Gröbner bases in symbolic analysis : [D2 Workshop on Gröbner Bases in Symbolic Analysis (May 8-17, 2006) ; RICAM Special Semester on Gröbner Bases and Related Methods

This volume contains survey articles and original research papers, presenting the state of the art on applying the symbolic approach of Gröbner bases and related methods to differential and difference equations. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods hosted by the Johann Radon Institute of Computational and Applied Mathematics, Linz, Austria, in May 2006. Preface 5 Gröbner Bases in Algebraic Analysis: New Perspectives for Applications 9 Solving Systems of Linear Partial Difference and Differential Equations with Constant Coefficients Using Gröbner Bases 31 Computation of the Strength of Systems of Difference Equations via Generalized Gröbner Bases 51 Editors' Note in Memory of Giuseppa Carra Ferro 83 A Survey on Differential Gröbner Bases 85 Differential Elimination and Biological Modelling 117 Janet Bases and Applications 147 Spencer Cohomology, Differential Equations, and Pommaret Bases 177 Differential Invariants for Lie Pseudo-groups 225 Invariant Theory and Differential Operators 253 Compatibility Complexes for Overdetermined Boundary Problems 275 On Initial Value Problems for Ordinary Differential-Algebraic Equations 291 Index 349