LEADER 05247nam 2200625Ia 450 001 9910451315903321 005 20200520144314.0 010 $a981-277-843-8 035 $a(CKB)1000000000407160 035 $a(EBL)1681017 035 $a(OCoLC)855899649 035 $a(SSID)ssj0000138855 035 $a(PQKBManifestationID)11954247 035 $a(PQKBTitleCode)TC0000138855 035 $a(PQKBWorkID)10101447 035 $a(PQKB)10581841 035 $a(MiAaPQ)EBC1681017 035 $a(WSP)00004768 035 $a(Au-PeEL)EBL1681017 035 $a(CaPaEBR)ebr10201210 035 $a(CaONFJC)MIL505461 035 $a(EXLCZ)991000000000407160 100 $a20020710d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aDifferential algebra and related topics$b[electronic resource] $eproceedings of the International Workshop, Newark Campus of Rutgers, The State University of New Jersey, 2-3 November 2000 /$feditors, Li Guo ... [et al.] 210 $aSingapore ;$aHong Kong $cWorld Scientific$dc2002 215 $a1 online resource (320 p.) 300 $aDescription based upon print version of record. 311 $a981-02-4703-6 320 $aIncludes bibliographical references. 327 $aContents ; 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 Sets 327 $a6 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 ; References 327 $aDifferential 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 reduction 327 $a13 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 ; References 327 $aModel 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 ; References 327 $aInverse Differential Galois Theory 330 $a 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 comput 606 $aDifferential algebra$vCongresses 606 $aAlgebraic fields$vCongresses 608 $aElectronic books. 615 0$aDifferential algebra 615 0$aAlgebraic fields 676 $a515.35 701 $aGuo$b Li$0611852 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451315903321 996 $aDifferential algebra and related topics$92078189 997 $aUNINA