Dear Willem and gap-forum,
That's too bad. A simple "substitution rule" or "evaluation map"
for algebras would be a useful feature to have in GAP.
BTW, this problem occurs outside the WeylAlg package.
Here's another simple example with lie algebras:
A:=SimpleLieAlgebra("A",1,Rationals);
U:=UniversalEnvelopingAlgebra(A);
g:=GeneratorsOfAlgebraWithOne(U);
a:=g[1];
hom:=AlgebraWithOneGeneralMappingByImages(U,U,g,g);
# This gets stuck
b:=Image(hom,a);
Regards,
R.N.
Willem de Graaf <[EMAIL PROTECTED]> wrote:
Dear Tsai,
You noted the following behaviour:
> Read("weylalg.gap");
> A:=WeylAlgebra(Rationals,1);
> g:=GeneratorsOfAlgebra(A);
> h:=[g[1],g[2]-g[3],g[2]+g[3]];
> hom:=AlgebraWithOneGeneralMappingByImages(A,A,g,h);
> a:=g[2];
> # This operation gets stuck
> b:=Image(hom,a);
>
> Any ideas why this is happening?
As far as I can see the following happens.
Unfortunately, GAP doesn't know how to compute the image in this
case, i.e., there is no special method implemented. So GAP
falls back on a method that is based on computing a basis
of the algebra in question. But because the algebra here is
infinite dimensional, this never terminates.
Best wishes,
Willem de Graaf
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