Holonomic closure properties over PiSigma-fields

Given two holonomic recurrences (i.e., recurrences with polynomial coeffcients), one can compute a recurrence whoses solutions contain, e.g., the addition (or multiplication) of all solutions of the input recurrences. In this master thesis the underlying algorithms for such closure properties are generalized and implemented in the setting of difference rings. Special emphasis will be put on concrete examples coming from symbolic summation in difference rings (using, e.g., the summation package Sigma).