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Differential and Difference Dimension Polynomials
Preface. I. Preliminaries. II. Numerical Polynomials. III. Basic Notion of Differential and Difference Algebra. IV. Grobner Bases. V. Differential Dimension Polynomials. VI. Dimension Polynomials inExpand
Algorithms and Methods for Solving Scheduling Problems and Other Extremum Problems on Large-Scale Graphs
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 areExpand
Differential Dimension Polynomials
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 DExpand
Jacobi’s bound for systems of algebraic differential equations
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 differentialExpand
Parallel algorithms for Gröbner-basis construction
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 problemExpand
Some Approaches to Construction of Standard Bases in Commutative and Differential Algebra
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 andExpand
Dimension Polynomials in Difference and Difference-Differential Algebra
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 elementExpand
Some Application of Dimension Polynomials in Difference-Differential Algebra
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 theExpand
Basic Notions of Differential and Difference Algebra
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 beExpand