Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials

DOI10.1007/978-3-211-99314-9_2zbMath1191.14071OpenAlexW59564462MaRDI QIDQ3576571

Daniel J. Bates, Jonathan D. Hauenstein, Chris Peterson, Andrew John Sommese

Publication date: 30 July 2010

Published in: Texts and Monographs in Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-211-99314-9_2

zbMATH Keywords

homotopy continuationGrassmannianspolynomial systemirreducible componentsnumerical algebraic geometryrank deficiencymatrix of polynomials

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Grassmannians, Schubert varieties, flag manifolds (14M15) Computational aspects of higher-dimensional varieties (14Q15) Matrices over function rings in one or more variables (15A54) Computational aspects and applications of commutative rings (13Pxx)

Related Items (7)

Exceptional Stewart--Gough Platforms, Segre Embeddings, and the Special Euclidean Group ⋮ Isosingular sets and deflation ⋮ Witness sets of projections ⋮ Machine learning the real discriminant locus ⋮ Computing Geometric Feature Sizes for Algebraic Manifolds ⋮ A singular value homotopy for finding critical parameter values ⋮ Algebraic boundaries of Hilbert’s SOS cones

Uses Software

• CoCoA
• Kronecker
• Macaulay2
• PHCpack
• SINGULAR

Cites Work

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• SINGULAR
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• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Varieties Defined by Quadratic Equations
• A Gröbner free alternative for polynomial system solving

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