The package EvaluateMultiSums

Short Description

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 in the 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 Carsten Schneider, 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 Peter Paule. 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 <<"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 consists of the file

• EvaluateMultiSums.m    (encoded)

For a demo we refer to the Mathematica notebook Demo.nb.

Literature

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]
• C. Schneider. Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction. In: Proc. ACAT 2013, J. Phys.: Conf. Ser.523/012037, pp. 1-17.2014.[url] [bib]
  

Bugs

Sigma is developed for Mathematica 11 and higher versions and might not run properly on earlier versions. Please report any bugs to Carsten Schneider.