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Re: [Axiom-developer] Eval in Axiom/Aldor

From: Ralf Hemmecke
Subject: Re: [Axiom-developer] Eval in Axiom/Aldor
Date: Wed, 15 Nov 2006 13:14:07 +0100
User-agent: Thunderbird (X11/20061025)

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 ...

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.


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