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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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Main Authors: Cox, David A. (Author, http://id.loc.gov/vocabulary/relators/aut), Little, John. (http://id.loc.gov/vocabulary/relators/aut), O'Shea, Donal. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition:4th ed. 2015.
Series:Undergraduate Texts in Mathematics,
Subjects:
Algebraic geometry.
Commutative algebra.
Commutative rings.
Mathematical logic.
Computer software.
Algebraic Geometry.
Commutative Rings and Algebras.
Mathematical Logic and Foundations.
Mathematical Software.
Online Access:https://doi.org/10.1007/978-3-319-16721-3
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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