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
, returns the quotient
.
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
-