Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem
Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem
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利用对称性的空间曲线多面体方法应用于循环 n 根问题
DOI：
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发表时间：
2011
期刊：
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通讯作者：
J. Verschelde
中科院分区：
文献类型：
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作者：
Danko Adrovic;J. Verschelde
我们提出了一个多面体算法来操纵正维解集。使用面法线作为pretropisms牛顿多面体，我们专注于前两个条款的一个Puixix系列扩展。该系列的主导力量是通过热带前品种计算。这种多面体算法非常适合于利用对称性，当它出现在多项式系统。在同一组轨道中具有pretropisms的初始形式系统仅求解一次，允许冗余数据的系统过滤。使用cddlib、Gfan、PHCpack和Sage的计算在循环n根多项式系统上进行了说明。
We present a polyhedral algorithm to manipulate positive dimensional solution sets. Using facet normals to Newton polytopes as pretropisms, we focus on the first two terms of a Puiseux series expansion. The leading powers of the series are computed via the tropical prevariety. This polyhedral algorithm is well suited for exploitation of symmetry, when it arises in systems of polynomials. Initial form systems with pretropisms in the same group orbit are solved only once, allowing for a systematic filtration of redundant data. Computations with cddlib, Gfan, PHCpack, and Sage are illustrated on cyclic n-roots polynomial systems.