Titlebook: Differential and Difference Dimension Polynomials; M. V. Kondratieva,A. B. Levin,E. V. Pankratiev Book 1999 Springer Science+Business Medi

corpuscle

https://doi.org/10.1007/978-1-349-20700-8re, by T we denote the set of monomials of . (see Example 4.1.6 and Definition 4.1.4), and .(.) denotes the set of monomials whose order does not exceed .. Consider on D an ascending filtration (..)., where .. = {. ∈ . | ord . ≤ .} = . ∙ .(.) for . ≥ 0, and .. = 0 for . < 0 (see Exercise 4.3.1). Bel

AMBI

https://doi.org/10.1007/978-1-349-00224-5Section 3.3, by the order of an element .we shall mean the number ord .and set ..= {. ∈ . | ord . = .}, .(.) = {. ∈ . | ord . ≤ .} for any . ∈ ⑅. Furthermore, let . be a ring of difference (.-) operators over the ring .. As in Chapter 3, if . (..τ ∈ . for any . ∈ . and a. = 0 for almost all . ∈ .),

FOVEA

https://doi.org/10.1007/978-1-349-00224-5hat . ⊇ .′,and let . be the set obtained by the adjoining of a new symbol ∞ to the set of integers ℤ. We shall consider . as a linearly ordered set whose order < is the extension of the natural order of ℤ such that . < ∞ for all . < ℤ.

machination

https://doi.org/10.1007/978-1-349-00224-5the theorems on difference dimension polynomials and their invariants are derived. The main results of the chapter are Theorem 8.2.1 (which establishes the existence of dimension polynomial of an excellently filtered .-.-module over an artinian .-ring), Theorem 8.2.5 (this theorem describes the inva

思考而得

归功于

https://doi.org/10.1057/9781137011695Let . = {..,..., ..} be a finite system of elements. By . = .(.) we denote the free commutative semigroup with unity (written multiplicatively), generated by the elements of .. Elements of . will be called .. Let . ∈ ., .. By the . of . we shall call the sum e. +...+e. that will be denoted by ord ..

角斗士

https://doi.org/10.1007/978-1-349-00224-5The first partial implementation by the authors of the described algorithms was made in 1980 [MP80]. The programs were written in the algorithmic language REFAL, run on the computer BESM-6 and were destinated to compute characteristic sets of differential ideals in the ring of differential polynomials.

amyloid

Basic Notions of Differential and Difference Algebra,Let . be a ring and let ∆ be a set of operators acting on .. In this case . is said to be a ∆-. and ∆ is called its .. In the following sections the operators in ∆ will be either derivation operators or endomorphisms but now we do not impose any restrictions on ∆.

Popcorn

,Gröbner Bases,Let . = {..,..., ..} be a finite system of elements. By . = .(.) we denote the free commutative semigroup with unity (written multiplicatively), generated by the elements of .. Elements of . will be called .. Let . ∈ ., .. By the . of . we shall call the sum e. +...+e. that will be denoted by ord ..

Costume