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

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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Autors principals: Cox, David A. (Autor), Little, John (Autor), O'Shea, Donal (Autor)
Autor corporatiu: SpringerLink (Online service)
Format: Electrònic eBook
Idioma:anglès
Publicat: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Edició:5th ed. 2025.
Col·lecció:Undergraduate Texts in Mathematics,
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Accés en línia:https://doi.org/10.1007/978-3-031-91841-4
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Taula de continguts:
  • 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.