Software available from the RISC Combinatorics Group


The source code for our packages is password protected. To get the password send an email to Peter Paule. It will be given for free to all researchers and non-commercial users.

Please note, the distribution of RISC Software from other sources than RISC by JKU policy, is not allowed.

Available Packages

The researchers on combinatorics at RISC provide the following software, mainly packages for the computer algebra system Mathematica. To download them, please follow the guidelines given on each page. Most of the Mathematica packages are contained in the RISCErgosum bundle.

Symbolic Summation

Hypergeometric Summation
  • fastZeil, the Paule/Schorn implementation of Gosper's and Zeilberger's algorithm in Mathematica (by P. Paule, M. Schorn, and A. Riese).
  • Zeilberger, a Maxima implementation of Gosper's and Zeilberger's algorithm (by F. Caruso).
  • MultiSum, a Mathematica package for proving hypergeometric multi-sum identities (by K. Wegschaider and A. Riese).

q-Hypergeometric Summation

  • qZeil, a Mathematica implementation of q-analogues of Gosper's and Zeilberger's algorithm (by A. Riese).
  • Bibasic Telescope (pqTelescope), a Mathematica implementation of a generalization of Gosper's algorithm to bibasic hypergeometric summation (by A. Riese).
  • qMultiSum, a Mathematica package for proving q-hypergeometric multi-sum identities (by A. Riese).

Multi-Summation in Difference Rings and Fields

  • Sigma, a Mathematica package for discovering and proving multi-sum identities (by C. Schneider).
  • EvaluateMultiSums, a Mathematica package based on Sigma that tries to evaluate automatically multi-sums to expressions in terms of indefinite nested sums defined over (q-)hypergeometric products (by C. Schneider).

Symbolic Summation for Stirling Numbers

  • Stirling, a Mathematica package for computing recurrence equations of sums involving Stirling numbers or Eulerian numbers (by M. Kauers).

Symbolic Summation and Integration for Holonomic Functions

  • HolonomicFunctions, a Mathematica package for dealing with multivariate holonomic functions, including closure properties, summation, and integration (by C. Koutschan).

Sequences and Power Series

  • Asymptotics, a Mathematica package for computing asymptotic series expansions of univariate holonomic sequences (by M. Kauers).
  • Dependencies, a Mathematica package for computing algebraic relations of C-finite sequences and multi-sequences (by M. Kauers and B. Zimmermann).
  • Engel, a Mathematica implementation of q-Engel Expansion (by B. Zimmermann).
  • GeneratingFunctions, a Mathematica package for manipulations of univariate holonomic functions and sequences (by C. Mallinger).
  • Guess, a Mathematica package for guessing multivariate recurrence equations (by M. Kauers).
  • ore_algebra, a Sage package for doing computations with Ore operators (by M. Kauers, M. Jaroschek, F Johansson).
  • PositiveSequence, a Mathematica package for showing positivity of univariate C-finite and holonomic sequences
  • qGeneratingFunctions, a Mathematica package for manipulations of univariate q-holonomic functions and sequences (by C. Koutschan).
  • RLangGFun, a Maple implementation of the inverse Schützenberger methodology (by C. Koutschan).

Special Function Algorithms for Indefinite Nested Sums and Integrals

  • HarmonicSums, a Mathematica package for dealing with harmonic sums, generalized harmonic sums and cyclotomic sums and their related integral representations (by J. Ablinger).

Permutation Groups

  • PermGroup, a Mathematica package for permutation groups, group actions and Polya theory (by T. Bayer).

Partition Analysis

  • Omega, a Mathematica implementation of Partition Analysis (by A. Riese).
  • GenOmega, a Mathematica implementation of Guo-Niu Han's general Algorithm for MacMahon's Partition Analysis (by M. Wiesinger).

Difference/Differential Equations

  • DiffTools, a Mathematica implementation of several algorithms for solving linear difference equations with polynomial coefficients (by C. Weixlbaumer).
  • OreSys, a Mathematica implementation of several algorithms for uncoupling systems of linear Ore operator equations (by S. Gerhold).
  • RatDiff, a Mathematica implementation of Mark van Hoeij's algorithm for finding rational solutions of linear difference equations (by A. Riese).
  • SumCracker, a Mathematica implementation of several algorithms for identities and inequalities of special sequences, including summation problems (by M. Kauers).


  • Singular, a Mathematica interface to the Singular system (by M. Kauers and V. Levandovskyy).
  • ModularGroup, a Mathematica package providing basic algorithms and visualization routines related to the modular group, e.g. for drawing the tessellation of the upper half-plane (by T. Ponweiser).
  • math4ti2, a Mathematica interface to the 4ti2. (by R. Hemmecke and S. Radu).
  • RaduRK, a Mathematica implementation of Radu's Ramanujan-Kolberg Algorithm (by N. Smoot)
  • DrawFunDoms, a Mathematica package for drawing fundamental dmains for congruence subgroups in the modular Group SL2(ℤ) (by P. Kainberger).
  • QEta, a FriCAS package to compute with Dedekind eta functions (by R. Hemmecke).