Clear();
Print ("Beginning demo program: test_2_1.txt\n\n");
Print ("This demonstrates the use of the following procedures:\n");
Print ("   ConvolutionTable_f( group, elements, func )\n");
Print ("   Convolution_AsList( CL, list1, list2 )\n");
Print ("   Convolution_AsMultiset( CL, multset1, multset2 )\n\n");
Sleep(5);

# This demo file tests out the convolution capabilities of
# DifSets.txt.  Let's again look at the dihedral group.

group    := SmallGroup(8,3);
elements := Elements(group);
func     := x->x^-1;
CL       := ConvolutionTable_f(group, elements, func);

Print ("   Let's construct the dihedral group of order 8 and look\n");
Print ("at the convolution table generated by the inverse function:\n");
Print ("   group    := SmallGroup(8,3);;\n");
Print ("   elements := Elements(group);;\n");
Print ("   func     := x->x^-1;;\n");
Print ("   CL       := ConvolutionTable_f(group, elements, func);\n\n");
PrintArray (CL);
Print ("\n\n");
Sleep(8);


# So if we look at < R90 >,
# and convolve it with a subgroup of order 2 :

sub_R90 := NormalSubgroups(group)[3];
sub_O2  := NormalSubgroups(group)[2];
list1   := CharacteristicFunction(group, Elements(sub_R90) );
list2   := CharacteristicFunction(group, Elements(sub_O2) );
prod    := Convolution_AsList( CL, list1, list2 );

Print ("   Let's construct < R90 > and convolve it with a subgroup\n");
Print ("of order 2.\n");
Print ("   sub_R90 := NormalSubgroups(group)[3];;\n");
Print ("   sub_O2  := NormalSubgroups(group)[2];;\n");
Print ("   list1   := CharacteristicFunction(group, Elements(sub_R90) );;\n");
Print ("   list2   := CharacteristicFunction(group, Elements(sub_O2) );;\n");
Print ("   prod    := Convolution_AsList( CL, list1, list2 );\n\n");
PrintArray (prod);
Print ("\n\n");
Sleep(8);

# And now the same thing, but with multisets...

mult1 := ListToMultiset(list1);
mult2 := ListToMultiset(list2);
prod  := Convolution_AsMultiset( CL, mult1, mult2 );

Print ("   And now let's do the same thing with multisets.\n");
Print ("   mult1 := ListToMultiset(list1);;\n");
Print ("   mult2 := ListToMultiset(list2);;\n");
Print ("   prod  := Convolution_AsMultiset( CL, mult1, mult2 );\n\n");
PrintArray (prod);
Print ("\n\n");