Normalization in Riemann Tensor Polynomial Ring

作者：Liu, Jiang^*

来源：Journal of Systems Science and Complexity, 2018, 31(2): 569-580.

DOI：10.1007/s11424-017-6325-z

• Canonical form
• Einstein summation convention
• monoid ring
• nD symbolic computation
• Riemann tensor

It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grobner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grobner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grobner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grobner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.

• 出版日期2018-4
• 单位东华大学; 上海理工大学