Clear();
Print ("Beginning demo program: test_1_1.txt\n");
Print ("This demonstrates the use of the following procedures:\n");
Print ("   RightTranslates( group, subset )\n");
Print ("   ConjugateTranslates( group, subset )\n");
Print ("   GroupMatrixRt( rep, group, elements )\n\n");
Sleep(5);

# This first bit tests out the RightTranslates function
# on the dihedral group of 8 elements.

group    := Group( (1,2,3,4), (1,3) );
elements := Elements(group);

Print ("Let's look at the symmetric group generated by (1,2,3,4)\n");
Print ("and (1,3).  This subgroup of S4 is isomorphic to D4, or the\n");
Print ("dihedral group of eight elements.\n\n");
Print ("   group := Group( (1,2,3,4), (1,3) );\n");
Print (group, "\n\n");
Print ("   elements := Elements(group);\n");
Print (elements, "\n\n");
Sleep(8);


subset    := [];
subset[1] := elements[1];
subset[2] := elements[4];
subset[3] := elements[5];

Print ("Now we need to create a subset of the group.\nsubset := ");
Print (subset, "\n\n");
Sleep(5);


rTrans := RightTranslates(group, subset);

Print ("Now here are the right translates.\n");
Print ("   rTrans := RightTranslates( group, subset );\n");
Print (rTrans, "\n\n");
Sleep(8);


# If we use ConjugateTranslates, but let the elements form a
# normal subroup... .

normal    := [];
normal[1] := elements[1];
normal[2] := elements[6];

Print ("Let's try creating a normal subgroup.\nnormal := ");
Print (normal, "\n\n");
Sleep(5);


cTrans := ConjugateTranslates(group, normal);

Print ("And then look at all of the conjugates.\n");
Print ("   cTrans := ConjugateTranslates( group, normal );\n");
Print (cTrans, "\n\n");
Sleep(5);


# Now let's look at the GroupMatrixRt of D8 with representatives:
# e D H R90 D' R180 R270 V

rep := [ " e  ", " D  ", " H  ", "R90 ", " D' ", "R180", "R270", " V  " ];
mat := GroupMatrixRt( rep, group, elements );

Print ("Now let's look at the GroupMatrixRt of D8 with representatives:\n");
Print ("   rep := [ \" e  \", \" D  \", \" H  \", \"R90 \", \" D' \", \"R180\", \"R270\", \" V  \" ];\n");
Print ("   mat := GroupMatrixRt( rep, group, elements );\n");
PrintArray(mat);
Print ("\n");
Sleep(8);


# And let's try an improper call of the previous function...

rep := [ " e  ", " D  ", " H  " ];

Print ("This is what happens if you do no have enough representatives\n");
Print ("for your group.\n\n");
Print ("   rep := [ \" e  \", \" D  \", \" H  \" ];\n");
mat := GroupMatrixRt( rep, group, elements );
Print ("\n\n");