About Gordan's algorithm for binary forms

DOI10.1007/s10208-016-9324-xzbMath1408.13017arXiv1403.2283OpenAlexW1581624903MaRDI QIDQ1692130

Marc Olive

Publication date: 26 January 2018

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.2283

zbMATH Keywords

covariantsbinary formsclassical invariant theoryGordan's algorithm

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Actions of groups on commutative rings; invariant theory (13A50) Computational aspects in algebraic geometry (14Q99)

Related Items

Isotropic invariants of a completely symmetric third-order tensor, A minimal integrity basis for the elasticity tensor, Algorithms for fundamental invariants and equivariants of finite groups, An irreducible function basis of isotropic invariants of a third order three-dimensional symmetric tensor, Covariant algebra of the binary nonic and the binary decimic, Computation of minimal covariants bases for 2D coupled constitutive laws, Dynamical systems of correspondences on the projective line I: Moduli spaces and multiplier maps, 3D geometric moment invariants from the point of view of the classical invariant theory, Combinatorial algorithm for the computation of cyclically standard regular bracket monomials, Generic separating sets for three-dimensional elasticity tensors, Rational invariants of even ternary forms under the orthogonal group, Reconstructing plane quartics from their invariants, Invariant rings of sums of fundamental representations of \(\operatorname{SL}_n\) and colored hypergraphs, Minimal functional bases for elasticity tensor symmetry classes, An algebraic independence result related to a conjecture of Dixmier on binary form invariants, On differential invariants of parabolic surfaces, An irreducible polynomial functional basis of two-dimensional Eshelby tensors, Characterization of the symmetry class of an elasticity tensor using polynomial covariants, Effective rationality of second-order symmetric tensor spaces

Uses Software

• Macaulay2
• Normaliz
• Poincare_Series
• noether.lib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sylvester versus Gundelfinger
• On anisotropic polynomial relations for the elasticity tensor
• Normaliz: Algorithms for affine monoids and rational cones
• SL\(_{2}\)-modules of small homological dimension
• On the Poincaré series of the invariants of binary forms
• Brill-Gordan loci, transvectants and an analogue of the Foulkes conjecture
• Combinatorics, transvectants and superalgebras. An elementary constructive approach to Hilbert's finiteness theorem
• The invariants of the binary nonic
• The invariants of the binary decimic
• The higher transvectants are redundant
• The rise of Cayley's invariant theory (1841--1862)
• The decline of Cayley's invariant theory (1863-1895)
• Efficient solution of linear diophantine equations
• Graph theory and classical invariant theory
• Computation of invariants for reductive groups
• Gordan ideals in the theory of binary forms
• On the polynomial invariants of the elasticity tensor
• Computational invariant theory
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• Quadratic involutions on binary forms
• Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects
• A complete minimal system of covariants for the binary form of degree 7
• Computing invariants of algebraic groups in arbitrary characteristic
• The death of a mathematical theory. A study in the sociology of knowledge
• Invariant theory, old and new
• Isotropic invariants of a completely symmetric third-order tensor
• ON THE VOLUME CONJECTURE FOR CLASSICAL SPIN NETWORKS
• A Course in Commutative Algebra
• Efficient Algorithms for Computing Nœther Normalization
• Série de Poincaré et systèmes de paramètres pour les invariants des formes binaires de degré 7
• The invariant theory of binary forms
• The structure of null Lagrangians
• Using Algebraic Geometry
• Invariants de plusieurs formes binaires
• Covariant algebra of the binary nonic and the binary decimic
• On the Graded Ring of Invariants of Binary Octavics
• Combinatorics and commutative algebra
• Algorithms in invariant theory