About algebraic Puiseux series in several variables

JOURNAL OF ALGEBRA

卷:527

Article

关键词: Multivariate polynomials;    Algebraic power series;    Implicitization;    Closed form for coefficients;   

DOI  :  10.1016/j.jalgebra.2019.02.004

来源: Elsevier

【 摘 要 】

We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the results from [8]. We show that the algebraicity of such a series for given bounded degrees is determined by a finite number of explicit universal polynomial formulas. Conversely, given a vanishing polynomial, there is a closed-form formula for the coefficients of the series in terms of the coefficients of the polynomial and of a bounded initial part of the series. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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