An Extension of Grobner Basis Theory to Indexed Polynomials Without Eliminations  

作　　者：LIU Jiang 

机构地区：[1]Department of Systems Science,University of Shanghai for Science and Technology,Shanghai 200093,China

出　　处：《Journal of Systems Science & Complexity》2020年第5期1708-1718,共11页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11701370。

摘　　要：In computer algebra,it remains to be challenging to establish general computational theories for determining the equivalence of indexed polynomials.In previous work,the author solved the equivalence determination problem for Riemann tensor polynomials by extending Grobner basis theory.This paper extends the previous work to more general indexed polynomials that involve no eliminations of indices and functions,by the method of ST-restricted rings.A decomposed form of the Grobner basis of the defining syzygy set in each ST-restricted ring is provided,and then the canonical form of an indexed polynomial proves to be the normal form with respect to the Grobner basis in the ST-fundamental restricted ring.

关 键 词：Canonical form Einstein summation convention free commutative monoid ring Grobner basis 

分 类 号：O174.14[理学—数学]