An introduction to Gröbner bases
著者
書誌事項
An introduction to Gröbner bases
（Pure and applied mathematics）
John Wiley & sons, c1997
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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. Groebner 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 Groebner Bases. The inclusion of exercises, lists of further reading and related literature make this a practical approach to introducing Groebner 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
* Groebner Bases
* Algebraic Sets
* Solving Systems of Polynomial Equations
* Applications of Groebner Bases
* Homogeneous Algebra
* Hilbert Series
* Variations of Groebner Bases
* Improvements to Buchberger's Algorithms
* Software
目次
Rings.
Fields, and Ideals.
Monomial Ideals.
Groebner Bases.
Algebraic Sets.
Primary Decomposition of Ideals.
Solving Systems of Polynomial Equations.
Applications of Groebner Bases.
Homogeneous Algebras.
Projective Varieties.
The Associated Graded Ring.
Hilbert Series.
Variations of Groebner Bases.
Improvements to Buchberger's Algorithm.
Software.
Hints to Some Exercises.
Answers to Exercises.
Bibliography.
Index.
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