Isolated points, duality and residues
Isolated points, duality and residues
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DOI：
10.1016/s0022-4049(97)00023-6
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发表时间：
1997-05
影响因子：
0.8
通讯作者：
B. Mourrain
中科院分区：
文献类型：
--
作者：
B. Mourrain
在本文中，我们感兴趣的是使用对偶多项式的有效计算。我们将域K上多项式代数R的对偶元素表示为微分算子中的形式级数∈ K[[]]。我们利用R的理想与K的向量空间之间的对应关系，通过导子稳定且对于（λ）-adic拓扑是闭的，来构造孤立点的局部逆系统。我们提出了一种算法，它计算正交D的主要组成部分，这个孤立的点，通过积分的多项式在对偶空间K[]，具有良好的复杂性界限。然后将该算法应用于局部残数的计算、局部完备交曲线的真实的分支的分析、齐次多项式结式的计算。
In this paper, we are interested in the use of duality in effective computations on polynomials. We represent the elements of the dual of the algebra R of polynomials over the field K as formal series ∈ K[[∂]] in differential operators. We use the correspondence between ideals of R and vector spaces of K[[∂]], stable by derivation and closed for the (∂)-adic topology, in order to construct the local inverse system of an isolated point. We propose an algorithm, which computes the orthogonal D of the primary component of this isolated point, by integration of polynomials in the dual space K[∂], with good complexity bounds. Then we apply this algorithm to the computation of local residues, the analysis of real branches of a locally complete intersection curve, the computation of resultants of homogeneous polynomials.