> < ^ Date: Thu, 21 Aug 2003 09:30:00 -0600 (MDT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
> < ^ Subject: Re: Matrice powers

Dear GAP-Forum,

Nicola Sottocornola wrote:

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,

The problem is a missing method for `DefaultFieldOfMatrixGroup'. Such a method
will be added in the next release, I also append code for it to this email.

(We are aware of several further problems in working with matrix groups over
algebraic extensions. These will be rectified in the next release but some
of them are not ameneable to a simple patch for 4.3.)

Thank you for the bug report,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke

```#############################################################################
##
#M  DefaultFieldOfMatrixGroup( <elms> )
##
InstallMethod(DefaultFieldOfMatrixGroup,"alg elms",
[IsGroup and IsAlgebraicElementCollCollColl and HasGeneratorsOfGroup],0,
function(g)
local l,f,i,j,k,gens;
l:=GeneratorsOfGroup(g);
if Length(l)=0 then
l:=[One(g)];
fi;
gens:=l[1][1];
f:=DefaultFieldByGenerators(gens); # ist row
# are all elts in this?
for i in l do
for j in i do
for k in j do
if not k in f then
gens:=Concatenation(gens,[k]);
f:=DefaultFieldByGenerators(gens);
fi;
od;
od;
od;
return f;
end);
```

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