Viktor Levandovskyy Publications of Viktor Levandovskyy
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Refereed Papers
2017
Christian Schilli, Eva Zerz and Viktor Levandovskyy : Controlled and conditioned invariance for polynomial and rational feedback systems . In: Algebraic and Symbolic Computation Methods in Dynamical Systems, Advances in Delays and Dynamics (ADD). Springer (2017)
Albert Heinle and Viktor Levandovskyy : A Factorization Algorithm for G-Algebras and its Applications . Journal of Symbolic Computation (2017)
Johannes Hoffmann and Viktor Levandovskyy : A constructive approach to arithmetics in Ore localizations . In: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 17). ACM Press (2017)
2016
Albert Heinle and Viktor Levandovskyy : A Factorization Algorithm for G-Algebras and Applications . In: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 16). ACM Press (2016), 263-270
Christian Schilli, Eva Zerz and Viktor Levandovskyy : Controlled and conditioned invariant varieties for polynomial control systems with rational feedback . In: Proceedings of the International Symposium on Mathematical Theory of Networks and Systems (MTNS 2016), Minneapolis. (2016), 182-187
Jason Bell, Albert Heinle and Viktor Levandovskyy : On noncommutative finite factorization domains . Transactions of the AMS 369 (2017), 2675-2695
2015
Mark Giesbrecht, Albert Heinle and Viktor Levandovskyy : Factoring Linear Partial Differential Operators in n Variables . Journal of Symbolic Computation 75 (2016), 127-148
Jonathan Hauenstein and Viktor Levandovskyy : Certifying solutions to square systems of polynomial-exponential equations . Journal of Symbolic Computation (2015)
Brigita Fercec, Viktor Levandovskyy, Valery G. Romanovski and Douglas Shafer : Bifurcations of critical periods of polynomial systems . Journal of Differential Equations 259,8 (2015), 3825-3853, bibtex.
Albert Heinle and Viktor Levandovskyy : The SDEval Benchmarking Toolkit . ACM Communications in Computer Algebra 49,1 (2015), 1-9, bibtex.
2014
Mark Giesbrecht, Albert Heinle and Viktor Levandovskyy : Factoring Differential Operators in n Variables . In: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 14). ACM Press (2014), 194-201, bibtex.
Christian Schilli, Eva Zerz and Viktor Levandovskyy : Controlled and conditioned invariant varieties for polynomial control systems . In: Proceedings of the International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen. (2014), 1691-1698, bibtex.
Viktor Levandovskyy and Anne Shepler : Corrigendum to Example in Quantum Drinfeld Hecke Algebras . Canadian Journal of Mathematics 66 (2014), 902-902
Viktor Levandovskyy and Anne Shepler : Quantum Drinfeld Hecke Algebras . Canadian Journal of Mathematics 66 (2014), 874-901, bibtex.
2013
Viktor Levandovskyy, Grischa Studzinski and Benjamin Schnitzler : Enhanced Computations of Gröbner Bases in Free Algebras as a New Application of the Letterplace Paradigm . In: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 13). ACM Press (2013), 259-266, bibtex.
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
2012
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
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.
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
2011
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.
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.
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
2010
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.
Viktor Levandovskyy, Eva Zerz and Kristina Schindelar : Exact linear modeling using Ore algebras . Journal of Symbolic Computation 46,11 (2011), 1189-1204, bibtex.
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.
2009
Viktor Levandovskyy, Alessandro Logar and Valery Romanovski : The cyclicity of a cubic system . Open Systems & Information Dynamics 16,4 (2009), 429-439, bibtex.
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.
Roberto La Scala and Viktor Levandovskyy : Letterplace ideals and non-commutative Gröbner bases . Journal of Symbolic Computation 44,10 (2009), 1374-1393, bibtex.
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.
2008
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.
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.
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.
2007
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.
2006
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.
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)
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)
2005
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)
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)
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)
Viktor Levandovskyy : Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation . (2005), Ph.D. Thesis
2001 - 2004
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)
Viktor Levandovskyy : On Gröbner bases for noncommutative G-algebras . In: Proceedings of the 8th Rhine Workshop on Computer Algebra, Mannheim, Germany. (2002)
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)
Preprints and Technical Reports
Wolfram Decker and Christian Eder and Viktor Levandovskyy and Sharwan K. Tiwari : Modular Techniques For Noncommutative Gröbner Bases . (2017)
Albert Heinle and Viktor Levandovskyy : A Factorization Algorithm for G-Algebras and its Applications . (2017)
Jason P. Bell and Albert Heinle and Viktor Levandovskyy : On Noncommutative Finite Factorization Domains . (2014)
Mark Giesbrecht, Albert Heinle and Viktor Levandovskyy : Factoring Differential Operators in n Variables . (2014)
Albert Heinle and Viktor Levandovskyy and Andreas Nereike : SymbolicData:SDEval - Benchmarking for Everyone . (2013)
Albert Heinle and Viktor Levandovskyy : Factorization of Z-homogeneous polynomials in the First (q)-Weyl Algebra . (2013)
Viktor Levandovskyy and Anne Shepler : Quantum Drinfeld Hecke Algebras . (2011)
Viktor Levandovskyy and Kristina Schindelar : Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases . (2011)
Viktor Levandovskyy, Christoph Koutschan and Oleksandr Motsak : On Two-generated Non-commutative Algebras Subject to the Affine Relation . (2011)
Jonathan Hauenstein and Viktor Levandovskyy : Certifying solutions to square systems of polynomial-exponential equations . (2011)
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
Roberto La Scala and Viktor Levandovskyy : Skew polynomial rings, Gröbner bases and the letterplace embedding of the free associative algebra . (2010)
Christian Dingler and Viktor Levandovskyy : Algebraic Foundations for Finite Difference Schemes . (2010)
Viktor Levandovskyy and Bernd Martin : A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations . (2010)
Viktor Levandovskyy, Kristina Schindelar and Eva Zerz : Exact linear modeling using Ore algebras . (2010)
Viktor Levandovskyy and Kristina Schindelar : Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases . (2010)
Viktor Levandovskyy and Jorge Martín-Morales : Algorithms for Checking Rational Roots of $b$-functions and their Applications . (2010)
Daniel Andres, Viktor Levandovskyy and Jorge Martín-Morales : Effective Methods for the Computation of Bernstein-Sato polynomials for Hypersurfaces and Affine Varieties . (2010)
Viktor Levandovskyy and Eva Zerz : Obstructions to Genericity in Study of Parametric Problems in Control Theory . (2007)
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)
Viktor Levandovskyy : Intersection of Ideals with Non-commutative Subalgebras . In: Technical report no. 2006-14. J. Kepler University Linz (2006)
Manuel Kauers and Viktor Levandovskyy : An Interface between Mathematica and Singular . In: Technical report no. 2006-29. J. Kepler University Linz (2006)
(Co-)edited Special Issues
"Symbolic Computation and its Applications", Special Issue of the Journal of Symbolic Computation, Volume 47, Issue 10 (2012), Foreword from the Editors .
"Non-commutative Gröbner Bases and Applications", Special Issue of the Journal of Symbolic Computation, Volume 42, Number 11-12 (2007), Foreword from the Editor .
Software (incl. SINGULAR and PLURAL libraries)
Gert-Martin Greuel, Viktor Levandovskyy and Hans Schönemann : PLURAL (2000-2005). Non-commutative Extension of SINGULAR .
Manuel Kauers and Viktor Levandovskyy : Singular.m (2006). An Interface between Mathematica and Singular.
Viktor Levandovskyy : ncdecomp.lib (2004). Library for decomposition of a module into its central characters.
Viktor Levandovskyy and Jorge Martín-Morales : dmod.lib (2005). Library for computations with algebraic D-modules .
Viktor Levandovskyy and Daniel Andres : dmodapp.lib (2007). Library for applications of algebraic D-modules.
Viktor Levandovskyy : freegb.lib (2008). Library for computations of two-sided Gröbner bases in free algebras via letterplace.
Viktor Levandovskyy and Kristina Schindelar : jacobson.lib (2009). Computation of a diagonal and Jacobson forms for matrices over Ore Euclidean domains .
Daniel Andres and Viktor Levandovskyy and Jorge Martín-Morales : dmodvar.lib (2010). Library for computations with D-modules for affine varieties.
Posters
Viktor Levandovskyy : (poster in A0 format, pdf) . In: Poster session of ISSAC 2010 conference. (2010)
Viktor Levandovskyy : Computer Algebra System Singular 2-2-0 Goes Noncommutative (poster in A1 format, pdf) . In: Poster session of ISSAC 2004 conference. (2004)
Viktor Levandovskyy and H.Schönemann : Using computer algebra system Singular::Plural for computations in noncommutative polynomial algebras (poster in A0 format, pdf) . In: Poster session of ISSAC 2003 conference. (2003)
RWTH Aachen University Division of Mathematics Lehrstuhl D für Mathematik