Differential standard bases under composition

被引：0
|
作者：
Zobnin A.I. [1 ]
机构：
[1] Faculty of Mechanics and Mathematics, Moscow State University, Moscow
来源：
Journal of Mathematical Sciences | 2008年 / 152卷 / 4期
基金：
俄罗斯基础研究基金会;
关键词：
Standard Basis; Polynomial Ring; Computer Algebra System; Membership Problem; Monomial Ordering;
D O I：
10.1007/s10958-008-9080-9
中图分类号：
学科分类号：
摘要：
We generalize Hoon Hong's theorem on Gröbner bases under composition to the case of differential standard bases in the ordinary ring of differential polynomials ℱ {y}. In particular, we prove that some ideals have finite differential standard bases. We construct special orderings on differential monomials such that ideals generated by some power of a quasi-linear polynomial acquire finite differential standard bases. © 2008 Springer Science+Business Media, Inc.
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页码：522 / 539
页数：17
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