Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals

DOI10.1016/j.jalgebra.2014.09.040zbMath1327.12003arXiv1304.7967OpenAlexW2963989919MaRDI QIDQ479803

Roberto La Scala, Vladimir P. Gerdt

Publication date: 5 December 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.7967

zbMATH Keywords

Gröbner basesinvariant idealsdifference algebras

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) Difference algebra (12H10)

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Uses Software

• SINGULAR
• DifferentialThomas
• DIFFALG
• Letterplace

Cites Work

• Unnamed Item
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• Letterplace
• Gröbner bases of symmetric ideals
• Transforming linear functional systems into fully integrable systems
• Algorithmic Thomas decomposition of algebraic and differential systems
• Letterplace ideals and non-commutative Gröbner bases.
• Computing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules
• A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic \(n\)-roots
• The diamond lemma for ring theory
• Differential Gröbner bases in one variable and in the partial case
• Skew polynomial rings, Gröbner bases and the letterplace embedding of the free associative algebra.
• Computer algebra methods for equivariant dynamical systems
• Difference algebra
• Gröbner bases and generation of difference schemes for partial differential equations
• Computation of difference Gröbner bases
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations
• Consistency of finite difference approximations for linear PDE systems and its algorithmic verification
• Finite generation of symmetric ideals
• On Consistency of Finite Difference Approximations to the Navier-Stokes Equations
• SINGULAR
• Admissible orderings and finiteness criteria for differential standard bases
• Ordering by Divisibility in Abstract Algebras

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