Using symmetries in the eigenvalue method for polynomial systems

DOI10.1016/j.jsc.2008.11.009zbMath1174.14053OpenAlexW1968321788MaRDI QIDQ731929

Karin Gatermann, Ilias S. Kotsireas, Robert M. Corless

Publication date: 9 October 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.11.009

zbMATH Keywords

symmetrieseigenvalue methodsolving polynomial systems

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational aspects in algebraic geometry (14Q99)

Related Items

Galois/Monodromy Groups for Decomposing Minimal Problems in 3D Reconstruction, Multiplication matrices and ideals of projective dimension zero

Uses Software

• Macaulay2
• Maple
• SINGULAR

Cites Work

• Computing the isolated roots by matrix methods
• SAGBI and SAGBI-Gröbner bases over principal ideal domains
• Using SAGBI bases to compute invariants
• The \(n\)-body problem and mutual distances
• Applications of SAGBI-bases in dynamics
• Computational invariant theory
• Gröbner bases, invariant theory and equivariant dynamics
• Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
• Analogs of Gröbner bases in polynomial rings over a ring
• H-bases for polynomial interpolation and system solving
• Computer algebra methods for equivariant dynamical systems
• On the complexity of sparse elimination
• Parallel integer relation detection: Techniques and applications
• Invariants of finite groups and their applications to combinatorics
• Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman
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