\'Equations aux q-diff\'erences lin\'eaires: factorisation, r\'esolution et th\'eor\`emes d'indices

TL;DR

This paper presents explicit algorithms for factoring and solving linear q-difference equations, providing a concrete approach to well-known theoretical results in the field.

Contribution

It offers a clear, explicit algorithmic framework for factorizing and solving q-difference operators, enhancing practical understanding of these classical results.

Findings

Explicit algorithms for q-difference operator factorization

Concrete methods for solving q-difference equations

Clarification of well-known theoretical results

Abstract

We describe explicit algorithms for factoring q-difference operators and solving q-difference equations. These are well known results, presented in a "concrete" form. ----- Nous decrivons des algorithmes explicites pour la factorisation d'operateurs et la resolution d'equations aux q-differences. Il s'agit d'une presentation "concrete" de resultats bien connus.