> < ^ From:

> < ^ Subject:

In his message, John Neil asked:

>

> I have need to do calculations with group rings of ag-groups. Does GAP know

> how to deal with this already or am I looking at defining a new domain? If

> someone has already done something with this, I would appreciate knowing what

> it is.

>

Group Rings are not a built-in object. If the groups, in which you want to

compute are not too big (basically this means, that you can keep a list of

all group elements in memory at the same time and you are prepared to wait

for multiplications --- multiplication is done by simple distributive

expansion of sums, thus requires a lot of products to be computed), I can

provide some basic routines, I wrote some time ago. They provide a group

algebra as an vector space of dimension $|G|$, the basis corresponding to

the group elements. Thus elements are represented as sums of group elements.

Supported operations are almost only the basic ring operations +, -, *.

Alexander Hulpke

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