/* 1. Standard Lattice of rank 8 and degree 8 Determinant: 38416 Factored Determinant: 2^4 * 7^4 Minimum: 6 Inner Product Matrix: [ 6 0 0 2 0 0 -3 3] [ 0 6 2 0 -2 -2 -3 3] [ 0 2 6 -3 -3 -3 -2 0] [ 2 0 -3 6 0 0 0 2] [ 0 -2 -3 0 6 0 0 0] [ 0 -2 -3 0 0 6 2 -2] [-3 -3 -2 0 0 2 6 -3] [ 3 3 0 2 0 -2 -3 6] |Aut| = [ <2, 8>, <3, 2> ] St.mod. = true LatDB = 8QF.8.e */ // Data Liste:=[ PowerStructure(Lat) | LatticeWithGram(MatrixRing(IntegerRing(), 8) ! \[ 6, 0, 0, 2, 0, 0, -3, 3, 0, 6, 2, 0, -2, -2, -3, 3, 0, 2, 6, -3, -3, -3, -2, 0, 2, 0, -3, 6, 0, 0, 0, 2, 0, -2, -3, 0, 6, 0, 0, 0, 0, -2, -3, 0, 0, 6, 2, -2, -3, -3, -2, 0, 0, 2, 6, -3, 3, 3, 0, 2, 0, -2, -3, 6 ]:CheckPositive:=false) ];