The package EvaluateMultiSums
is a Mathematica package that tries to simplify automatically
multi-sums to expressions in terms of indefinite nested sums defined over
hypergeometric products. As backbone it uses the summation package Sigma
setting of difference rings/fields that has to be loaded in addition. In addition, one can load the package HarmonicSums
to activate its full functionality (in particular if infinite sums are
involved and limit calculations are necessary).
The package has been developed by
, a member 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
It will be given for free to all researchers and non-commercial users.
Copyright © 1999–2019 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
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...).
consists of the file
For a demo we refer to the Mathematica notebook
For further details we refer, e.g., to the articles
- C. Schneider. Simplifying
Multiple Sums in Difference Fields. In: Computer Algebra in Quantum
Field Theory: Integration, Summation and Special
Functions, J. Blümlein, C. Schneider (ed.), Texts and Monographs in Symbolic
Computation. 2013. Springer. [url] [bib]
- Modern Summation Methods for Loop
Integrals in Quantum Field Theory: The Packages
Sigma, EvaluateMultiSums and SumProduction. In: Proc. ACAT 2013, J. Phys.: Conf. Ser.523012037, pp. 1-17.2014.[url] [bib]
Sigma is developed for Mathematica 11 and higher versions and might not run properly on
earlier versions. Please report any bugs