稀疏系统与算法等维分解
Sparse systems and algorithmic equidimensional decomposition
AI总结：
本文提出了一种概率算法，用于稀疏多项式系统中等维分量的计算与分解。
摘要：
我们提出了一种新的概率算法，用于刻画由任意稀疏多项式系统定义的仿射代数簇的等维分量。对于每个等维分量，该算法计算一个见证集，即通过将分量与一个互补维数的通用线性子空间相交而得到的有限集。该算法的复杂度与所涉及多项式支持相关的组合不变量呈多项式关系。
英文摘要：
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
