[GAP Forum] trace of an algebraic element

Thomas Breuer thomas.breuer at math.rwth-aachen.de
Tue Sep 29 10:17:27 BST 2009

Dear GAP Forum,

xiaolei zhang wrote

> I try to calculate the trace of an element, like this:
> GAP4, Version: 4.4.12 of 17-Dec-2008, x86_64-unknown-linux-gnu-gcc
> gap> F2:=GF(2);
> GF(2)
> gap> x:=X(GF(2), "x");
> x
> gap> F:=AlgebraicExtension(F2, x^2+x+1);
> <field of size 4>
> gap> r:=RootOfDefiningPolynomial(F);
> a
> gap> Trace(r);
> Error, no method found! For debugging hints type ?Recovery from NoMethodFound
> Error, no 1st choice method found for `AsDivisionRing' on 2 arguments
> called ......

Thanks for this report.
This bug will be fixed in the next version of GAP.

For the moment, the code appended below can be used to avoid the error.
Simply read it into your GAP session before you start your calculations.

All the best,
Thomas Breuer


# Replace a too general implication by an appropriate one.
l:= List( [ IsFieldControlledByGaloisGroup, IsField and IsFinite ],
          f -> TRUES_FLAGS( FLAGS_FILTER( f ) ) );;
for p in Filtered( IMPLICATIONS, p -> l = List( p, TRUES_FLAGS ) ) do
  p[2]:= FLAGS_FILTER( IsField and IsFFECollection );

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