#13215: Skew polynomials
----------------------------------------------------------+-----------------
Reporter: caruso | Owner: tbd
Type: enhancement | Status:
needs_review
Priority: major | Milestone:
sage-5.11
Component: algebra | Resolution:
Keywords: skew polynomials | Work issues:
Report Upstream: N/A | Reviewers:
Burcin Erocal
Authors: Xavier Caruso | Merged in:
Dependencies: #13214, #13303, #13640, #13641, #13642 | Stopgaps:
----------------------------------------------------------+-----------------
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 tickets #13214 (Frobenius endomorphisms over
> finite fields), #13303 (which fixes a bug in
> quotient_polynomial_ring_element.pyx), #13640 (some q-numbers), #13641
> (short representation for morphisms), #13642 (fast modular
> exponentiation, only for speed). You need to apply the corresponding
> patches first.
>
> 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.
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]
--
Comment (by caruso):
I've posted an updated version of this patch which should apply at the top
of sage 5-10 (hopefully).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13215#comment:23>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
