[GAP Forum] elements of algebra

[Stefan Kohl]

Dear Forum,

Alper Odabaş wrote:

> Good day.
> I have some (maybe stupid) questions:
> How can I get all elements of given algebra?

If your algebra is finite, then you can use `AsList'. E.g.:

gap> A := FullMatrixAlgebra(GF(2),2);
( GF(2)^[ 2, 2 ] )
gap> AsList(A);
[ [ <an immutable GF2 vector of length 2>, <an immutable GF2 vector of length
         2> ],

[ ... (rest of output omitted for saving space) ... ]

> For elements a,b in group G the command a^b in GAP computes (b^-1ab). How can I compute it in algebra case. 

In general you cannot.

The reason for this is simply that in general not all elements
of an algebra are invertible.

> is GAP best way in Commutative Algebra??? or CoCoA, Magma 

I feel that I am not a neutral person in this respect, thus prefer to leave
commenting on this to other people.

Hope this helps,

     Stefan Kohl