关于多元代数Puixix级数
About algebraic Puiseux series in several variables
摘要：
本文利用多元迭代Pui-x级数系数的性质讨论了其代数性。我们的目的是把[HM 15]的结果推广到多个变量。我们表明，这样一个系列的代数给定的有界度是由有限数量的显式通用多项式公式。相反，给定一个消失多项式，有一个关于多项式系数和级数有界初始部分的级数系数的封闭式公式。
英文摘要：
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 [HM15]. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
