In the last years, the author developed in a series of papers powerful algorithms for definite and indefinite symbolic summation and implemented them in a summation package Sigma realized in the computer algebra system Mathematica [Discrete Math. Theor. Comput. Sci. 6, No. 2, 365–386 (2004; Zbl 1066.68164); J. Difference Equ. Appl . 11, No. 9, 799–821 (2005; Zbl 1087.33011)]. Starting point of his work are papers by M. Karr who described algorithms for symbolic summation in the setting of difference fields [J. Assoc. Comput. Mach. 28, 305–350 (1981; Zbl 0494.68044)].
In this paper the author uses a denominator elimination strategy which enables him to look for polynomial solutions of the parameterized linear difference equations coming up in summation problems instead of searching for rational function solutions. He illustrates his algorithms by some well-chosen examples.