HolonomicFunctions
Short Description
The HolonomicFunctions.m package provides commands for a variety of
tasks. The central concern is to deal with multivariate holonomic
($\partial$-finite) functions in an algorithmic fashion. For this
purpose the package can compute annihilating ideals and execute
closure properties for such functions. Also summation and integration
can be performed via creative telescoping. As subtasks, the following
items have been implemented in HolonomicFunctions: computations in Ore
algebras (noncommutative polynomial arithmetic with mixed
difference-differential operators), noncommutative Gröbner bases,
and solving of coupled linear systems of differential or difference
equations.
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 © 1999–2008 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 package is contained in the Mathematica input file
and is accompanied by the Mathematica notebook (last updated on February 2, 2010)
Literature
The theoretical background of the algorithms implemented in
HolonomicFunctions and how to use the package, is described in
- Advanced Applications of the Holonomic Systems Approach. Christoph Koutschan.
RISC-Linz, Johannes Kepler University. PhD Thesis. September 2009.
[pdf]
All the commands that are contained in HolonomicFunctions are in detail described in the documentation
- HolonomicFunctions (User's Guide). Christoph Koutschan.
Technical report no. 10-01 in RISC Report Series, University of Linz, Austria. January 2010.
[pdf]
Versions and Bugs
Right now you are using Version 1.3 released on January 25, 2010.
This version is compatible with Mathematica versions from 5.2 to 7.0.
Please report any bugs and comments to
Christoph Koutschan.