理想.簇与算法-第3版

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
　1. introduction
　2. orderings on the monomials in k[xl  xn]
　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
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