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.
| Download
GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 41838420 Hilbert basis elements 8 Hilbert basis elements of degree 1 20 extreme rays 16 support hyperplanes embedding dimension = 16 rank = 8 external index = 1 size of triangulation = 48 resulting sum of |det|s = 48 grading: 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 degrees of extreme rays: 1: 8 2: 12 multiplicity = 21/2 Hilbert series: 1 4 18 36 50 36 18 4 1 denominator with 8 factors: 1: 4 2: 4 degree of Hilbert Series as rational function = -4 The numerator of the Hilbert Series is symmetric. Hilbert series with cyclotomic denominator: 1 4 18 36 50 36 18 4 1 cyclotomic denominator: 1: 8 2: 4 Hilbert quasi-polynomial of period 2: 0: 480 1136 1216 784 330 89 14 1 1: 390 1051 1186 779 330 89 14 1 with common denominator = 480 rank of class group = 8 class group is free *********************************************************************** 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 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