GAP Manual: 16. Algebraic extensions of fields

If we adjoin a root alpha of an irreducible polynomial p inK[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 sfGAP 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, bfAll information in this chapter is subject to change in future versions.

This chapter contains the following sections:

[next] [prev] [up]