Dear GAP - Forum,

David Joyner wrote:

Is the following behavior a bug?

gap> S:=PolynomialRing(Rationals,["x"]);
<algebra-with-one over Rationals, with 1 generators>
gap> p0:=UnivariatePolynomial(Rationals,[1,1,1,1,1,1,1,1,1,1],1);
1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9
gap> p0:=UnivariatePolynomial(Rationals,[1,1,1,1,1,1,1,1,1,1,1],1);
1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10
gap> C11:=FieldExtension(Rationals,p0);
<field in characteristic 0>
gap> IsAbelianNumberField(C11);
value property is already set the other way at
SetIsPrimeField( P, true );
PrimeField( F ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop, you can 'quit;' to quit to outer
loop,
or you can return to set it anyhow to continue
brk>

In version 4.2 fix #7, according to my observations, there is just no method found
that is able to compute the degree of a certain field F over its prime field, where the
field F arises during the computation (one method is applicable, but gives up) :

gap> S:=PolynomialRing(Rationals,["x"]);
<algebra-with-one over Rationals, with 1 generators>
gap> p0:=UnivariatePolynomial(Rationals,[1,1,1,1,1,1,1,1,1,1,1],1);
1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10
gap> C11:=FieldExtension(Rationals,p0);
<field in characteristic 0>
gap> IsAbelianNumberField(C11);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error no 2nd choice method found for `DegreeOverPrimeField' on 1 arguments at
Error( no_method_found );
DegreeOverPrimeField( F ) called from
IsPrimeField( CF ) called from
IsSubset( D, F ) called from
AsField( PrimeField( F ), F ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop, you can 'quit;' to quit to outer loop,
or you can return to continue
brk>

The field F seems to have some nasty properties that make GAP unable to
do even very easy calculations with it -- for example, determining its characteristic,
or checking whether it is equal to C11 ...

Best wishes,

Stefan