Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra - Rilegato

Cox, David; Little, John; O'Shea, Donal

 
9780387946801: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Rilegato
ISBN 10: 0387946802 ISBN 13: 9780387946801
Casa editrice: Springer Verlag, 2006

Sinossi

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 in 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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Recensione

"I consider the book to be wonderful...The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging...offers the heart and soul of modern commutative and algebraic geometry." -The American Mathematical Monthly

Contenuti

Geometry, Algebra, and Algorithms.- Groebner Bases.- Elimination Theory.- The Algebra-Geometry Dictionary.- Polynomial and Rational Functions on a Variety.- Robotics and Automatic Geometric Theorem Proving.- Invariant Theory of Finite Groups.- Projective Algebraic Geometry.- The Dimension of a Variety.- Some Concepts from Algebra.- Pseudocode.- Computer Algebra Systems.- Independent Projects.

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Editore
Springer Verlag
Data di pubblicazione
2006
Lingua
Inglese
ISBN 10 
0387946802
ISBN 13 
9780387946801
Rilegatura
Copertina rigida
Numero edizione
2
Numero di pagine
549
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

Friedrich-Karl-Str. 9
Hamburg
Germania

Altre edizioni note dello stesso titolo

9780387978475: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra

Edizione in evidenza

ISBN 10:  038797847X ISBN 13:  9780387978475
Casa editrice: Springer, 1992
Rilegato