Viktor Levandovskyy Projects of Viktor Levandovskyy
(For) Students
Thirs-Party-Funded Projects
PPP Project "Computations with Ore polynomials" with Canada, funded by DAAD, 2013-2014.
"Development, implementation and applications of fundamental algorithms, relying on Gröbner bases in free associative algebras", funded by the DFG (LE 2697/2-1) in the framework of Priority Programme SPP 1489, joint project with Prof. M. Kreuzer, Passau. 2011-2013.
PPP Project "Computational D-Module Theory", funded by DAAD and Acciones Integradas Hispano-Alemanas. 2012-2013.
Numerous small-scale projects, joint with Prof. Eva Zerz, funded by the Undergraduate Research Fund of RWTH Aachen, 2008-2010.
"Development of Fast Rational Noncommutative Gröbner Bases in Ore-Localized Algebras of Operators and Applications to Special Functions", funded by the Transnational Access Programme of the project SCIence (Symbolic Computation Infrastructure for Europe) of the European Union.
"Symbolic Computation in Studies of Dynamical Systems", funded by the Transnational Access Programme of the project SCIence (Symbolic Computation Infrastructure for Europe) of the European Union, partner Prof. V. Romanovski.
Joint project "Implementierung einer kontrolltheoretischen Programmbibliothek im Computeralgebrasystem Singular" with Prof. Eva Zerz, supported by the Forschungsschwerpunkt "Mathematik und Praxis" des Landes Rheinland-Pfalz, Kaiserslautern University, 2004-2005.
"Entwicklung, Implementierung und Anwendung von auf Gröbnerbasen beruhenden Algorithmen für eine Klasse nichtkommutativer Algebren", project by Prof. G.-M. Greuel, funded by the DFG (Gr 640/11-1), 2002-2004.
"Representations and homology of algebras", funded by CRDF Award UM2-2094, project leader Prof. Y. A. Drozd, 2000--2001.
Software-related Projects
SINGULAR and PLURAL . I have been involved in the development of these systems since 1997. In 2005 PLURAL became an integral part of SINGULAR . See more at My Singular. There are several important variations of non-commutative Gröbner bases, on which I either already work or plan to work in the near future. News: ongoing development of the following projects:
SINGULAR : LETTERPLACE - Gröbner bases for modules over free and finitely presented algebras.
SINGULAR : LOCAPAL - Gröbner bases and basics over OLGA's, that is over certain (rational) localizations of G-algebras.
D-modules suite: several libraries, providing powerful implementations to the algorithms of computational D-module theory and algebraic analysis.
C L I P S a.k.a. Control Library In Plural and Singular, formerly supported by the Forschungsschwerpunkt "Mathematik und Praxis". Current state: in the SINGULAR library control.lib there have been implemented important (and easy-to-use) functions for systems with constant coefficients (that is, at present we work over commutative rings). Future plans: extend the functionality to the cases of polynomial and rational coefficients.
Databases, Benchmarking, Collection of Examples
The development of the database Gröbner Bases Implementations. Functionality Check and Comparison was initiated by me and enthusiastically supported by Bruno Buchberger during the Gröbner Bases Special Semester in 2006 at RISC. The database is currently being filled up with the data on contemporary computer algebra systems. Thanks to Camelia Rosenkranz for its programming!
SymbolicData. A project maintained by Hans-Gert Gräbe from Leipzig. We have tested the possibility to handle non-commutative PBW-like structures back in 2004. News:
The toolbox has been updated by H.-G. Gräbe with the XML-like syntax. We are working on bringing various non-commutative test sets together in the framework of SymbolicData.
There is ongoing work to provide FreeAlgebra types of examples and to implement connections to/from SINGULAR : LETTERPLACE , Magma, GAP and Bergman.
RWTH Aachen University Division of Mathematics Lehrstuhl B für Mathematik