Polar Varieties and Computation of one Point in each Connected Component of a Smooth Real Algebraic Set

机译：光滑实代数集的每个连通分量的极点多样性和一个点的计算

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Let /f_1, ..., f_s be polynomials in Q[X_1,.... X_n] that generate a radical ideal and let V be their complex zero-set. Suppose that V is smooth and equidimensional; then we show that computing suitable sections of the polar varieties associated to generic projections of V gives at least one point in each connected component of V ∩ R~n. We deduce an algorithm that extends that of Bank, Giusti, Heintz and Mbakop to non-compact situations. Its arithmetic complexity is polynomial in the complexity of evaluation of the input system, an intrinsic algebraic quantity and a combinatorial quantity.

机译：令/ f_1，...，f_s为Q [X_1，.... X_n]中的多项式，这些多项式生成一个根理想，并使V为其复零集。假设V是光滑的和等维的；然后我们表明，计算与V的一般投影相关的极地变种的适当部分，可以在V∩R〜n的每个连通分量中至少给出一个点。我们推导了一种将Bank，Giusti，Heintz和Mbakop的算法扩展到非紧凑情况的算法。它的算术复杂度是输入系统评估的复杂度，内在代数量和组合量的多项式。

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《International Symposium on Symbolic and Algebraic Computation Aug 3-6, 2003 Philadelphia, Pennsylvania, USA》|2003年|p.224-231|共8页
会议地点 Philadelphia PA(US);Philadelphia PA(US)
作者
Mohab Safey El Din; Eric Schost;
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作者单位

LIP6, Universite Paris 6 75005 Paris, France;

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会议组织
原文格式 PDF
正文语种 eng
中图分类 O2;
关键词
polynomial system solving; real solutions; complexity;

机译：多项式系统求解实解复杂性;

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专利

1. Properness defects of projections and computation of at least one point in each connected component of a real algebraic set [J] . El Din MS, Schost E Discrete & computational geometry . 2004,第3期

机译：对真实代数集的每个连接分量中的至少一个点的预测和计算的正确性缺陷
2. Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra [J] . Makai Endre Jr., Zemanek Jaroslav Czechoslovak Mathematical Journal . 2016,第3期

机译：Banach代数中的代数元素集的连接组件中的漂亮连接路径
3. Nice connecting paths in connected components of sets of algebraic elements in aBanach algebra [J] . Endre Makai Jr., Jaroslav Zemánek Czechoslovak Mathematical Journal . 2016,第3期

机译：Banach代数中的一组代数元素的连接组件中的漂亮连接路径
4. Polar varieties and computation of one point in each connected component of a smooth real algebraic set [C] . Mohab Safey El Din, Eric Schost International symposium on Symbolic and algebraic computation . 2003

机译：极数变体和光滑实代数集的每个连通分量中的一个点的计算
5. Algebraic cycles on real varieties and Z(2)-equivariant homotopy theory. [D] . dos Santos, Pedro Ferreira. 1999

机译：实数和Z（2）-等价同构理论的代数循环。
6. PACC: Large scale connected component computation on Hadoop and Spark [O] . Ha-Myung Park, Namyong Park, Sung-Hyon Myaeng, 2020

机译：PACC：Hadoop和Spark上的大规模连接组件计算
7. Polar Varieties and Computation of one Point in each Connected Component of a Smooth Real Algebraic Set [O] . Mohab Safey El Din, Éric Schost 2003

机译：平滑实代数集中每个连通分量中一个点的极性变种与计算
8. Maintenance of 2- and 3-Connected Components of Graphs, Part 2: 2- and 3-Edge-Connected Components and 2-Vertex-Connected Components. [R] . La Poutre, J. A. 1991

机译：图2的2和3连接组件的维护，第2部分：2和3边连接组件和2顶点连接组件。

Polar Varieties and Computation of one Point in each Connected Component of a Smooth Real Algebraic Set

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