Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
Inhalt
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.- Appendix A Some Concepts from Algebra.- Fields and Rings.- Groups.- Determinants.- Appendix B Pseudocode.- Inputs, Outputs, Variables, and Constants.- Assignment Statements.- Looping Structures.- Branching Structures.- Appendix C Computer Algebra Systems.- Maple.- Mathematica.- REDUCE.- Other Systems.- Appendix D Independent Projects.- General Comments.- Suggested Projects.- References.