Clear();
Print ("Beginning demo program: test_2_3.txt\n\n");
Print ("This demonstrates the use of the following procedures:\n");
Print ("   RightTransversalList( group, elements, normal ) \n");
Print ("   TransversalListSpecific( group, elements, normal ) \n");
Print ("   Expand( TL, d )  \n");
Print ("   InverseExpand( TL, d )  \n\n");
Sleep(5);


# This test program tests out the functionality of the
# RightTransversalList group of functions.

# Let's begin with D4, and a normal subgroup

group    := SmallGroup(8,3);
elements := Elements(group);
normal   := NormalSubgroups( group )[2];
TL       := RightTransversalList(group, elements, normal);

Print ("Let's begin with D4 and a normal subgroup:\n");
Print ("   group    := SmallGroup(8,3);;\n");
Print ("   elements := Elements(group);;\n");
Print ("   normal   := NormalSubgroups( group )[2];;\n");
Print ("   TL       := RightTransversalList(group, elements, normal);\n\n");
PrintArray (TL);
Print ("\n\n");
Sleep(10);


TL := TransversalListSpecific( group, elements, normal );

Print ("Using the same parameters, except the 'Specific' function:\n");
Print ("   TL := TransversalListSpecific( group, elements, normal );\n\n");
PrintArray (TL);
Print ("\n\n");
Sleep(5);


# Now let's try Expand and InverseExpand...

TL     := [ [1,2], [3,4], [5,6] ]; 
d      := [ 1,3,5 ];
output := Expand(TL, d);
d2     := InverseExpand(TL, output);

Print ("Now let's try the Expand and InverseExpand procedures:\n");
Print ("   TL     := [ [1,2], [3,4], [5,6] ];;\n");
Print ("   d      := [ 1, 3, 5 ];; \n");
Print ("   output := Expand(TL, d);\n\n");
Print (output, "\n\n");
Sleep(5);

Print ("   d2 := InvserseExpand(TL, output);\n\n");
Print (d2, "\n\n");