Index
Adjacency Decomposition Method, 137
Recursive , 139
adjacent
Delone polytope, 57
face, 132
adjoint form, 35
algorithm
of Fincke and Pohst, 31
graph traversal , 31
Las Vegas , 72
Minkowski’s , 20
randomized , 72
reduction , 17
Voronoi’s , 31
approximation
Euclidean norm best , 25
simultaneous , 24
arithmetic group, 66
arithmetical minimum, 3
surface, 27
generalized , 38
representatives of , 3
arithmetically equivalent, 2
automorphism group
of Delone triangulation, 92
of a polyhedral cone, 74
of periodic form, 46
of quadratic form, 33
GLt
d
(Z)-restricted , 49
linear , 134
projective , 134
(T, t)-∼ , 50
Balinski’s theorem, 138
Baranovskii cone, 75
Barnes-Wall lattice, 54, 126
basic closed semialgebraic set, 39
basis, 5
bcc-lattice, 141
best approximation
first kind , 23
second kind , 23
bistellar
flip, 58
neighbor, 58, 68
T -flip, 68
Bravais
group, 50
manifold, 34
canonical representative, 136
cell of polyhedral complex, 133
centroid, 97
certificate, 86
characteristic form, 73
chirotope, 62
Cholesky decomposition, 5
circumradius, 86
closest vector problem, 38
coarsening, 57
coefficient
inner , 4
outer , 4
cohomology, 37
compactification, 36, 66
complex lattice, 52
cone
Baranovskii , 75
convex , 3
hypermetric , 75
normal , 29
outer normal , 94
polyhedral , 132
secondary , 57
support, 31
congruence subgroup, 46
conic hull, 132
contiguous
perfect form, 30
secondary cone, 67
E-∼ , G-∼ , 53
continued fraction, 23
expansion, 23
Hermite’s , 25
multidimensional , 24
ordinary , 23
convergent, 23
matrix, 24
155
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