| 书目名称 | Differential and Difference Dimension Polynomials | | 编辑 | M. V. Kondratieva,A. B. Levin,E. V. Pankratiev | | 视频video | | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 描述 | The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]‘ but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi‘s results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi‘s bound) remains open. There are some generalization of the problem of Jacobi‘s bound to the par | | 出版日期 | Book 1999 | | 关键词 | Combinatorics; algebra; difference equation; number theory; partial differential equation; partial differ | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-017-1257-6 | | isbn_softcover | 978-90-481-5141-7 | | isbn_ebook | 978-94-017-1257-6 | | copyright | Springer Science+Business Media Dordrecht 1999 |
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发表于 2025-3-21 18:47:28
