منابع مشابه
Point Configurations and Cayley-Menger Varieties
Equivalence classes of n-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger varieties arise in the Euclidean case, and have relevance for mechanical linkages, polygon spaces and rigidity theory. Applications include upper bounds for realizati...
متن کاملCausal association of electromagnetic signals using the Cayley–Menger determinant
determinant Samuel Picton Drake, Brian D. O. Anderson, and Changbin Yu Defence Science and Technology Organisation, Edinburgh, South Australia 5111, Australia and School of Chemistry and Physics, The University of Adelaide, Adelaide, South Australia 5005, Australia Research School of Information Sciences and Engineering, Australian National University, Canberra, Australian Capital Territory 020...
متن کاملPolynomial Complexity Recognizing a Tropical Linear Variety
A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.
متن کاملCoordinate-Free Formulation of a 3-2-1 Wire-Based Tracking Device Using Cayley-Menger Determinants
This paper deals with the problem of estimating the pose of a rigid moving object by measuring the length of six wires attached to it. Among all possible locations for the attachments on the moving object, the “3-2-1” configuration exhibits the highest number of favorable properties. A closed-form coordinate-free solution to the forward kinematics of this particular configuration is given in te...
متن کاملAn Algorithm for Lifting Points in a Tropical Variety
The aim of this paper is to give a constructive proof of one of the basic theorems of tropical geometry: given a point on a tropical variety (defined using initial ideals), there exists a Puiseux-valued “lift” of this point in the algebraic variety. This theorem is so fundamental because it justifies why a tropical variety (defined combinatorially using initial ideals) carries information about...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2019
ISSN: 0895-4801,1095-7146
DOI: 10.1137/19m1237582