Thomas Decomposition of Algebraic and Differential Systems

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these system into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness 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 given paper is a revised version of B

• Type: Journal
• Year: 2010
• Where: CASC
• Authors: Thomas Bächler, Vladimir P. Gerdt, Markus Lange-Hegermann, Daniel Robertz
• Keywords: CASC 2010, Decomposition Algorithms, Mathematics, Simplicity, So-called Simple Subsystems