Deformation Techniques for Sparse Systems
Deformation Techniques for Sparse Systems
复制标题
稀疏系统的变形技术
DOI：
10.1007/s10208-008-9024-2
复制
发表时间：
2006
影响因子：
3
通讯作者：
A. Waissbein
中科院分区：
文献类型：
--
作者：
Gabriela Jeronimo;G. Matera;P. Solernó;A. Waissbein
我们给出了一个求解零维稀疏系统的概率符号算法。我们的算法结合了基于仿射簇的某种态射的平坦变形的符号同伦过程和Huber和Sturmfels的多面体变形。该算法的复杂性在输入系统的组合结构的大小上是立方的。该尺寸主要由输入多项式的牛顿多面体的基数和混合体积以及与所考虑的变形相关的混合体积的算术模拟来表示。
We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system. This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration.