Ideals, Varieties, and Algorithms

David A. Cox is Emeritus Professor of Mathematics at Amherst College.John Little is Emeritus Professor of Mathematics at College of the Holy Cross.Donal O'Shea is past President and Emeritus Professor of Mathematics at New College of Florida.

• 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.