On Testing a Bivariate Polynomial for Analytic Reducibility
On Testing a Bivariate Polynomial for Analytic Reducibility
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关于测试二元多项式的解析可归约性
DOI：
10.1006/jsco.1997.0150
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
S. McCallum
中科院分区：
文献类型：
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作者：
S. McCallum
设K是特征为零的代数闭域。我们给出了一个有效的算法来确定给定的多项式f(x，y)在Kx，y上是否在原点上解析可约。提出的算法是基于Kuo(1989)提出的一种非正式方法，而该方法又是从Abhyankar(1988)的思想中推导出来的。文中着重证明了算法的正确性和终止性，并适合于计算机实现。对于算法的一个部分版本，证明了多项式最坏情况时间复杂度的界。
LetKbe an algebraically closed field of characteristic zero. We present an efficient algorithm for determining whether or not a given polynomialf(x,y) inKx,y is analytically reducible overKat the origin. The algorithm presented is based upon an informal method sketched by Kuo (1989) which is in turn derived from ideas of Abhyankar (1988). The presentation contained herein emphasises the proofs of the algorithm's correctness and termination, and is suitable for computer implementation. A polynomial worst case time complexity bound is proved for a partial version of the algorithm.