AlgebraicExtension( pol )
constructs the algebraic extension L corresponding to the polynomial pol. pol must be an irreducible polynomial defined over a ``defining'' field K. The elements of K are embedded into L in the canonical way. As L is a field, all field functions are applicable to L. Similarly, all field element functions apply to the elements of L.
L is considered implicitely to be a field over the subfield K. This
means, that functions like
Norm relative to subfields are
gap> x:=X(Rationals);;x.name:="x";; gap> p:=x^4+3*x^2+1; x^4 + 3*x^2 + 1 gap> e:=AlgebraicExtension(p); AlgebraicExtension(Rationals,x^4 + 3*x^2 + 1) gap> e.name:="e";; gap> IsField(e); true gap> y:=X(GF(2));;y.name:="y";; gap> q:=y^2+y+1; Z(2)^0*(y^2 + y + 1) gap> f:=AlgebraicExtension(q); AlgebraicExtension(GF(2),Z(2)^0*(y^2 + y + 1))
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