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The MultiIntegrate package allows to compute multi-dimensional integrals over hyperexponential integrands in terms of (generalized) harmonic sums.
AuthorsThe MultiIntegrate package allows to compute multi-dimensional integrals over hyperexponential integrands in terms of (generalized) harmonic sums. This package uses variations and extensions of the multivariate Alkmkvist-Zeilberger algorithm.
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 © 2009–2019 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.
The Package The package is contained in the Mathematica input file and is accompanied by the Mathematica notebook:
Right now you are using Version 1.0 released on October 11, 2018. This version is compatible with Mathematica versions from 9.0 to 11.3.
- demo.nb (for Mathematica version 11.3)
Literature The theoretical background of the algorithms implemented in MultiIntegrate is described in
The PhD thesis also contains a chapter about how to use the package.
- Computer Algebra Algorithms for Special Functions in Particle Physics (PhD Thesis). RISC, Johannes Kepler University, April 2012.[pdf]
- J. Ablinger, A. Behring, J. Blümlein,A. De Freitas,A. von Manteuffel and C. Schneider. Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra.Comput. Phys. Comm. 202, pp. 33-112. 2016. ISSN 0010-4655. arXiv:1509.08324 [hep-ph].[url]
Bugs Please report any bugs, comments and requests to Jakob Ablinger.