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.

Bin Packing 3D

Repository containing the codes for solving the orthogonal 3D Bin Packing Problem, programmed by Muamer Hrncic.
https://github.com/MuamerHr/BPP3D-Bin-Packing-Problem

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