Pruning Algorithms for Pretropisms of Newton Polytopes

DOI10.1007/978-3-319-45641-6_31zbMath1453.52015arXiv1512.01594OpenAlexW2421942443MaRDI QIDQ2830024

Jeff Sommars, Jan Verschelde

Publication date: 9 November 2016

Published in: Computer Algebra in Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01594

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Computational aspects related to convexity (52B55) Foundations of tropical geometry and relations with algebra (14T10)

Related Items (3)

Computing tropical varieties over fields with valuation ⋮ Computing All Space Curve Solutions of Polynomial Systems by Polyhedral Methods ⋮ Pruning Algorithms for Pretropisms of Newton Polytopes

Uses Software

• DEMiCs
• MixedVol
• PHCpack
• polymake
• R
• SageMath
• Gfan
• PPL
• polyhedra
• lattice_polytope
• VolEsti
• VortexCalculations

Cites Work

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• The number of roots of a system of equations
• Mixed volume computation for semi-mixed systems
• Computing mixed volume and all mixed cells in quermassintegral time
• Efficient incremental algorithms for the sparse resultant and the mixed volume
• Computing convex hulls and counting integer points with \texttt{polymake}
• Computing tropical varieties
• Computing All Space Curve Solutions of Polynomial Systems by Polyhedral Methods
• Pruning Algorithms for Pretropisms of Newton Polytopes
• An output-sensitive algorithm for computing projections of resultant polytopes
• Algorithm 846
• Finiteness of stationary configurations of the four-vortex problem
• Polyhedral Methods in Numerical Algebraic Geometry
• Lectures on Polytopes
• Algorithm 795
• Efficient Random-Walk Methods for Approximating Polytope Volume
• Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem
• Computing Puiseux series for algebraic surfaces

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