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