### The Invertibility of Rational Univariate Representations

XIAO Shuijing, ZENG Guangxing

1. Department of Mathematics, Nanchang University, Nanchang 330031, China
• Received:2021-03-13 Revised:2021-07-02 Online:2022-11-25 Published:2022-12-23
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant No. 12161057.

XIAO Shuijing, ZENG Guangxing. The Invertibility of Rational Univariate Representations[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2430-2451.

In this paper, the so-called invertibility is introduced for rational univariate representations, and a characterization of the invertibility is given. It is shown that the rational univariate representations, obtained by both Rouillier's approach and Wu's method, are invertible. Moreover, the ideal created by a given rational univariate representation is defined. Some results on invertible rational univariate representations and created ideals are established. Based on these results, a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.
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