Holonomic Summation in Difference Rings

Summation of holonomic sequences (sequences that satisy homogeneous recurrences) relies on non-trivial computer algebra techniques such as Groebner basis algorithms, decoupling algorithms of coupled recurrence systems and solvers of scalar recurrences. Alternatively, there exists a simplified algorithmic version for definite multi-sums that is free of Groebner basis and decoupling algorithms. As a bonus, these ideas work in general difference rings where one can handle also recurrences with inhomogeneous parts that depend on indefinite nested sums. In this bachelor thesis the basic ideas of this holonomic/difference ring approach is elaborated and the available functionality within the summation package Sigma is applied to concrete examples.