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Differential and Difference Dimension Polynomials

- M. Kondratieva, A. Levin, A. Mikhalev, E. V. Pankratiev
- Mathematics
- 30 November 1998

Preface. I. Preliminaries. II. Numerical Polynomials. III. Basic Notion of Differential and Difference Algebra. IV. Grobner Bases. V. Differential Dimension Polynomials. VI. Dimension Polynomials in… Expand

Algorithms and Methods for Solving Scheduling Problems and Other Extremum Problems on Large-Scale Graphs

- E. V. Pankratiev, A. Chepovskiy, E. A. Cherepanov, S. Chernyshev
- Mathematics
- 1 August 2005

We consider a large-scale directed graph G = (V, E) whose edges are endowed with a family of characteristics. A subset of vertices of the graph, V′ ⊂ V, is selected and some additional conditions are… Expand

Differential Dimension Polynomials

- M. Kondratieva, A. Levin, A. Mikhalev, E. V. Pankratiev
- Mathematics
- 1999

Let R be a differential ring with a basic set ∆ = {d 1,..., d m }, D be the ring of linear differential operators over R (see Definition 3.2.38). As before, by T we denote the set of monomials of D… Expand

Jacobi’s bound for systems of algebraic differential equations

- M. Kondratieva, A. Mikhalev, E. V. Pankratiev
- Mathematics
- 14 November 2009

This review paper is devoted to the Jacobi bound for systems of partial differential polynomials. We prove the conjecture for the system of n partial differential equations in n differential… Expand

Parallel algorithms for Gröbner-basis construction

- V. A. Mityunin, E. V. Pankratiev
- Mathematics
- 1 April 2007

The problem of the Gröbner-basis construction is important both from the theoretical and applied points of view. As examples of applications of Gröbner bases, one can mention the consistency problem… Expand

Some Approaches to Construction of Standard Bases in Commutative and Differential Algebra

- E. V. Pankratiev
- 2002

In this talk I would like to present the directions of research and some results obtained by the Moscow team involved in INTAS grant 99-1222 related to the theory of standard bases in polynomial and… Expand

Dimension Polynomials in Difference and Difference-Differential Algebra

- M. Kondratieva, A. Levin, A. Mikhalev, E. V. Pankratiev
- Mathematics
- 1999

Let R be a difference ring with a basic set σ = {α l,...,α n } and let T = T σ be a free commutative semigroup generated by the elements α l,...,α n . As in Section 3.3, by the order of an element… Expand

Kolchin Seminar, March 15, 2003 STANDARD BASES IN COMMUTATIVE AND DIFFERENTIAL ALGEBRA

- E. V. Pankratiev
- 2003

Some Application of Dimension Polynomials in Difference-Differential Algebra

- M. Kondratieva, A. Levin, A. Mikhalev, E. V. Pankratiev
- Mathematics
- 1999

Let R be a commutative ring, M an R-module and U a family of R-submodules of M. Furthermore, let B U denote the set of all pairs (N, N′) ∈ U × U such that N ⊇ N′,and let \(\overline {\Bbb Z}\) be the… Expand

Basic Notions of Differential and Difference Algebra

- M. Kondratieva, A. Levin, A. Mikhalev, E. V. Pankratiev
- Mathematics
- 1999

Let R be a ring and let ∆ be a set of operators acting on R. In this case R is said to be a ∆-ring and ∆ is called its basic set of operators. In the following sections the operators in ∆ will be… Expand

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