Opened 10 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: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### 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:

- a basic implementation of skew polynomials over any commutative ring (including addition, multiplication, euclidean division, gcd...)
- a more complete implementation of skew polynomials over finite fields (including factoring)

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