一种计算参数微分理想根正则表示的新算法

IF 0.1 Q4 MATHEMATICS
Shahnaz Fakouri, S. Rahmany, Abdolali Basiri
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引用次数: 1

摘要

微分理想根的正则表示在求解隶属度问题、计算解的泰勒展开、寻找李对称以及求解动力系统等方面具有广泛的应用。对于具有参数系数的多项式微分理想,目前还没有一种算法能给出所有可能参数值的所有正则表示。在这篇文章中,我们提出了一个新的算法,计算所有不同的正则表示相对于所有可能的状态的参数。此外,我们还提出了一个有效的判据来减少一些无效的计算。在Maple中实现了该算法,文中给出的几个实例证明了该算法的高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A new algorithm for computing regular representations for radicals of parametric differential ideals
Abstract The regular representation of the radical of a differential ideal has various applications such as solving the membership problem, computing Taylor expansion of solutions, finding the Lie symmetries, and solving dynamical systems. Presently, there is no algorithm giving all regular representations for all possible values of the parameters for a polynomial differential ideal with parametric coefficients. In this article, we propose a new algorithm that computes all different regular representations with respect to all possible states of the parameters. Also, we present an efficient criterion to reduce some ineffectual computations. Implementing the algorithm in Maple and several examples reported in this article demonstrate the high efficiency of the algorithm.
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