Real monodromy action

Jonathan D. Hauenstein

doi:10.1016/j.amc.2019.124983

2020-05-01

Jonathan D. Hauenstein

Margaret H. Regan *

DOI：10.1016/j.amc.2019.124983

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摘要

En 中文

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.

Keyword:

Monodromy group

Numerical algebraic geometry

Real algebraic geometry

Real monodromy structure

Homotopy continuation

Parameter homotopy

Kinematics