Effective algorithms for computing Noetherian representations of zero-dimensional ideals
Effective algorithms for computing Noetherian representations of zero-dimensional ideals
复制标题
计算零维理想的诺特表示的有效算法
DOI：
10.1007/s00200-022-00570-7
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
K. Nabeshima and S. Tajima
中科院分区：
文献类型：
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作者：
重松 潤;尾形 明子;伊藤 義徳;伊藤亜矢子;Chihiro Kemuriyama & Olivia C. OGAWA;K. Nabeshima and S. Tajima
我们认为诺特算子的背景下，符号计算。利用完整模理论，我们给出了一个计算零维理想Noether算子的新方法。提出了一种有效的算法，主要由线性代数技术计算它们。作为应用，利用Noether算子讨论了多项式理想的新的计算方法。
We consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic-modules, we present a new method for computing Noetherian operators associated to a zero-dimensional ideal. An effective algorithm that consists mainly of linear algebra techniques is proposed for computing them. Moreover, as applications, new computation methods of polynomial ideals are discussed by utilizing the Noetherian operators.