Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials

DOI10.1007/s11075-015-0095-2zbMath1349.14177arXiv1505.05241OpenAlexW2234351191MaRDI QIDQ312198

Matthew E. Niemerg, Jonathan D. Hauenstein, Daniel J. Bates, Frank J. Sottile

Publication date: 14 September 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.05241

zbMATH Keywords

polynomial systemGale dualityreal algebraic geometryDescartes' rulefewnomialKhovanskii-Rolle continuation

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Real algebraic sets (14P05) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational aspects in algebraic geometry (14Q99)

Uses Software

• Bertini
• alphaCertified
• ISOLATE
• galeDuality

Cites Work

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• ISOLATE
• Khovanskii-Rolle continuation for real solutions
• Gale duality for complete intersections
• Semidefinite characterization and computation of zero-dimensional real radical ideals
• Factoring polynomials with rational coefficients
• Solving zero-dimensional systems through the rational univariate representation
• A methodology for solving chemical equilibrium systems
• A new exclusion test.
• Numerically computing real points on algebraic sets
• Improving the efficiency of exclusion algorithms
• Algorithm 921
• Descartes’ Rule of Signs for Polynomial Systems Supported on Circuits
• Some Geometrical Aspects of Control Points for Toric Patches
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Bounds on the Number of Real Solutions to Polynomial Equations
• Finding at least one point in each connected component of a real algebraic set defined by a single equation
• Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

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