Dear GAP-Forum, dear Alexander Hulpke,

thank you for your suggestion. Now it is possible to compute negative
powers of A but not to work with groups. For instance if I have, as in
my first post,

Indeterminate(Rationals,"x");;
p:=UnivariatePolynomial(Rationals,[1,-2,-2,-2,1],1);;
e:=FieldExtension(Rationals,p);;
t:=RootOfDefiningPolynomial(e);
si:=2*t/(1+t2); co:=(1-t2)/(1+t2);
idm:=IdentityMat(5,e);; 
A:=idm*[[0,0,0,0,1],
[1,0,0,0,0],
[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0]];;

and I write

gap> g:=Group(A);;

I obtain

gap> Size(g);
Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 2nd choice method found for
`GeneratorsOfLeftOperatorRingWithOne' on 1 arguments called from
GeneratorsOfLeftOperatorRingWithOne( A ) called from
GeneratorsOfLeftOperatorRing( A ) called from
Basis( V ) called from
Enumerator( D ) called from
Field( fg ) called from

How can I construct groups with matrix like these?

Thanks, Nicola

Alexander Hulpke wrote:

Dear GAP-Forum,

Nicola Sottocornola reported some problem with inverting a matrix defined
over an algebraic extension.

This problem stems from the fact that the algebraic extension (in GAP) did
not know that it has no zero divisors. This error will be corrected in the
next release.

As a workaround until then, you can read in the attached method into GAP4.3.

Best wishes,

Alexander Hulpke