1. From analytical mechanical problems to rewriting theory through M. Janet's work
- Author
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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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