"Source: Text/Algebra/AlgClff.text";
"Line: 683";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgClff.text, line: 683
// Example: H97E14 ()
print "Example: H97E14";
ei := GetEchoInput();
SetEchoInput(true);
q := 3;
r := 4;
K := GF(3);
Q := StandardQuadraticForm(2*r,K);
C,V,f := CliffordAlgebra(Q);
x := func< k,t |
  k eq 1 select f(t*V.(r+2))*f(V.(r+1))-One(C)
  else f(t*V.(r-k+2))*f(V.(r+k))-One(C) >;
y := func< k,t |
  k eq 1 select f(t*V.r)*f(V.(r-1))-One(C)
  else f(t*V.(r-k+1))*f(V.(r+k-1))-One(C) >;
n := func< k, t | x(k,t)*y(k,-t^-1)*x(k,t) >;
h := func< k, t | n(k,t)*n(k,-1) >;
w := n(1,1)*n(2,1)*n(3,1)*n(4,1);
S := MinimalRightIdeals(C : Limit := 1)[1];
Dimension(S);
X := sub<GL(16,K) | ActionMatrix(S,h(2,2)), ActionMatrix(S,y(1,1)*x(3,1)*w) >;
LieType(X,3);
LMGOrder(X);
assert $1 eq 19808719257600;
Z := LMGCentre(X);
#Z, IsElementaryAbelian(Z);
SS := SpinPlus(8,K);
#SS;
E, phi := EvenSubalgebra(C);
T := MinimalRightIdeals(E : Limit := 1)[1];
Dimension(T);
Y := sub<GL(8,K) | ActionMatrix(T,h(2,2)@@phi), 
                   ActionMatrix(T,(y(1,1)*x(3,1)*w)@@phi) >;
LieType(Y,3);
LMGOrder(Y);
SetEchoInput(ei);
