Representing sums in reduced difference rings

Michael Karr (1981) introduced reduced difference rings in which Liouvillian's Fundamental Theorem for Summation can be applied. Meanwhile there exist algorithms that can represent indefinite nested sums in such difference rings (or that can transform existing difference rings to such improved versions) but they have never been implemented. In this master thesis the underlying algorithms will be elaborated and implemented in Mathematica by using the available functionality of the summation package Sigma.