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

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these ch...

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Bibliographic Details
Main Authors: Cox, David A., Little, John (Author), O'Shea, Donal (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2015, 2015
Edition:4th ed. 2015
Series:Undergraduate Texts in Mathematics
Subjects:
Commutative Algebra
Algebraic Geometry
Commutative Rings And Algebras
Mathematical Logic
Computer Software
Commutative Rings
Mathematical Logic And Foundations
Mathematical Software
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • Notation for Sets and Functions
  • 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
  • 10. Additional Groebner Basis Algorithms
  • Appendix A. Some Concepts from Algebra
  • Appendix B. Pseudocode
  • Appendix C. Computer Algebra Systems
  • Appendix D. Independent Projects
  • References
  • Index.

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