16.4 Algebraic Extension Elements

According to Kronecker's construction, the elements of an algebraic extension are considered to be polynomials in the primitive element. Unless they are already in the defining field (in which case they are represented as elements of this field), they are represented by records in sf GAP (see Extension Element Records). These records contain a representation a polynomial in the primitive element. The extension corresponding to this primitive element is the default field for the algebraic element.

The usual field operations are applicable to algebraic elements.

    gap> r^3/(r^2+1);
    -1*alpha^3-1*alpha
    gap> DefaultField(r^2);
    e

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