An introduction to Gröbner bases

Ralf Fröberg

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: Monomial ldeas Grobner Bases Algebraic Sets Solving Systems of Polynomial Equations Applications of Grobner Bases Homogeneous Algebra Hilbert Series Variations of Grobner Bases Improvements to Buchberger's Algorithms Software

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[目次]

  • Rings. 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. Software. Hints to Some Exercises. Answers to Exercises. Bibliography. Index.

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この本の情報

書名 An introduction to Gröbner bases
著作者等 Fröberg, Ralf
Froberg Ralf
シリーズ名 Pure and applied mathematics
出版元 John Wiley & sons
刊行年月 c1997
ページ数 x, 177 p.
大きさ 24 cm
ISBN 0471974420
NCID BA32518217
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言語 英語
出版国 イギリス
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