Clear();
Print ("Beginning demo program: test_2_2.txt\n\n");
Print ("This demonstrates the use of the following procedures:\n");
Print ("   ImagesOfFixedSize( order, domain, im_order, range, printflag )\n\n");
Sleep(5);


# Here we attempt to test the ImagesOfFixedSize function.

# Let's first test all of the groups of order 8 that have
# C4 images... we should really know this already, so it's a
# good beginning point (C8, C4xC2).  

# These should be displayed as [1, 2], the groups:
# (8, 1) -- C8,
# (8, 2) -- C4xC2

# Remember that though D4 and Q4 have subgroups that are 
# isomorphic to C4, there exist no homomorphisms from D4 or Q4
# to C4.

solution := ImagesOfFixedSize(8, [], 4, [1], 0);

Print ("   Let's first test all of the groups of order 8 that have\n");
Print ("C4 images... we should really know this already, so it's a\n");
Print ("good beginning point:  C8 and C4xC2.\n");
Print ("   solution := ImagesOfFixedSize(8, [], 4, [1], 0);\n\n");
PrintArray (solution);
Print ("\n\n");
Sleep(8);

Print ("This means that SmallGroup(8,1) and SmallGroup(8,2) have\n");
Print ("such an image.\n\n");
Print ("   Remember that though D4 and Q4 have subgroups that are\n");
Print ("isomorphic to C4, there exist no homomorphisms from D4 or\n");
Print ("Q4 to C4.\n\n\n");
Sleep(8);


# Now let's try a few more:

Print ("Now let's try a few more:\n");

solution := ImagesOfFixedSize(16, [], 8, [1], 0);
Print ("Groups of order 16 with images of C8:\n");
Print ("   solution := ImagesOfFixedSize(16, [], 8, [1], 0);\n");
Print (solution, "\n\n");
Sleep(8);

solution := ImagesOfFixedSize(8, [], 4, [], 0);
Print ("Groups of order 8 with any image of size 4:\n");
Print ("   solution := ImagesOfFixedSize(8, [], 4, [], 0);\n");
Print (solution, "\n\n");
Sleep(8);

solution := ImagesOfFixedSize(8, [], 2, [], 0);
Print ("Groups of order 8 with any image of size 2:\n");
Print ("   solution := ImagesOfFixedSize(8, [], 2, [], 0);\n");
Print (solution, "\n\n");
Sleep(8);

solution := ImagesOfFixedSize(64, [], 16, [1], 0);
Print ("Groups of order 64 with images of C16:\n");
Print ("   solution := ImagesOfFixedSize(64, [], 16, [1], 0);\n");
Print (solution, "\n\n");
Print ("As you can see... this sometimes takes a while.\n\n");