Opened 9 years ago

Last modified 5 years ago

#13215 closed enhancement

Skew polynomials — at Version 2

Reported by: caruso Owned by: tbd
Priority: major Milestone: sage-7.4
Component: algebra Keywords: skew polynomials, sd75
Cc: tfeulner, caruso, burcin, jsrn, dlucas, tscrim Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #13214 Stopgaps:

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Description (last modified by caruso)

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...)
  2. a more complete implementation of skew polynomials over finite fields (including factoring)

NB: This ticket depends on ticket #13214 which implements Frobenius endomorphisms over finite fields. For convenience, I reattach the corresponding patch here.

Change History (3)

comment:1 Changed 9 years ago by caruso

  • Status changed from new to needs_review

comment:2 Changed 9 years ago by caruso

  • Dependencies set to #13214
  • Description modified (diff)

Changed 9 years ago by caruso

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