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DEPARTMENT OF MATHEMATICS

AAU1/...Department of Mathematics2/Publications3/Software

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.

Regular Secuences

This package, integrated into SageMath since version 10.1, was developed by Clemens Heuberger, Daniel Krenn and Gabriel Lipnik.

For further details, please see SageMath Ticket #21202.

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

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