"Source: Text/Algebra/AlgQEA.text";
"Line: 1093";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgQEA.text, line: 1093
// Example: H112E9 ()
print "Example: H112E9";
ei := GetEchoInput();
SetEchoInput(true);
R:= RootDatum("G2");
U:= QuantizedUEA(R);
b:= BarAutomorphism(U);
b(U.3);
U:= QuantizedUEA(RootDatum("C3"));
t:= AntiAutomorphismTau(U);
T:= AutomorphismTalpha(U, 3);
Ti:= Inverse(T);
f:= t*T*t;         
&and[ Ti(U.i) eq f(U.i) : i in [1..21] ];
assert $1;
U:= QuantizedUEA(RootDatum("D4"));
p:= SymmetricGroup(4)!(1,3,4);    
d:= DiagramAutomorphism(U, p);
e1:= CanonicalElements(U, [1,3,2,2]);
e2:= CanonicalElements(U, [2,3,1,2]);
&and[ d(x) in e2 : x in e1 ];
assert $1;
SetEchoInput(ei);
