"Source: Text/LieTheory/RootDtm.text";
"Line: 466";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/RootDtm.text, line: 466
// Example: H107E1 ()
print "Example: H107E1";
ei := GetEchoInput();
SetEchoInput(true);
RootDatum("E6");
RootDatum("E6" : Isogeny := "SC");
R := RootDatum("A5 B3" : Isogeny := [* 3, "Ad" *]);
R : Maximal;
RootDatum("E6 A3 B4" : Isogeny := "SC");
R := RootDatum("B3 T2 A2" : Isogeny := [* "SC", 0, "Ad" *]);
R;
Dimension(R), Rank(R);
SimpleCoroots(R);
G< a, b > := FundamentalGroup("D6");
G;
_, inj1 := sub< G | a >;
R1 := RootDatum("D6" : Isogeny := inj1);
_, inj2 := sub< G | b >;
R2 := RootDatum("D6" : Isogeny := inj2);
_, inj3 := sub< G | a*b >;
R3 := RootDatum("D6" : Isogeny := inj3);
SetEchoInput(ei);
