Clear();
Print ("Beginning demo program: test_1_2.txt\n\n");
Print ("This demonstrates the use of the following procedures:\n");
Print ("   PointsToInterval( design )\n");
Print ("   IncidenceMatrix( design )\n");
Print ("   CharacteristicFunction( group, normal )\n\n");
Sleep(5);


# first we need to create a design... let's do a (7, 3, 1)
# on (a, b, c, d, e, f, g)

design    := [];
design[1] := ["a", "b", "d"];
design[2] := ["b", "c", "e"];
design[3] := ["c", "d", "f"];
design[4] := ["d", "e", "g"];
design[5] := ["e", "f", "a"];
design[6] := ["f", "g", "b"];
design[7] := ["g", "a", "c"];

Print ("Let's create a (7,3,1)-design on the points (a,b,c,d,e,f,g).\n");
Print ("   design :=\n");
PrintArray (design);
Print ("\n\n");
Sleep(8);


# now we try PointsToInterval...

intDesign := PointsToInterval(design);

Print ("Now we use the PointsToInterval function on our design.\n");
Print ("   intDesign := PointsToInterval( design );\n");
PrintArray (intDesign);
Print ("\n\n");
Sleep(8);


# Let's create the incidence matrix of this design...

mat := IncidenceMatrix( design );

Print ("Next, let's create the incidence matrix of this design.\n");
Print ("   mat := IncidenceMatrix( design );\n");
PrintArray (mat);
Print ("\n\n");
Sleep(8);


# Going to the dihedral group, let's create an
# incidence list for a normal subgroup generated by R180

group     := Group( (1,2,3,4), (1,3) );
elements  := Elements(group);
normal    := [];
normal[1] := elements[1];
normal[2] := elements[6];
incList   := CharacteristicFunction( group, normal );

Print ("Looking at the dihedral group on 8 elements, let's create\n");
Print ("an incidence list for the normal subgroup generated by R180.\n");
Print ("   group    := Group( (1,2,3,4), (1,3) );\n");
Print ("   elements := Elements(group);\n");
Print ("   normal   := [ elements[1], elements[6] ];\n\n");
Print ("   incList  := CharacteristicFunction( group, normal );\n");
PrintArray (incList);
Print ("\n\n");