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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 in
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 are
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 D
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 differential
Parallel algorithms for Gröbner-basis construction
This paper analyzes the known algorithms for constructing the standard bases and considers some methods for increasing their efficiency and describes a technique for estimating the efficiency of paralleling the algorithms and presents some estimates.
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 and
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 element
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 the
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 be