稀疏系统的变形技术
Deformation techniques for sparse systems
摘要：
我们展示了一个概率符号算法求解零维稀疏系统。我们的算法结合了一个符号同伦过程，基于一个平面变形的仿射品种的某个态射，与多面体变形的Huber和Sturmfels。我们的算法的复杂性是二次的输入系统的组合结构的大小。该大小主要由输入多项式的牛顿多面体的混合体积和与所考虑的变形相关联的混合体积的算术模拟来表示。
英文摘要：
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 quadratic in the size of the combinatorial structure of the input system. This size is mainly represented by the mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration.
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