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The book assumes that the students will have access to a computer algebra system.Appendix C describes the features of AXIOM， Maple， Mathematica， and REDUCE that are most relevant to the text. We do not assume any prior experience with a com-puter. However， many of the algorithms in the book are described in pseudocode， which may be unfamiliar to students with no background in programming. Appendix B con-tains a careful descripLion of the pseudocode that we use in the text.
目次
Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
1 Geometry， Algebra， and Algoritlnns
1. Polynomials and Affine Space
2. Affine Varieties
3. Parametrizations of Affine Varieties
4. Ideals
5. Polynomials of One Variable
2. Groebner Bases
2. Orderings on the Monomials in k[xl xn]
1. Introduction
3. A Division Algorithm in k[xl Xn]
4. Monomial Ideals and Dickson's Lemma
5. The Hilbert Basis Theorem and Groebner Bases
6. Properties of Groebner Bases
7. Buchberger's Algorithm
8. First Applications of Groebner Bases
9. (Optional) Improvements on Buchberger's Algorithm
3. Elimination Theory
1. The Elimination and Extension Theorems
2. The Geometry of Elimination
3. Implicitization
4. Singular Points and Envelopes
5. Unique Factorization and Resultants
6. Resultants and the Extension Theorem
……
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
Appendix B.Pseudocode
Appendix C.Computer Algebra Systems
Appendix D.Independent Projects
References
Index
Preface to the Second Edition
Preface to the Third Edition
1 Geometry， Algebra， and Algoritlnns
1. Polynomials and Affine Space
2. Affine Varieties
3. Parametrizations of Affine Varieties
4. Ideals
5. Polynomials of One Variable
2. Groebner Bases
2. Orderings on the Monomials in k[xl xn]
1. Introduction
3. A Division Algorithm in k[xl Xn]
4. Monomial Ideals and Dickson's Lemma
5. The Hilbert Basis Theorem and Groebner Bases
6. Properties of Groebner Bases
7. Buchberger's Algorithm
8. First Applications of Groebner Bases
9. (Optional) Improvements on Buchberger's Algorithm
3. Elimination Theory
1. The Elimination and Extension Theorems
2. The Geometry of Elimination
3. Implicitization
4. Singular Points and Envelopes
5. Unique Factorization and Resultants
6. Resultants and the Extension Theorem
……
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
Appendix B.Pseudocode
Appendix C.Computer Algebra Systems
Appendix D.Independent Projects
References
Index
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