Algorithmic Thomas decomposition of algebraic and differential systems
Algorithmic Thomas decomposition of algebraic and differential systems
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DOI：
10.1016/j.jsc.2011.12.043
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
T. Bächler;V. Gerdt;Markus Lange-Hegermann;D. Robertz
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文献类型：
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作者：
T. Bächler;V. Gerdt;Markus Lange-Hegermann;D. Robertz
在本文中，我们考虑系统的代数和非线性偏微分方程和不等式。我们将这些系统分解成所谓的简单子系统，从而划分解决方案的集合。对于代数系统，简单性意味着三角性，无平方性和非零初始。微分简单性用对合性扩展了代数简单性。我们建立在J. M。托马斯和发展成一个新的算法不相交分解。本文是Bächler等人的修订版。（2010），并包括我们的分解算法的正确性和终止性的证明。此外，我们说明了进一步的指导性的例子，并描述了它的Maple实现与其他一些三角分解算法的实验比较。
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.