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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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Stillness in Nature: Eeo Stubblefield’s 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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https://doi.org/10.1007/978-1-349-20700-8ow, 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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https://doi.org/10.1007/978-1-349-00224-5hermore, let . be a ring of difference (.-) operators over the ring .. As in Chapter 3, if . (..τ ∈ . for any . ∈ . and a. = 0 for almost all . ∈ .), then the number ord . = max{ord . | a. ≠ 0} will be called the order of the element ..
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Springer Collected Works in Mathematicshttp://image.papertrans.cn/s/image/864189.jpg
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