Technical Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (ReUp) (0387946802)

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David Cox, John Little, "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra"

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.

The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered it the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric Theorem proving.

In preparing a new edition of "Ideals, Varieties and Algorithms" the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple, Mathematica and REDUCE.

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	Science/Engineering Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra Publisher: SpringerLanguage: EnglishISBN: 0387356509Paperback: 576 pagesData: Mar 2007Format: PDFDescription: The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is ...
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	Science/Engineering Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd Edition Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd Edition (Undergraduate Texts in Mathematics): David Cox, John Little, Donal O'Shea Springer \| ISBN: 0387356509 \| July 31, 2 ...
	Study An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics) Christian Peskine "An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics)"Cambridge University Press \| English \| 2009-04-09 \| ISBN: 0521108470 \| 244 pages \| PDF \| 5,7 MBIn t ...
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	Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) Author: Donal O'Shea, John Little, David CoxPublisher: Springer (2008)Binding: Hardcover, 560 pagespricer: $54.95ISBN-10: 0387356509editorialreviewsAlgebraic Geometry is the study of systems of polynomial equations in one or more variables, ...

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	Science/Engineering Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra Publisher: SpringerLanguage: EnglishISBN: 0387356509Paperback: 576 pagesData: Mar 2007Format: PDFDescription: The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is ...
	Science/Engineering The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative AlgebraPublisher: Springer \| Pages: 243 \| 2004-12-01 \| ISBN 0387222154 \| PDF \| 3 MBAlgebraic Geometry often seems very abstract, but in fact it is full ...
	Science/Engineering Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd Edition Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd Edition (Undergraduate Texts in Mathematics): David Cox, John Little, Donal O'Shea Springer \| ISBN: 0387356509 \| July 31, 2 ...
	Study An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics) Christian Peskine "An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics)"Cambridge University Press \| English \| 2009-04-09 \| ISBN: 0521108470 \| 244 pages \| PDF \| 5,7 MBIn t ...
	Science/Engineering Algebraic Statistics: Computational Commutative Algebra in Statistics (Monographs on Statistics and Applied Probability) (ReUp) Giovanni Pistone, Eva Riccomagno, Henry P. Wynn, "Algebraic Statistics: Computational Commutative Algebra in Statistics (Monographs on Statistics and Applied Probability)" Chapman & Hall/CRC 2000 \| ISBN-10: 1584882042 \| 184 Pages \| PDF ...
	Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) Author: Donal O'Shea, John Little, David CoxPublisher: Springer (2008)Binding: Hardcover, 560 pagespricer: $54.95ISBN-10: 0387356509editorialreviewsAlgebraic Geometry is the study of systems of polynomial equations in one or more variables, ...

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