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TitleAlgorithmic Thomas decomposition of algebraic and differential systems
Author(s) Thomas Bächler, Vladimir P. Gerdt, Markus Lange-Hegermann, Daniel Robertz
TypeArticle in Journal
AbstractIn 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.
KeywordsDisjoint triangular decomposition, Simple systems, Polynomial systems, Differential systems, Involutivity
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S074771711100246X
LanguageEnglish
JournalJournal of Symbolic Computation
Volume47
Number10
Pages1233 - 1266
Year2012
NoteSymbolic Computation and its Applications
Edition0
Translation No
Refereed No
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