Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
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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: 418346#############################################################################
##
#W In this file we prepare functions to loop over the 2,3 or 4 dimensional
#W crystallographic groups as matrix groups or pcp groups.
##
cryst4params:=
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[ 25, 6, 1, 5 ], [ 25, 6, 1, 6 ], [ 25, 6, 1, 7 ], [ 25, 6, 1, 8 ],
[ 25, 6, 2, 1 ], [ 25, 6, 2, 2 ], [ 25, 6, 2, 3 ], [ 25, 6, 2, 4 ],
[ 25, 6, 3, 1 ], [ 25, 6, 3, 2 ], [ 25, 6, 4, 1 ], [ 25, 6, 4, 2 ],
[ 25, 6, 4, 3 ], [ 25, 6, 4, 4 ], [ 25, 6, 4, 5 ], [ 25, 6, 4, 6 ],
[ 25, 6, 4, 7 ], [ 25, 6, 4, 8 ], [ 25, 6, 5, 1 ], [ 25, 6, 5, 2 ],
[ 25, 7, 1, 1 ], [ 25, 7, 1, 2 ], [ 25, 7, 1, 3 ], [ 25, 7, 1, 4 ],
[ 25, 7, 1, 5 ], [ 25, 7, 1, 6 ], [ 25, 7, 1, 7 ], [ 25, 7, 1, 8 ],
[ 25, 7, 1, 9 ], [ 25, 7, 1, 10 ], [ 25, 7, 1, 11 ], [ 25, 7, 1, 12 ],
[ 25, 7, 1, 13 ], [ 25, 7, 1, 14 ], [ 25, 7, 1, 15 ], [ 25, 7, 1, 16 ],
[ 25, 7, 2, 1 ], [ 25, 7, 2, 2 ], [ 25, 7, 2, 3 ], [ 25, 7, 2, 4 ],
[ 25, 7, 2, 5 ], [ 25, 7, 2, 6 ], [ 25, 7, 2, 7 ], [ 25, 7, 2, 8 ],
[ 25, 7, 3, 1 ], [ 25, 7, 3, 2 ], [ 25, 7, 3, 3 ], [ 25, 7, 3, 4 ],
[ 25, 7, 4, 1 ], [ 25, 7, 4, 2 ], [ 25, 7, 4, 3 ], [ 25, 7, 4, 4 ],
[ 25, 7, 4, 5 ], [ 25, 7, 4, 6 ], [ 25, 7, 4, 7 ], [ 25, 7, 4, 8 ],
[ 25, 7, 4, 9 ], [ 25, 7, 4, 10 ], [ 25, 7, 4, 11 ], [ 25, 7, 4, 12 ],
[ 25, 7, 4, 13 ], [ 25, 7, 4, 14 ], [ 25, 7, 4, 15 ], [ 25, 7, 4, 16 ],
[ 25, 7, 5, 1 ], [ 25, 7, 5, 2 ], [ 25, 7, 5, 3 ], [ 25, 7, 5, 4 ],
[ 25, 8, 1, 1 ], [ 25, 8, 1, 2 ], [ 25, 8, 1, 3 ], [ 25, 8, 1, 4 ],
[ 25, 8, 1, 5 ], [ 25, 8, 1, 6 ], [ 25, 8, 1, 7 ], [ 25, 8, 1, 8 ],
[ 25, 8, 1, 9 ], [ 25, 8, 1, 10 ], [ 25, 8, 1, 11 ], [ 25, 8, 1, 12 ],
[ 25, 8, 1, 13 ], [ 25, 8, 1, 14 ], [ 25, 8, 1, 15 ], [ 25, 8, 1, 16 ],
[ 25, 8, 2, 1 ], [ 25, 8, 2, 2 ], [ 25, 8, 2, 3 ], [ 25, 8, 2, 4 ],
[ 25, 8, 2, 5 ], [ 25, 8, 2, 6 ], [ 25, 8, 2, 7 ], [ 25, 8, 2, 8 ],
[ 25, 8, 3, 1 ], [ 25, 8, 3, 2 ], [ 25, 8, 3, 3 ], [ 25, 8, 3, 4 ],
[ 25, 8, 4, 1 ], [ 25, 8, 4, 2 ], [ 25, 8, 4, 3 ], [ 25, 8, 4, 4 ],
[ 25, 8, 4, 5 ], [ 25, 8, 4, 6 ], [ 25, 8, 4, 7 ], [ 25, 8, 4, 8 ],
[ 25, 8, 4, 9 ], [ 25, 8, 4, 10 ], [ 25, 8, 4, 11 ], [ 25, 8, 4, 12 ],
[ 25, 8, 4, 13 ], [ 25, 8, 4, 14 ], [ 25, 8, 4, 15 ], [ 25, 8, 4, 16 ],
[ 25, 8, 5, 1 ], [ 25, 8, 5, 2 ], [ 25, 8, 5, 3 ], [ 25, 8, 5, 4 ],
[ 25, 9, 1, 1 ], [ 25, 9, 1, 2 ], [ 25, 9, 1, 3 ], [ 25, 9, 1, 4 ],
[ 25, 9, 1, 5 ], [ 25, 9, 1, 6 ], [ 25, 9, 1, 7 ], [ 25, 9, 1, 8 ],
[ 25, 9, 2, 1 ], [ 25, 9, 2, 2 ], [ 25, 9, 2, 3 ], [ 25, 9, 2, 4 ],
[ 25, 9, 3, 1 ], [ 25, 9, 3, 2 ], [ 25, 9, 4, 1 ], [ 25, 9, 4, 2 ],
[ 25, 9, 4, 3 ], [ 25, 9, 4, 4 ], [ 25, 9, 4, 5 ], [ 25, 9, 4, 6 ],
[ 25, 9, 4, 7 ], [ 25, 9, 4, 8 ], [ 25, 9, 5, 1 ], [ 25, 9, 5, 2 ],
[ 25, 10, 1, 1 ], [ 25, 10, 1, 2 ], [ 25, 10, 1, 3 ], [ 25, 10, 1, 4 ],
[ 25, 10, 1, 5 ], [ 25, 10, 1, 6 ], [ 25, 10, 1, 7 ], [ 25, 10, 1, 8 ],
[ 25, 10, 1, 9 ], [ 25, 10, 1, 10 ], [ 25, 10, 1, 11 ], [ 25, 10, 1, 12 ],
[ 25, 10, 2, 1 ], [ 25, 10, 2, 2 ], [ 25, 10, 2, 3 ], [ 25, 10, 2, 4 ],
[ 25, 10, 3, 1 ], [ 25, 10, 3, 2 ], [ 25, 10, 3, 3 ], [ 25, 10, 4, 1 ],
[ 25, 10, 4, 2 ], [ 25, 10, 4, 3 ], [ 25, 10, 4, 4 ], [ 25, 10, 4, 5 ],
[ 25, 10, 4, 6 ], [ 25, 10, 4, 7 ], [ 25, 10, 4, 8 ], [ 25, 10, 5, 1 ],
[ 25, 10, 5, 2 ], [ 25, 11, 1, 1 ], [ 25, 11, 1, 2 ], [ 25, 11, 1, 3 ],
[ 25, 11, 1, 4 ], [ 25, 11, 1, 5 ], [ 25, 11, 1, 6 ], [ 25, 11, 1, 7 ],
[ 25, 11, 1, 8 ], [ 25, 11, 1, 9 ], [ 25, 11, 1, 10 ], [ 25, 11, 1, 11 ],
[ 25, 11, 1, 12 ], [ 25, 11, 1, 13 ], [ 25, 11, 1, 14 ], [ 25, 11, 1, 15 ],
[ 25, 11, 1, 16 ], [ 25, 11, 1, 17 ], [ 25, 11, 1, 18 ], [ 25, 11, 1, 19 ],
[ 25, 11, 1, 20 ], [ 25, 11, 1, 21 ], [ 25, 11, 1, 22 ], [ 25, 11, 1, 23 ],
[ 25, 11, 1, 24 ], [ 25, 11, 1, 25 ], [ 25, 11, 1, 26 ], [ 25, 11, 1, 27 ],
[ 25, 11, 1, 28 ], [ 25, 11, 1, 29 ], [ 25, 11, 1, 30 ], [ 25, 11, 1, 31 ],
[ 25, 11, 1, 32 ], [ 25, 11, 2, 1 ], [ 25, 11, 2, 2 ], [ 25, 11, 2, 3 ],
[ 25, 11, 2, 4 ], [ 25, 11, 2, 5 ], [ 25, 11, 2, 6 ], [ 25, 11, 2, 7 ],
[ 25, 11, 2, 8 ], [ 25, 11, 3, 1 ], [ 25, 11, 3, 2 ], [ 25, 11, 3, 3 ],
[ 25, 11, 3, 4 ], [ 25, 11, 4, 1 ], [ 25, 11, 4, 2 ], [ 25, 11, 4, 3 ],
[ 25, 11, 4, 4 ], [ 25, 11, 4, 5 ], [ 25, 11, 4, 6 ], [ 25, 11, 4, 7 ],
[ 25, 11, 4, 8 ], [ 25, 11, 4, 9 ], [ 25, 11, 4, 10 ], [ 25, 11, 4, 11 ],
[ 25, 11, 4, 12 ], [ 25, 11, 4, 13 ], [ 25, 11, 4, 14 ], [ 25, 11, 4, 15 ],
[ 25, 11, 4, 16 ], [ 25, 11, 4, 17 ], [ 25, 11, 4, 18 ], [ 25, 11, 4, 19 ],
[ 25, 11, 4, 20 ], [ 25, 11, 4, 21 ], [ 25, 11, 4, 22 ], [ 25, 11, 4, 23 ],
[ 25, 11, 4, 24 ], [ 25, 11, 4, 25 ], [ 25, 11, 4, 26 ], [ 25, 11, 4, 27 ],
[ 25, 11, 4, 28 ], [ 25, 11, 4, 29 ], [ 25, 11, 4, 30 ], [ 25, 11, 4, 31 ],
[ 25, 11, 4, 32 ], [ 25, 11, 5, 1 ], [ 25, 11, 5, 2 ], [ 25, 11, 5, 3 ],
[ 25, 11, 5, 4 ], [ 26, 1, 1, 1 ], [ 26, 2, 1, 1 ], [ 26, 2, 1, 2 ],
[ 27, 1, 1, 1 ], [ 27, 2, 1, 1 ], [ 27, 3, 1, 1 ], [ 27, 3, 2, 1 ],
[ 27, 4, 1, 1 ], [ 28, 1, 1, 1 ], [ 28, 2, 1, 1 ], [ 29, 1, 1, 1 ],
[ 29, 1, 2, 1 ], [ 29, 1, 2, 2 ], [ 29, 1, 3, 1 ], [ 29, 1, 3, 2 ],
[ 29, 2, 1, 1 ], [ 29, 2, 2, 1 ], [ 29, 3, 1, 1 ], [ 29, 3, 2, 1 ],
[ 29, 3, 2, 2 ], [ 29, 3, 3, 1 ], [ 29, 3, 4, 1 ], [ 29, 3, 5, 1 ],
[ 29, 3, 5, 2 ], [ 29, 4, 1, 1 ], [ 29, 4, 1, 2 ], [ 29, 4, 2, 1 ],
[ 29, 4, 3, 1 ], [ 29, 4, 4, 1 ], [ 29, 4, 4, 2 ], [ 29, 5, 1, 1 ],
[ 29, 5, 2, 1 ], [ 29, 6, 1, 1 ], [ 29, 6, 2, 1 ], [ 29, 6, 3, 1 ],
[ 29, 7, 1, 1 ], [ 29, 7, 2, 1 ], [ 29, 7, 3, 1 ], [ 29, 7, 4, 1 ],
[ 29, 8, 1, 1 ], [ 29, 8, 2, 1 ], [ 29, 8, 2, 2 ], [ 29, 8, 3, 1 ],
[ 29, 8, 3, 2 ], [ 29, 8, 4, 1 ], [ 29, 9, 1, 1 ], [ 29, 9, 2, 1 ],
[ 29, 9, 3, 1 ], [ 30, 1, 1, 1 ], [ 30, 2, 1, 1 ], [ 30, 3, 1, 1 ],
[ 30, 4, 1, 1 ], [ 30, 4, 2, 1 ], [ 30, 5, 1, 1 ], [ 30, 6, 1, 1 ],
[ 30, 7, 1, 1 ], [ 30, 8, 1, 1 ], [ 30, 9, 1, 1 ], [ 30, 10, 1, 1 ],
[ 30, 11, 1, 1 ], [ 30, 12, 1, 1 ], [ 30, 12, 2, 1 ], [ 30, 13, 1, 1 ],
[ 31, 1, 1, 1 ], [ 31, 1, 2, 1 ], [ 31, 1, 3, 1 ], [ 31, 1, 4, 1 ],
[ 31, 2, 1, 1 ], [ 31, 2, 2, 1 ], [ 31, 3, 1, 1 ], [ 31, 3, 1, 2 ],
[ 31, 3, 2, 1 ], [ 31, 3, 2, 2 ], [ 31, 4, 1, 1 ], [ 31, 4, 2, 1 ],
[ 31, 5, 1, 1 ], [ 31, 5, 1, 2 ], [ 31, 5, 2, 1 ], [ 31, 5, 2, 2 ],
[ 31, 6, 1, 1 ], [ 31, 6, 2, 1 ], [ 31, 7, 1, 1 ], [ 31, 7, 2, 1 ],
[ 32, 1, 1, 1 ], [ 32, 1, 2, 1 ], [ 32, 1, 2, 2 ], [ 32, 2, 1, 1 ],
[ 32, 2, 1, 2 ], [ 32, 2, 2, 1 ], [ 32, 2, 2, 2 ], [ 32, 3, 1, 1 ],
[ 32, 3, 1, 2 ], [ 32, 3, 2, 1 ], [ 32, 3, 2, 2 ], [ 32, 4, 1, 1 ],
[ 32, 4, 1, 2 ], [ 32, 4, 2, 1 ], [ 32, 4, 2, 2 ], [ 32, 4, 2, 3 ],
[ 32, 4, 2, 4 ], [ 32, 4, 2, 5 ], [ 32, 4, 2, 6 ], [ 32, 5, 1, 1 ],
[ 32, 5, 2, 1 ], [ 32, 5, 3, 1 ], [ 32, 6, 1, 1 ], [ 32, 6, 1, 2 ],
[ 32, 6, 1, 3 ], [ 32, 6, 2, 1 ], [ 32, 6, 2, 2 ], [ 32, 6, 2, 3 ],
[ 32, 6, 2, 4 ], [ 32, 7, 1, 1 ], [ 32, 7, 1, 2 ], [ 32, 7, 1, 3 ],
[ 32, 7, 2, 1 ], [ 32, 7, 2, 2 ], [ 32, 7, 2, 3 ], [ 32, 7, 2, 4 ],
[ 32, 8, 1, 1 ], [ 32, 8, 1, 2 ], [ 32, 8, 2, 1 ], [ 32, 8, 2, 2 ],
[ 32, 8, 2, 3 ], [ 32, 8, 2, 4 ], [ 32, 9, 1, 1 ], [ 32, 9, 1, 2 ],
[ 32, 9, 2, 1 ], [ 32, 9, 2, 2 ], [ 32, 9, 2, 3 ], [ 32, 9, 3, 1 ],
[ 32, 9, 3, 2 ], [ 32, 9, 3, 3 ], [ 32, 9, 4, 1 ], [ 32, 9, 4, 2 ],
[ 32, 9, 4, 3 ], [ 32, 9, 4, 4 ], [ 32, 9, 4, 5 ], [ 32, 9, 4, 6 ],
[ 32, 9, 5, 1 ], [ 32, 9, 5, 2 ], [ 32, 9, 5, 3 ], [ 32, 9, 5, 4 ],
[ 32, 9, 5, 5 ], [ 32, 9, 5, 6 ], [ 32, 10, 1, 1 ], [ 32, 10, 1, 2 ],
[ 32, 10, 2, 1 ], [ 32, 10, 2, 2 ], [ 32, 10, 2, 3 ], [ 32, 10, 2, 4 ],
[ 32, 10, 2, 5 ], [ 32, 10, 2, 6 ], [ 32, 10, 2, 7 ], [ 32, 11, 1, 1 ],
[ 32, 11, 1, 2 ], [ 32, 11, 2, 1 ], [ 32, 11, 3, 1 ], [ 32, 12, 1, 1 ],
[ 32, 12, 1, 2 ], [ 32, 12, 1, 3 ], [ 32, 12, 1, 4 ], [ 32, 12, 2, 1 ],
[ 32, 12, 2, 2 ], [ 32, 12, 2, 3 ], [ 32, 12, 2, 4 ], [ 32, 12, 2, 5 ],
[ 32, 12, 2, 6 ], [ 32, 13, 1, 1 ], [ 32, 13, 1, 2 ], [ 32, 13, 1, 3 ],
[ 32, 13, 1, 4 ], [ 32, 13, 2, 1 ], [ 32, 13, 2, 2 ], [ 32, 13, 2, 3 ],
[ 32, 13, 2, 4 ], [ 32, 13, 2, 5 ], [ 32, 13, 2, 6 ], [ 32, 13, 3, 1 ],
[ 32, 13, 3, 2 ], [ 32, 13, 3, 3 ], [ 32, 13, 3, 4 ], [ 32, 13, 3, 5 ],
[ 32, 13, 3, 6 ], [ 32, 13, 4, 1 ], [ 32, 13, 4, 2 ], [ 32, 13, 4, 3 ],
[ 32, 13, 4, 4 ], [ 32, 14, 1, 1 ], [ 32, 14, 1, 2 ], [ 32, 14, 1, 3 ],
[ 32, 14, 1, 4 ], [ 32, 14, 2, 1 ], [ 32, 14, 2, 2 ], [ 32, 14, 2, 3 ],
[ 32, 14, 2, 4 ], [ 32, 14, 3, 1 ], [ 32, 14, 3, 2 ], [ 32, 14, 3, 3 ],
[ 32, 14, 3, 4 ], [ 32, 14, 3, 5 ], [ 32, 14, 4, 1 ], [ 32, 14, 4, 2 ],
[ 32, 14, 4, 3 ], [ 32, 14, 4, 4 ], [ 32, 14, 4, 5 ], [ 32, 14, 4, 6 ],
[ 32, 14, 4, 7 ], [ 32, 14, 4, 8 ], [ 32, 14, 4, 9 ], [ 32, 14, 4, 10 ],
[ 32, 15, 1, 1 ], [ 32, 15, 1, 2 ], [ 32, 15, 1, 3 ], [ 32, 15, 1, 4 ],
[ 32, 15, 2, 1 ], [ 32, 15, 2, 2 ], [ 32, 15, 2, 3 ], [ 32, 15, 2, 4 ],
[ 32, 16, 1, 1 ], [ 32, 16, 2, 1 ], [ 32, 16, 2, 2 ], [ 32, 16, 3, 1 ],
[ 32, 17, 1, 1 ], [ 32, 17, 1, 2 ], [ 32, 17, 1, 3 ], [ 32, 17, 1, 4 ],
[ 32, 17, 1, 5 ], [ 32, 17, 1, 6 ], [ 32, 17, 1, 7 ], [ 32, 17, 1, 8 ],
[ 32, 17, 2, 1 ], [ 32, 17, 2, 2 ], [ 32, 17, 2, 3 ], [ 32, 17, 2, 4 ],
[ 32, 17, 2, 5 ], [ 32, 17, 2, 6 ], [ 32, 17, 2, 7 ], [ 32, 17, 2, 8 ],
[ 32, 18, 1, 1 ], [ 32, 18, 1, 2 ], [ 32, 18, 2, 1 ], [ 32, 18, 3, 1 ],
[ 32, 18, 3, 2 ], [ 32, 19, 1, 1 ], [ 32, 19, 1, 2 ], [ 32, 19, 2, 1 ],
[ 32, 19, 2, 2 ], [ 32, 19, 3, 1 ], [ 32, 19, 3, 2 ], [ 32, 20, 1, 1 ],
[ 32, 20, 1, 2 ], [ 32, 20, 2, 1 ], [ 32, 20, 2, 2 ], [ 32, 20, 3, 1 ],
[ 32, 21, 1, 1 ], [ 32, 21, 1, 2 ], [ 32, 21, 1, 3 ], [ 32, 21, 1, 4 ],
[ 32, 21, 2, 1 ], [ 32, 21, 2, 2 ], [ 32, 21, 3, 1 ], [ 32, 21, 3, 2 ],
[ 33, 1, 1, 1 ], [ 33, 2, 1, 1 ], [ 33, 3, 1, 1 ], [ 33, 3, 1, 2 ],
[ 33, 4, 1, 1 ], [ 33, 5, 1, 1 ], [ 33, 5, 1, 2 ], [ 33, 5, 1, 3 ],
[ 33, 6, 1, 1 ], [ 33, 6, 1, 2 ], [ 33, 7, 1, 1 ], [ 33, 8, 1, 1 ],
[ 33, 8, 1, 2 ], [ 33, 9, 1, 1 ], [ 33, 9, 1, 2 ], [ 33, 10, 1, 1 ],
[ 33, 10, 1, 2 ], [ 33, 11, 1, 1 ], [ 33, 12, 1, 1 ], [ 33, 12, 1, 2 ],
[ 33, 13, 1, 1 ], [ 33, 14, 1, 1 ], [ 33, 14, 2, 1 ], [ 33, 15, 1, 1 ],
[ 33, 16, 1, 1 ] ];
cryst3params :=
[ [ 1, 1, 1, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ],
[ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ], [ 2, 2, 1, 2 ], [ 2, 2, 2, 1 ],
[ 2, 2, 2, 2 ], [ 2, 3, 1, 1 ], [ 2, 3, 1, 2 ], [ 2, 3, 1, 3 ],
[ 2, 3, 1, 4 ], [ 2, 3, 2, 1 ], [ 2, 3, 2, 2 ], [ 3, 1, 1, 1 ],
[ 3, 1, 1, 2 ], [ 3, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 1 ],
[ 3, 1, 2, 2 ], [ 3, 1, 3, 1 ], [ 3, 1, 4, 1 ], [ 3, 1, 4, 2 ],
[ 3, 2, 1, 1 ], [ 3, 2, 1, 2 ], [ 3, 2, 1, 3 ], [ 3, 2, 1, 4 ],
[ 3, 2, 1, 5 ], [ 3, 2, 1, 6 ], [ 3, 2, 1, 7 ], [ 3, 2, 1, 8 ],
[ 3, 2, 1, 9 ], [ 3, 2, 1, 10 ], [ 3, 2, 2, 1 ], [ 3, 2, 2, 2 ],
[ 3, 2, 2, 3 ], [ 3, 2, 3, 1 ], [ 3, 2, 3, 2 ], [ 3, 2, 3, 3 ],
[ 3, 2, 3, 4 ], [ 3, 2, 4, 1 ], [ 3, 2, 4, 2 ], [ 3, 2, 5, 1 ],
[ 3, 2, 5, 2 ], [ 3, 2, 5, 3 ], [ 3, 3, 1, 1 ], [ 3, 3, 1, 2 ],
[ 3, 3, 1, 3 ], [ 3, 3, 1, 4 ], [ 3, 3, 1, 5 ], [ 3, 3, 1, 6 ],
[ 3, 3, 1, 7 ], [ 3, 3, 1, 8 ], [ 3, 3, 1, 9 ], [ 3, 3, 1, 10 ],
[ 3, 3, 1, 11 ], [ 3, 3, 1, 12 ], [ 3, 3, 1, 13 ], [ 3, 3, 1, 14 ],
[ 3, 3, 1, 15 ], [ 3, 3, 1, 16 ], [ 3, 3, 2, 1 ], [ 3, 3, 2, 2 ],
[ 3, 3, 2, 3 ], [ 3, 3, 2, 4 ], [ 3, 3, 2, 5 ], [ 3, 3, 2, 6 ],
[ 3, 3, 3, 1 ], [ 3, 3, 3, 2 ], [ 3, 3, 4, 1 ], [ 3, 3, 4, 2 ],
[ 3, 3, 4, 3 ], [ 3, 3, 4, 4 ], [ 4, 1, 1, 1 ], [ 4, 1, 1, 2 ],
[ 4, 1, 1, 3 ], [ 4, 1, 2, 1 ], [ 4, 1, 2, 2 ], [ 4, 2, 1, 1 ],
[ 4, 2, 2, 1 ], [ 4, 3, 1, 1 ], [ 4, 3, 1, 2 ], [ 4, 3, 1, 3 ],
[ 4, 3, 1, 4 ], [ 4, 3, 2, 1 ], [ 4, 3, 2, 2 ], [ 4, 4, 1, 1 ],
[ 4, 4, 1, 2 ], [ 4, 4, 1, 3 ], [ 4, 4, 1, 4 ], [ 4, 4, 1, 5 ],
[ 4, 4, 1, 6 ], [ 4, 4, 2, 1 ], [ 4, 4, 2, 2 ], [ 4, 5, 1, 1 ],
[ 4, 5, 1, 2 ], [ 4, 5, 1, 3 ], [ 4, 5, 1, 4 ], [ 4, 5, 1, 5 ],
[ 4, 5, 1, 6 ], [ 4, 5, 1, 7 ], [ 4, 5, 1, 8 ], [ 4, 5, 2, 1 ],
[ 4, 5, 2, 2 ], [ 4, 5, 2, 3 ], [ 4, 5, 2, 4 ], [ 4, 6, 1, 1 ],
[ 4, 6, 1, 2 ], [ 4, 6, 1, 3 ], [ 4, 6, 1, 4 ], [ 4, 6, 2, 1 ],
[ 4, 6, 2, 2 ], [ 4, 6, 2, 3 ], [ 4, 6, 2, 4 ], [ 4, 6, 3, 1 ],
[ 4, 6, 3, 2 ], [ 4, 6, 4, 1 ], [ 4, 6, 4, 2 ], [ 4, 7, 1, 1 ],
[ 4, 7, 1, 2 ], [ 4, 7, 1, 3 ], [ 4, 7, 1, 4 ], [ 4, 7, 1, 5 ],
[ 4, 7, 1, 6 ], [ 4, 7, 1, 7 ], [ 4, 7, 1, 8 ], [ 4, 7, 1, 9 ],
[ 4, 7, 1, 10 ], [ 4, 7, 1, 11 ], [ 4, 7, 1, 12 ], [ 4, 7, 1, 13 ],
[ 4, 7, 1, 14 ], [ 4, 7, 1, 15 ], [ 4, 7, 1, 16 ], [ 4, 7, 2, 1 ],
[ 4, 7, 2, 2 ], [ 4, 7, 2, 3 ], [ 4, 7, 2, 4 ], [ 5, 1, 1, 1 ],
[ 5, 1, 2, 1 ], [ 5, 1, 2, 2 ], [ 5, 2, 1, 1 ], [ 5, 2, 2, 1 ],
[ 5, 3, 1, 1 ], [ 5, 3, 2, 1 ], [ 5, 3, 2, 2 ], [ 5, 3, 3, 1 ],
[ 5, 3, 3, 2 ], [ 5, 4, 1, 1 ], [ 5, 4, 1, 2 ], [ 5, 4, 2, 1 ],
[ 5, 4, 2, 2 ], [ 5, 4, 3, 1 ], [ 5, 4, 3, 2 ], [ 5, 5, 1, 1 ],
[ 5, 5, 1, 2 ], [ 5, 5, 2, 1 ], [ 5, 5, 2, 2 ], [ 5, 5, 3, 1 ],
[ 5, 5, 3, 2 ], [ 6, 1, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 1, 1, 3 ],
[ 6, 1, 1, 4 ], [ 6, 2, 1, 1 ], [ 6, 3, 1, 1 ], [ 6, 3, 1, 2 ],
[ 6, 4, 1, 1 ], [ 6, 4, 1, 2 ], [ 6, 4, 1, 3 ], [ 6, 4, 1, 4 ],
[ 6, 5, 1, 1 ], [ 6, 5, 1, 2 ], [ 6, 5, 1, 3 ], [ 6, 5, 1, 4 ],
[ 6, 6, 1, 1 ], [ 6, 6, 1, 2 ], [ 6, 6, 2, 1 ], [ 6, 6, 2, 2 ],
[ 6, 7, 1, 1 ], [ 6, 7, 1, 2 ], [ 6, 7, 1, 3 ], [ 6, 7, 1, 4 ],
[ 7, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 1 ], [ 7, 1, 3, 1 ],
[ 7, 1, 3, 2 ], [ 7, 2, 1, 1 ], [ 7, 2, 1, 2 ], [ 7, 2, 1, 3 ],
[ 7, 2, 2, 1 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 1 ], [ 7, 2, 3, 2 ],
[ 7, 3, 1, 1 ], [ 7, 3, 1, 2 ], [ 7, 3, 1, 3 ], [ 7, 3, 2, 1 ],
[ 7, 3, 2, 2 ], [ 7, 3, 3, 1 ], [ 7, 3, 3, 2 ], [ 7, 4, 1, 1 ],
[ 7, 4, 1, 2 ], [ 7, 4, 2, 1 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 1 ],
[ 7, 4, 3, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 1, 2 ], [ 7, 5, 1, 3 ],
[ 7, 5, 1, 4 ], [ 7, 5, 2, 1 ], [ 7, 5, 2, 2 ], [ 7, 5, 2, 3 ],
[ 7, 5, 2, 4 ], [ 7, 5, 3, 1 ], [ 7, 5, 3, 2 ] ];
cryst2params :=
[ [ 1, 1, 1, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ],
[ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ], [ 2, 2, 1, 2 ], [ 2, 2, 1, 3 ],
[ 2, 2, 2, 1 ], [ 3, 1, 1, 1 ], [ 3, 2, 1, 1 ], [ 3, 2, 1, 2 ],
[ 4, 1, 1, 1 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 4, 3, 1, 1 ],
[ 4, 4, 1, 1 ] ];
NumberSpaceGroups := function( dim )
if dim = 4 then return 4783; fi;
if dim = 3 then return 219; fi;
if dim = 2 then return 17; fi;
end;
SpaceGroup := function( dim, nr )
local type;
if dim = 4 then
type := cryst4params[nr];
return SpaceGroupBBNWZ( 4, type[1], type[2], type[3], type[4] );
elif dim = 3 then
type := cryst3params[nr];
return SpaceGroupBBNWZ( 3, type[1], type[2], type[3], type[4] );
elif dim = 2 then
type := cryst2params[nr];
return SpaceGroupBBNWZ( 2, type[1], type[2], type[3], type[4] );
else
return fail;
fi;
end;
PointGroupByNumber := function( dim, nr )
local type;
if dim = 4 then
type := cryst4params[nr];
return MatGroupZClass( 4, type[1], type[2], type[3] );
elif dim = 3 then
type := cryst3params[nr];
return MatGroupZClass( 3, type[1], type[2], type[3] );
elif dim = 2 then
type := cryst2params[nr];
return MatGroupZClass( 2, type[1], type[2], type[3] );
fi;
end;
SpaceGroupPcpGroup := function( dim, nr )
local G, iso, H, F, n;
G := SpaceGroup( dim, nr );
iso := IsomorphismPcpGroup( G );
if IsBool( iso ) then return fail; fi;
H := Image( iso );
n := Length( Igs(H) );
F := Subgroup( H, Igs(H){[n-dim+1..n]} );
SetFittingSubgroup( H, F );
return H;
end;