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

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Mathematics and Its Applicationshttp://image.papertrans.cn/d/image/278811.jpg
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Ethics, Evolution, Ecology, and Performancem some parts of algebra for understanding the subsequent chapters. The reader may read the chapter as a whole, or use its appropriate parts for references while reading the latter text (as for those readers who have mastered the whole material covered by the book [Lang71]).
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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.
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978-90-481-5141-7Springer Science+Business Media Dordrecht 1999
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Numerical Polynomials,acted to the univariate dimension polynomials associated with subsets of ℕ., because the problem of determination of such polynomials is a part of the problem of computing Kolchin’s differential dimension polynomial of finitely generated differential field extensions.
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Differential Dimension Polynomials,ow, if the contrary is not said explicitly, by a filtration on . we shall mean this filtration. By a . we shall mean a .-module . with exhaustive and separable filtration (..).. It means that . = ⋃... and there exists .. ∈ ℤ such that .. = 0 for all . < .., .. ⊆ .. and .... ⊆ .. for all ., . ∈ ℤ.
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