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An Introduction to Grobner Bases : Pure and Applied Mathematics - Ralf Fröberg

An Introduction to Grobner Bases

Pure and Applied Mathematics


Published: 7th October 1997
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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. Grobner 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 Grobner Bases. The inclusion of exercises, lists of further reading and related literature make this a practical approach to introducing Grobner 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:<br> * Monomial ldeas<br> * Grobner Bases<br> * Algebraic Sets<br> * Solving Systems of Polynomial Equations<br> * Applications of Grobner Bases<br> * Homogeneous Algebra<br> * Hilbert Series<br> * Variations of Grobner Bases<br> * Improvements to Buchberger's Algorithms<br> * Software


Fields, and Ideals.

Monomial Ideals.

Grobner Bases.

Algebraic Sets.

Primary Decomposition of Ideals.

Solving Systems of Polynomial Equations.

Applications of Grobner Bases.

Homogeneous Algebras.

Projective Varieties.

The Associated Graded Ring.

Hilbert Series.

Variations of Grobner Bases.

Improvements to Buchberger's Algorithm.


Hints to Some Exercises.

Answers to Exercises.



ISBN: 9780471974420
ISBN-10: 0471974420
Series: Pure and Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 190
Published: 7th October 1997
Country of Publication: GB
Dimensions (cm): 23.6 x 15.65  x 1.73
Weight (kg): 0.36
Edition Number: 1