Details:
Title  Algorithmic Thomas decomposition of algebraic and differential systems  Author(s)  Thomas Bächler, Vladimir P. Gerdt, Markus LangeHegermann, Daniel Robertz  Type  Article in Journal  Abstract  In this paper, we consider systems of algebraic and nonlinear partial differential equations and inequations. We decompose these systems into socalled simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, squarefreeness and nonvanishing 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.  Keywords  Disjoint triangular decomposition, Simple systems, Polynomial systems, Differential systems, Involutivity  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771711100246X 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  10  Pages  1233  1266  Year  2012  Note  Symbolic Computation and its Applications  Edition  0  Translation 
No  Refereed 
No 
