The Resource Using algebraic geometry, David A. Cox, John Little, Donal O'Shea
Using algebraic geometry, David A. Cox, John Little, Donal O'Shea
Resource Information
The item Using algebraic geometry, David A. Cox, John Little, Donal O'Shea represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Using algebraic geometry, David A. Cox, John Little, Donal O'Shea represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 "The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules."Jacket
 Language
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (xii, 572 pages)
 Contents

 Introduction. Polynomials and ideals. Monomial orders and polynomial division. Gröbner bases. Affine varieties
 Solving polynomial equations. Solving polynomial systems by elimination. Finitedimensional algebras. Gröbner basis conversion. Solving equations via eigenvalues and eigenvectors. Real root location and isolation
 Resultants. The resultant of two polynomials. Multipolynomial resultants. Properties of resultants. Computing resultants. Solving equations via resultants. Solving equations via eigenvalues and eigenvectors
 Computation in local rings. Local rings. Multiplicities and Milnor numbers. Term orders and division in local rings. Standard bases in local rings. Applications of standard bases
 Modules. Modules over rings. Monomial orders and Gröbner bases for modules. Computing syzygies. Modules over local rings
 Free resolutions. Presentations and resolutions of modules. Hilbert's Syzygy Theorem. Graded resolutions. Hilbert polynomials and geometric applications
 Polytopes, resultants, and equations. Geometry of polytopes. Sparse resultants. Toric varieties. Minkowski sums and mixed volumes. Bernstein's Theorem. Computing resultants and solving equations
 Polyhedral regions and polynomials. Integer programming. Integer programming and combinatorics. Multivariate polynomial splines. The Gröbner fan of an ideal. The Gröbner walk
 Algebraic coding theory. Finite fields. Errorcorrecting codes. Cyclic codes. ReedSolomon decoding algorithms
 The BerlekampMasseySakata decoding algorithm. Codes from order domains. The overall structure of the BMS algorithm. The details of the BMS algorithm
 Isbn
 9780387271057
 Label
 Using algebraic geometry
 Title
 Using algebraic geometry
 Statement of responsibility
 David A. Cox, John Little, Donal O'Shea
 Language
 eng
 Summary
 "The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules."Jacket
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Cox, David A
 Dewey number
 516.3/5
 Illustrations
 illustrations
 Index
 index present
 Language note
 English
 LC call number
 QA564
 LC item number
 .C6883 2005eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName

 Little, John B
 O'Shea, Donal
 Series statement
 Graduate texts in mathematics
 Series volume
 185
 http://library.link/vocab/subjectName

 Geometry, Algebraic
 Algorithms
 Geometry, Algebraic
 Mathematics
 Algebraic geometry
 Symbolic and Algebraic Manipulation
 Algebra
 Geometry, Algebraic
 Geometria algébrica
 Label
 Using algebraic geometry, David A. Cox, John Little, Donal O'Shea
 Bibliography note
 Includes bibliographical references (pages 533545) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction. Polynomials and ideals. Monomial orders and polynomial division. Gröbner bases. Affine varieties  Solving polynomial equations. Solving polynomial systems by elimination. Finitedimensional algebras. Gröbner basis conversion. Solving equations via eigenvalues and eigenvectors. Real root location and isolation  Resultants. The resultant of two polynomials. Multipolynomial resultants. Properties of resultants. Computing resultants. Solving equations via resultants. Solving equations via eigenvalues and eigenvectors  Computation in local rings. Local rings. Multiplicities and Milnor numbers. Term orders and division in local rings. Standard bases in local rings. Applications of standard bases  Modules. Modules over rings. Monomial orders and Gröbner bases for modules. Computing syzygies. Modules over local rings  Free resolutions. Presentations and resolutions of modules. Hilbert's Syzygy Theorem. Graded resolutions. Hilbert polynomials and geometric applications  Polytopes, resultants, and equations. Geometry of polytopes. Sparse resultants. Toric varieties. Minkowski sums and mixed volumes. Bernstein's Theorem. Computing resultants and solving equations  Polyhedral regions and polynomials. Integer programming. Integer programming and combinatorics. Multivariate polynomial splines. The Gröbner fan of an ideal. The Gröbner walk  Algebraic coding theory. Finite fields. Errorcorrecting codes. Cyclic codes. ReedSolomon decoding algorithms  The BerlekampMasseySakata decoding algorithm. Codes from order domains. The overall structure of the BMS algorithm. The details of the BMS algorithm
 Control code
 262679966
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xii, 572 pages)
 Form of item
 online
 Isbn
 9780387271057
 Lccn
 2003070363
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/b138611
 Other physical details
 illustrations
 http://library.link/vocab/ext/overdrive/overdriveId
 9780387207063
 Specific material designation
 remote
 System control number
 (OCoLC)262679966
 Label
 Using algebraic geometry, David A. Cox, John Little, Donal O'Shea
 Bibliography note
 Includes bibliographical references (pages 533545) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction. Polynomials and ideals. Monomial orders and polynomial division. Gröbner bases. Affine varieties  Solving polynomial equations. Solving polynomial systems by elimination. Finitedimensional algebras. Gröbner basis conversion. Solving equations via eigenvalues and eigenvectors. Real root location and isolation  Resultants. The resultant of two polynomials. Multipolynomial resultants. Properties of resultants. Computing resultants. Solving equations via resultants. Solving equations via eigenvalues and eigenvectors  Computation in local rings. Local rings. Multiplicities and Milnor numbers. Term orders and division in local rings. Standard bases in local rings. Applications of standard bases  Modules. Modules over rings. Monomial orders and Gröbner bases for modules. Computing syzygies. Modules over local rings  Free resolutions. Presentations and resolutions of modules. Hilbert's Syzygy Theorem. Graded resolutions. Hilbert polynomials and geometric applications  Polytopes, resultants, and equations. Geometry of polytopes. Sparse resultants. Toric varieties. Minkowski sums and mixed volumes. Bernstein's Theorem. Computing resultants and solving equations  Polyhedral regions and polynomials. Integer programming. Integer programming and combinatorics. Multivariate polynomial splines. The Gröbner fan of an ideal. The Gröbner walk  Algebraic coding theory. Finite fields. Errorcorrecting codes. Cyclic codes. ReedSolomon decoding algorithms  The BerlekampMasseySakata decoding algorithm. Codes from order domains. The overall structure of the BMS algorithm. The details of the BMS algorithm
 Control code
 262679966
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xii, 572 pages)
 Form of item
 online
 Isbn
 9780387271057
 Lccn
 2003070363
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/b138611
 Other physical details
 illustrations
 http://library.link/vocab/ext/overdrive/overdriveId
 9780387207063
 Specific material designation
 remote
 System control number
 (OCoLC)262679966
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