Algorithmic Thomas decomposition of algebraic and differential systems

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• 作者：Thomas Bä ; chler ^{thomas@momo.math.rwth-aachen.de} ; Vladimir Gerdt¹ ; ^{gerdt@jinr.ru} ; Markus Lange-Hegermann² ; ^{markus@momo.math.rwth-aachen.de} ; Daniel Robertz ^{daniel@momo.math.rwth-aachen.de}
• 关键词：Disjoint triangular decomposition ; Simple systems ; Polynomial systems ; Differential systems ; Involutivity
• 刊名：Journal of Symbolic Computation
• 出版年：2012
• 期刊代码：140_07477171
• 类别：cp
• 出版时间：October, 2012
• 卷：47
• 期：10
• 页码：1233-1266
• 文件大小：460 K

摘要

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 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.