An Extension of Gr(o)bner Basis Theory to Indexed Polynomials Without Eliminations

• 作者: LIU Jiang
• 来源期刊: 系统科学与复杂性学报（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 1708-1718
• 页数: 11页
• 语种: 英文
• DOI: 10.1007/s11424-020-9135-7

摘要

In computer algebra,it remains to be challenging to establish general computational the ories for determining the equivalence of indexed polynomials.In previous work,the author solved the equivalence determination problem for Riemann tensor polynomials by extending Gr(o)bner 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 Gr(o)bner 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 Gr(o)bner basis in the ST-fundamental restricted ring.