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| Slurmfels B. — Solving systems of polynomial equations |
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| Предметный указатель |
Algebraic function 8 33
Algebraic torus 31 123
Alon — Jaeger — Tarsi conjecture 69
Amoebas 119
Artin's theorem 95
Bergman complex 124
Bernstein's theorem 31 37 123
Bezout matrix 44 48
Bezout's theorem 29 123
Binary random variable 103 107
binomial 32 62 104
Birch's theorem 114
Bisection 5
Castelnuovo — Mumford regularity 70
Cholesky decomposition 88
Circuit ideal 113 143
Companion matrix 4 11 17—20 22 26 57
Companion matrix, resultant formula 44
Complete intersection 29 63 67 107 131
Cubic surface 26
Derangement 82
Descartes's rule of signs 5
Discriminant 10 11 23 135 139
Discriminant of symmetric matrix 96—99
Discriminant, computation of 1—2 29—30
Ehrenpreis — Palamodov theorem 133 141 142
Eigenvalues 4 11 17—22 87—88 96—99
Elimination ideal 14—15
Elimination theory 49 51 52
Elliptic curve 27 122
Entire function 134 136
Fewnomial 38
Fibonacci number 64
Floating point 3 87 88
Galois group 2—3 26
Game in normal form 71
Gel'fand — Kapranov — Zelevinsky 10 50 124
Gorenstein 135 139-140
Graphical model 82 101 103 104
Grassmannian 127 131
Groebner basis 29 90 93 105 107 127
Groebner basis and Bergman fan 125
Groebner basis of adjacent minors 64
Groebner basis of decomposable graph 104
Groebner basis of lattice walks 111
Groebner basis of subpermanents 67 68
Groebner basis of totally mixed Nash equilibria 74
Groebner basis of zero-dimensional ideal 13—27 89 90
Groebner basis, computation, compared to Hermite normal form 33
Groebner basis, implicitizing rational plane curve using 45
Groebner basis, statistics and 101
Groebner basis, universal 127
Groebner cone 125—127
Groebner duality 135
Groebner fan 125—127
Hammersley — Clifford theorem 104
Harmonic polynomial 139
Hermite normal form 32
Hilbert series 98
Homotopy method 37 82
Hypergeometric differential equations 10
Hypergeometric function 9
Ideal quotient 15—17 137
Ilyushechkin's theorem 98
Initial form 125
Initial ideal 125—127 129
Initial monomial 52
Initial monomial ideal 13 60 127
Integral representation 144
Irreducible variety 59 103 108 125 141
Iterative proportional scaling 116
Jordan canonical form 11
Khovanskii's theorem 38
Laurent polynomial 22 24 31 49 52 124
Laurent series 6
Lexicographic term order 15 26 44
Linear programming 17 89 94
Local ring 16 17 135
Lower facet 35
Macaulay 2 14 59
Mathieu's problem 24 27
Matroid 127
Maximal ideal 15 17 136 137
Maximum likelihood 115
Minkowski sum 31 35 80 123
Mixed volume 37 50 73 80 84
Moment map 115
Monomial ideal 62 140
Multiplicity 1 6 15 16 133—136
Multiplicity, not in trace form 20
Multiplicity, standard monomials and 13 16
| Multiplicity, tropical 123
Nash equilibrium 71
Newton polytope 30—37 51 52 55 73 79—81
Newton polytope, amoeba and 124
Newton polytope, Bergman fan and 125
Newton polytope, Puiseux series and 7
Newton polytope, tropical curves with 123
Nodal curve 27 131
Non-radical ideal, scheme structure of 134
Normal form 14 17 89 138
Optimization 91
Partial differential equations 8 16 133
Payoff matrix 71
Permanent 67 68 83 145
Petersen graph 127
PHCpack 82
Piecewise-linear 7 34—36 119
Polytope 30
Positive semidefinite 88 92
Primary decomposition 17 26 59—70
Primary decomposition of binomial ideal 62 104
Primary decomposition of circuit ideals 113 114
Primary decomposition of graphical models 103 104
Primary decomposition of ideal of partial differential operators 136 137 142
Primary decomposition, Markov chains and 101
Primary decomposition, random walks and 111 112 117
Prime ideal 15 18 59 60 65 102—104 125 144
Puiseux series 6—11 34—35 37 41
Puiseux series, valuation and 119 130
Quadratic form 20 48 87 88 90 139
Radical ideal 13—15 17—18 26 59 74
Radical ideal and associated primes 60—61
Radical ideal and primary decomposition 61
Radical ideal and primary ideal 17 62 136
Radical ideal in univariate polynomial ring 4—5
Radical ideal of adjacent minors 64—66
Radical ideal of adjacent minors of embedded component 66
Radical ideal of adjacent minors, primary decomposition 66
Radical ideal of binomial ideal 62
Radical ideal of circuit ideal 113
Radical ideal of graphical model 103 105
Radical ideal of independence model 106
Radical ideal of subpermanents 67—68 70
Radical ideal of univariate polynomial 4
Radical ideal, close to zero-dimensional ideal 26
Radical ideal, computing in Macaulay 2 68
Radical ideal, Ehrenpreis — Palamodov pairs of 142
Radical ideal, maximizing polynomial modulo 92
Radical ideal, maximum likelihood ideal as 115
Radical ideal, zero-dimensional 14
Rational univariate representation 15
Real Nullstellensatz 94
Regular subdivision 121
Resultant 2 30 43—57
Resultant, companion matrix formula 44
Saturated independence condition 104—114
Saturation 15—17 106 125
Scheme 16 134 142
Semidefinite programming 87 88 90
Shape lemma 15
Sign changes 5—6 21
Sign changes in characteristic polynomial 22
singular 15 23 59
Solving the quintic 9
SOStools 89
Sparse Polynomial 3 29—41 49 79 80
Sparse resultant 49—57
Squarefree 4 14 60
Standard monomials 13 14 89 90 137—140
Standard monomials in resultant computation 55
Standard monomials, multiplicity and 16
Standard pairs 140 142
State polytope 125
Strategy 71 74
Sturm sequence 5
Sufficient statistic 114
Sylvester matrix 2 44 48 55
Symbolic power 144
Toric deformation 33
Toric ideal 104 106
Toric Jacobian 40
Trilinear equation 55 76
Tropical curve 120
Tropical semiring 119
Tropical variety 130
Unmixed 38 52 55
Zero-dimensional ideal 13—27 47 59 89—92
Zero-dimensional ideal of partial differential operators 136 137 141 142
Zero-dimensional ideal, complete intersection 63
Zero-dimensional ideal, Gorenstein 139
Zero-dimensional ideal, maximum likelihood ideal 115
Zero-dimensional ideal, monomial 140
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