Factoring and Irreducibility Related Methods in Skew Polynomials

[arpitdm]

We propose the addition of the following methods and classes to skew polynomials:

1. def random_irreducible in class SkewPolynomialRing_general in skew_polynomial_ring.py

2. Following functions to the class SkewPolynomial_finite_field_dense:

• def is_irreducible
• def bound
• def type
• cdef SkewPolynomial_finite_field_dense _rdivisor_c
• def irreducible_divisor
• def irreducible_divisor_with_norm
• def irreducible_divisors
• def _irreducible_divisors
• def count_irreducible_divisors
• cdef _factor_c
• cdef _factor_uniform_c
• def factor(self,distribution=None):
• def count_factorizations(self):
• def count_factorisations(self):
• def factorizations
• def factorisations

Note: The original ticket #13215 first introduced this functionality. That was subsequently modified to support the basic implementation of skew polynomials and the factoring and irreducibility related methods from that ticket that were removed are being reintroduced here.

[arpitdm]

Please also note that the current code is more or less just what was in the original patch for #13215 related to Factoring and Irreducibility methods. No effort has been made yet to accommodate for changes in #13215 since this addition was factored out.