A unified method for multivariate polynomial factorizations
A unified method for multivariate polynomial factorizations
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DOI：
10.1007/bf03167201
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发表时间：
1993-02
影响因子：
0.9
通讯作者：
Tateaki Sasaki;M. Sasaki
中科院分区：
文献类型：
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作者：
Tateaki Sasaki;M. Sasaki
最近，Sasaki等人提出了一种多元多项式的近似因式分解算法。该算法通过研究近似根的相同幂的线性组合来计算不可约因子。在本文中，我们表明，各种多元多项式因式分解可以执行这种方法。我们提出了幂级数环、整数、代数数域（包括代数闭域）和代数函数域上多元多项式因式分解的算法。此外，我们讨论了这种方法的适用性，一元多项式因式分解。
Recently, Sasaki et al. presented an approximate factorization algorithm of multivariate polynomials. The algorithm calculates irreducible factors by investigating linear combinations of the same power of approximate roots. In this paper, we show that various kinds of multivariate polynomial factorizations can be performed by this method. We present algorithms for factorization of multivariate polynomials over power-series rings, over the integers, over algebraic number fields including algebraically closed fields, and over algebraic function fields. Furthermore, we discuss applicability of this method to univariate polynomial factorization.