Ideals, varieties and algorithms [ Livre] : an introduction to computational algebraic geometry and commutative algebra / Cox David ; O'shea Donal ; Little John

Langue: Anglais.Publication : Springer, 1997Description : XIII-536 p.ISBN: 0387946802.Collection: Undergraduate texts in mathematicsClassification: 514.1 Géométrie algébriqueRésumé: Reviews 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 1960s. 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 led to some interesting applications - for example, in robotics and in geometric theorem proving. .Sujet - Nom commun: Géométrie algébrique -- Informatique | Complexité de calcul (informatique) | Communication, Théorie mathématique de la | Algorithmes | Algèbres commutatives -- Informatique
Current location Call number Status Notes Date due Barcode
ENS Rennes - Bibliothèque
Mathématiques
514.1 COX (Browse shelf) Available 514.1 Géométrie algébrique 00003016

Reviews
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 1960s. 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 led to some interesting applications - for
example, in robotics and in geometric theorem proving.

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