Thomas Decomposition of Algebraic and Differential Systems
Commutative Algebra
2015-05-19 v1 Analysis of PDEs
Abstract
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple.
Cite
@article{arxiv.1008.3767,
title = {Thomas Decomposition of Algebraic and Differential Systems},
author = {Thomas Bächler and Vladimir Gerdt and Markus Lange-Hegermann and Daniel Robertz},
journal= {arXiv preprint arXiv:1008.3767},
year = {2015}
}