An Introduction to Gröbner Bases
Wiley Series in Pure and Applied Mathematics
1. Edition August 1997
X, 180 Pages, Hardcover
Wiley & Sons Ltd
Short Description
Gröbner Bases is a relatively new technique in computational algebraic geometry. This book defines this technique with proofs and introductions to rings and fields. It also covers monomial ideals, orders of algebraic sets, Buchberger's algorithms and Hilbert series.
As algebra becomes more widely used in a variety of applications and computers are developed to allow efficient calculations in the field, so there becomes a need for new techniques to further this area of research. Gröbner Bases is one topic which has recently become a very popular and important area of modern algebra. This book provides a concrete introduction to commutative algebra through Gröbner Bases. The inclusion of exercises, lists of further reading and related literature make this a practical approach to introducing Gröbner Bases. The author presents new concepts and results of recent research in the area allowing students and researchers in technology, computer science and mathematics to gain a basic understanding of the technique. A first course in algebra is the only prior knowledge required for this introduction. Chapter titles include:
* Monomial ldeas
* Gröbner Bases
* Algebraic Sets
* Solving Systems of Polynomial Equations
* Applications of Gröbner Bases
* Homogeneous Algebra
* Hilbert Series
* Variations of Gröbner Bases
* Improvements to Buchberger's Algorithms
* Software
Fields, and Ideals.
Monomial Ideals.
Gröbner Bases.
Algebraic Sets.
Primary Decomposition of Ideals.
Solving Systems of Polynomial Equations.
Applications of Gröbner Bases.
Homogeneous Algebras.
Projective Varieties.
The Associated Graded Ring.
Hilbert Series.
Variations of Gröbner Bases.
Improvements to Buchberger's Algorithm.
Software.
Hints to Some Exercises.
Answers to Exercises.
Bibliography.
Index.
