Gröbner bases and applications /:
This book provides an easy-to-read account of the theory of Gröbner bases and applications. It is in 2 parts, the first consists of tutorial lectures, and the second, 17 original research papers on Gröbner bases.
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. ; New York :
Cambridge University Press,
1998.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
251. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides an easy-to-read account of the theory of Gröbner bases and applications. It is in 2 parts, the first consists of tutorial lectures, and the second, 17 original research papers on Gröbner bases. |
| Beschreibung: | Papers from an intensive course for researchers (Jan. 1998) and a conference "33 Years of Gröbner Bases" held at RISC-Linz, Feb. 2-4, 1998. |
| Beschreibung: | 1 online resource (viii, 552 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107362697 1107362695 9780511565847 0511565844 |
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MARC
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| 245 | 0 | 0 | |a Gröbner bases and applications / |c edited by B. Buchberger & F. Winkler. |
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 251 | |
| 500 | |a Papers from an intensive course for researchers (Jan. 1998) and a conference "33 Years of Gröbner Bases" held at RISC-Linz, Feb. 2-4, 1998. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 520 | 8 | |a This book provides an easy-to-read account of the theory of Gröbner bases and applications. It is in 2 parts, the first consists of tutorial lectures, and the second, 17 original research papers on Gröbner bases. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; Programme Committee; Tutorials; Introduction to Grobner Bases; Outline; 1 Grobner Bases at Work; 1.1 Example: Fermat Ideals; 1.2 Example: Geometry Theorem Proving; 1.3 Example: Invariant Theory; 1.4 Example: Systems of Polynomial Equations; 2 The Main Theorem on Grobner Bases; 2.1 Polynomials; 2.2 Polynomial Ideals; 2.3 Admissible Orderings on Power Products; 2.4 Order Dependent Decomposition of Polynomials; 2.5 Admissible Orderings on Polynomials; 2.6 Reduction Modulo Polynomials; Definition (Reduction Modulo Polynomials) | |
| 505 | 8 | |a Proposition (Noetherianity of Reduction Modulo Polynomials)Proposition (Property of Reduction Algorithm):; Proposition (Property of Cofactor Algorithm); Proposition (Compatibility of Reduction); Proposition (Relation Between Reduction and Congruence); 2.7 Some General Properties of Noetherian ReductionRelations; 2.8 Grobner Bases; 2.9 S-Polynomials; 2.10 The Main Theorem: Algorithmic Characterizationof Grobner Bases by S-Polynomials; 2.11 An Algorithm for Constructing Grobner Bases; Proposition (Correctness of the Grobner-Basis Algorithm):; Definition (Reduced Grobner Bases) | |
| 505 | 8 | |a Proposition (Canonicality):2.12 Other Characterizations of Grobner Bases; 3 Applications of Grobner Bases; 3.1 Overview; 3.2 Ideal Membership, Canonical Simplification, IdealIdentity; 3.3 Radical Membership; 3.4 Computation in Residue Class Rings Modulo Ideals; 3.5 Leading Power Products; 3.6 Polynomial Equations; 3.7 Linear Syzygies; 3.8 Hilbert Functions; 3.9 Elimination Ideals; 3.10 Ideal Operations; 3.11 Algebraic Relations and Implicitization; 3.12 Inverse Mappings; 3.13 Miscellaneous; References; Symbolic Summation and Symbolic Integration; Introduction | |
| 505 | 8 | |a 1 Indefinite Summation and Integration1.1 Ore Operators, Ore Algebras, Annihilating Ideals; 1.2 Grobner Bases in Ore Algebras; Contiguity Relations for the Appell F4 Bivariate HypergeometricFunction; 1.3 5-Finite Functions; 1.4 Indefinite Summation and Integration; Particular Solutions; Multivariate Extension; 2 Definite Summation and Integration; 2.1 Creative Telescoping and Elimination by GrobnerBases; 2.2 Multiple Summations and Integrations; 2.3 Takayama's Algorithm and Grobner Bases of Modules; Gordon's Generalization of the Rogers-Ramanujan Identities | |
| 505 | 8 | |a 2.4 Zeilberger's Fast Algorithm and its <9-Finite ExtensionCalkin's Curious Identity; 3 Closure Properties; 3.1 Addition, Product and Derivation of 5-Finite Functionsby the FGLM Algorithm; 3.2 Indefinite Summation and Integration by GrobnerBases; 4 Dimension and Holonomy; Acknowledgements; References; Grobner Bases and Invariant Theory; 0 Introduction; 1 Basic definitions and problems; 2 Algorithms for finite groups; 3 Algorithms for linearly reductive groups; References; A Tutorial on Generic Initial Ideals; Why is the gin Borel-fixed?; Why does the rlex gin compute satiety and regularity? | |
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| contents | Cover; Title; Copyright; Contents; Preface; Programme Committee; Tutorials; Introduction to Grobner Bases; Outline; 1 Grobner Bases at Work; 1.1 Example: Fermat Ideals; 1.2 Example: Geometry Theorem Proving; 1.3 Example: Invariant Theory; 1.4 Example: Systems of Polynomial Equations; 2 The Main Theorem on Grobner Bases; 2.1 Polynomials; 2.2 Polynomial Ideals; 2.3 Admissible Orderings on Power Products; 2.4 Order Dependent Decomposition of Polynomials; 2.5 Admissible Orderings on Polynomials; 2.6 Reduction Modulo Polynomials; Definition (Reduction Modulo Polynomials) Proposition (Noetherianity of Reduction Modulo Polynomials)Proposition (Property of Reduction Algorithm):; Proposition (Property of Cofactor Algorithm); Proposition (Compatibility of Reduction); Proposition (Relation Between Reduction and Congruence); 2.7 Some General Properties of Noetherian ReductionRelations; 2.8 Grobner Bases; 2.9 S-Polynomials; 2.10 The Main Theorem: Algorithmic Characterizationof Grobner Bases by S-Polynomials; 2.11 An Algorithm for Constructing Grobner Bases; Proposition (Correctness of the Grobner-Basis Algorithm):; Definition (Reduced Grobner Bases) Proposition (Canonicality):2.12 Other Characterizations of Grobner Bases; 3 Applications of Grobner Bases; 3.1 Overview; 3.2 Ideal Membership, Canonical Simplification, IdealIdentity; 3.3 Radical Membership; 3.4 Computation in Residue Class Rings Modulo Ideals; 3.5 Leading Power Products; 3.6 Polynomial Equations; 3.7 Linear Syzygies; 3.8 Hilbert Functions; 3.9 Elimination Ideals; 3.10 Ideal Operations; 3.11 Algebraic Relations and Implicitization; 3.12 Inverse Mappings; 3.13 Miscellaneous; References; Symbolic Summation and Symbolic Integration; Introduction 1 Indefinite Summation and Integration1.1 Ore Operators, Ore Algebras, Annihilating Ideals; 1.2 Grobner Bases in Ore Algebras; Contiguity Relations for the Appell F4 Bivariate HypergeometricFunction; 1.3 5-Finite Functions; 1.4 Indefinite Summation and Integration; Particular Solutions; Multivariate Extension; 2 Definite Summation and Integration; 2.1 Creative Telescoping and Elimination by GrobnerBases; 2.2 Multiple Summations and Integrations; 2.3 Takayama's Algorithm and Grobner Bases of Modules; Gordon's Generalization of the Rogers-Ramanujan Identities 2.4 Zeilberger's Fast Algorithm and its <9-Finite ExtensionCalkin's Curious Identity; 3 Closure Properties; 3.1 Addition, Product and Derivation of 5-Finite Functionsby the FGLM Algorithm; 3.2 Indefinite Summation and Integration by GrobnerBases; 4 Dimension and Holonomy; Acknowledgements; References; Grobner Bases and Invariant Theory; 0 Introduction; 1 Basic definitions and problems; 2 Algorithms for finite groups; 3 Algorithms for linearly reductive groups; References; A Tutorial on Generic Initial Ideals; Why is the gin Borel-fixed?; Why does the rlex gin compute satiety and regularity? |
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| discipline | Mathematik |
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| indexdate | 2024-11-27T13:25:17Z |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Gröbner bases and applications / edited by B. Buchberger & F. Winkler. Cambridge, U.K. ; New York : Cambridge University Press, 1998. 1 online resource (viii, 552 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 251 Papers from an intensive course for researchers (Jan. 1998) and a conference "33 Years of Gröbner Bases" held at RISC-Linz, Feb. 2-4, 1998. Includes bibliographical references and index. This book provides an easy-to-read account of the theory of Gröbner bases and applications. It is in 2 parts, the first consists of tutorial lectures, and the second, 17 original research papers on Gröbner bases. Print version record. Cover; Title; Copyright; Contents; Preface; Programme Committee; Tutorials; Introduction to Grobner Bases; Outline; 1 Grobner Bases at Work; 1.1 Example: Fermat Ideals; 1.2 Example: Geometry Theorem Proving; 1.3 Example: Invariant Theory; 1.4 Example: Systems of Polynomial Equations; 2 The Main Theorem on Grobner Bases; 2.1 Polynomials; 2.2 Polynomial Ideals; 2.3 Admissible Orderings on Power Products; 2.4 Order Dependent Decomposition of Polynomials; 2.5 Admissible Orderings on Polynomials; 2.6 Reduction Modulo Polynomials; Definition (Reduction Modulo Polynomials) Proposition (Noetherianity of Reduction Modulo Polynomials)Proposition (Property of Reduction Algorithm):; Proposition (Property of Cofactor Algorithm); Proposition (Compatibility of Reduction); Proposition (Relation Between Reduction and Congruence); 2.7 Some General Properties of Noetherian ReductionRelations; 2.8 Grobner Bases; 2.9 S-Polynomials; 2.10 The Main Theorem: Algorithmic Characterizationof Grobner Bases by S-Polynomials; 2.11 An Algorithm for Constructing Grobner Bases; Proposition (Correctness of the Grobner-Basis Algorithm):; Definition (Reduced Grobner Bases) Proposition (Canonicality):2.12 Other Characterizations of Grobner Bases; 3 Applications of Grobner Bases; 3.1 Overview; 3.2 Ideal Membership, Canonical Simplification, IdealIdentity; 3.3 Radical Membership; 3.4 Computation in Residue Class Rings Modulo Ideals; 3.5 Leading Power Products; 3.6 Polynomial Equations; 3.7 Linear Syzygies; 3.8 Hilbert Functions; 3.9 Elimination Ideals; 3.10 Ideal Operations; 3.11 Algebraic Relations and Implicitization; 3.12 Inverse Mappings; 3.13 Miscellaneous; References; Symbolic Summation and Symbolic Integration; Introduction 1 Indefinite Summation and Integration1.1 Ore Operators, Ore Algebras, Annihilating Ideals; 1.2 Grobner Bases in Ore Algebras; Contiguity Relations for the Appell F4 Bivariate HypergeometricFunction; 1.3 5-Finite Functions; 1.4 Indefinite Summation and Integration; Particular Solutions; Multivariate Extension; 2 Definite Summation and Integration; 2.1 Creative Telescoping and Elimination by GrobnerBases; 2.2 Multiple Summations and Integrations; 2.3 Takayama's Algorithm and Grobner Bases of Modules; Gordon's Generalization of the Rogers-Ramanujan Identities 2.4 Zeilberger's Fast Algorithm and its <9-Finite ExtensionCalkin's Curious Identity; 3 Closure Properties; 3.1 Addition, Product and Derivation of 5-Finite Functionsby the FGLM Algorithm; 3.2 Indefinite Summation and Integration by GrobnerBases; 4 Dimension and Holonomy; Acknowledgements; References; Grobner Bases and Invariant Theory; 0 Introduction; 1 Basic definitions and problems; 2 Algorithms for finite groups; 3 Algorithms for linearly reductive groups; References; A Tutorial on Generic Initial Ideals; Why is the gin Borel-fixed?; Why does the rlex gin compute satiety and regularity? Gröbner bases. http://id.loc.gov/authorities/subjects/sh92005856 Bases de Gröbner. MATHEMATICS Group Theory. bisacsh Gröbner bases fast Commutatieve algebra's. gtt Gröbner, Bases de. ram Buchberger, Bruno. Winkler, Franz, 1955- https://id.oclc.org/worldcat/entity/E39PBJvXk98BYCTj3pd6Wfp3wC http://id.loc.gov/authorities/names/n97118345 Print version: Gröbner bases and applications. Cambridge, U.K. ; New York : Cambridge University Press, 1998 0521632986 (DLC) 97044181 (OCoLC)38042878 London Mathematical Society lecture note series ; 251. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552422 Volltext |
| spellingShingle | Gröbner bases and applications / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; Programme Committee; Tutorials; Introduction to Grobner Bases; Outline; 1 Grobner Bases at Work; 1.1 Example: Fermat Ideals; 1.2 Example: Geometry Theorem Proving; 1.3 Example: Invariant Theory; 1.4 Example: Systems of Polynomial Equations; 2 The Main Theorem on Grobner Bases; 2.1 Polynomials; 2.2 Polynomial Ideals; 2.3 Admissible Orderings on Power Products; 2.4 Order Dependent Decomposition of Polynomials; 2.5 Admissible Orderings on Polynomials; 2.6 Reduction Modulo Polynomials; Definition (Reduction Modulo Polynomials) Proposition (Noetherianity of Reduction Modulo Polynomials)Proposition (Property of Reduction Algorithm):; Proposition (Property of Cofactor Algorithm); Proposition (Compatibility of Reduction); Proposition (Relation Between Reduction and Congruence); 2.7 Some General Properties of Noetherian ReductionRelations; 2.8 Grobner Bases; 2.9 S-Polynomials; 2.10 The Main Theorem: Algorithmic Characterizationof Grobner Bases by S-Polynomials; 2.11 An Algorithm for Constructing Grobner Bases; Proposition (Correctness of the Grobner-Basis Algorithm):; Definition (Reduced Grobner Bases) Proposition (Canonicality):2.12 Other Characterizations of Grobner Bases; 3 Applications of Grobner Bases; 3.1 Overview; 3.2 Ideal Membership, Canonical Simplification, IdealIdentity; 3.3 Radical Membership; 3.4 Computation in Residue Class Rings Modulo Ideals; 3.5 Leading Power Products; 3.6 Polynomial Equations; 3.7 Linear Syzygies; 3.8 Hilbert Functions; 3.9 Elimination Ideals; 3.10 Ideal Operations; 3.11 Algebraic Relations and Implicitization; 3.12 Inverse Mappings; 3.13 Miscellaneous; References; Symbolic Summation and Symbolic Integration; Introduction 1 Indefinite Summation and Integration1.1 Ore Operators, Ore Algebras, Annihilating Ideals; 1.2 Grobner Bases in Ore Algebras; Contiguity Relations for the Appell F4 Bivariate HypergeometricFunction; 1.3 5-Finite Functions; 1.4 Indefinite Summation and Integration; Particular Solutions; Multivariate Extension; 2 Definite Summation and Integration; 2.1 Creative Telescoping and Elimination by GrobnerBases; 2.2 Multiple Summations and Integrations; 2.3 Takayama's Algorithm and Grobner Bases of Modules; Gordon's Generalization of the Rogers-Ramanujan Identities 2.4 Zeilberger's Fast Algorithm and its <9-Finite ExtensionCalkin's Curious Identity; 3 Closure Properties; 3.1 Addition, Product and Derivation of 5-Finite Functionsby the FGLM Algorithm; 3.2 Indefinite Summation and Integration by GrobnerBases; 4 Dimension and Holonomy; Acknowledgements; References; Grobner Bases and Invariant Theory; 0 Introduction; 1 Basic definitions and problems; 2 Algorithms for finite groups; 3 Algorithms for linearly reductive groups; References; A Tutorial on Generic Initial Ideals; Why is the gin Borel-fixed?; Why does the rlex gin compute satiety and regularity? Gröbner bases. http://id.loc.gov/authorities/subjects/sh92005856 Bases de Gröbner. MATHEMATICS Group Theory. bisacsh Gröbner bases fast Commutatieve algebra's. gtt Gröbner, Bases de. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh92005856 |
| title | Gröbner bases and applications / |
| title_auth | Gröbner bases and applications / |
| title_exact_search | Gröbner bases and applications / |
| title_full | Gröbner bases and applications / edited by B. Buchberger & F. Winkler. |
| title_fullStr | Gröbner bases and applications / edited by B. Buchberger & F. Winkler. |
| title_full_unstemmed | Gröbner bases and applications / edited by B. Buchberger & F. Winkler. |
| title_short | Gröbner bases and applications / |
| title_sort | grobner bases and applications |
| topic | Gröbner bases. http://id.loc.gov/authorities/subjects/sh92005856 Bases de Gröbner. MATHEMATICS Group Theory. bisacsh Gröbner bases fast Commutatieve algebra's. gtt Gröbner, Bases de. ram |
| topic_facet | Gröbner bases. Bases de Gröbner. MATHEMATICS Group Theory. Gröbner bases Commutatieve algebra's. Gröbner, Bases de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552422 |
| work_keys_str_mv | AT buchbergerbruno grobnerbasesandapplications AT winklerfranz grobnerbasesandapplications |