Ideals, Varieties, and Algorithms
An Introduction to Computational Algebraic Geometry and Commutative Algebra
2nd Edition
Published on 9. March 2013
XIII, 538 pages
978-1-4757-2693-0 (ISBN)
Description
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. In preparing a new edition of "Ideals, Varieties and Algorithms" the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple, Mathematica and REDUCE.
Reviews / Votes
"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 MonthlyMore details
Other editions
New editions
David A. Cox | John Little | DONAL OSHEA
Ideals, Varieties, and Algorithms
An Introduction to Computational Algebraic Geometry and Commutative Algebra
E-Book
08/2007
3rd Edition
Springer
€46.99
Available for download
Additional editions
David Cox | John Little | DONAL OSHEA
Ideals, Varieties, and Algorithms
An Introduction to Computational Algebraic Geometry and Commutative Algebra
Book
02/2006
2nd Edition
Springer
€85.59
Article exhausted; check for reprint
Previous edition
David Cox | John Little | DONAL OSHEA
Ideals, Varieties, and Algorithms
An Introduction to Computational Algebraic Geometry and Commutative Algebra
E-Book
04/2013
1st Edition
Springer
€85.59
Available for download
Content
1. Geometry, Algebra, and Algorithms.- 2. Groebner Bases.- 3. Elimination Theory.- 4. The Algebra-Geometry Dictionary.- 5. Polynomial and Rational Functions on a Variety.- 6. Robotics and Automatic Geometric Theorem Proving.- 7. Invariant Theory of Finite Groups.- 8. Projective Algebraic Geometry.- 9. The Dimension of a Variety.- Appendix A. Some Concepts from Algebra.- §1 Fields and Rings.- §2. Groups.- §3. Determinants.- Appendix B. Pseudocode.- §1. Inputs, Outputs, Variables, and Constants.- §2. Assignment Statements.- §3. Looping Structures.- §4. Branching Structures.- Appendix C. Computer Algebra Systems.- §1. AXIOM.- §2. Maple.- §3. Mathematica.- §4. REDUCE.- §5. Other Systems.- Appendix D. Independent Projects.- §1. General Comments.- §2. Suggested Projects.- References.
