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 Gröbner 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 Gröbner 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 Gröbner basis in the ST-fundamental restricted ring.

在计算机代数中，建立通用计算理论来确定索引多项式的等价性仍然具有挑战性。在先前的工作中，作者通过扩展Gröbner基理论解决了黎曼张量多项式的等价确定问题。本文通过ST约束环的方法将先前的工作扩展到不涉及索引和函数消除的更一般的索引多项式。提供每个ST限制环中定义的sysygy的Gröbner基础的分解形式，然后证明索引多项式的规范形式相对于ST基本限制环中的Gröbner基础是标准形式。