Beyond polyhedral homotopies

DOI10.1016/j.jsc.2018.06.019zbMath1435.14053arXiv1706.03520OpenAlexW2963833143MaRDI QIDQ1994128

Anton Leykin, Josephine Yu

Publication date: 1 November 2018

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03520

zbMATH Keywords

homotopy continuationnumerical algebraic geometrytropical geometrynonlinear algebrasolving polynomial equations

Mathematics Subject Classification ID

Combinatorial aspects of tropical varieties (14T15) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational aspects of higher-dimensional varieties (14Q15) Numerical algebraic geometry (65H14)

Related Items

Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians ⋮ Probabilistic Saturations and Alt’s Problem

Uses Software

• HOM4PS
• PHCpack
• PHoM
• Gfan
• Hom4PS-3

Cites Work

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• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
• An algorithm for lifting points in a tropical variety
• HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
• PHoM -- a polyhedral homotopy continuation method for polynomial systems
• Computing tropical varieties
• Hom4PS-3: A Parallel Numerical Solver for Systems of Polynomial Equations Based on Polyhedral Homotopy Continuation Methods
• Introduction to Numerical Continuation Methods
• Algorithm 795
• A Polyhedral Method for Solving Sparse Polynomial Systems
• A Singular Mathematical Promenade
• Stable intersections of tropical varieties