Solving multivariate algebraic equation by Hensel construction
Solving multivariate algebraic equation by Hensel construction
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DOI：
10.1007/bf03167329
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发表时间：
1999-06
影响因子：
0.9
通讯作者：
Tateaki Sasaki;F. Kako
中科院分区：
文献类型：
--
作者：
Tateaki Sasaki;F. Kako
给定多变量多项式F（x，y，.，z），本文讨论了形式幂级数或分数幂级数的根的计算，ofFw.r.t.xin z.若问题是正则的，即展开点不是根的奇点，则计算容易，本文考虑的是非正则情况。我们稍微扩展了广义Hensel构造，使它可以应用到不规则的情况。这种扩展允许我们计算二元多项式F（x，y）的根，对于多元多项式F（x，y，...，z），我们考虑将根展开成分数幂级数w.r.t. y的总度数，...，z，根用简单得多的多项式的根来表示。
Given a multivariate polynomial F(x, y, ...,z), this paper deals with calculating the roots ofFw.r.t.xin terms of formal power series or fractional-power series iny, ...,z.If the problem is regular, i.e. the expansion point is not a singular point of a root, then the calculation is easy, and the irregular case is considered in this paper. We extend the generalized Hensel construction slightly so that it can be applied to the irregular case. This extension allows us to calculate the roots of bivariate polynomial F(x, y) in terms of Puiseux series iny.For multivariate polynomial F(x, y, ...,z), we consider expanding the roots into fractional-power series w.r.t. the total-degree ofy, ...,z, and the roots are expressed in terms of the roots of much simpler polynomials.