A Streamlined Difference Ring Theory: Indefinite Nested Sums, the Alternating Sign, and the Parameterized Telescoping Problem - Schneider, Carsten (2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2014)
We present an algebraic framework to represent indefinite nested sums over hyper geometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been extended to a ring theory in which also the alternating sign can be expressed. The underlying machinery relies on algorithms that compute all solutions of a given parameterized telescoping equation. As a consequence, we can solve the telescoping and creative telescoping problem in such difference rings.