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Publications
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Links
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Refereed Papers
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2013 |
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Viktor Levandovskyy and Anne Shepler : Quantum Drinfeld Hecke Algebras .
Canadian Journal of Mathematics (2013), in press
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Roberto La Scala and Viktor Levandovskyy : Skew polynomial rings, Gröbner bases and the letterplace embedding
of the free associative algebra .
Journal of Symbolic Computation 48,1 (2013), 110-131
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Jonathan Hauenstein and Viktor Levandovskyy : Certifying solutions to square systems of polynomial-exponential equations .
(2013), submitted
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2012 |
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Viktor Levandovskyy and Jorge Martín-Morales : Algorithms for Checking Rational Roots of $b$-functions and their
Applications .
Journal of Algebra 352,1 (2012), 408-429
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Viktor Levandovskyy and Bernd Martin : A Symbolic Approach to Generation and Analysis of Finite Difference
Schemes of Partial Differential Equations .
In: U. Langer, P. Paule: Numerical and Symbolic Scientific Computing: Progress and Prospects. Springer (2012), 123-156, bibtex.
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Viktor Levandovskyy and Kristina Schindelar : Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases .
Journal of Symbolic Computation 47,10 (2012), 1214-1232
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2011 |
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Eva Zerz, Viktor Levandovskyy and Kristina Schindelar : Exact linear modeling with polynomial coefficients .
Multidimensional Systems and Signal Processing 22,1-3 (2011), 55-65, bibtex.
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Viktor Levandovskyy, Christoph Koutschan and Oleksandr Motsak : On Two-generated Non-commutative Algebras Subject to the Affine Relation .
In: Gerdt, V., Koepf. W., Mayr, E. and Vorozhtsov, E.: Proceedings of CASC 2011. LNCS 6885, Springer (2011), 309-320, bibtex.
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Viktor Levandovskyy, Gerhard Pfister and Valery Romanovski : Evaluating cyclicity of cubic systems with algorithms of computational
algebra .
Communications on Pure and Applied Analysis 11,5 (2011), 2023--2035
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2010 |
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Daniel Andres, Michael Brickenstein, Viktor Levandovskyy, Jorge Martín-Morales and Hans Schönemann : Constructive D-module Theory with SINGULAR .
Mathematics in Computer Science 4,2-3 (2010), 359-383, bibtex.
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Viktor Levandovskyy, Eva Zerz and Kristina Schindelar : Exact linear modeling using Ore algebras .
Journal of Symbolic Computation 46,11 (2011), 1189-1204, bibtex.
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Viktor Levandovskyy and Kristina Schindelar : Computing diagonal form and Jacobson normal form of a matrix using
Gröbner bases .
Journal of Symbolic Computation 46,5 (2011), 595-608, bibtex.
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2009 |
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Viktor Levandovskyy, Alessandro Logar and Valery Romanovski : The cyclicity of a cubic system .
Open Systems & Information Dynamics 16,4 (2009), 429-439, bibtex.
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Daniel Andres, Viktor Levandovskyy and Jorge Martín-Morales : Principal Intersection and Bernstein-Sato Polynomial of an Affine Variety .
In: Proceedings of the International Symposium on Symbolic and
Algebraic Computation (ISSAC 09). ACM Press (2009), 231-238, bibtex.
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Roberto La Scala and Viktor Levandovskyy : Letterplace ideals and non-commutative Gröbner bases .
Journal of Symbolic Computation 44,10 (2009), 1374-1393, bibtex.
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Viktor Levandovskyy, Valery Romanovski and Douglas Shafer : The cyclicity of a cubic system with nonradical Bautin ideal .
Journal of Differential Equations 246,3 (2009), 1274-1287, bibtex.
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2008 |
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Kristina Schindelar, Viktor Levandovskyy and Eva Zerz : Linear exact modeling with variable coefficients .
In: Proceedings of the International Symposium on Mathematical Theory
of Networks and Systems (MTNS 08), Blacksburg. SIAM (2008), bibtex.
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Viktor Levandovskyy and Jorge Martín-Morales : Computational D-module Theory with Singular, Comparison with Other Systems and Two New Algorithms .
In: Proceedings of the International Symposium on Symbolic and
Algebraic Computation (ISSAC 08). ACM Press (2008), bibtex.
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Christoph Koutschan and Viktor Levandovskyy : Computing one of Victor Moll's irresistible integrals with computer algebra .
Computer Science Journal of Moldova 16,1(46) (2008), 35-49, bibtex.
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2007 |
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Viktor Levandovskyy and Eva Zerz : Obstructions to Genericity in Study of Parametric Problems in Control Theory .
In: Gröbner Bases in Control Theory and Signal Processing. de Gruyter (2007), 191-214, bibtex.
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2006 |
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Viktor Levandovskyy : Intersection of Ideals with Non-commutative Subalgebras .
In: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2006), Genova, Italy. ACM Press (2006), bibtex.
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Viktor Levandovskyy : PLURAL, a Non-commutative Extension of SINGULAR: Past, Present and Future .
In: A. Iglesias, N. Takayama: Proceedings of International Congress on Mathematical Software. LNCS 4151, Springer (2006)
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Viktor Levandovskyy and Eva Zerz : Algebraic systems theory and computer algebraic methods for some classes of linear control systems .
In: Y. Yamamoto: Proc. of the International Symposium on Mathematical Theory of Networks and Systems (MTNS'06). (2006)
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2005 |
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Viktor Levandovskyy and Eva Zerz : Computer algebraic methods for the structural analysis of linear control systems .
In: Proceedings in Applied Mathematics and Mechanics (PAMM). Wiley-VCH (2005)
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Viktor Levandovskyy : PBW Bases, Non-Degeneracy Conditions and Applications .
In: Buchweitz, R.-O. and Lenzing, H. (eds.): Proceedings of the ICRA X conference, Toronto, Canada. AMS. Fields Institute Communications (2005)
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Viktor Levandovskyy : On preimages of ideals in certain non-commutative algebras .
In: Pfister G., Cojocaru S. and Ufnarovski, V. (eds.): Computational Commutative and Non-Commutative Algebraic Geometry. IOS Press (2005)
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Viktor Levandovskyy : Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation .
(2005), Ph.D. Thesis
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2001 - 2004 |
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Viktor Levandovskyy and H.Schönemann : PLURAL - a Computer Algebra System for Noncommutative Polynomial Algebras .
In: M. Bronstein: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2003), Philadelfia, USA. ACM Press (2003)
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Viktor Levandovskyy : On Gröbner bases for noncommutative G-algebras .
In: Proceedings of the 8th Rhine Workshop
on Computer Algebra, Mannheim, Germany. (2002)
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Viktor Levandovskyy : Theory and applications of Gröbner bases in noncommutative
polynomial algebras (in Ukrainian) .
In: Proceedings of the 3rd Algebraic Conference in Ukraine, Sumy, Ukraine. (2001)
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Preprints and Technical Reports
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Viktor Levandovskyy and Anne Shepler : Quantum Drinfeld Hecke Algebras .
(2011)
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Viktor Levandovskyy and Kristina Schindelar : Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases .
(2011)
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Viktor Levandovskyy, Christoph Koutschan and Oleksandr Motsak : On Two-generated Non-commutative Algebras Subject to the Affine Relation .
(2011)
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Jonathan Hauenstein and Viktor Levandovskyy : Certifying solutions to square systems of polynomial-exponential equations .
(2011)
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S. Cojocaru, A. Colesnicov, A. Heinle, V. Levandovskyy, L. Malahov, G. Studzinski and V. Ufnarovski : Creation of a Knowledge Framework for Non-Commutative Computer Algebra .
In: Proc. 7th International Conference on Microelectronics and Computer Science, Chisinau, Moldova. (2011), 166-169
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Roberto La Scala and Viktor Levandovskyy : Skew polynomial rings, Gröbner bases and the letterplace embedding of the free associative algebra .
(2010)
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Christian Dingler and Viktor Levandovskyy : Algebraic Foundations for Finite Difference Schemes .
(2010)
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Viktor Levandovskyy and Bernd Martin : A Symbolic Approach to Generation and Analysis of Finite Difference
Schemes of Partial Differential Equations .
(2010)
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Viktor Levandovskyy, Kristina Schindelar and Eva Zerz : Exact linear modeling using Ore algebras .
(2010)
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Viktor Levandovskyy and Kristina Schindelar : Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases .
(2010)
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Viktor Levandovskyy and Jorge Martín-Morales : Algorithms for Checking Rational Roots of $b$-functions and their Applications .
(2010)
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Daniel Andres, Viktor Levandovskyy and Jorge Martín-Morales : Effective Methods for the Computation of Bernstein-Sato polynomials for Hypersurfaces and Affine Varieties .
(2010)
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Viktor Levandovskyy and Eva Zerz : Obstructions to Genericity in Study of Parametric Problems in Control Theory .
(2007)
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Viktor Levandovskyy : PLURAL, a Non-commutative Extension of SINGULAR: Past, Present and Future .
In: Reports On Computer Algebra no. 36,. Centre for Computer Algebra, University of Kaiserslautern, (2006)
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Viktor Levandovskyy : Intersection of Ideals with Non-commutative Subalgebras .
In: Technical report no. 2006-14. J. Kepler University Linz (2006)
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Manuel Kauers and Viktor Levandovskyy : An Interface between Mathematica and Singular .
In: Technical report no. 2006-29. J. Kepler University Linz (2006)
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(Co-)edited Special Issues
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Software (incl.
SINGULAR
and
PLURAL
libraries)
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Gert-Martin Greuel, Viktor Levandovskyy and Hans Schönemann :
PLURAL
(2000-2005). Non-commutative Extension of
SINGULAR
.
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Manuel Kauers and Viktor Levandovskyy : Singular.m (2006). An Interface between Mathematica and Singular.
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Viktor Levandovskyy : ncdecomp.lib (2004). Library for
decomposition of a module into its central characters.
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Viktor Levandovskyy and Jorge Martín-Morales : dmod.lib (2005). Library for computations with algebraic D-modules .
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Viktor Levandovskyy and Daniel Andres : dmodapp.lib (2007). Library for
applications of algebraic D-modules.
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Viktor Levandovskyy : freegb.lib (2008). Library for
computations of two-sided Gröbner bases in free algebras via letterplace.
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Viktor Levandovskyy and Kristina Schindelar : jacobson.lib (2009). Computation of a diagonal and Jacobson forms for
matrices over Ore Euclidean domains .
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Daniel Andres and Viktor Levandovskyy and Jorge Martín-Morales : dmodvar.lib (2010). Library for computations with D-modules for affine varieties.
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Posters
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