16.1 AlgebraicExtension

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 Trace and Norm relative to subfields are not supported.

    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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