Registration
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.
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.
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
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qZeil,
a Mathematica implementation of q-analogues of Gosper's
and Zeilberger's algorithm (by A. Riese).
-
Bibasic Telescope,
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 Fields
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Sigma,
a Mathematica package for discovering and proving multi-sum identities (by C. Schneider). The first Sigma version is released!
Symbolic Summation for Stirling Numbers
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Stirling.m,
a Mathematica package for computing recurrence equations of sums
involving Stirling numbers or Eulerian numbers (by M. Kauers).
Sequences and Power Series
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Dependencies,
a Mathematica package for computing algebraic relations of C-finite sequences
and multi-sequences (by M. Kauers and B. Zimmermann).
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Engel,
a Mathematica implementation of q-Engel Expansion
(by B. Zimmermann).
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GeneratingFunctions,
a Mathematica package for manipulations of
univariate holonomic functions and sequences (by C. Mallinger).
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qGeneratingFunctions (q-GFUN),
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).
Permutation Groups
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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).
Difference/Differential Equations
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DiffTools,
a Mathematica implementation of several algorithms for
solving linear difference equations with polynomial coefficients (by C. Weixlbaumer).
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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).
Misc
-
Singular,
a Mathematica interface to the Singular system
(by M. Kauers and V. Levandovskyy).
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Warning:
Due to an efficiency problem with Mathematica's multivariate rational function
arithmetic in versions 4.x, we strongly recommend not to use our packages
with these versions.
External Packages
With the kind permission of the corresponding authors we have slightly
modified the following packages not developed by our group to
make them work with our software. They can be downloaded without password.
Note that our changes are not user-visible.
Difference Equations
-
Hyper, a Mathematica package for finding hypergeometric solutions
of linear recurrences (by
Marko Petkovšek, University of Ljubljana, Slovenia).
-
qHyper, a Mathematica package for finding q-hypergeometric
solutions of linear recurrences (by
Marko Petkovšek, University of Ljubljana, Slovenia).
