Opened 9 years ago

Last modified 5 years ago

#13215 closed enhancement

Skew polynomials — at Initial Version

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

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