qZeil
Short Description
qZeil is a Mathematica implementation of
q-analogues of Gosper's
and Zeilberger's algorithm for proving and finding indefinite and definite
q-hypergeometric summation identities.
The package has been developed by
Axel Riese,
a Ph.D. student of the
RISC Combinatorics group.
Registration and Legal Notices
The source code for this package 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.
Copyright © 1999–2011 The RISC Combinatorics Group, Austria — all rights reserved.
Commercial use of the software is prohibited without prior written permission.
A Note on Encoded Files
This package contains one or more Mathematica input files which are encoded. Those files
cannot be read or modified directly as plain text, but can be loaded into
Mathematica just like any normal input file (i.e., with
<<"file" or
Get["file"]).
There is no need (and also no way) to decode them by using additional software
or a special key.
If loading an encoded file causes a syntax error, open it with a
text editor and remove any blank lines at the beginning (for some
reason your Mac could have inserted them silently...).
The Package
The
qZeil package consists of the Mathematica input file
an ASCII-documentation of all changes and new features since version 1.4
a Mathematica notebook consisting of about 500 examples
and the add-on for Bailey pair related functions (optional !)
Alternatively, you can download the whole package as a compressed archive file
Screenshot
Click
here to see
the
q-Gosper and
q-Zeilberger algorithm in action.
Literature
Information on the installation and use of the package (together with its
theoretical background) can be found in the paper
P. Paule and A. Riese,
A Mathematica q-Analogue
of Zeilberger's Algorithm Based on an Algebraically Motivated
Approach to q-Hypergeometric Telescoping,
in Special
Functions, q-Series and Related Topics,
Fields Inst. Commun., Vol. 14, pp. 179-210,
1997.
[pdf]
Moreover, an up-to-date manual for the package is presented in my Ph.D. thesis
A. Riese,
Contributions to Symbolic q-Hypergeometric Summation,
Ph.D. Thesis, RISC, J. Kepler University, Linz, 1997.
[pdf]
Methods for tuning the algorithm are described in the paper
A. Riese,
Fine-Tuning Zeilberger's Algorithm: The Methods of Automatic Filtering and
Creative Substituting,
in Symbolic Computation, Number Theory, Special Functions, Physics
and Combinatorics (F.G. Garvan and M.E.H. Ismail, eds.),
Developments in Mathematics, Vol. 4, pp. 243-254, Kluwer, 2001.
[pdf]
Versions and Bugs
The current version of the package is 2.42 last updated on February 18, 2005.
Please report any bugs and comments to
Ralf Hemmecke.