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Combinatorial Resultants in the Algebraic Rigidity Matroid
[article]
2021
arXiv
pre-print
Motivated by a rigidity-theoretic perspective on the Localization Problem in 2D, we develop an algorithm for computing circuit polynomials in the algebraic rigidity matroid associated to the Cayley-Menger ideal for n points in 2D. We introduce combinatorial resultants, a new operation on graphs that captures properties of the Sylvester resultant of two polynomials in the algebraic rigidity matroid. We show that every rigidity circuit has a construction tree from K_4 graphs based on this
arXiv:2103.08432v1
fatcat:psdqebn445bwfdsx3tqf7ovute