Coverart for item
The Resource Using algebraic geometry, David A. Cox, John Little, Donal O'Shea

Using algebraic geometry, David A. Cox, John Little, Donal O'Shea

Label
Using algebraic geometry
Title
Using algebraic geometry
Statement of responsibility
David A. Cox, John Little, Donal O'Shea
Creator
Contributor
Subject
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
Member of
Is part of
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
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 533-545) 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. Finite-dimensional 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. Error-correcting codes. Cyclic codes. Reed-Solomon decoding algorithms -- The Berlekamp-Massey-Sakata 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
978-0-387-20706-3
Specific material designation
remote
System control number
(OCoLC)262679966
Label
Using algebraic geometry, David A. Cox, John Little, Donal O'Shea
Publication
Bibliography note
Includes bibliographical references (pages 533-545) 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. Finite-dimensional 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. Error-correcting codes. Cyclic codes. Reed-Solomon decoding algorithms -- The Berlekamp-Massey-Sakata 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
978-0-387-20706-3
Specific material designation
remote
System control number
(OCoLC)262679966

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