Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra / David Cox, John Little, Donald O'Shea
By: Cox, David
Contributor(s): Little, John | O'Shea, DonaldMaterial type: Text; Format: print Series: Undergraduate texts in mathematicsPublisher: San Francisco : Springer, 2007Edition: 3rd edDescription: XV, 551 p. : gráf. ; 24 cmISBN: 0-387-35650-9Subject(s): Álgebra conmutativa | Algebra y Geometria | Geometría algebraica
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|Monografías||01. BIBLIOTECA CAMPUS JEREZ||Ma-1057 (Browse shelf)||Checked out||PREST. LIBROS||31/01/2022||3741824089|
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Bibliografía: p. 535-539
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. INDICE: 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.
Other editions of this work
|Ideals, varieties, and algorithms :
by Cox, David
Springer, (Berlín :) , 1997 Xi, 513 p.