Theory

Source files, computed values, declared values, and values that are not decided.

Lattices, the chosen basis and the Gram tensor, orthogonal sums, twists, and the invariants of every lattice.

Notation for the named lattices of the catalogue, and the chosen basis of each one.

The dual lattice, the discriminant group and its form, unimodular and 2-elementary lattices, and Nikulin's invariants.

Integral overlattices of a lattice, counted through the discriminant form, and the genus symbol.

Invariants of definite lattices, and the sign convention for negative definite forms.

Isotropic, hyperbolic and reflective lattices.

Roots of a lattice and the root sublattice \(R(L) = \mathbb{Z}\Phi(L)\).

Morphisms of lattices and their block matrices.

The series \(F_{L,\Gamma}(z, w)\) of the numbers of \(\Gamma\)-orbits of primitive vectors of each norm, for eight subgroups \(\Gamma\) of \(O(L)\).

The primes of bad reduction of the quadric Q(x) = n, the character of the discriminant, the points over finite fields, and the zeta functions.