Checking whether two algebras are isomorphic with MAGMA

Question

I want to use MAGMA to check whether to given finite dimensional algebras over a field are isomorphic. Here my attempt:

K := RationalField();
A<x,y> := FPAlgebra<K, x,y |
      x^2,y^2,(x+y)^2>;
A;

B<x,y> := FPAlgebra<K, x,y |
      x*y,y*(x+y),(x+y)*x>;
B;
IsIsomorphic(A,B);

It gives the error: Runtime error in 'IsIsomorphic': Bad argument types Argument types given: AlgFP, AlgFP in the online magma calculator http://magma.maths.usyd.edu.au/calc/ .

Question: Is there an easy fix to this? How can one check whether the two algebras are isomorphic using MAGMA?

Answer 1

For finite fields you could do this:

f:=GF(31);
FA<e1,x,y>:=FreeAlgebra(f,3);
rrr:=[x*x,y*y,(x+y)*(x+y)];
A:=BasicAlgebra(FA,rrr,1,[<1,1>,<1,1>]);
A;

Basic algebra of dimension 4 over GF(31)

Number of projective modules: 1

Number of generators: 3

FB<e,a,b>:=FreeAlgebra(f,3);
RRR:=[a*b,b*(a+b),(a+b)*a];
B:=BasicAlgebra(FB,RRR,1,[<1,1>,<1,1>]);
B;

Basic algebra of dimension 4 over GF(31)

Number of projective modules: 1

Number of generators: 3

IsIsomorphic(A,B);

false
[ 0]

I don't know if it is implemented for infinite fields. I get an error message when I enter it with f:=RationalField();