| 1 |
Polynomials and affine space, affine varieties |
p. 5: 2, {6b}; p. 12: {6}, 8, 10 |
| 2 |
Parameterizations of affine varieties, ideals |
p. 22: 1, 3, 4, {11}; p. 34: 3b, {9}, 10 |
| 3 |
Polynomials of one variable, orderings on the monomials in k[x1,...,xn] |
p. 46: {9}, 10; p. 52: 5; p. 60: {2}, 10 |
| 4 |
A division algorithm in k[x1,...,xn], monomial ideals and Dickson's lemma |
p. 68: {1}; p. 73: 3, {9} |
| 5 |
The Hilbert basis theorem and Groebner bases, properties of Groebner bases |
p. 80: {1}, 10; p. 87: 1, {12} |
| 6 |
Buchberger's algorithm, first applications of Groebner bases |
p. 94: 2a, {3a}; p. 100: {1}, 7 |
| 7 |
The elimination and extension theorems, the geometry of elimination |
p. 121: 1, {6}; p. 127: {3}, 5 |
| 8 |
Implicitization, singular points and envelopes |
p. 135: 9, {11}; p. 148: 4, {10} |
| 9 |
Unique factorization and resultants |
p. 159: 1, {4}; p. 159: 11, {17} |
| 10 |
Resultants and the extension theorem, the nullstellensatz |
p. 166: {2}, 3, 8; p. 174: 1, {2} |
| 11 |
Radical ideals and the ideal-variety correspondence, sums, products, and intersections of ideal |
p. 182: 2, {7a}; p. 191: 1, {11a-d} |
| 12 |
Zariski closure and quotients of ideals, irreducible varieties and prime ideals |
p. 197: {1}, 4; p. 203: 5, {12} |
| 13 |
Decomposition of a variety into irreducibles, polynomial mappings |
p. 209: 1, {9}; p. 220: 8, 10 |
| 14 |
Quotients of polynomials R, algorithmic computations in k[x1,...,xn]/I |
p. 228: 1, 6; p. 237: 6, {8} |
| 15 |
The coordinate ring of an affine variety, rational functions on a variety |
p. 246: 8, 9; p. 256: {9}, 10 |
| 16 |
Proof of the Closure theory, geometric description of robots, the forward kinematics problem |
p. 263: {5}, 8; p. 269: 4; p. 277: {4} |
| 17 |
The inverse kinematic problem and motion planning, automatic geometric theorem proving |
p. 287: {3}, 6; p. 303: 9, 13d |
| 18 |
Wu's method, symmetric polynomials |
p. 315: 3, 6a; p. 324: {8}, 14 |
| 19 |
Finite matrix groups and rings of invariants, generators for the ring of invariants |
p. 333: 11, 14; p. 342: {5}, 7 |
| 20 |
Relations among generators and the geometry of orbits, the projective plane, projective space and projective varieties |
p. 354: 6, 13; p. 375: 4, {7} |
| 21 |
The projective algebra-geometry dictionary, the projective closure of an affine variety |
p. 385: 15; p. 385:{10}; p. 391: {2}, 9 |
| 22 |
Projective elimination theory |
p. 406: 7, {9}; p. 406: 17, 18 |
| 23 |
The geometry of quadric hypersurfaces, the variety of a monomial ideal |
p. 419: 7, 10, {15}; p. 442: {2}, 5 |
| 24 |
The complement of a monomial ideal, the Hilbert function and the dimension of a variety |
p. 453: 3, 12; p. 465: 10, {12} |
| 25 |
Elementary properties of dimension, dimension and algebraic independence |
p. 474: 6, 10; p. 482: 7, 13 |
| 26 |
Dimension and nonsingularity, the tangent cone |
p. 493: 13, 17; p. 504: 6, 13 |