People interested
Xavier Caruso, Jérémy Le Borgne
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 a X = \sigma(a) X (a \in K)
This ring is closely related to \sigma-modules over k (which arises in p-adic Hodge theory).
The aim of the project is to implement basic arithmetic 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 constant