[GAP Forum] algebra mapping problem

[Willem de Graaf]

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