典型文献
Normalization of Indexed Differentials by Extending Gr?bner Basis Theory
文献摘要：
It is a fundamental problem to determine the equivalence of indexed differential polynomi-als in both computer algebra and differential geometry.However,in the literature,there are no general computational theories for this problem.The main reasons are that the ideal generated by the basic syzygies cannot be finitely generated,and it involves eliminations of dummy indices and functions.This paper solves the problem by extending Gr?bner basis theory.The authors first present a division of the set of elementary indexed differential monomials E(?)into disjoint subsets,by defining an equivalence relation on E(?)based on Leibniz expansions of monomials.The equivalence relation on E(?)also induces a division of a Gr?bner basis of basic syzygies into disjoint subsets.Furthermore,the authors prove that the dummy index numbers of the sim-monomials of the elements in each equivalence class of E(?)have upper bounds,and use the upper bounds to construct fundamental restricted rings.Finally,the canonical form of an indexed differential polynomial proves to be the normal form with respect to a subset of the Gr?bner basis in the fundamental restricted ring.
文献关键词：
中图分类号：
作者姓名：
LIU Jiang;NI Feng;SONG Shihang;DU Mingjun
作者机构：
Department of Systems Science,University of Shanghai for Science and Technology,Shanghai 200093,China
文献出处：
引用格式：
[1]LIU Jiang;NI Feng;SONG Shihang;DU Mingjun-.Normalization of Indexed Differentials by Extending Gr?bner Basis Theory)[J].系统科学与复杂性学报（英文版）,2022(05):2016-2028
A类：
Differentials,polynomi,syzygies,eliminations
B类：
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AB值：
0.494342
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