Numerical irreducible decomposition over a number field

DOI10.1142/S0219498818501955zbMath1408.14194OpenAlexW2761385847MaRDI QIDQ4561486

Timothy McCoy, Chris Peterson, Andrew John Sommese

Publication date: 6 December 2018

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498818501955

zbMATH Keywords

multiplicityGalois grouphomotopy continuationpolynomial systemalgebraic setirreducible componentnumerical algebraic geometrynumber fieldprimary decompositionalgebraic varietywitness setgeneric pointcascade homotopynumerical irreducible decomposition

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Real polynomials: location of zeros (26C10) Computational aspects in algebraic geometry (14Q99)

Uses Software

• Bertini

Cites Work

• Isosingular sets and deflation
• Théoremes de Bertini et applications
• A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set
• Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
• The Distribution of Galois Groups and Hilbert's Irreducibility Theorem
• Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
• Computing the multiplicity structure in solving polynomial systems
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Galois theory
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