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arXiv · 1607.04732

Difference Index of Quasi-Prime Difference Algebraic Systems

Jie Wang
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Abstract

This paper is devoted to studying difference indices of quasi-prime difference algebraic systems. We define the quasi dimension polynomial of a quasi-prime difference algebraic system. Based on this, we give the definition of the difference index of a quasi-prime difference algebraic system through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved. In particular, an upper bound of difference indices is given. As applications, an upper bound of the Hilbert-Levin regularity and an upper bound of orders for difference ideal membership problem are deduced.

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Jie Wang. 2016-07-16. Difference Index of Quasi-Prime Difference Algebraic Systems. https://arxiv.org/abs/1607.04732

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