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Projects
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Thirs-Party-Funded Projects
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PPP Project "Computations with Ore polynomials" with Canada, funded by DAAD,
2013-2014.
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"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.
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PPP Project "Computational D-Module Theory", funded by DAAD and Acciones
Integradas Hispano-Alemanas. 2012-2013.
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Numerous small-scale projects, joint with Prof. Eva Zerz, funded by the Undergraduate Research Fund of RWTH Aachen, 2008-2010.
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"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.
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"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.
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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.
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"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.
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"Representations and homology of algebras", funded by CRDF Award
UM2-2094, project leader Prof. Y. A. Drozd, 2000--2001.
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Software-related Projects
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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:
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SINGULAR
:
LETTERPLACE
- Gröbner bases for modules over free and finitely presented algebras.
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SINGULAR
:
LOCAPAL
- Gröbner bases and basics over OLGA's, that is over certain (rational) localizations of G-algebras.
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D-modules suite: several libraries, providing powerful
implementations to the algorithms of computational D-module theory and algebraic analysis.
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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.
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Databases, Benchmarking, Collection of Examples
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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!
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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:
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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.
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There is ongoing work to provide FreeAlgebra types of examples and to implement
connections to/from
SINGULAR
:
LETTERPLACE
, Magma, GAP and Bergman.
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