A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Sparse elimination and applications in kinematics
Sparse elimination and applications in kinematics
Efficient incremental algorithms for the sparse resultant and the mixed volume
Journal of Symbolic Computation
Mathematics of Computation
How to count efficiently all affine roots of a polynomial system
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
The Number of Embeddings of Minimally Rigid Graphs
Discrete & Computational Geometry
Planar minimally rigid graphs and pseudo-triangulations
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Combinatorial genericity and minimal rigidity
Proceedings of the twenty-fourth annual symposium on Computational geometry
Algebraic methods for counting euclidean embeddings of rigid graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
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Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the viewpoint of Bernstein's Theorem. The focus of the paper is to provide methods to study the mixed volume of suitable systems of polynomial equations obtained from the edge length constraints. While in most cases the resulting bounds are weaker than the best known bounds on the number of embeddings, for some classes of graphs the bounds are tight.