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gap> L:=SimpleLieAlgebra("D",8,Rationals);
<Lie algebra of dimension 120 over Rationals>
gap> rs:=RootSystem(L);
<root system of rank 8>
gap> w:=WeylGroup(rs);
<matrix group with 8 generators>
gap> gens:=GeneratorsOfGroup(w);;
gap> pabs:=List(gens, g -> Group(Difference(gens, [g])));
[ <matrix group with 7 generators>, <matrix group with 7 generators>,
<matrix group with 7 generators>, <matrix group with 7 generators>,
<matrix group with 7 generators>, <matrix group with 7 generators>,
<matrix group with 7 generators>, <matrix group with 7 generators> ]
gap> g:=Group(gens);
<matrix group with 8 generators>
gap> cg:=CosetGeometry(g,pabs);;
gap> cham:=RandomChamber(cg);; # Time of last command: 23945 ms
gap> FlagToStandardFlag(cg,cham); # Time of last command: 1720 ms
[ [ 0, 0, 0, 0, 1, -1, 0, 0 ], [ 0, 0, 0, 1, 0, -1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, -1, -1 ], [ 1, -1, 0, 1, 0, 0, -1, -1 ],
[ 0, -1, 0, 1, 0, 0, -1, -1 ], [ 0, -1, 0, 1, 0, 0, 0, -2 ],
[ 0, -1, 1, 0, 0, 0, 0, -1 ], [ 0, -1, 0, 1, 0, 0, 0, -1 ] ]
gap> cham^last = StandardFlagOfCosetGeometry(cg); # Time of last command:1005 ms
true
[ Dauer der Verarbeitung: 0.3 Sekunden
(vorverarbeitet)
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