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

DOI10.1007/s00407-020-00255-yzbMath1467.01007arXiv1911.09703OpenAlexW3048292655MaRDI QIDQ2659144

Philippe Malbos, Kenji Iohara

Publication date: 25 March 2021

Published in: Archive for History of Exact Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.09703

zbMATH Keywords

formal methodsJanet's basessystems of linear PDEs

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) Other special methods applied to PDEs (35A25) History of partial differential equations (35-03)

Related Items (1)

Confluence of algebraic rewriting systems

Cites Work

• On the genesis of the Cartan-Kähler theory
• Differential forms -- Cartan to De Rham
• An algorithm for determining the size of symmetry groups
• The diamond lemma for ring theory
• Gröbner bases and involutive methods for algebraic and differential equations
• Frobenius, Cartan, and the problem of Pfaff
• Exterior differential systems and the calculus of variations
• Resolution of singularities of an algebraic variety over a field of characteristic zero. II
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Über das Macaulaysche inverse System und dessen Bedeutung für die Theorie der linearen Differentialgleichungen mit konstanten Koeffizienten
• From Analytical Mechanics Problems to Rewriting Theory Through M. Janet’s Work
• A Simple Criterion for Involutivity
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