Intro -- 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 Sets -- 6 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 -- Differential 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 -- 13 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 -- Model 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 -- Inverse Differential Galois Theory -- 1 Introduction -- 2 The derivation approach to the inverse problem -- 3 The inverse problem for a 2 x 2 upper triangular matrix group -- 4 Solvable groups -- References -- Differential Galois Theory Universal Rings and Universal Groups -- 1 The basic concepts -- 2 Universal Picard-Vessiot rings -- 3 Regular singular equations -- 4 Formal differential equations -- 5 Multisummation and Stokes maps.

6 Meromorphic differential equations -- References -- Cyclic Vectors -- 1 Introduction -- 2 Linear Differential Equations -- 3 The Algorithm -- 4 Remarks on the Algorithm -- 5 Remarks on the Hypotheses -- 6 Counterexamples -- 7 An Alternate Approach -- Appendix - A MAPLE implementation -- References -- Differential Algebraic Techniques in Hamiltonian Dynamics -- 1 Integrals of Ordinary Differential Equations -- 2 Linearized Equations -- 3 Hamiltonian Systems - The Classical Formulation -- 4 Normal Variational Equations -- 5 Differential Galois Theory and Non-Integrability -- 6 Preliminaries to the Applications -- 7 Applications -- References -- Moving Frames and Differential Algebra -- Introduction -- 1 Moving frames a tutorial -- 2 Comparison of {uaK||K|>=0} with {IaK||K|>=0} -- 3 Calculations with invariants -- References -- Baxter Algebras and Differential Algebras -- 0 Introduction -- 1 Definitions examples and basic properties -- 2 Free Baxter algebras -- 3 Further applications of free Baxter algebras -- References.

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 computational methods such as symbolic integration, and symmetry analysis of differential equations. This volume includes tutorial and survey papers presented at workshop. Contents: The Ritt-Kolchin Theory for Differential Polynomials (W Y Sit); Differential Schemes (J J Kovacic); Differential Algebra - A Scheme Theory Approach (H Gillet); Model Theory and Differential Algebra (T Scanlon); Inverse Differential Galois Theory (A R Magid); Differential Galois Theory, Universal Rings and Universal Groups (M van der Put); Cyclic Vectors (R C Churchill & J J Kovacic); Differential Algebraic Techniques in Hamiltonian Mechanics (R C Churchill); Moving Frames and Differential Algebra (E L Mansfield); Baxter Algebras and Differential Algebras (L Guo). Readership: Graduate students, pure mathematicians, logicians, algebraic geometers, applied mathematicians and physicists.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.