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

[Ralf Hemmecke]

Hi Antoine,

I don't know whether this is the right way to go, but at least it 
compiles and it might let you go further.

Suggestion:

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

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

Maybe you can make that shorter. In particular the numer/denom part is 
perhaps too much, but that is what I have found to work, ehm compile.

Now, don't ask me how to relate x and z. The reason why I have 
introduced that z lies in the definition of UP. It is not defined as 
PolynomialCategory as such, but the code says...

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

and there you already see that in a category default, you have no chance 
of seeing the x.

But then it says...

UnivariatePolynomialCategory(R:Ring): Category ==
 Join(PolynomialCategory(R, NonNegativeInteger, SingletonAsOrderedSet),

which let me to define z as the only element of SingletonAsOrderedSet.

Maybe that helps a bit.

Ralf


On 11/13/2006 11:44 PM, Antoine Hersen wrote:
> Hello,
>
> I am having some issue with the eval function, any ideas ?
> I have reduced my problem to the simplest form.
> It is making me crazy !!!
>
> Because UP, which is a PolynomialCat, has InnerEvalable
>
> PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet):
>         Category ==
>   Join(PartialDifferentialRing VarSet, FiniteAbelianMonoidRing(R, E),
>        Evalable %, InnerEvalable(VarSet, R),
>        InnerEvalable(VarSet, %), RetractableTo VarSet,
>        FullyLinearlyExplicitRingOver R)
>
> What am I missing ?
>
> Prog :
>
> #include "axiom.as <http://axiom.as>"
>
> TestEval( x:Symbol , F:Field): with {}
> == add {
>
>
>     import from UnivariatePolynomial(x,F) ;
>     import from Fraction UnivariatePolynomial(x,F) ;
>
>     test(a:Fraction UnivariatePolynomial(x,F)):Fraction 
> UnivariatePolynomial(x,F) == {
>         eval(a, x, 1)
>     }
>
> And here his the error message :
>
>  aldor -M no-abbrev -O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete 
> -DAxiom -Y $AXIOM/algebra eval.as <http://eval.as>
> #1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
> "eval.as <http://eval.as>", line 11:                 eval(a, x, 1)
>                     ................^
> [L11 C17] #2 (Error) No one possible return type satisfies the context type.
>   These possible return types were rejected:
>           -- Fraction(UnivariatePolynomial(x, F))
>   The context requires an expression of type 
> Fraction(UnivariatePolynomial(x, F)).
> The following could be suitable if imported:
>   eval: (Fraction(UnivariatePolynomial(x, F)), Symbol pretend 
> SetCategory, UnivariatePolynomial(x, F) pretend Type) -> 
> Fraction(UnivariatePolynomial(x, F)) from 
> Fraction(UnivariatePolynomial(x, F)), if UnivariatePolynomial(x, F) has 
> InnerEvalable(Symbol, UnivariatePolynomial(x, F))
>
> Thanks
>
> Antoine Hersen
> }
>
>
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