#13215: Skew polynomials
-------------------------------------+-------------------------------------
Reporter: caruso | Owner: tbd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: algebra | Resolution:
Keywords: skew polynomials | Merged in:
Authors: Xavier Caruso | Reviewers: Burcin Erocal
Report Upstream: N/A | Work issues: see comment #25
Branch: | Commit:
u/arpitdm/skew_polynomials | e189fec13d005a7fba39a429876c501fe95c05da
Dependencies: #13214, #13303, | Stopgaps:
#13640, #13641, #13642 |
-------------------------------------+-------------------------------------
Description changed by arpitdm:
Old description:
> If R is a ring equipped with an endomorphism sigma, the ring of skew
> polynomials over (R,sigma) is the ring of usual polynomials over R with
> the modified multiplication given by the rule X*a = sigma(a)*X.
>
> Skew polynomials play an important role in several domains like coding
> theory or Galois representations theory in positive characteristic.
>
> The attached patch provides:
>
> 1. a basic implementation of skew polynomials over any commutative ring
> (including addition, multiplication, euclidean division, gcd...)
> 1. a more complete implementation of skew polynomials over finite fields
> (including factoring)
>
> NB: This ticket depends on
> - ticket #13214: Frobenius endomorphisms over finite fields
> - ticket #13642: Fast modular exponentiation (only for speed)
>
> ----
> Apply: [attachment:trac_13215_skew_polynomials.patch]
New description:
If R is a ring equipped with an endomorphism sigma, the ring of skew
polynomials over (R,sigma) is the ring of usual polynomials over R with
the modified multiplication given by the rule X*a = sigma(a)*X.
Skew polynomials play an important role in several domains like coding
theory or Galois representations theory in positive characteristic.
This ticket provides:
1. a basic implementation of skew polynomials over any commutative ring
(including addition, multiplication, euclidean division, gcd...)
2. construction of skew polynomial rings
--
--
Ticket URL: <https://trac.sagemath.org/ticket/13215#comment:58>
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