Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets
Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets
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DOI：
10.1007/978-3-319-72453-9_8
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Daniel J. Bates;Daniel A. Brake;J. Hauenstein;A. Sommese;C. Wampler
中科院分区：
文献类型：
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作者：
Daniel J. Bates;Daniel A. Brake;J. Hauenstein;A. Sommese;C. Wampler
给定一个多项式系统f，本文给出了同伦的一般构造方法，该同伦的每个连通分支至少有一个点在的解的集合上。这种算法的方法，然后被用来计算一个超集的孤立点的图像中的代数集，出现在许多应用中，如计算临界集用于分解的真实的代数集。一个例子表明了这种方法的有效性。
Given a polynomial systemf, this article provides a general construction for homotopies that yield at least one point of each connected component on the set of solutions of. This algorithmic approach is then used to compute a superset of the isolated points in the image of an algebraic set which arises in many applications, such as computing critical sets used in the decomposition of real algebraic sets. An example is presented which demonstrates the efficiency of this approach.