Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
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The work Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
Resource Information
The work Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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 Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
 Title remainder
 An Introduction to Computational Algebraic Geometry and Commutative Algebra
 Statement of responsibility
 by David Cox, John Little, Donal O’Shea
 Language

 eng
 eng
 Summary
 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. 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
 Dewey number

 516.3/5
 516.35
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 HVOpXOucMj4
 IMW1F3VNHGY
 FE1gCVmacE8
 Language note
 English
 LC call number
 QA564609
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Undergraduate Texts in Mathematics,
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