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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

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