Ideals in Univariate Polynomial Rings.

AUTHORS:

  • David Roe (2009-12-14) – initial version.
class sage.rings.polynomial.ideal.Ideal_1poly_field(ring, gen)

Bases: sage.rings.ideal.Ideal_pid

An ideal in a univariate polynomial ring over a field.

residue_class_degree()

Returns the degree of the generator of this ideal.

This function is included for compatibility with ideals in rings of integers of number fields.

EXAMPLES:

sage: R.<t> = GF(5)[]
sage: P = R.ideal(t^4 + t + 1)
sage: P.residue_class_degree()
4
residue_field(names=None, check=True)

If this ideal is P \subset F_p[t], returns the quotient F_p[t]/P.

EXAMPLES:

sage: R.<t> = GF(17)[]; P = R.ideal(t^3 + 2*t + 9)
sage: k.<a> = P.residue_field(); k
Residue field in a of Principal ideal (t^3 + 2*t + 9) of Univariate Polynomial Ring in t over Finite Field of size 17