An Extension of Gröbner Basis Theory to Indexed Polynomials Without Eliminations

Abstract

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.