Real monodromy action

被引：2

作者：

Hauenstein, Jonathan D. ^{[1
]}

Regan, Margaret H. ^{[1
]}

机构：

[1] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 373卷

基金：

美国国家科学基金会;

关键词：

Monodromy group; Numerical algebraic geometry; Real algebraic geometry; Real monodromy structure; Homotopy continuation; Parameter homotopy; Kinematics; POLYNOMIAL SYSTEMS; GALOIS-GROUPS;

D O I：

10.1016/j.amc.2019.124983

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The monodromy group is an invariant for parameterized systems of polynomial equations that encodes structure of the solutions over the parameter space. Since the structure of real solutions over real parameter spaces are of interest in many applications, real monodromy action is investigated here. A naive extension of monodromy action from the complex numbers to the real numbers is shown to be very restrictive. Therefore, we introduce a real monodromy structure which need not be a group but contains tiered characteristics about the real solutions over the parameter space. An algorithm is provided to compute the real monodromy structure. In addition, this real monodromy structure is applied to an example in kinematics which summarizes all the ways performing loops parameterized by leg lengths can cause a mechanism to change poses. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：13

共 23 条

[11] Homotopy techniques for tensor decomposition and perfect identifiability [J].

Hauenstein, Jonathan D. ;

Oeding, Luke ;

Ottaviani, Giorgio ;

Sommese, Andrew J. .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2019, 753 :1-22

[12] Numerical Computation of Galois Groups [J].

Hauenstein, Jonathan D. ;

Rodriguez, Jose Israel ;

Sottile, Frank .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2018, 18 (04) :867-890

[13]

Hayes M., 1999, Kinematics of general planar stewart-gough platforms

[14]

Hermite C, 1851, CR HEBD ACAD SCI, V32, P458

[15] Non-singular assembly mode change in 3-RPR-parallel manipulators [J].

Husty, Manfred L. .

COMPUTATIONAL KINEMATICS, PROCEEDINGS, 2009, :51-60

[16] Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators [J].

Innocenti, C ;

Parenti-Castelli, V .

JOURNAL OF MECHANICAL DESIGN, 1998, 120 (01) :73-79

[17]

Kuramoto Y., 1984, CHEM TURBULENCE

[18] GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION [J].

Leykin, Anton ;

Sottile, Frank .

MATHEMATICS OF COMPUTATION, 2009, 78 (267) :1749-1765

[19]

Macho E., 2007, P IFTOMM 2007, P1

[20]

Sommese AJ, 2005, NUMERICAL SOLUTION OF SYSTEMS OF POLYNOMIALS: ARISING IN ENGINEERING AND SCIENCE, P1, DOI 10.1142/9789812567727

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