代数几何应用-第2版

preface to the second edition

preface to the first edition

introduction

1   polynomials and ideals

　2  monomial orders and polynomial division

　3  gr6bner bases

　4  affine varieties

2　solving polynomial equations

　1   solving polynomial systems by elimination

　2  finite-dimensional algebras

　3   gr6bner 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 miinor numbers

　3  term orders and division in local rings

　4  standard bases in local rings

　5  applications of standard bases

5  modules

　1   modules over rings

　2   monomial orders and gr6bner bases for modules

　3   computing syzygies

　4  modules over local rings

6  free resolutions

　i   presentations and resolutions of modules

　2  hilbert's syzygy theorem

　3   graded resolutions

　4   hilbert polynomials and geometricapplications 

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 gr6bner fan of an ideal

　5   the gr6bner 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