Bibliothèque de L'IMIST/CNRST

Includes bibliographical references and index.

The homogeneous case. Polynomial rings graded by matrices ; Degree forms and macaulay bases ; Homogenization ; Term orderings of DegRev type ; Homogeneous gröbner bases ; Minimal homogeneous systems of generators ; Minimal homogeneous presentations ; Minimal graded free resolutions -- Hilbert functions. Basic properties of hilbert functions ; Hilbert series ; Computation of hilbert series ; Dimension, multiplicity, and hilbert polynomials ; Bounds for hilbert functions ; Affine hilbert functions and krull dimension ; Independent sets of indeterminates ; General hilbert functions -- Further applications. Toric ideals and hilbert bases ; Liftings of ideals and distractions ; Finite sets of points ; Border bases ; Filtrations ; SAGBI bases ; Automatic theorem proving -- The ABC of CoCoA -- One graphical interface for everybody -- More on CoCoA programming -- Suggestions for further reading -- Hints for selected exercises.