Diff for "padicSageDays/Projects/SkewPolynomials"

People interested

Xavier Caruso, Jérémy Le Borgne

Description

If k is a field and σ a ring endomorphism of k, the ring of skew polynomials k[X,σ] is the usual vector space of polynomials over k equipped with the multiplication deduced from the rule aX=σ(a)X (a∈K)

This ring is closely related to σ-modules over k (which arises in p-adic Hodge theory).

The aim of the project is to implement basic arithmetic on k[X,σ] when k is a finite field

Progress

A class has been written (for now, in python). It supports the following functions:

• - basic arithmeric (addition, multiplication, euclidean division, gcd)

  - computation of the center Z(k[X,σ]) -- need to add a coercion map - computation of the so-called map Ψ:k[X,σ]→Z(k[X,σ]) - computation of the associated Galois representation (via the corresponding σ-module) - factorization -- in progress

Bugs

Do not derive from PolynomialRing_general since this class assumes that the variable commutes with the constant