Gcd Modulo a Primary Triangular Set of Dimension Zero
Gcd Modulo a Primary Triangular Set of Dimension Zero
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DOI：
10.1145/3087604.3087612
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
X. Dahan
中科院分区：
文献类型：
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作者：
X. Dahan
在多项式理想理论中，计算三角集合T上的gcd是某些三角分解方法的核心程序。因此，它已经被深入研究，并在几种情况下得到很好的理解和实现，特别是在系数在激进三角集上的情况下;在非激进三角集上不是这种情况。本文介绍了一个gcd概念在这种情况下，当另外为简单起见T被假定为主要的。它建立在系数环的Hensel性质上，并且是自然的，因为它与a和B模T的子结式序列相联系。一般的算法仍然依赖于一些假设，除了一个变量的三角形集的情况。
Computing gcd over a triangular set T is the core routine of the machinery of some triangular decomposition methods, in the realm of polynomial ideal theory. As such it has been studied intensively and is well-understood and implemented in several situations, especially in the case where coefficients are over a radical triangular set; It is not the case over a non-radical one. This paper introduces a gcd notion in this case, when additionally for simplicity T is assumed to be primary. It is built upon the Henselian property of the coefficient ring, and is natural in that it is linked with the subresultant sequence of a and b modulo T. A general algorithm still relies on some assumptions, except for the case of a triangular set of one variable.