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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 13:25:40 +0100
User-agent: Thunderbird (X11/20061025)

On 11/15/2006 07:44 AM, Page, Bill wrote:
On Tuesday, November 14, 2006 6:20 PM Antoine Hersen wrote:
I get nasty FOAM run time error with Ralf solution (I used it
in a more involved context)

Ralf wrote:

Replace "eval(a, x, 1)" by

    z: SingletonAsOrderedSet := create();
    eval(numer a, z, 1)/eval(denom a, z, 1);

I don't understand why Ralf introduces a new variable z. But
I think that is the right idea.

Since I worked backwards to find where "eval" is implemented. That compiled and I was in a rush. I don't claim it is the way to go.



  UnivariatePolynomial(x, F) has

is true so one way that does work is:

    import from UnivariatePolynomial(x, F);
    import from NonNegativeInteger;

    test1(a:Fraction UnivariatePolynomial(x,F)):Fraction
UnivariatePolynomial(x,F) == {
        eval(numer a, monomial(1$F,1),1)/eval(denom a,

monomial(1$F,1) is just one way to get x in the right form.
(Perhaps Ralf missed this possibility.)

I hope you see that the eval from above is not the same function as the eval here.

I considered the definitions ...

UnivariatePolynomial(x:Symbol, R:Ring):
  UnivariatePolynomialCategory(R) with ...

UnivariatePolynomialCategory(R:Ring): Category ==
 Join(PolynomialCategory(R, NonNegativeInteger, SingletonAsOrderedSet),
      Eltable(R, R), Eltable(%, %), DifferentialRing,
      DifferentialExtension R) with ...

PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet):
        Category ==
  Join(PartialDifferentialRing VarSet, FiniteAbelianMonoidRing(R, E),
       Evalable %, InnerEvalable(VarSet, R),
       InnerEvalable(VarSet, %), RetractableTo VarSet,
       FullyLinearlyExplicitRingOver R) with

while I am using InnerEvalable(VarSet, R) (which has nothing to do with the symbol x from UnivariatePolynomial, you suggested

InnerEvalable(%, %)

from UnivariatePolynomial(x,F) where I must say, that I would have to dig deeper in the category hierarchy of UP in order to find that signature.

Two different "eval"s, where yours is probably a bit more general. I don't believe that they end up in the same implementation.


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