Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra - Softcover
Synopsis
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.- §1 Fields and Rings.- §2. Groups.- §3. Determinants.- Appendix B. Pseudocode.- §1. Inputs, Outputs, Variables, and Constants.- §2. Assignment Statements.- §3. Looping Structures.- §4. Branching Structures.- Appendix C. Computer Algebra Systems.- §1. AXIOM.- §2. Maple.- §3. Mathematica.- §4. REDUCE.- §5. Other Systems.- Appendix D. Independent Projects.- §1. General Comments.- §2. Suggested Projects.- References.
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