"Source: Text/LieTheory/RootDtm.text";
"Line: 1923";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/RootDtm.text, line: 1923
// Example: H107E19 ()
print "Example: H107E19";
ei := GetEchoInput();
SetEchoInput(true);
DynkinDiagram(RootDatum("E6"));
R := RootDatum("E6" : Twist:=2 ); R;
OrbitsOnSimples(R);
DistinguishedOrbitsOnSimples(R) eq OrbitsOnSimples(R);
assert $1;
AnisotropicSubdatum(R);
RR := RelativeRootDatum(R);RR;
_,pi := RelativeRootSpace(R);
DynkinDiagram(RR);
[ Position(Roots(RR), pi(Root(R,i)) ) : i in [1,6, 3,5, 4, 2]];
R := RootDatum("E6" : Twist := <{{2},{4}},2> ); R;
OrbitsOnSimples(R);
DistinguishedOrbitsOnSimples(R);
AnisotropicSubdatum(R);
RR := RelativeRootDatum(R);RR;
DynkinDiagram(RR);
_,pi := RelativeRootSpace(R);
[ Position(Roots(RR), pi(Root(R,i)) ) : i in [2,4]];
R := RootDatum("E6" : Twist := <{{2},{1,6}},2> ); R;
OrbitsOnSimples(R);
DistinguishedOrbitsOnSimples(R);
AnisotropicSubdatum(R);
RR := RelativeRootDatum(R);RR;
DynkinDiagram(RR);
_,pi := RelativeRootSpace(R);
[ Position(Roots(RR), pi(Root(R,i)) ) : i in [2, 1,6]];
T := RootDatum( "D4" : Twist:=<{{2}},6> );
T;
RelativeRootDatum(T);
GammaOrbitsRepresentatives(T,1);
GammaOrbitsRepresentatives(T,2);
SetEchoInput(ei);
