=== People interested ===

Xavier Caruso, Jérémy Le Borgne

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=== Description ===

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

This ring is closely related to $\sigma$-modules over $k$ and, consequently, to Galois representations.

The aim of the project is to implement usual functions on $k[X,\sigma]$ 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 $Z(k[X,\sigma])$ -- need to add a coercion map
 * computation of the so-called map $\Psi : k[X,\sigma] \to Z(k[X,\sigma])$
 * computation of the associated Galois representation (via the corresponding $\sigma$-module)
 * factorization -- in progress

=== Bugs ===

Do not derive from !PolynomialRing_general since this class assumes that the variable commutes with the constants (probably rather hard: need to rewrite many things)