Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety

DOI10.1016/j.amc.2013.12.165zbMath1410.65205OpenAlexW2109499536WikidataQ57443171 ScholiaQ57443171MaRDI QIDQ1644578

Gerhard Pfister, Charles W. Wampler, Wolfram Decker, Frank-Olaf Schreyer, Chris Peterson, Daniel J. Bates, Jonathan D. Hauenstein, Andrew John Sommese

Publication date: 21 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.12.165

zbMATH Keywords

homotopy continuationsymbolic computationpolynomial systemnumerical computationcomputational algebraic geometryprimary decomposition

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational aspects of higher-dimensional varieties (14Q15)

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Uses Software

• HOM4PS
• PHCpack
• SINGULAR
• Bertini
• alphaCertified

Cites Work

• Bertini
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• Efficient path tracking methods
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• Numerical homotopies to compute generic points on positive dimensional algebraic sets
• Ideals of adjacent minors
• Newton's method with deflation for isolated singularities of polynomial systems
• The evaluation of the zeros of ill-conditioned polynomials. I, II
• Associative differential operations
• Algorithm 921
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• Regeneration homotopies for solving systems of polynomials
• Algorithm 857
• Adaptive Multiprecision Path Tracking
• Finding All Solutions to a System of Polynomial Equations
• Numerical calculation of the multiplicity of a solution to algebraic equations
• Algorithm 795
• SINGULAR
• Computing the multiplicity structure in solving polynomial systems
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• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
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