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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
  
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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra [Hardcover]

4.0 out of 5 stars  See all reviews (3 customer reviews)


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Product Details

  • Hardcover: 551 pages
  • Publisher: Springer
  • Language: English
  • ISBN-10: 0387356517
  • ISBN-13: 978-0387356518
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #8,367,095 in Books (See Top 100 in Books)

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Average Customer Review
4.0 out of 5 stars (3 customer reviews)
 
 
 
 
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10 of 12 people found the following review helpful:
4.0 out of 5 stars Careful about production error, February 10, 2008
This is the 3rd edition of a popular reference on the subject. There was some production error with earlier version of the book. Even with the latest version, the authors have provided 14-page worth of corrections for the 1st printing of the 3rd edition. See www.cs.amherst.edu/~dac/iva/3ed1.pdf.
So buyers may be better off waiting for a corrected later version from the publisher.
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7 of 8 people found the following review helpful:
5.0 out of 5 stars Very clearly written., February 11, 2009
This book explains the concepts well and the proofs are written carefully and clearly. This is a math book, so you should expect the usual Definition-Theorem-Proof format, but the exposition is progressive, and the material is very well motivated. I had to implement an algorithm for the computation of Groebner bases, and I borrowed this book from the University library to learn about the Buchberger algorithm and related topics, and thanks to this book I was able to understand this algorithm and its correctness proof without the help of anyone. Of course Buchberger's algorithm is only a small part of this book, and you can find a lot of important topics in it.
Finally, note that the second part of Madhu Sudan's Algebra and Computation course at MIT follows this book closely. So at least one top expert in the field seems to have a good opinion of the book.
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2 of 12 people found the following review helpful:
3.0 out of 5 stars Good book (for Math people), February 18, 2010
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I actually haven't gone through the entire book, but the parts that I did go through were interesting. The book was (I thought) a little confusing to understand, but that may just be because it is for higher level abstract math. Lost of proofs and interesting things if your interested in abstract math!
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Inside This Book (learn more)
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Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
projective algebraic geometry, elimination theory, circle theorem, first elimination ideal, ideal description problem, grlex order, cyclic matrix group, using lex order, finite matrix group, many homogeneous invariants, grevlex order, reduced row echelon matrices, monomial ideal, implicitization problem, monomial order, reduced row echelon matrix, intermediate dividend, using elimination theory, ideal membership problem, polynomial parametrization, affine variety, coordinate subspace, most computer algebra systems, smallest variety containing, projective closure
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Extension Theorem, Use Exercise, Bezout's Theorem, Hilbert Basis Theorem, Closure Theorem, Euclidean Algorithm, Weak Nullstellensatz, Prove Proposition, The Algebra-Geometry Dictionary, Use Theorem, Hilbert's Nullstellensatz, Elimination Theorem, Invariant Theory of Finite Groups, Pappus's Theorem, The Geometry of Quadric Hypersurfaces, Parametrizations of Affine Varieties, Rational Functions, Dickson's Lemma, Use Definition, Quotients of Polynomial Rings, Algorithmic Computations, Polynomials of One Variable, Intersections of Ideals, Repeat Exercise, Use Corollary
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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