Sinossi
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 partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.
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Contenuti
Preface. I. Preliminaries. II. Numerical Polynomials. III. Basic Notion of Differential and Difference Algebra. IV. Gröbner Bases. V. Differential Dimension Polynomials. VI. Dimension Polynomials in Difference and Difference-Differential Algebra. VII. Some Application of Dimension Polynomials in Difference-Differential Algebra. VIII. Dimension Polynomials of Filtered G-modules and Finitely Generated G-Fields Extensions. IX. Computation of Dimension Polynomials. References. Index.
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M. 444 pp. Englisch. Codice articolo 9780792354840
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 d. Codice articolo 5968690
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Buch. Condizione: Neu. Differential and Difference Dimension Polynomials | Alexander V. Mikhalev (u. a.) | Buch | xiii | Englisch | 1998 | Springer Netherland | EAN 9780792354840 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Codice articolo 102550347
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Buch. Condizione: Neu. Neuware -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 partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 444 pp. Englisch. Codice articolo 9780792354840
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M. Codice articolo 9780792354840
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