Currently sf GAP only allows extension fields of fields K , when K itself is not an extension field. As it is planned to modify the representation of field extensions to unify vector space structures and to speed up computations, bf All information in this chapter is subject to change in future versions. 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. IsAlgebraicExtension returns true if the object D is an algebraic field extension and false otherwise. So, for example, a matrix ring may in fact be a field extension, yet IsAlgebraicExtension would return false . This root is called the primitive element of this extension. According to Kronecker's construction, the elements of an algebraic extension are considered to be polynomials in the primitive element.