Module splitting_field 

Contains implementations to extend crate::rings::extension::number_field::NumberFields by adjoining additional roots of polynomials.

Functions

extend_galois_fieldunstable-enable

Availability

extend_number_fieldunstable-enable

Given a number field K and an irreducible polynomial f, computes a representation of the number field L = K[X]/(f). The result is returned by the inclusion K -> L and the element that corresponds to the coset of X, i.e. a root of f in L. Note that the canonical generator of L does not have to be a root of f (this might even be impossible, e.g. if f in ZZ[X] but K != QQ).

extend_number_field_promise_is_irreducibleunstable-enable

Given a number field K and an irreducible polynomial f, computes a representation of the number field L = K[X]/(f). The result is returned by the inclusion K -> L and the element that corresponds to the coset of X, i.e. a root of f in L. Note that the canonical generator of L does not have to be a root of f (this might even be impossible, e.g. if f in ZZ[X] but K != QQ).

splitting_fieldunstable-enable

Given a polynomial f in K[X] over a field K, this computes an extension L of K such that f splits in L.

variety_from_lex_gbunstable-enable

The closure create_field should, when given a field K' and an irreducible polynomial g in K'[X], compute an extension field K'', and return both the embedding K' -> K'' and a root a in K'' of g.