Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.
Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.
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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: 4183844398 Hilbert basis elements 4398 Hilbert basis elements of degree 1 83 extreme rays 25 support hyperplanes embedding dimension = 5 rank = 5 (maximal) external index = 1 size of triangulation = 620 resulting sum of |det|s = 65126 grading: 0 0 0 0 1 degrees of extreme rays: 1: 83 Hilbert basis elements are of degree 1 multiplicity = 65126 Hilbert series: 1 4393 33752 25439 1541 denominator with 5 factors: 1: 5 degree of Hilbert Series as rational function = -1 Hilbert polynomial: 12 268 3059 16874 32563 with common denominator = 12 rank of class group = 20 class group is free *********************************************************************** 4398 Hilbert basis elements of degree 1: 0 0 2 9 1 0 0 2 10 1 0 0 2 11 1 0 0 2 12 1 0 0 3 7 1 0 0 3 8 1 0 0 3 9 1 0 0 3 10 1 0 0 3 11 1 0 0 3 12 1 0 0 4 5 1 0 0 4 6 1 0 0 4 7 1 0 0 4 8 1 0 0 4 9 1 0 0 4 10 1 0 0 4 11 1 0 0 5 3 1 0 0 5 4 1 0 0 5 5 1 0 0 5 6 1 0 0 5 7 1 0 0 5 8 1 0 0 5 9 1 0 0 5 10 1 0 0 6 2 1 0 0 6 3 1 0 0 6 4 1 0 0 6 5 1 0 0 6 6 1 0 0 6 7 1 0 0 6 8 1 0 0 6 9 1 0 0 7 2 1 0 0 7 3 1 0 0 7 4 1 0 0 7 5 1 0 0 7 6 1 0 0 7 7 1 0 0 7 8 1 0 0 8 1 1 0 0 8 2 1 0 0 8 3 1 0 0 8 4 1 0 0 8 5 1 0 0 8 6 1 0 0 8 7 1 0 0 9 1 1 0 0 9 2 1 0 0 9 3 1 0 0 9 4 1 0 0 9 5 1 0 0 9 6 1 0 0 10 0 1 0 0 10 1 1 0 0 10 2 1 0 0 10 3 1 0 0 10 4 1 0 0 10 5 1 0 0 11 0 1 0 0 11 1 1 0 0 11 2 1 0 0 11 3 1 0 0 11 4 1 0 0 12 0 1 0 0 12 1 1 0 0 12 2 1 0 0 12 3 1 0 0 13 0 1 0 0 13 1 1 0 0 13 2 1 0 0 14 0 1 0 0 14 1 1 0 0 15 0 1 0 1 2 6 1 0 1 2 7 1 0 1 2 8 1 0 1 2 9 1 0 1 2 10 1 0 1 3 4 1 0 1 3 5 1 0 1 3 6 1 0 1 3 7 1 0 1 3 8 1 0 1 3 9 1 0 1 3 10 1 0 1 4 3 1 0 1 4 4 1 0 1 4 5 1 0 1 4 6 1 0 1 4 7 1 0 1 4 8 1 0 1 4 9 1 0 1 4 10 1 0 1 5 2 1 0 1 5 3 1 0 1 5 4 1 0 1 5 5 1 0 1 5 6 1 0 1 5 7 1 0 1 5 8 1 0 1 5 9 1 0 1 5 10 1 0 1 6 1 1 0 1 6 2 1 0 1 6 3 1 0 1 6 4 1 0 1 6 5 1 0 1 6 6 1 0 1 6 7 1 0 1 6 8 1 0 1 6 9 1 0 1 7 1 1 0 1 7 2 1 0 1 7 3 1 0 1 7 4 1 0 1 7 5 1 0 1 7 6 1 0 1 7 7 1 0 1 7 8 1 0 1 8 0 1 0 1 8 1 1 0 1 8 2 1 0 1 8 3 1 0 1 8 4 1 0 1 8 5 1 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1 0 2 13 0 1 0 2 13 1 1 0 2 14 0 1 0 3 2 3 1 0 3 2 4 1 0 3 2 5 1 0 3 2 6 1 0 3 3 2 1 0 3 3 3 1 0 3 3 4 1 0 3 3 5 1 0 3 3 6 1 0 3 4 2 1 0 3 4 3 1 0 3 4 4 1 0 3 4 5 1 0 3 4 6 1 0 3 5 1 1 0 3 5 2 1 0 3 5 3 1 0 3 5 4 1 0 3 5 5 1 0 3 5 6 1 0 3 6 1 1 0 3 6 2 1 0 3 6 3 1 0 3 6 4 1 0 3 6 5 1 0 3 6 6 1 0 3 7 0 1 0 3 7 1 1 0 3 7 2 1 0 3 7 3 1 0 3 7 4 1 0 3 7 5 1 0 3 7 6 1 0 3 8 0 1 0 3 8 1 1 0 3 8 2 1 0 3 8 3 1 0 3 8 4 1 0 3 8 5 1 0 3 8 6 1 0 3 9 0 1 0 3 9 1 1 0 3 9 2 1 0 3 9 3 1 0 3 9 4 1 0 3 9 5 1 0 3 10 0 1 0 3 10 1 1 0 3 10 2 1 0 3 10 3 1 0 3 10 4 1 0 3 11 0 1 0 3 11 1 1 0 3 11 2 1 0 3 11 3 1 0 3 12 0 1 0 3 12 1 1 0 3 12 2 1 0 3 13 0 1 0 3 13 1 1 0 3 14 0 1 0 4 2 3 1 0 4 2 4 1 0 4 3 2 1 0 4 3 3 1 0 4 3 4 1 0 4 4 2 1 0 4 4 3 1 0 4 4 4 1 0 4 5 1 1 0 4 5 2 1 0 4 5 3 1 0 4 5 4 1 0 4 6 1 1 0 4 6 2 1 0 4 6 3 1 0 4 6 4 1 0 4 7 1 1 0 4 7 2 1 0 4 7 3 1 0 4 7 4 1 0 4 8 0 1 0 4 8 1 1 0 4 8 2 1 0 4 8 3 1 0 4 8 4 1 0 4 9 0 1 0 4 9 1 1 0 4 9 2 1 0 4 9 3 1 0 4 9 4 1 0 4 10 0 1 0 4 10 1 1 0 4 10 2 1 0 4 10 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2 1 15 0 3 3 1 15 1 0 0 1 15 1 0 1 1 15 1 0 2 1 15 1 0 3 1 15 1 0 4 1 15 1 0 5 1 15 1 0 6 1 15 1 1 0 1 15 1 1 1 1 15 1 1 2 1 15 1 1 3 1 15 1 1 4 1 15 1 1 5 1 15 1 2 0 1 15 1 2 1 1 15 1 2 2 1 15 1 2 3 1 15 1 3 0 1 15 1 3 1 1 15 2 0 0 1 15 2 0 1 1 15 2 0 2 1 15 2 0 3 1 15 2 0 4 1 15 2 0 5 1 15 2 1 0 1 15 2 1 1 1 15 2 1 2 1 15 2 1 3 1 15 2 2 0 1 15 2 2 1 1 15 3 0 0 1 15 3 0 1 1 15 3 0 2 1 15 3 0 3 1 15 3 1 0 1 15 3 1 1 1 15 4 0 0 1 15 4 0 1 1 16 0 0 0 1 16 0 0 1 1 16 0 0 2 1 16 0 0 3 1 16 0 0 4 1 16 0 0 5 1 16 0 0 6 1 16 0 1 0 1 16 0 1 1 1 16 0 1 2 1 16 0 1 3 1 16 0 1 4 1 16 0 1 5 1 16 0 2 0 1 16 0 2 1 1 16 0 2 2 1 16 0 2 3 1 16 1 0 0 1 16 1 0 1 1 16 1 0 2 1 16 1 0 3 1 16 1 0 4 1 16 1 0 5 1 16 1 1 0 1 16 1 1 1 1 16 1 1 2 1 16 1 1 3 1 16 1 2 0 1 16 1 2 1 1 16 2 0 0 1 16 2 0 1 1 16 2 0 2 1 16 2 0 3 1 16 2 1 0 1 16 2 1 1 1 16 3 0 0 1 16 3 0 1 1 17 0 0 0 1 17 0 0 1 1 17 0 0 2 1 17 0 0 3 1 17 0 0 4 1 17 0 0 5 1 17 0 1 0 1 17 0 1 1 1 17 0 1 2 1 17 0 1 3 1 17 1 0 0 1 17 1 0 1 1 17 1 0 2 1 17 1 0 3 1 17 1 1 0 1 17 1 1 1 1 17 2 0 0 1 17 2 0 1 1 18 0 0 0 1 18 0 0 1 1 18 0 0 2 1 18 0 0 3 1 18 1 0 0 1 18 1 0 1 1 0 further Hilbert basis elements of higher degree: 83 extreme rays: 0 0 2 9 1 0 0 2 12 1 0 0 3 12 1 0 0 5 3 1 0 0 6 2 1 0 0 10 0 1 0 0 15 0 1 0 1 2 6 1 0 1 3 4 1 0 1 5 10 1 0 1 6 1 1 0 1 8 0 1 0 1 15 0 1 0 2 2 4 1 0 2 5 1 1 0 2 7 0 1 0 3 2 3 1 0 3 3 2 1 0 3 7 0 1 0 3 8 6 1 0 3 14 0 1 0 4 2 3 1 0 4 2 4 1 0 4 3 2 1 0 4 5 1 1 0 4 8 0 1 0 4 9 4 1 0 4 13 0 1 1 0 1 12 1 1 0 3 12 1 1 0 15 0 1 1 4 9 4 1 1 4 13 0 1 2 0 0 9 1 2 0 0 11 1 2 1 0 6 1 2 1 0 10 1 2 2 0 4 1 2 3 0 3 1 2 4 0 3 1 2 4 0 4 1 3 0 0 12 1 3 1 0 4 1 3 3 0 2 1 3 4 0 2 1 3 4 12 0 1 5 0 0 3 1 5 0 13 0 1 5 2 0 1 1 5 4 0 1 1 5 4 10 1 1 6 0 0 2 1 6 1 0 1 1 6 1 12 0 1 7 0 0 12 1 7 2 0 0 1 7 3 0 0 1 7 4 6 4 1 7 4 7 3 1 8 1 0 0 1 8 1 10 1 1 8 4 0 0 1 10 0 0 0 1 10 1 0 10 1 10 3 3 6 1 10 3 4 5 1 11 0 7 3 1 11 2 1 8 1 12 1 0 9 1 12 2 0 8 1 13 0 0 9 1 13 0 4 5 1 13 3 0 6 1 13 4 0 4 1 14 3 0 5 1 14 4 0 3 1 15 4 0 0 1 15 4 0 1 1 17 0 0 5 1 18 0 0 0 1 18 0 0 3 1 18 1 0 0 1 18 1 0 1 1 25 support hyperplanes: -2 -2 -2 -1 39 -1 -2 -1 -2 32 -1 -2 -1 -1 25 -1 -1 -2 -2 31 -1 -1 -1 -1 22 -1 -1 -1 0 19 -1 0 -1 0 18 0 -2 0 -1 12 0 -1 -1 -1 17 0 -1 0 0 4 0 0 -1 -1 15 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 -1 1 3 -4 1 -1 2 -1 9 1 0 0 0 0 1 0 1 0 -2 1 0 1 1 -5 1 0 1 2 -7 1 1 1 1 -8 1 1 1 2 -9 1 2 1 2 -10 2 2 2 1 -12 2 3 2 1 -13