Our research activities often lead to the development of software, which we set out here for reasons of transparency and reproducability.
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
For further details, please see SageMath Ticket #15078.
For further details, please see SageMath Ticket #17601.
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.
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.
|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|