"Source: Text/Algebra/AlgLie.text";
"Line: 2382";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgLie.text, line: 2382
// Example: H110E26 ()
print "Example: H110E26";
ei := GetEchoInput();
SetEchoInput(true);
R := RootDatum("G2");
L := LieAlgebra(R, GF(3));
pos,neg,cart := StandardBasis(L);
shrt := [ i : i in [1..NumPosRoots(R)] | IsShortRoot(R, i) ];
shrt;
I := ideal<L | pos[shrt]>;
assert Dimension(I) eq 7;
_, str1 := ReductiveType(I); str1;
LI, proj, pb, pbsub := QuotientWithPullback(L, I);
_, str2 := ReductiveType(LI); str2;
proj(pos[1]);
y := LI![0,1,1,1,1,0,1];
y;
x, V := pb(y);
x;
#V;
assert $1 eq 2187;
assert #V eq #I;
{* proj(x + v) eq y : v in V *};
assert forall{v : v in V | proj(x+v) eq y };
M := pbsub(y);
M, M meet I;
assert Dimension(M) eq 8;
assert Dimension(M meet I) eq 7;
_,str3 := ReductiveType(M);    
str3;
SetEchoInput(ei);
