How do I construct the group algebra of a group in GAP?

Question

I tried the following:

gap> C3 := CyclicGroup(3);
<pc group of size 3 with 1 generators>
gap> A := Algebra(Rationals, GeneratorsOfGroup(C3));
<algebra over Rationals, with 1 generators>

but:

gap> Dimension(A);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `IsFiniteDimensional' on 1 arguments at /proc/cygdrive/E/gap-4.10.0/lib/methsel2.g:250 called from
IsFiniteDimensional( V ) at /proc/cygdrive/E/gap-4.10.0/lib/modfree.gi:318     called from
<function "unknown">( <arguments> )
 called from read-eval loop at *stdin*:490
type 'quit;' to quit to outer loop
brk> quit;

and even:

gap> Zero(A);
Error, no method found! For debugging hints type ?Recovery from     NoMethodFound
Error, no 1st choice method found for `ZeroMutable' on 1 arguments at     /proc/cygdrive/E/gap-4.10.0/lib/methsel2.g:250 called from
ZERO_MUT( elm ) at /proc/cygdrive/E/gap-4.10.0/lib/arith.gi:79 called from
Zero( Representative( A ) ) at /proc/cygdrive/E/gap-    4.10.0/lib/addmagma.gi:605 called from
<function "unknown">( <arguments> )
 called from read-eval loop at *stdin*:490
type 'quit;' to quit to outer loop
brk> quit;

Answer 1

To construct a group ring, use GroupRing:

gap> G := CyclicGroup(3);
<pc group of size 3 with 1 generators>
gap> QG := GroupRing(Rationals,G);
<algebra-with-one over Rationals, with 1 generators>
gap> Dimension(QG);
3
gap> Zero(QG);
<zero> of ...
gap> One(QG);
(1)*<identity> of ...
gap> Random(QG);
(1)*f1+(-1)*f1^2

Please see also this question. In GAP, see Magma rings documentation. There are also some packages related to group rings, primarily LAGUNA and Wedderga.