16 Algebraic extensions of fields

If we adjoin a root alpha of an irreducible polynomial p in K[x] to the field K we get an algebraic extension K(alpha), which is again a field. By Kronecker's construction, we may identify K(alpha) with the factor ring K[x]/(p), an identification that also provides a method for computing in these extension fields.

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.

Subsections

1. AlgebraicExtension
2. IsAlgebraicExtension
3. RootOf
4. Algebraic Extension Elements
5. Set functions for Algebraic Extensions
6. IsNormalExtension
7. MinpolFactors
8. GaloisGroup for Extension Fields
9. ExtensionAutomorphism
10. Field functions for Algebraic Extensions
11. Algebraic Extension Records
12. Extension Element Records
13. IsAlgebraicElement
14. Algebraic extensions of the Rationals
15. DefectApproximation
16. GaloisType
17. ProbabilityShapes
18. DecomPoly