Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra /

• Main Authors: Cox, David (Author), Little, John (Author), O’Shea, Donal (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2007.
• Edition: Third Edition.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Computer software.; Mathematical logic.; Algebraic Geometry.; Commutative Rings and Algebras.; Mathematical Logic and Foundations.; Mathematical Software.

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 o...

Table of Contents:

• 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.