SumCracker: A Mathematica implementation of several algorithms for identities and inequalities of special sequences, including summation problems

This package is part of the RISCErgoSum bundle. See Download and Installation.

Short Description

The SumCracker package contains routines for manipulating a large class of sequences (admissible sequences). It can prove identities and inequalities for these sequences, simplify expressions, evaluate symbolic sums, and solve certain difference equations.

SumCracker is developed for Mathematica 7 and might not run properly on earlier versions of Mathematica.

Accompanying files

Literature

To use the implementation it is sufficient to study the notebook demo.nb. It contains a few examples to start with.

Further information can be found in the following papers.

  • M. Kauers, Algorithms for Nonlinear Higher Order Difference Equations, Ph.D. Thesis, RISC, J. Kepler University Linz, 2005, [ps]
  • M. Kauers, SumCracker: A Package for Manipulating Symbolic Sums and Related Objects, Journal of Symbolic Computation 41(9), 2006, pp. 1039-1057, [pdf from JSC] [local pdf]