Solving polynomial systems via homotopy continuation and monodromy

DOI10.1093/imanum/dry017zbMath1462.65055arXiv1609.08722OpenAlexW2963247163MaRDI QIDQ5854360

Jeff Sommars, Timothy Duff, Anton Leykin, Kisun Lee, Cvetelina Hill, Anders Nedergaard Jensen

Publication date: 16 March 2021

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08722

zbMATH Keywords

homotopy continuationpolynomial system solvers

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)

Related Items (17)

Decomposable sparse polynomial systems ⋮ The steady-state degree and mixed volume of a chemical reaction network ⋮ Galois/Monodromy Groups for Decomposing Minimal Problems in 3D Reconstruction ⋮ Equations for GL invariant families of polynomials ⋮ Signatures of algebraic curves via numerical algebraic geometry ⋮ Using monodromy to recover symmetries of polynomial systems ⋮ Landau discriminants ⋮ \(u\)-generation: solving systems of polynomials equation-by-equation ⋮ Line Multiview Varieties ⋮ Polyhedral homotopies in Cox coordinates ⋮ A numerical toolkit for multiprojective varieties ⋮ On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs ⋮ Real monodromy action ⋮ Solving decomposable sparse systems ⋮ MonodromySolver ⋮ Likelihood equations and scattering amplitudes ⋮ Using monodromy to statistically estimate the number of solutions

Uses Software

• HOM4PS
• Macaulay2
• PHCpack
• Bertini
• alphaCertified
• NumericalAlgebraicGeometry
• gfanlib
• pss5
• NumericalCertification

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