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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

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