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