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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 1.5.0.8 (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.
Ralf

**[Axiom-developer] Eval in Axiom/Aldor**, *Antoine Hersen*, `2006/11/13`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Ralf Hemmecke*, `2006/11/13`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Martin Rubey*, `2006/11/14`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Antoine Hersen*, `2006/11/14`
**RE: [Axiom-developer] Eval in Axiom/Aldor**, *Page, Bill*, `2006/11/15`
**Re: [Axiom-developer] Eval in Axiom/Aldor**,
*Ralf Hemmecke* **<=**
**RE: [Axiom-developer] Eval in Axiom/Aldor**, *Page, Bill*, `2006/11/15`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Ralf Hemmecke*, `2006/11/15`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Gabriel Dos Reis*, `2006/11/15`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Ralf Hemmecke*, `2006/11/16`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Gabriel Dos Reis*, `2006/11/16`
**Re: [Axiom-developer] Eval in Axiom/Aldor**, *Ralf Hemmecke*, `2006/11/15`