Ideals, Varieties, and Algorithms - David A. Cox

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Résumé :
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....

Biographie:
the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz&mdash...

Sommaire:

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 chapters are covered. In addition to the fundamentals of algebraic geometry&mdash...