05247nam 2200625Ia 450 991045131590332120200520144314.0981-277-843-8(CKB)1000000000407160(EBL)1681017(OCoLC)855899649(SSID)ssj0000138855(PQKBManifestationID)11954247(PQKBTitleCode)TC0000138855(PQKBWorkID)10101447(PQKB)10581841(MiAaPQ)EBC1681017(WSP)00004768(Au-PeEL)EBL1681017(CaPaEBR)ebr10201210(CaONFJC)MIL505461(EXLCZ)99100000000040716020020710d2002 uy 0engur|n|---|||||txtccrDifferential algebra and related topics[electronic resource] proceedings of the International Workshop, Newark Campus of Rutgers, The State University of New Jersey, 2-3 November 2000 /editors, Li Guo ... [et al.]Singapore ;Hong Kong World Scientificc20021 online resource (320 p.)Description based upon print version of record.981-02-4703-6 Includes bibliographical references.Contents ; Foreword ; Workshop Participants ; Workshop Program ; The Ritt-Kolchin Theory for Differential Polynomials ; Preface ; 1 Basic Definitions ; 2 Triangular Sets and Pseudo-Division ; 3 Invertibility of Initials ; 4 Ranking and Reduction Concepts ; 5 Characteristic Sets6 Reduction Algorithms 7 Rosenfeld Properties of an Autoreduced Set ; 8 Coherence and Rosenfeld's Lemma ; 9 Ritt-Raudenbush Basis Theorem ; 10 Decomposition Problems ; 11 Component Theorems ; 12 The Low Power Theorem ; Appendix: Solutions and hints to selected exercises ; ReferencesDifferential Schemes 1 Introduction ; 2 Differential rings ; 3 Differential spectrum ; 4 Structure sheaf ; 5 Morphisms ; 6 A-Schemes ; 7 A-Zeros ; 8 Differential spectrum of R ; 9 AAD modules ; 10 Global sections of AAD rings ; 11 AAD schemes ; 12 AAD reduction13 Based schemes 14 Products ; References ; Differential Algebra - A Scheme Theory Approach ; Introduction ; 1 Differential Rings ; 2 Kolchin's Irreducibility Theorem ; 3 Descent for Projective Varieties ; 4 Complements and Questions ; ReferencesModel Theory and Differential Algebra 1 Introduction ; 2 Notation and conventions in differential algebra ; 3 What is model theory? ; 4 Differentially closed fields ; 5 O-minimal theories ; 6 Valued differential fields ; 7 Model theory of difference fields ; ReferencesInverse Differential Galois Theory Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computDifferential algebraCongressesAlgebraic fieldsCongressesElectronic books.Differential algebraAlgebraic fields515.35Guo Li611852MiAaPQMiAaPQMiAaPQBOOK9910451315903321Differential algebra and related topics2078189UNINA