标题： 光滑完全交实代数集每个连通分支的至少一个点的计算的细化位复杂度 显示英文标题

标题： Refined bit complexity for the computation of at least onepoint per connected component of a smooth completeintersection real algebraic set

摘要： 我们对计算光滑实代数集每个连通分支至少一个点的算法的位复杂度分析进行了改进，与之前的工作相比，相对于变量数量实现了指数级加速。 所分析的算法基于临界点方法，将问题简化为计算与通用投影在直线上的限制相关的临界点。 我们的改进以及随后的复杂度陈述的提升来自于对编码这些临界点集合的多项式系统的多仿射结构的更好利用。 通过这种改进，该算法产生的输出大小的位大小估计也得到了改善。 显示英文摘要

摘要： We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior works. The algorithm which is analyzed is based on the critical point method, reducing the problem to computations of critical points associated to the restriction of generic projections on lines to the studied variety. Our refinement, and the subsequent improved complexity statement, comes from a better utilization of the multi-affine structure of polynomial systems encoding these sets of critical points. The bit-size estimates on the size of the output produced by this algorithm are also improved by this refinement.