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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 4183845742 Hilbert basis elements 54 Hilbert basis elements of degree 1 9 extreme rays 9 support hyperplanes embedding dimension = 9 rank = 9 (maximal) external index = 1 size of nested triangulation = 4 resulting sum of |det|s = 3932160 grading: 1 0 0 0 0 0 0 0 0 degrees of extreme rays: 1: 5 5: 4 multiplicity = 786432/5 Hilbert series: 1 46 1695 21504 82823 140913 156027 155433 136184 73957 16786 1043 20 denominator with 9 factors: 1: 8 5: 1 degree of Hilbert Series as rational function = -1 Hilbert series with cyclotomic denominator: -1 -46 -1695 -21504 -82823 -140913 -156027 -155433 -136184 -73957 -16786 -1043 -20 cyclotomic denominator: 1: 9 5: 1 Hilbert quasi-polynomial of period 5: 0: 1575 7785 9802 10332 21952 6720 9856 3072 6144 1: 9387 7785 9802 10332 21952 6720 9856 3072 6144 2: 5355 7785 9802 10332 21952 6720 9856 3072 6144 3: 7119 7785 9802 10332 21952 6720 9856 3072 6144 4: 11655 7785 9802 10332 21952 6720 9856 3072 6144 with common denominator = 1575 *********************************************************************** 54 Hilbert basis elements of degree 1: 1 -2 1 2 -2 2 -1 -2 3 1 -2 3 -2 1 -2 3 -2 1 1 -1 0 1 -1 1 0 -1 1 1 -1 0 1 0 1 -1 -1 2 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 0 0 0 0 -1 1 1 -1 1 0 0 0 0 0 0 1 -1 1 0 0 0 1 -1 1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 1 0 -1 2 1 -1 2 -1 1 -1 2 -1 1 1 0 -2 0 3 0 -2 0 1 1 0 -1 0 0 0 1 0 -1 1 0 -1 0 1 0 -1 0 1 1 0 -1 0 1 0 0 0 0 1 0 -1 0 2 0 -1 0 1 1 0 0 -1 0 -1 1 0 1 1 0 0 -1 0 0 1 0 0 1 0 0 0 -2 0 0 0 3 1 0 0 0 -1 0 0 0 1 1 0 0 0 -1 0 0 0 2 1 0 0 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 -1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 2 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 -1 0 -1 1 0 1 1 0 1 0 0 0 -1 0 -1 1 0 1 0 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 2 0 1 0 2 0 1 1 1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 0 -1 0 1 2 1 1 0 -1 -1 -1 0 1 1 1 1 0 -1 -1 -1 1 1 2 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 2 -1 -2 -2 -2 1 2 3 1 2 1 2 1 2 1 2 1 5688 further Hilbert basis elements of higher degree: 2 -3 2 1 -1 0 1 -2 2 2 -3 3 -1 0 0 0 0 0 2 -2 0 1 0 2 -2 -1 2 2 -2 0 2 -1 0 0 0 0 2 -2 0 2 -1 1 -1 -1 2 2 -2 1 -1 2 -1 0 0 0 2 -2 1 -1 2 -1 1 -2 2 2 -2 1 0 -1 2 -1 0 0 2 -2 1 0 0 -1 2 -1 0 2 -2 1 0 0 0 -1 2 -2 2 -2 1 0 0 0 0 -2 4 2 -2 1 0 0 0 0 -1 2 2 -2 1 0 0 0 0 0 0 2 -2 1 0 0 1 -2 1 0 2 -2 1 0 0 1 0 -2 2 2 -2 1 0 1 -1 1 -1 1 2 -2 1 0 1 0 0 -2 2 2 -2 1 0 2 0 0 -2 3 2 -2 1 1 -2 1 -1 0 2 2 -2 1 1 -2 2 -1 -1 2 2 -2 1 1 -1 1 -1 -1 2 2 -2 1 1 -1 1 -1 0 0 2 -2 1 1 -1 1 -1 0 1 2 -2 1 1 -1 1 0 -2 3 2 -2 1 1 -1 2 -1 -1 2 2 -2 1 1 0 0 0 -2 2 2 -2 1 1 0 1 -1 0 1 2 -2 1 2 -1 1 0 -1 2 2 -2 2 -2 1 -1 2 -1 0 2 -2 2 -1 -1 0 1 -1 2 2 -2 2 -1 0 -1 1 0 0 2 -2 2 -1 0 -1 2 -2 2 2 -2 2 -1 0 -1 2 -1 1 2 -2 2 -1 0 0 0 0 0 2 -2 2 -1 0 0 1 -1 0 2 -2 2 -1 0 0 1 -1 1 2 -2 2 -1 0 0 2 -2 1 2 -2 2 -1 1 -2 2 -1 0 2 -2 2 -1 1 -2 3 -1 0 2 -2 2 -1 1 -1 1 0 0 2 -2 2 -1 1 0 1 -1 1 2 -2 2 -1 2 -1 1 -2 2 2 -2 2 0 -2 0 1 -2 4 2 -2 2 0 -1 0 1 -2 2 2 -2 2 0 -1 0 1 -2 3 2 -2 2 0 -1 0 1 -2 4 2 -2 2 0 -1 1 1 -3 2 2 -2 2 0 0 -1 1 -1 0 2 -2 2 0 0 -1 2 -2 1 2 -2 2 0 0 -1 2 -1 1 2 -2 2 0 0 1 -1 1 0 2 -2 2 1 -1 2 0 -1 2 2 -2 2 1 0 1 0 -2 3 2 -2 3 -2 1 -1 2 -1 0 2 -2 3 -1 0 -1 2 -2 2 2 -2 3 -1 1 -1 2 0 0 2 -2 3 0 -1 0 2 -2 4 2 -2 3 0 0 0 2 -2 2 2 -2 3 0 1 0 2 -2 3 2 -1 -2 2 1 -1 0 0 0 2 -1 -1 0 1 1 -1 0 0 2 -1 -1 0 2 -1 0 0 0 2 -1 -1 0 2 0 -2 1 0 2 -1 -1 0 2 0 -1 -1 2 2 -1 -1 0 2 1 -2 0 1 2 -1 -1 1 0 -1 1 1 -2 2 -1 -1 1 0 0 -1 0 2 2 -1 -1 1 0 0 0 0 0 2 -1 -1 1 0 1 -2 -1 4 2 -1 -1 1 1 -1 0 0 0 2 -1 -1 1 1 -1 0 1 -1 2 -1 -1 1 1 0 -1 0 0 2 -1 -1 1 1 0 -1 0 1 2 -1 -1 1 1 1 -2 -1 2 2 -1 -1 1 2 0 -1 0 1 2 -1 -1 2 -1 -1 1 0 0 2 -1 -1 2 0 -1 1 0 0 2 -1 0 -2 2 0 1 -1 0 2 -1 0 -1 0 1 0 1 -2 2 -1 0 -1 0 1 1 -1 0 2 -1 0 -1 1 -1 1 -1 2 2 -1 0 -1 1 -1 1 0 0 2 -1 0 -1 1 0 -2 2 0 2 -1 0 -1 1 0 -1 1 0 2 -1 0 -1 1 0 0 0 0 2 -1 0 -1 1 0 1 -1 0 2 -1 0 -1 1 1 -1 1 -1 2 -1 0 -1 2 -1 0 -1 3 2 -1 0 -1 2 -1 0 0 1 2 -1 0 -1 2 -1 1 -1 0 2 -1 0 -1 2 0 -1 0 0 2 -1 0 -1 2 0 0 -1 1 2 -1 0 -1 2 0 0 0 0 2 -1 0 -1 3 -1 0 -1 1 2 -1 0 -1 3 -1 1 -1 1 2 -1 0 0 -2 2 0 -1 2 2 -1 0 0 -1 0 0 1 0 2 -1 0 0 -1 1 -1 0 2 2 -1 0 0 -1 1 0 -1 2 2 -1 0 0 -1 1 0 0 0 2 -1 0 0 -1 2 0 -1 0 2 -1 0 0 -1 2 0 -1 1 2 -1 0 0 0 -3 3 0 0 2 -1 0 0 0 -2 2 0 0 2 -1 0 0 0 -1 1 0 0 2 -1 0 0 0 -1 1 1 -1 2 -1 0 0 0 0 -1 0 2 2 -1 0 0 0 0 -1 1 0 2 -1 0 0 0 0 -1 1 1 2 -1 0 0 0 0 0 -1 2 2 -1 0 0 0 0 0 0 0 2 -1 0 0 0 0 0 0 1 2 -1 0 0 0 0 0 1 -2 2 -1 0 0 0 0 0 1 -1 2 -1 0 0 0 0 1 -1 1 2 -1 0 0 0 1 -1 0 0 2 -1 0 0 0 1 -1 0 1 2 -1 0 0 0 1 0 -1 1 2 -1 0 0 0 1 0 0 0 2 -1 0 0 0 2 0 -1 1 2 -1 0 0 1 -1 0 0 0 2 -1 0 0 1 -1 1 -1 0 2 -1 0 0 1 -1 1 0 0 2 -1 0 0 1 0 -1 0 0 2 -1 0 0 1 0 -1 1 -1 2 -1 0 0 1 0 -1 1 0 2 -1 0 0 1 0 0 1 -1 2 -1 0 0 1 1 -2 0 0 2 -1 0 0 1 1 -1 -1 1 2 -1 0 0 1 1 -1 0 1 2 -1 0 0 2 -2 1 -1 0 2 -1 0 0 2 -1 0 -1 1 2 -1 0 0 2 -1 0 0 0 2 -1 0 0 2 0 -1 1 0 2 -1 0 1 -2 0 0 0 2 2 -1 0 1 -2 1 -1 -1 4 2 -1 0 1 -1 -1 1 0 1 2 -1 0 1 -1 0 0 -1 2 2 -1 0 1 -1 0 0 0 0 2 -1 0 1 -1 0 0 0 1 2 -1 0 1 -1 0 0 0 2 2 -1 0 1 -1 1 -1 -1 2 2 -1 0 1 -1 2 -1 -2 2 2 -1 0 1 0 -1 0 1 -2 2 -1 0 1 0 -1 1 -1 0 2 -1 0 1 0 -1 1 0 -1 2 -1 0 1 0 -1 1 0 0 2 -1 0 1 0 -1 1 1 -1 2 -1 0 1 0 0 -1 0 0 2 -1 0 1 0 0 0 -1 1 2 -1 0 1 0 0 0 0 0 2 -1 0 1 0 0 0 0 1 2 -1 0 1 0 0 0 1 -1 2 -1 0 1 0 0 1 0 0 2 -1 0 1 0 1 -1 0 1 2 -1 0 1 1 -1 1 0 0 2 -1 0 1 1 0 -1 -1 1 2 -1 0 1 1 0 0 0 1 2 -1 0 1 1 1 -2 0 1 2 -1 0 2 -2 0 0 -1 2 2 -1 0 2 -1 0 0 -1 0 2 -1 0 2 -1 0 0 -1 1 2 -1 0 2 0 -1 2 0 0 2 -1 0 2 0 0 0 -1 1 2 -1 0 2 0 1 -2 -2 2 2 -1 1 -2 0 -1 2 0 0 2 -1 1 -2 0 0 2 -1 0 2 -1 1 -2 1 -1 1 0 1 2 -1 1 -2 1 0 2 -1 0 2 -1 1 -2 2 -2 1 -1 2 2 -1 1 -2 2 -2 2 -1 2 2 -1 1 -1 -1 -2 2 0 2 2 -1 1 -1 -1 -1 1 0 2 2 -1 1 -1 -1 -1 2 -1 2 2 -1 1 -1 -1 0 -1 2 0 2 -1 1 -1 -1 0 0 1 1 2 -1 1 -1 -1 0 1 -1 2 2 -1 1 -1 0 -2 2 0 0 2 -1 1 -1 0 -2 2 0 1 2 -1 1 -1 0 -1 0 1 0 2 -1 1 -1 0 -1 1 0 0 2 -1 1 -1 0 -1 1 1 0 2 -1 1 -1 0 -1 2 -1 0 2 -1 1 -1 0 -1 2 -1 1 2 -1 1 -1 0 0 -1 2 0 2 -1 1 -1 0 0 0 0 0 2 -1 1 -1 0 0 0 1 -1 2 -1 1 -1 0 0 0 1 0 2 -1 1 -1 0 0 1 -1 0 2 -1 1 -1 0 0 2 -2 0 2 -1 1 -1 0 1 -1 1 -2 2 -1 1 -1 0 1 0 0 -1 2 -1 1 -1 0 1 0 1 -1 2 -1 1 -1 0 1 1 -1 0 2 -1 1 -1 1 -2 2 0 1 2 -1 1 -1 1 -1 0 -1 2 2 -1 1 -1 1 -1 0 0 0 2 -1 1 -1 1 -1 2 -1 0 2 -1 1 -1 1 0 0 -1 0 2 -1 1 -1 1 0 0 0 0 2 -1 1 -1 1 0 0 1 0 2 -1 1 -1 1 0 1 -2 1 2 -1 1 -1 1 0 1 0 0 2 -1 1 -1 2 -1 0 -1 0 2 -1 1 -1 3 -1 0 -1 1 2 -1 1 0 -1 -1 1 -1 2 2 -1 1 0 -1 0 -1 1 0 2 -1 1 0 -1 0 0 1 1 2 -1 1 0 -1 1 -1 0 0 2 -1 1 0 -1 1 -1 1 1 2 -1 1 0 -1 1 0 0 1 2 -1 1 0 -1 1 0 0 2 2 -1 1 0 0 -2 2 -1 0 2 -1 1 0 0 -1 1 -1 0 2 -1 1 0 0 0 -1 0 0 2 -1 1 0 0 0 -1 1 -2 2 -1 1 0 0 0 -1 1 -1 2 -1 1 0 0 0 0 -2 2 2 -1 1 0 0 0 0 1 -1 2 -1 1 0 0 1 -1 0 0 2 -1 1 0 0 1 -1 1 -1 2 -1 1 0 0 1 -1 1 0 2 -1 1 0 0 1 0 0 1 2 -1 1 0 0 1 1 0 0 2 -1 1 0 1 -2 2 -1 0 2 -1 1 0 1 -1 0 -1 0 2 -1 1 0 1 -1 1 0 0 2 -1 1 0 1 -1 2 0 0 2 -1 1 0 1 0 -1 1 -1 2 -1 1 0 1 0 0 1 0 2 -1 1 0 1 1 -1 1 0 2 -1 1 0 1 1 0 0 1 2 -1 1 1 -1 0 1 0 2 2 -1 1 1 -1 1 -1 -2 2 2 -1 1 1 -1 2 0 -2 2 2 -1 1 1 0 -1 1 -1 0 2 -1 1 1 0 0 1 0 0 2 -1 1 1 0 0 1 0 1 2 -1 1 1 0 1 -1 0 1 2 -1 1 1 0 1 -1 1 0 2 -1 1 1 0 1 0 1 0 2 -1 1 1 1 0 1 0 1 2 -1 1 2 -2 1 -1 -2 2 2 -1 1 2 -1 1 -1 -2 2 2 -1 1 2 -1 2 -1 -1 3 2 -1 1 2 0 2 -1 0 2 2 -1 1 2 0 2 0 -1 3 2 -1 1 3 -1 2 0 0 2 2 -1 2 -2 0 -2 2 -1 2 2 -1 2 -2 0 -2 2 0 1 2 -1 2 -2 0 -2 3 -1 2 2 -1 2 -2 0 -1 1 0 0 2 -1 2 -2 0 -1 2 -1 1 2 -1 2 -2 0 -1 2 0 1 2 -1 2 -2 1 -1 2 -2 0 2 -1 2 -2 1 -1 3 -2 0 2 -1 2 -2 1 0 3 -1 0 2 -1 2 -1 -1 -1 1 -1 2 2 -1 2 -1 -1 -1 2 -1 3 2 -1 2 -1 0 -2 2 -1 1 2 -1 2 -1 0 -1 1 -1 0 2 -1 2 -1 0 -1 1 -1 1 2 -1 2 -1 0 -1 2 -2 1 2 -1 2 -1 0 -1 2 -1 1 2 -1 2 -1 0 -1 3 -1 2 2 -1 2 -1 0 0 0 2 0 2 -1 2 -1 0 0 1 -2 0 2 -1 2 -1 0 0 2 -2 1 2 -1 2 -1 1 -2 2 -2 0 2 -1 2 -1 1 -1 1 -1 0 2 -1 2 -1 1 -1 3 -1 0 2 -1 2 -1 1 0 1 0 0 2 -1 2 -1 1 0 2 0 0 2 -1 2 -1 2 -1 3 -1 1 2 -1 2 0 -1 -1 1 -2 2 2 -1 2 0 0 -1 1 -2 0 2 -1 2 0 0 -1 1 -2 1 2 -1 2 0 0 1 0 0 0 2 -1 2 0 0 1 1 -1 1 2 -1 2 0 0 1 1 0 1 2 -1 2 0 1 -2 3 -1 0 2 -1 2 0 1 -1 1 -2 1 2 -1 2 0 1 -1 2 0 0 2 -1 2 0 1 0 0 -1 1 2 -1 2 0 1 0 1 1 0 2 -1 2 1 -1 1 1 -1 4 2 -1 2 1 0 0 1 -1 1 2 -1 2 1 0 2 -1 2 0 2 -1 2 2 -1 1 0 -2 2 2 -1 3 -1 0 -1 2 -1 2 2 -1 3 -1 0 -1 3 -1 3 2 -1 3 -1 1 -2 2 -2 0 2 -1 3 -1 1 -1 2 -1 0 2 -1 3 -1 1 -1 3 -1 1 2 -1 3 -1 2 -1 2 -1 1 2 0 -2 -1 1 2 0 -1 0 2 0 -2 -1 2 1 -1 0 0 2 0 -2 0 1 -1 0 1 0 2 0 -2 0 1 0 -1 0 2 2 0 -2 0 2 -1 -1 1 1 2 0 -2 0 2 0 -1 0 0 2 0 -2 1 0 -2 1 1 0 2 0 -2 1 2 -1 -1 0 0 2 0 -1 -2 0 2 1 0 -2 2 0 -1 -1 -1 1 1 0 0 2 0 -1 -1 -1 2 1 -1 0 2 0 -1 -1 0 0 -1 1 2 2 0 -1 -1 0 0 0 0 2 2 0 -1 -1 0 0 0 1 0 2 0 -1 -1 0 0 1 0 0 2 0 -1 -1 0 1 0 0 0 2 0 -1 -1 0 1 0 0 1 2 0 -1 -1 0 1 1 0 -2 2 0 -1 -1 0 1 1 0 -1 2 0 -1 -1 0 2 1 -1 0 2 0 -1 -1 1 -1 0 1 1 2 0 -1 -1 1 0 -1 1 0 2 0 -1 -1 1 0 -1 1 1 2 0 -1 -1 1 0 0 0 0 2 0 -1 -1 1 1 0 -1 0 2 0 -1 -1 1 1 0 0 -1 2 0 -1 -1 1 1 0 0 0 2 0 -1 -1 1 1 1 0 -1 2 0 -1 -1 2 -1 -1 0 2 2 0 -1 -1 2 0 -1 1 1 2 0 -1 -1 2 0 0 -1 0 2 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