From Analytical Mechanics Problems to Rewriting Theory Through M. Janet’s Work

DOI10.1007/978-3-030-26454-3_1zbMath1446.13022OpenAlexW2781489572MaRDI QIDQ3294886

Kenji Iohara, Philippe Malbos

Publication date: 29 June 2020

Published in: Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-26454-3_1

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) History of commutative algebra (13-03)

Related Items (1)

Maurice Janet's algorithms on systems of linear partial differential equations

Uses Software

• DifferentialThomas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algorithmic Thomas decomposition of algebraic and differential systems
• Higher-dimensional normalisation strategies for acyclicity
• Formal algorithmic elimination for PDEs
• An example of a smooth linear partial differential equation without solution
• Involution. The formal theory of differential equations and its applications in computer algebra
• History and basic features of the critical-pair/completion procedure
• An algorithm for determining the size of symmetry groups
• The diamond lemma for ring theory
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Gröbner bases and involutive methods for algebraic and differential equations
• The infinite groups of Lie and Cartan. I: The transitive groups
• Involutive bases of polynomial ideals
• Minimal involutive bases
• Exterior differential systems and the calculus of variations
• Gröbner deformations of hypergeometric differential equations
• Convergent presentations and polygraphic resolutions of associative algebras
• Resolution of singularities of an algebraic variety over a field of characteristic zero. II
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Über die Deformation isolierter Singularitäten analytischer Mengen
• Über das Macaulaysche inverse System und dessen Bedeutung für die Theorie der linearen Differentialgleichungen mit konstanten Koeffizienten
• On theories with a combinatorial definition of 'equivalence'
• Polygraphs of finite derivation type
• On E. Cartan's Prolongation Theorem of Exterior Differential Systems
• Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems
• Term Rewriting and All That
• Recursive Unsolvability of a problem of Thue
• A Simple Criterion for Involutivity
• An algebraic model of transitive differential geometry

This page was built for publication: From Analytical Mechanics Problems to Rewriting Theory Through M. Janet’s Work