Symbolic Summation and Combinatorial Identities - Period I (Subproject of SFB F 13 Numerical and Symbolic Scientific Computation)

The general project goal is the development of computer algebra algorithms for automated proving or closed-form evaluation of summation identities arising in combinatorial context. In order to accomplish this goal, the problem of proving or closed-form evaluation will be transformed into problems of solving. This, for instance, means: solving linear systems of equations with rational function coefficients, finding (symbolic) solutions of difference equations, or finding (e.g., by applying Gröbner bases theory) certain operators in annihilating ideals that arise in the context of certain noncommutative difference operator algebras and corresponding (left-)modules. It is a fundamental aspect of the proposed research that its goals can only be achieved by effective interaction of mathematical theory and practical implemantation of efficient algorithms.