"Source: Text/Algebra/AlgLie.text";
"Line: 3142";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgLie.text, line: 3142
// Example: H110E35 ()
print "Example: H110E35";
ei := GetEchoInput();
SetEchoInput(true);
R := RootDatum("E7");
L1 := LieAlgebra(R, GF(2));
p1,n1,c1 := StandardBasis(L1);
assert IsChevalleyBasis(L1, R, p1, n1, c1);
L1;
DynkinDiagram(R);      
S, proj := sub<R | [1..6]>;
S;
#proj;
assert $1 eq 72;
projpos := [i : i in proj | i le NumPosRoots(R)];
#projpos;
assert $1 eq 36;
L2 := sub<L1 | p1[projpos], n1[projpos]>;                
L2;
H2 := L2 meet SplitMaximalToralSubalgebra(L1);
H2;
p2,n2,c2 := ChevalleyBasis(L2, H2, RootDatum("E6"));
ok := IsChevalleyBasis(L2, RootDatum("E6"), p2, n2, c2);      
ok;
assert ok;
SetEchoInput(ei);
