TY  - BOOK
AU  - Cox,David A
AU  - Little,John B
AU  - O'Shea,Donal
TI  - Using algebraic geometry
T2  - Graduate texts in mathematics
SN  - 0387207066
AV  - QA564 .C688 2005
PY  - 2005///]
CY  - New York
PB  - Springer
KW  - Geometry, Algebraic
N1  - Includes bibliographical references (pages 533-545) and index; Table Of Contents; Preface to the Second Edition; Preface to the First Edition; 1 Introduction; 1 Polynomials and Ideals; 2 Monomial Orders and Polynomial Division; 3 Grobner Bases; 4 Affine Varieties; 2 Solving Polynomial Equations; 1 Solving Polynomial Systems by Elimination; 2 Finite-Dimensional Algebras; 3 Grobner Basis Conversion; 4 Solving Equations via Eigenvalues and Eigenvectors; 5 Real Root Location and Isolation; 3 Resultants; 1 The Resultant of Two Polynomials; 2 Multipolynomial Resultants; 3 Properties of Resultants; 4 Computing Resultants; 5 Solving Equations via Resultants; 6 Solving Equations via Eigenvalues and Eigenvectors; 4 Computation in Local Rings; 1 Local Rings; 2 Multiplicities and Milnor Numbers; 3 Term Orders and Division in Local Rings; 4 Standard Bases in Local Rings; 5 Applications of Standard Bases; 5 Modules; l Modules over Rings; 2 Monomial Orders and Grobner Bases for Modules; 3 Computing Syzygies; 4 Modules over Local Rings; 6 Free Resolutions; 1 Presentations and Resolutions of Modules; 2 Hilbert's Syzygy Theorem; 3 Graded Resolutions; 4 Hilbert Polynomials and Geometric Applications; 7 Polytopes, Resultants, and Equations; 1 Geometry of Polytopes; 2 Sparse Resultants; 3 Toric Varieties; 4 Minkowski Sums and Mixed Volumes; 5 Bernstein's Theorem; 6 Computing Resultants and Solving Equations; 8 Polyhedral Regions and Polynomials; 1 Integer Programming; 2 Integer Programming and Combinatorics; 3 Multivariate Polynomial Splines; 4 The Grobner Fan of an Ideal; 5 The Grobner Walk; 9 Algebraic Coding Theory; 1 Finite Fields; 2 Error-Correcting Codes; 3 Cyclic Codes; 4 Reed-Solomon Decoding Algorithms; 10 The Berlekamp-Massey-Sakata Decoding Algorithm; 1 Codes from Order Domains; 2 The Overall Structure of the BMS Algorithm; 3 The Details of the BMS Algorithm; References; Index
ER  -