Gröbner bases, invariant theory and equivariant dynamics

DOI10.1006/jsco.1998.0277zbMath0939.68171OpenAlexW2058981827MaRDI QIDQ1808673

Frédéric Guyard, Karin Gatermann

Publication date: 25 November 1999

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

Full work available at URL: https://semanticscholar.org/paper/5505c28bd201d3131b8609fd759f7b691156ff4c

zbMATH Keywords

algorithmic invariant theory

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Actions of groups on commutative rings; invariant theory (13A50)

Related Items (4)

Algorithms for fundamental invariants and equivariants of finite groups ⋮ Symmetry in multivariate ideal interpolation ⋮ Using symmetries in the eigenvalue method for polynomial systems ⋮ Preface

Uses Software

• moregroebner

Cites Work

• Group theoretic methods in bifurcation theory. With an appendix by P. Olver
• The Gröbner fan of an ideal
• Standard bases and geometric invariant theory. I: Initial ideals and state polytopes
• Computing combinatorial decompositions of rings
• Computation of Hilbert functions
• Heteroclinic cycles and modulated travelling waves in a system with \(D_ 4\) symmetry
• Singularities and groups in bifurcation theory. Volume II
• Finding sparse systems of parameters
• Zeros of equivariant vector fields: Algorithms for an invariant approach
• Bifurcation analysis for spherically symmetric systems using invariant theory
• The 1:2 resonance with \(O(2)\) symmetry and its applications in hydrodynamics
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• Semi-invariants, equivariants and algorithms
• Calculating invariant rings of finite groups over arbitrary fields
• Forced reflectional symmetry breaking of an O(2)-symmetric homoclinic cycle
• Admissible orders and linear forms
• Bifurcation from rotationally invariant states
• Automatic classification of normal forms
• Linearization of vector fields on the orbit space of the action of a compact Lie group
• Introduction to Lie Algebras and Representation Theory
• Algorithms in invariant theory
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