"Source: Text/Group/GrpMatFF.text";
"Line: 1659";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatFF.text, line: 1659
// Example: H67E10 ()
print "Example: H67E10";
ei := GetEchoInput();
SetEchoInput(true);
G := Sp (6, 5^3);
G := ExteriorSquare (G);
f, m1, m2, m3, m4, E, W := ClassicalConstructiveRecognition( G, "Sp", 6, 5^3 );
Q, R := ClassicalStandardPresentation ("Sp", 6, 5^3);
#{Evaluate( r, E ) : r in R} eq 1;
x := Random (G);
y := m1 (x);
y;
w := m3 (x);
"Length of SLP is ", #w;
Evaluate (w, [G.i: i in [1..Ngens (G)]]) eq x;
E eq Evaluate( W, [G.i : i in [ 1 .. Ngens( G )]]);                   
G := PSL( 6, 4 );
f, m1, m2, m3, m4, E, W := ClassicalConstructiveRecognition( G, "SL", 6, 4 );
E eq Evaluate( W, [G.i : i in [ 1 .. Ngens( G )]]);                   
Q, rels := ClassicalStandardPresentation( "SL" , 6, 4);
#{Evaluate( r, E ) : r in rels} eq 1;
g := Random( G );
s := m1( g );
s in SL(6,4);
m2( s ) eq g;
h := Random( SL( 6, 4 ) ); 
g := m2( h );
g in G;
m1( g ) eq h;
IsScalar( m1( g ) * h^-1 );
w := m3( g );
w in WordGroup( G );
m4( w ) eq g;
g eq Evaluate( w, [G.i : i in [ 1 .. Ngens( G )]]);
SetEchoInput(ei);
