Finding optimal representation of nested products

Using difference ring theory and linear algebra techniques (like the Smith Normal Form) one can find optimal representations of hypergemeomtric products. This means that the reduced products (evaluated as sequences) are algebraically independent among each other and the number of products (the transendental degree) is minimal. In this master thesis the existing techneques will be generalized to nested hypergeometric products and the algorithmic ideas will be implemented in a new Mathematica package (using the summation package Sigma) for concrete problem solving.