24 citations · 128 across the 26 of their papers we have counts for
7 papers · 1 filter
Skew polynomial rings, Groebner bases and the letterplace embedding of the free associative algebra
Roberto La Scala, Viktor Levandovskyy
In this paper we introduce an algebra embedding from the free associative algebra generated by a finite or countable set into the skew monoid ring $S =…
A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations
Viktor Levandovskyy, Bernd Martin
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with c…
Constructive -module Theory with \textsc{Singular}
Daniel Andres, Michael Brickenstein, Viktor Levandovskyy +2
We overview numerous algorithms in computational -module theory together with the theoretical background as well as the implementation in the computer algebra system \textsc{Sin…
Exact linear modeling using Ore algebras
Kristina Schindelar, Viktor Levandovskyy, Eva Zerz
Linear exact modeling is a problem coming from system identification: Given a set of observed trajectories, the goal is find a model (usually, a system of partial differential and/…
Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
Viktor Levandovskyy, Kristina Schindelar
In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gröbner bases. This c…
Algorithms for Checking Rational Roots of -functions and their Applications
Viktor Levandovskyy, Jorge Martín-Morales
Bernstein-Sato polynomial of a hypersurface is an important object with numerous applications. It is known, that it is complicated to obtain it computationally, as a number of open…
Effective Methods for the Computation of Bernstein-Sato polynomials for Hypersurfaces and Affine Varieties
Daniel Andres, Viktor Levandovskyy, Jorge Martín-Morales
This paper is the widely extended version of the publication, appeared in Proceedings of ISSAC'2009 conference \citep*{ALM09}. We discuss more details on proofs, present new algori…