发表机构
North Carolina State University; University of Notre Dame（北卡罗来纳州立大学; 圣母大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二元多项式系统中牛顿同伦追踪起始点空间划分的几何结构，分析胞腔边界与数量，为高效实解算法提供基础。
AI 中文摘要
计算实代数几何中的一个标准问题是计算具有实系数的多项式方程组的所有实解。一种经典且有前景的方法是沿着由牛顿同伦定义的实曲线的连通分量进行追踪，该同伦依赖于所选的起始点。随着起始点的变化，可能获得实解的不同子集。这产生了起始点空间的一个划分，理解该划分的结构对于开发基于牛顿同伦的高效算法至关重要。本文研究了二元系统中此类胞腔边界的结构以及相应划分中的胞腔数量。文中包含多个示例以展示所得结果。
英文摘要
A standard question in computational real algebraic geometry is to compute all real solutions to a system of polynomial equations with real coefficients. One classical and promising approach is to track along a connected component of a real curve defined by a Newton homotopy, which is dependent upon the selected start point. As the start point varies, different subsets of real solutions may be obtained. This yields a partition of the space of start points into cells, and it is important to understand the structure of this partition in order to develop efficient algorithms based on Newton homotopies. The structure of the boundary of such cells and the number of cells in the corresponding partition are investigated for bivariate systems. Several examples are included to demonstrate the results.
Comments23 pages, 22 figures. Submitted to Journal of Algebra and its Applications
