|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Kreuzer M., Robbiano L. — Computational commutative algebra 1 |
|
|
|
| Предметный указатель |
Left-cancellation law 42
Lemma of Dickson 43
Lemma of Gaub 33
Lemma of Krull — Azumaya 76
Lemma of Nakayama 81
Lemma of Seidenberg 250
Lexicographic term ordering 51
Lifting computation 109 180
Lifting existence 106 180
Lifting of a linear map 180
Lifting of syzygies 106 109
Line 144
Line in projective space 204
Line segment 67
Linear algebra 119 178
Linear map 18
Linear map, homogeneous 78
localization 213
Logarithm 22
Macaulay's basis theorem 62 115
Matrix group 236
Matrix notation 147
Matrix, associated to a linear map 182
Maximal ideal 19
Maximal ideal, structure theorem 137 141
MEL-Rule 272
Method of tag variables 196
Minimal Groebner basis 118
Minimal polynomial 227
Minimal polynomial of an algebraic number 89 98
Minimal risk portfolio 270
Modern portfolio theory 267
Modular law 173
Module 18
Module annihilator 166
Module basis 19
Module colon 169
Module depth 193
Module elimination 48 196
Module monomial 44
Module of fractions 213
Module of homomorphisms 181
Module of syzygies 100
Module ordering 54
Module rank 19
Module, cyclic 19
Module, defined over a field 116
Module, finitely generated 19
Module, free 19
Module, graded 77
Module, graded free 78
Module, Noetherian 112
Module, projective 191
Module, term ordering 54
Molien's theorem 238
Monic polynomial 60
Monic tuple 118
Monoid 17 41
Monoid module 41
Monoid with cancellation law 42
Monoid, commutative 17
Monoid, ideal 41
Monoid, Noetherian 42
Monoid, ordering 50
Monoideal 41
Monomial ideal 44
Monomial module 44
Monomial module, structure theorem 44
Monomodule 41
Monomodule, Noetherian 46
Morphism of Affine spaces 234
Multiplicatively closed set 212
Nakayama's lemma 81
Natural spline 158
Newton polytope 67
Newton's identities 239
Nilpotent element 18
Noetherian module 112
Noetherian monoid 42
Noetherian monomodule 46
Non-zerodivisor 18
Non-zerodivisor for a module 171 176
Normal  -position 254
Normal form 73 113
Normal remainder 73 75
Normal remainder algorithm 75
Normal selection strategy 124
Nullstellensatz, field-theoretic version 136
Nullstellensatz, strong version 140
Nullstellensatz, weak version 139
Number field, algebraic closure 98
Number field, Gaubian 36
Number field, quadratic 24
Ordering induced by a tuple 149
Ordering of a monoid 50
Ordering of a monomodule 54
Ordering of terms 50
Ordering RevLex 52
Ordering, compatible 55
Ordering, represented by a matrix 52 57
Ordering, reverse-lexicographic 52
Outer product 184
Palindromic verse 241
Parametrically defined space curve 196
Perfect field 37 247
Permutation group 237
Pluecker relations 207
Point 137
Point in projective space 204
Polynomial 20
Polynomial dense 262
Polynomial derivative 35
Polynomial map 234
Polynomial representation 24 60 66
Polynomial ring 20
Polynomial ring, factoriality 33
Polynomial ring, surjective homomorphism 230
Polynomial ring, univariate 20
Polynomial, binomial 127
Polynomial, content 33
Polynomial, elementary symmetric 66
Polynomial, homogeneous 77 83
Polynomial, invariant 237
Polynomial, Lagrange interpolation 156
Polynomial, Laurent 208
Polynomial, minimal 89 227
Polynomial, monic 28 60
Polynomial, multivariate 20
Polynomial, primitive 33
Polynomial, squarefree part 37
Polynomial, strange 261
Polynomial, symmetric 66 129 230
Polynomial, univariate 20
Polynomial, zero 137
Polytope 67
Polytope, Newton 67
Polytope, vertex 67
Portfolio 268
Power product 22
Preimage computation 162
Presentation of a module 164
Presentation of a subquotient 164
Presentation of an algebra 23
Presentation of the image 178 228
Presentation of the kernel 178
Presentation via generators and relations 164
Primary decomposition 264
Primary ideal 264
Prime element 29
Prime ideal 19
| Prime, associated 175
Primitive Element Theorem 256
Primitive polynomial 33
Principal ideal domain 19
Projection 235
Projective hyperplane 204
Projective line 204
Projective module 191
Projective point 204
Projective space 204
Pullback 191
Pullback, universal property 192
Pythagorean triple 173
Pythagorean triple, fundamental 173
Pythagorean triple, positive 173
Radical 139
Radical ideal 48 139
Radical membership test 219
Radical of a zero-dimensional ideal 247
Radical of a zero-dimensional ideal, computation 251
Rank 19
Reduced Groebner basis 115 120
Reduces in one step 92
Reducible element 29
Reducible ideal 142
Reducible topological space 142
Reduction step 92
Reflection group 237
Reflexivity 50 54
Regular sequence 171
Regular sequence in an ideal 193
Regular sequence test 172
Relation 50
Relation, algebraic 23
Relation, complete 50
Relation, rewrite 92
Relatively prime elements 31
Reverse-lexicographic ordering 52
Rewrite relation 92
Rewrite relation, confluent 95
Rewrite rule 92
Reynolds operator 238
Right-cancellation law 42
Ring 17
Ring homomorphism 18
Ring of invariants 238
Ring polynomial 20
Ring, graded 76
Ring, unique factorization 30
Rotation group 237
Running example 100
S-polynomial 122
S-vector 122
Saturation 215
Saturation and localization 216
Saturation, computation 215 217 220
Saturation, exactness properties 220
Scalar multiplication 18
Seidenberg's lemma 250
Set of zeros 138
Set, Affine 144
Set, convex 67
Set, disconnected 142
Set, multiplicatively closed 212
Shape lemma 257
Shifting degrees 78
Special generation of submodules 87
SPLINE 155
Spline degree 157
Spline Function 156
Spline, natural 158
Squarefree part 31
Squarefree part, computation 249
Stable ideal 119
Standard deviation 268
Standard grading 77
Strong Law of Large Numbers 271
Subalgebra of a function field 240
Subalgebra, membership test 230
Submodule 18
Submodule, membership test 114
Submonomodule 41
Substitution homomorphism 23 226
Support 22
Symmetric group 66
Symmetric polynomial 66 129 230
System of Diophantine equations 207
System of Diophantine inequalities 207
System of generators of a module 19
System of generators of a monoideal 41
System of generators of a monomodule 42
System of generators of an algebra 23
System of generators of leading term module 88
System of generators, homogeneous 79
System of generators, irredundant 154
System of generators, minimal homogeneous 81
System of generators, minimal monomial 45
System of generators, special 87
System of polynomial equations 241
Syzygy 100
Syzygy module 100
Syzygy module of a Groebner basis 151
Syzygy module of elements of a monomial module 104 108
Syzygy module, computation 152 203
Syzygy of terms 104
Syzygy theorem of Hilbert 159
Syzygy, trivial 125
Taylor expansion 272
Tensor product 184
Term 22
Term ordering 50
Term ordering module 54
Term ordering, classication 58
Term ordering, compatible 55
Term ordering, cost compatible 210
Term ordering, DegLex 51
Term ordering, degree compatible 52
Term ordering, degree-lexicographic 51
Term ordering, degree-reverse-lexicographic 51
Term ordering, DegRevLex 51
Term ordering, Elim(L) 52
Term ordering, elimination 52 196
Term ordering, induced by a tuple 149
Term ordering, Lex 51
Term ordering, lexicographic 51
Term ordering, Ord(V) 52
Term ordering, PosTo 55
Term ordering, represented by a matrix 52
Term ordering, ToPos 55
Term, extended 208
Term, leading 60
Term, of a module 22
Theorem of Hilbert 113 159
Theorem of Macaulay 62 115
Theorem of Molien 238
Theorem, Chinese remainder 39 245
Theorem, primitive element 256
Toric ideal 222
Total return 267
Transcendental element 227
Transitive closure 92
Transitivity 50 54
Trivial reduction 92
Trivial syzygy 125
Twisted cubic curve 201
Twisted cubic curve, tangent surface 233
Unique factorization domain 30
Universal property of localization 219
Universal property of polynomial rings 23
Universal property of the pullback 192
|
|
|
| Реклама |
|
|
|
|
|
О проекте