16.11 Algebraic Extension Records

Since every algebraic extension is a field, it is represented as a record. This record contains all components, a field record will contain (see Field Records). Additionally, it contains the components isAlgebraicExtension, minpol, primitiveElm and may contain the components isNormalExtension, minpolFactors and galoisType.

isAlgebraicExtension:

is always true. This indicates that F is an algebraic extension.

minpol:

is the defining polynomial of F.

primitiveElm:

contains RootOf(F.minpol).

isNormalExtension:

indicates, whether F is a normal extension field.

minpolFactors:

contains a factorization of F.minpol over F.

galoisType:

contains the Galois type of the normal closure of F. See section GaloisType.

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