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3 results on '"01-08, 13P10, 12H05, 35A25, 58A15, 68Q42"'

1. From analytical mechanical problems to rewriting theory through M. Janet

Author

Iohara, Kenji and Malbos, Philippe

Subjects
Mathematics - History and Overview, Mathematics - Commutative Algebra, 01-08, 13P10, 12H05, 35A25, 58A15, 68Q42
Abstract

This note surveys the historical background of the Gr\"obner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developed in algebra throughout the twentieth century. We recall the work of M. Janet on the algebraic analysis on linear partial differential systems that leads to the notion of involutive division. We present some generalizations of the division introduced by M. Janet and their relations with Gr\"obner basis theory., Comment: Lecture note of the Kobe-Lyon summer school 2015

Published
2017

2. From analytical mechanical problems to rewriting theory through M. Janet's work

Author

Philippe Malbos, Kenji Iohara, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Polynomial ring, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], 010102 general mathematics, Elimination theory, 01-08, 13P10, 12H05, 35A25, 58A15, 68Q42, 010103 numerical & computational mathematics, 01 natural sciences, Algebra, Algebraic equation, symbols.namesake, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, symbols, Homological algebra, Ideal (order theory), Rewriting, 0101 mathematics, Computational problem, Mathematics, Hilbert–Poincaré series
Abstract

This chapter is devoted to a survey of the historical background of Grobner bases for D-modules and linear rewriting theory largely developed in algebra throughout the twentieth century and to present deep relationships between them. Completion methods are the main streams for these computational theories. In the theory of Grobner bases, they were motivated by algorithmic problems in elimination theory such as computations in quotient polynomial rings modulo an ideal, manipulating algebraic equations, and computing Hilbert series. In rewriting theory, they were motivated by computation of normal forms and linear bases for algebras and computational problems in homological algebra.

Published
2020
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3. From analytical mechanical problems to rewriting theory through M. Janet

Author

Iohara , Kenji, Malbos , Philippe, Algèbre, géométrie, logique ( AGL ), Institut Camille Jordan [Villeurbanne] ( ICJ ), École Centrale de Lyon ( ECL ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ) -École Centrale de Lyon ( ECL ), and Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
Mathematics::Commutative Algebra, History and Overview (math.HO), Mathematics - History and Overview, FOS: Mathematics, Computer Science::Symbolic Computation, 01-08, 13P10, 12H05, 35A25, 58A15, 68Q42, Commutative Algebra (math.AC), Mathematics - Commutative Algebra, [ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]
Abstract

This note surveys the historical background of the Gr\"obner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developed in algebra throughout the twentieth century. We recall the work of M. Janet on the algebraic analysis on linear partial differential systems that leads to the notion of involutive division. We present some generalizations of the division introduced by M. Janet and their relations with Gr\"obner basis theory., Comment: Lecture note of the Kobe-Lyon summer school 2015

Published
2017

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