Properness defects of projections and computation of at least one point in each connected component of a real algebraic set

El Din MS; Schost E

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Properness defects of projections and computation of at least one point in each connected component of a real algebraic set

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

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Computing at least one point in each connected component of a real algebraic set is a basic subroutine to decide emptiness of semi-algebraic sets, which is a fundamental algorithmic problem in effective real algebraic geometry. In this article we propose a new algorithm for the former task, which avoids a hypothesis of properness required in many of the previous methods. We show how studying the set of non-properness of a linear projection Pi enables us to detect the connected components of a real algebraic set without critical points for Pi. Our algorithm is based on this observation and its practical counterpoint, using the triangular representation of algebraic varieties. Our experiments show its efficiency on a family of examples.

机译：计算实际代数集的每个连接组件中的至少一个点是基本子程序，以决定半代数集的空虚，这是有效的真实代数几何形状中的基本算法问题。在本文中，我们提出了一种新的任务算法，这避免了许多先前方法所需的正确性假设。我们展示了如何研究线性投影PI的非适用性，使我们能够检测实际代数集的连接部件，而没有PI的关键点。我们的算法基于这种观察及其实际对应点，使用代数品种的三角形表示。我们的实验表明了它对一个例子的效率。

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来源
《Discrete & computational geometry》 |2004年第3期|共14页
作者
El Din MS; Schost E;
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作者单位

Univ Paris 06 LIP6 F-75015 Paris France;

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原文格式 PDF
正文语种 eng
中图分类几何、拓扑;
关键词
DIMENSIONAL SYSTEMS; POLYNOMIAL SYSTEMS; ELIMINATION THEORY; EXISTENTIAL THEORY; POLAR VARIETIES; GROBNER BASES; COMPLEXITY; EQUATION; ALGORITHM;

机译：尺寸系统;多项式系统;消除理论;存在理论;极地品种;Grobner基础;复杂性;方程式;算法;

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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. Approximation of Analytic Sets with Proper Projection by Algebraic Sets [J] . Marcin Bilski Constructive Approximation . 2012,第3期

机译：用代数集逼近具有正确投影的解析集。
3. 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
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. BOOLEAN-VALUED MODELS OF SET THEORY WHEN THE BOOLEAN ALGEBRA IS A PROPER CLASS IN THE GROUND MODEL. [D] . PELLETIER, DONALD HECTOR. 1971

机译：当布尔代数是地面模型中的适当类时，集合论的布尔值模型。
6. Shallow Sparsely-Connected Autoencoders for Gene Set Projection [O] . Maxwell P. Gold, Alexander LeNail, Ernest Fraenkel -1

机译：用于基因集投影的浅稀疏连接自动编码器
7. Properness defects of projections and computation of at least one point in each connected component of a real algebraic set [O] . Safey El Din, Mohab, Schost, Eric 2004

机译：实数代数集的每个连通分量中的投影性质缺陷和至少一个点的计算
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。

Properness defects of projections and computation of at least one point in each connected component of a real algebraic set

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