIdealMember : (List %,%) -> Union(List %,"failed")
...
wholePart : % -> UnivariatePolynomial(x,Fraction Integer)
-----------
Regards,
Bill Page.
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