GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
20 Hilbert basis elements 8 Hilbert basis elements of degree 1 20 extreme rays 1 module generators over original monoid 16 support hyperplanes embedding dimension = 16 rank = 8 external index = 1 internal index = 1 original monoid is integrally closed size of partial triangulation = 0 resulting sum of |det|s = 0 grading: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 with denominator = 4 degrees of extreme rays: 1: 8 2: 12 Monoid is Gorenstein Generator of interior: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 *********************************************************************** 8 Hilbert basis elements of degree 1: 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 12 further Hilbert basis elements of higher degree: 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 2 0 0 0 0 1 0 1 0 0 2 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 2 0 0 0 0 1 1 0 0 0 1 1 0 2 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 2 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0 1 0 1 0 0 0 0 2 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 2 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 20 extreme rays: 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 2 0 0 0 0 1 0 1 0 0 2 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 2 0 0 0 0 1 1 0 0 0 1 1 0 2 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 2 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0 1 0 1 0 0 0 0 2 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 2 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 module generators over original monoid: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 support hyperplanes: 0 0 0 -1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 -1 -1 1 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 2 -1 -1 0 0 -1 0 0 0 0 0 0 0 1 0 -1 -1 1 1 -1 0 1 0 0 0 0 0 0 0 1 0 0 -1 1 0 -1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 8 equations: 1 0 0 0 0 0 0 -1 0 0 0 -1 1 0 0 0 0 1 0 0 0 0 0 -1 0 1 -1 -1 1 1 0 -1 0 0 1 0 0 0 0 1 0 -1 1 1 -2 -1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 -1 -1 -1 0 0 0 0 0 1 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 -2 -1 -1 0 0 0 0 0 0 0 1 -1 0 1 0 -1 1 0 0 -1 0 0 0 0 0 0 0 0 1 1 1 1 -1 -1 -1 -1 8 basis elements of lattice: 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 -1 0 0 0 0 1 0 0 0 1 0 -1 2 0 1 2 -1 -1 0 0 0 0 1 0 0 -1 0 1 -1 0 -1 -1 1 1 0 0 0 0 0 1 0 -1 0 0 -1 1 0 -1 1 0 0 0 0 0 0 0 1 -1 0 -1 0 1 0 1 -1 0 0 0 0 0 0 0 0 0 1 1 -1 -1 -1 -1 1 1