Index
algebraic function , 8 , 3 3
algebraic torus , 31, 123
Alon-Jaeger-Tarsi conjecture , 6 9
amoebas, 11 9
Artin's Theorem , 9 5
Bezout matrix , 44 , 4 8
Bezout's Theorem , 29 , 123
Bergman complex , 124
Bernstein's Theorem , 31, 37, 123
binary rando m variable , 103, 107
binomial, 32 , 62 , 104
Birch's Theorem , 11 4
bisection, 5
Castelnuovo-Mumford regularity , 7 0
Cholesky decomposition , 8 8
circuit ideal , 113, 143
companion matrix , 4 , 11, 17-20, 22 , 26 , 5 7
resultant formula , 4 4
complete intersection , 29 , 63 , 67, 107, 131
cubic surface , 2 6
derangement, 8 2
Descartes's Rul e o f Signs , 5
discriminant, 10, 11, 23, 135, 139
computation of , 1-2, 29-3 0
of symmetri c matrix , 96-9 9
Ehrenpreis-Palamodov Theorem , 133, 141,
142
eigenvalues, 4 , 11, 17-22, 87-88 , 96-9 9
elimination ideal , 14-15
elimination theory , 49 , 51, 52
elliptic curve , 27 , 122
entire function , 134, 136
fewnomial, 3 8
Fibonacci number , 6 4
floating point , 3 , 87, 8 8
Galois group , 2-3 , 2 6
game i n norma l form , 7 1
Gel'fand-Kapranov-Zelevinsky, 10, 50 , 124
Gorenstein, 135, 139-140
Grobner duality , 135
graphical model , 82 , 101, 103, 104
Grassmannian, 127, 131
Grobner basis , 29 , 90 , 93 , 105, 107, 127
and Bergma n fan , 125
computation, compare d t o Hermit e nor -
mal form , 3 3
implicitizing rationa l plan e curv e using ,
45
of adjacen t minors , 6 4
of decomposabl e graph , 104
of lattic e walks , 111
of subpermanents , 67 , 6 8
of totall y mixe d Nas h equilibria , 7 4
of zero-dimensiona l ideal , 13-27, 89 , 9 0
statistics and , 101
universal, 127
Grobner cone , 125-127
Grobner fan , 125-127
Hammersley-Clifford Theorem , 104
harmonic polynomial , 139
Hermite norma l form , 3 2
Hilbert series , 9 8
homotopy method , 37 , 8 2
hypergeometric differentia l equations , 10
hypergeometric function , 9
ideal quotient , 15-17, 137
Ilyushechkin's Theorem , 9 8
initial form , 125
initial ideal , 125-127, 129
initial monomial , 5 2
initial monomia l ideal , 13, 60, 127
integral representation , 144
irreducible variety , 59 , 103, 108, 125, 141
iterative proportiona l scaling , 116
Jordan canonica l form , 11
Khovanskii's Theorem , 3 8
Laurent polynomial , 22 , 24 , 31, 49, 52 , 124
Laurent series , 6
lexicographic ter m order , 15, 26, 4 4
linear programming , 17, 89, 9 4
local ring , 16, 17, 135
lower facet , 3 5
Macaulay 2 , 14, 5 9
Mathieu's problem , 24 , 2 7
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