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