Algorithmic Thomas Decomposition of Algebraic and Differential Systems

Thomas Bächler , Vladimir P. Gerdt , Markus Lange-Hegermann und Daniel Robertz,
Oct 2012

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The present paper is a revised version of Bächler et al. (2010) and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms.

Literatur Beschaffung: Elsevier
author= {Bächler, Thomas and Gerdt, Vladimir P. and Lange-Hegermann, Markus and Robertz, Daniel},
title= {Algorithmic Thomas Decomposition of Algebraic and Differential Systems},
howpublished= {},
month= {Oct},
year= {2012},
note= {},