微分消去算法中的新阶界
New order bounds in differential elimination algorithms
摘要：
本文给出了Rosene-Groebner算法中导数阶的一个新的上界。该算法计算特征为零的微分域上的微分多项式环中的根微分理想的正则分解，其中任意个数的可交换导子。这个分解可以用来检验在给定的根微分理想中的隶属关系。特别是，该算法允许我们确定系统的多项式偏微分方程是一致的。在此之前，唯一已知的阶上界是由Golubitsky、Kondratieva、Moreno Maza和Ovchinnikov针对单次求导给出的。我们实现了我们的界限相关联的算法反链序列的长度可以使用莱昂桑切斯和Ovchinnikov的结果有界。
英文摘要：
We present a new upper bound for the orders of derivatives in the Rosenfeld-Groebner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in the ring of differential polynomials over a differential field of characteristic zero with an arbitrary number of commuting derivations. This decomposition can then be used to test for membership in the given radical differential ideal. In particular, this algorithm allows us to determine whether a system of polynomial PDEs is consistent. Previously, the only known order upper bound was given by Golubitsky, Kondratieva, Moreno Maza, and Ovchinnikov for the case of a single derivation. We achieve our bound by associating to the algorithm antichain sequences whose lengths can be bounded using the results of Leon Sanchez and Ovchinnikov.
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