Eckhard Pfuegel, Kingston College, London

A Monomial-by-Monomial Method for Computing Regular Solutions of Systems of Pseudo-Linear Equations

This talk deals with the local analysis of systems of pseudo-linear equations. We define regular solutions and use this as a 
unifying theoretical framework for discussing the structure and existence of regular solutions of various systems of linear 
functional equations. We then give a generic and flexible algorithm for the computation of a basis of regular solutions. 
We have implemented this algorithm in the Computer Algebra System Maple in order to provide novel functionality for solving 
systems of linear differential, difference and $q$-difference equations given in various input formats.