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Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra /

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This text covers topics in algebraic geometry and commutative algebra with careful attention to their 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 cha...

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Bibliographic Details
Main Authors: Cox, David A. (Author), Little, John (Author), Shea, Donal (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer, 2025.
Edition:Fifth edition.
Series:Undergraduate texts in mathematics,
Subjects:
Geometry, Algebraic > Data processing.
Commutative algebra > Data processing.
Electronic books.
Online Access:Connect to the full text of this electronic book
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.