Software
Our research activities often lead to the development of software, which we set out here for reasons of transparency and reproducability.
Discrete Mathematics
SageMath
SageMath is free open-source mathematics software. This software is used and developed in the Department during research. As is standard procedure in mathematics, SageMaths source code is peer-reviewed. Students of mathematics also learn to use the Python programming language that forms the basis for SageMath as part of a range of courses and in doing so, how to solve tasks from varied fields of mathematics.
The following introduces the contributions and software modules of the members of the department, contributing to further development of SageMath and which are integrated into the mathematics software.
Finite state machines, Automata, Transducers
This package, integrated into SageMath since version 5.13 was developed by Clemens Heuberger, Daniel Krenn and Sara Kropf.
For further details, please see SageMath Ticket #15078.
Asymptotic Expansions
This package, integrated into SageMath since version 6.9, was developed by Benjamin Hackl, Clemens Heuberger and Daniel Krenn.
For further details, please see SageMath Ticket #17601.
All Contributions
All contributions by SageMath developers at the department can be found on SageMath’s trac-Server.
Optimisation
BiqMac Solver
The BiqMac Solver is the result of a joint project involving Giovanni Rinaldi (IASI-CNR, Rome) and Franz Rendl along with Angelika Wiegele (both Department of Mathematics, AAU). It can be used to solve the Max-Cut problem on graphs exactly or approximately. In addition, unrestricted binary quadratic optimisation problems can be solved or approximated using BiqMac.
The actual Solver can be found at biqmac.aau.at/ and several test cases are at biqmac.aau.at/biqmaclib.html. In addition, BiqMac is available via NEOS Server neos-server.org/neos/.
Vizing’s Conjecture
Matlab as well as SageMath codes from the project on Vizing’s Conjecture via Semidefinite Programming and Sums-of-Squares can be found at gitlab.com/dakrenn/vizing-sdp-sos.
Diverse Matlab-Files
| Description | Authors | Year | Data |
| Random instances used in Expedis | N. Gusmeroli | 2019 | RandomInstances.tar.gz |
| DADAL — Using a Factored Dual in Augmented Lagrangian Methods for Semidefinite Programming | M. De Santis, F. Rendl, A. Wiegele | 2017 | DADAL |
| Version of mprw with initial scaling of entries | J. Malick, J. Povh, F. Rendl, A. Wiegele | 2011 | mprw2.m |
| Boundary Point Method for solving SDPs | J. Malick, J. Povh, F. Rendl, A. Wiegele | 2007 | mprw.m |
| A Boundary Point Method for computing the Theta number | J. Povh, F. Rendl, A. Wiegele | 2005 | theta_bp.m |
| Matlab files for a variant of Karger-Motwani-Sudan’s graph coloring heuristic | I. Dukanovic and F. Rendl | 2005 | colorKMS.tgz |
| Matlab files to compute strengthenings of theta function | I. Dukanovic and F. Rendl | 2005 | Linux version / Windows version (without LAPACK) |
| Matlab m-file to compute basic SDP relaxation for Max-Cut | F. Rendl | 2003 | mc_psd.m |
| Matlab files to compute the theta function | G. Gruber and F. Rendl | 2002 | theta_ml.tar.gz |
| Convex Quadratic Programming over the Standard Simplex | F. Rendl | 2003 | qp_prjct.m |
| An infeasible active set method for convex problems with simple bounds | K. Kunisch and F. Rendl | 2001 | active-ml.tar |
| Random data sets for equipartition in MATLAB binary format | A. Lisser and F.Rendl | 2000 | rand.zip |
| Matlab generators for sparse SDP | F. Rendl | 2000 | rand_sdps.m, rand_sdpsqr.m |
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