000			04131nam a22005535i 4500
001			978-0-387-35651-8
003			DE-He213
005			20161121231121.0
007			cr nn 008mamaa
008			130217s2007 xxu| s |||| 0|eng d
020			_a9780387356518 _9978-0-387-35651-8
024	7		_a10.1007/978-0-387-35651-8 _2doi
050		4	_aQA564-609
072		7	_aPBMW _2bicssc
072		7	_aMAT012010 _2bisacsh
082	0	4	_a516.35 _223
100	1		_aCox, David. _eauthor.
245	1	0	_aIdeals, Varieties, and Algorithms _h[electronic resource] : _bAn Introduction to Computational Algebraic Geometry and Commutative Algebra / _cby David Cox, John Little, Donal O’Shea.
250			_aThird Edition.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2007.
300			_aXV, 553 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056
505	0		_aGeometry, 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.
520			_aAlgebraic 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. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: A significantly updated section on Maple in Appendix C Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3 From the 2nd Edition: "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.
650		0	_aMathematics.
650		0	_aAlgebraic geometry.
650		0	_aCommutative algebra.
650		0	_aCommutative rings.
650		0	_aComputer software.
650		0	_aMathematical logic.
650	1	4	_aMathematics.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aCommutative Rings and Algebras.
650	2	4	_aMathematical Logic and Foundations.
650	2	4	_aMathematical Software.
700	1		_aLittle, John. _eauthor.
700	1		_aO’Shea, Donal. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387356501
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-35651-8
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c508855 _d508855