Factoring and Irreducibility Related Methods in Skew Polynomials

[arpitdm]

This ticket implements the following methods (all related to factorization and irreducible divisors) for skew polynomials over finite fields

• is_irreducible
• right_irreducible_divisor, left_irreducible_divisor (return a divisor)
• right_irreducible_divisors, left_irreducible_divisors (return an iterator over all divisors)
• count_irreducible_divisors
• factor (return a factorization)
• factorizations (return an iterator over all factorizations)
• count_factorizations

CC: @tscrim @xcaruso @johanrosenkilde @sagetrac-dlucas @vbraun

Component: algebra

Author: Xavier Caruso

Branch/Commit: d107cce

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/21264

[arpitdm]

Branch: u/arpitdm/irreducibility_factoring_skew_polynomials

[arpitdm]

comment:2

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.

[arpitdm]

Changed branch from u/arpitdm/irreducibility_factoring_skew_polynomials to none

[arpitdm]

Author: Xavier Caruso

[xcaruso]

comment:4

Where is the code of this ticket?

Should I copy it from https://github.com/sagemath/sage-prod/files/10655943/trac_13215_skew_polynomials.patch.gz or can I find it somewhere on git?

[xcaruso]

Branch: u/caruso/skew_polynomial_finite_field

[xcaruso]

comment:6

OK, I found it.

---

Last 10 new commits:

16ce9e3	add testsuite
318a179	Merge branch 'pickling_frobenius' into skew_polynomial_finite_order
1ce658d	fix comparison of morphisms
2598cf2	implement a factory
75c220a	skip test_category
c7b937c	fix pyflakes
9e4ed51	fix non ascii and blocks
11fa8eb	100% coverage
20794e7	added factoring and irreducibility based methods as is, from the original #13215 ticket
4826d12	Merge branch 'u/arpitdm/irreducibility_factoring_skew_polynomials' of git://trac.sagemath.org/sage into skew_polynomial_finite_field

[xcaruso]

Commit: 4826d12

[sagetrac-git]

Changed commit from 4826d12 to 14d9f26

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

86b0bdc	factorize methods _left_lcm_cofactor and _right_lcm_cofactor
49c64bb	remove class CenterSkewPolynomialRing and add doctest
1b0092f	Merge branch 'skew_polynomial_finite_order' into skew_polynomial_finite_field
dc6995c	remove CenterSkewPolynomial_generic_dense in pxd
1725800	Merge branch 'skew_polynomial_finite_order' into skew_polynomial_finite_field
81228f5	remove CenterSkewPolynomial_generic_dense and duplicate methods
1c513ff	fix import
253200f	remove obsolete import
7e4f15e	change coercion defaults
14d9f26	refactor code

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

1eee2b4	improve error message when coercion/conversion fails for the center
19c9e67	add doctests
5f3188c	default variable name for the center
a171b19	typos
9d11ad3	Merge branch 'skew_polynomial_finite_order' into skew_polynomial_finite_field
e8f2b32	working_center
84f7d9e	Merge branch 'skew_polynomial_finite_order' into skew_polynomial_finite_field
1bcdf9a	use working_center
3db3ff2	reduced norm of a constant polynomial
858c9e7	Merge branch 'skew_polynomial_finite_order' into skew_polynomial_finite_field