LamanGraphs swMATH ID: 39185 Software Authors: Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels; Schicho, Josef Description: dataset LamanGraphs: The number of realizations of a Laman graph. Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursive formula for the number of complex solutions of such systems. Homepage: https://zenodo.org/record/1245517#.YN19ei35wRE Keywords: Laman graph; minimally rigid graph; tropical geometry; Euclidean embedding; Puiseux series; graph realization; graph embedding Related Software: PHCpack; OEIS; phcpy; FGb; NetworkX; Bezout; MonodromySolver; MULTIRES; Scikit; Matplotlib; FlexRiLoG; NumericalAlgebraicGeometry; Bertini.m2; Traces; Bertini; nauty; Mathematica; Macaulay2 Cited in: 13 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The number of realizations of a Laman graph. Zbl 1439.14182Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels; Schicho, Josef 2018 all top 5 Cited by 21 Authors 5 Schicho, Josef 4 Grasegger, Georg 3 Bernstein, Daniel Irving 3 Koutschan, Christoph 2 Bartzos, Evangelos 2 Capco, Jose 2 Emiris, Ioannis Z. 2 Gallet, Matteo 2 Legerský, Jan 2 Lubbes, Niels 2 Tsigaridas, Elias P. 1 Farnsworth, Cameron 1 Garamvölgyi, Dániel 1 Gortler, Steven J. 1 Jackson, Bill 1 Jordán, Tibor 1 Krone, Robert 1 Mc Glue, Ciaran 1 Owen, John C. 1 Rodriguez, Jose Israel 1 Stokes, Klara all top 5 Cited in 11 Serials 2 SIAM Journal on Applied Algebra and Geometry 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Journal of Pure and Applied Algebra 1 Journal of Symbolic Computation 1 SIAM Journal on Discrete Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Applicable Algebra in Engineering, Communication and Computing 1 Experimental Mathematics 1 Journal of Integer Sequences 1 Forum of Mathematics, Sigma all top 5 Cited in 7 Fields 11 Combinatorics (05-XX) 9 Convex and discrete geometry (52-XX) 5 Algebraic geometry (14-XX) 2 Mechanics of particles and systems (70-XX) 1 Commutative algebra (13-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Computer science (68-XX) Citations by Year