Clear();
Print ("Beginning demo program: test_1_3.txt\n\n");
Print ("This demonstrates the use of the following procedures:\n");
Print ("   IntegerToList( intIn, length, base )\n");
Print ("   ListToInteger( vector, length, base )\n");
Print ("   ListToMultiset( list )\n");
Print ("   MultisetToList( multiset, listlength )\n\n");
Sleep(5);


# Let's try to represent some integers as lists

int1 := IntegerToList(   21, 2, 10 );
int2 := IntegerToList(  103, 5, 10 );
int3 := IntegerToList( 1451, 2, 10 );

Print ("Let's try to represent some integers as lists in base 10.\n\n");
Print ("   int1 := IntegerToList(   21, 2, 10 )\n", int1, "\n\n");
Print ("   int2 := IntegerToList(  103, 5, 10 )\n", int2, "\n\n");
Print ("   int3 := IntegerToList( 1451, 2, 10 )\n", int3, "\n\n");
Print ("\n");
Sleep(8);


# Okay, now how about with different bases?

int1 := IntegerToList(   21,  5,  3 );
int2 := IntegerToList(  103, 10,  2 );
int3 := IntegerToList( 1451,  4, 16 );

Print ("Okay, same trick with different bases.\n\n");
Print ("   int1 := IntegerToList(   21,  5,  3 )\n", int1, "\n\n");
Print ("   int2 := IntegerToList(  103, 10,  2 )\n", int2, "\n\n");
Print ("   int3 := IntegerToList( 1451,  4, 16 )\n", int3, "\n\n");
Print ("\n");
Sleep(8);


# Let's go backward...

list1 := [ 0, 0, 0, 1, 1, 0, 0, 1, 1, 1 ];
list2 := [ 0, 5, 10, 12 ];

Print ("Let's go backward...\nStarting with:\n\nlist1 := ");
PrintArray (list1);
Print ("list2 := ");
PrintArray (list2);
Print ("\n");


int1 := ListToInteger( list1,  2 );
int2 := ListToInteger( list2, 16 );
int3 := ListToInteger( list1,  3 );

Print ("   int1 := ListToInteger( list1,  2 );\n", int1, "\n\n");
Print ("   int2 := ListToInteger( list2, 16 );\n", int2, "\n\n");
Print ("   int3 := ListToInteger( list1,  3 );\n", int3, "\n\n");
Print ("\n");
Sleep(10);


# So basically, we can do really trivial things in
# really creative ways:

int1 := ListToInteger( IntegerToList( 1000, 10, 3 ), 3);

Print ("Now we change 1000 to a list and immediately change back:\n");
Print ("   int1 := ListToInteger( IntegerToList( 1000, 10, 3 ), 3);\n");
Print (int1, "\n\n");
Sleep(3);


# Or interesting truncations:

int1 := ListToInteger( IntegerToList( 1000, 4, 3 ), 3);

Print ("We can do the same thing but truncate the list before we\n");
Print ("reconstruct the integer.\n");
Print ("   int1 := ListToInteger( IntegerToList( 1000, 4, 3 ), 3);\n");
Print (int1, "\n\n");
Sleep(5);


# Now we can test our multiset functions.

list := [1, 2, 1, 0, 0, 3];
mult := ListToMultiset( list );

Print ("Start with a list:\n   list := ", list, "\n");
Print ("   mult := ListToMultiSet( list );\n", mult, "\n\n");
Sleep(3);


# and back...

newlist := MultisetToList( mult, Size(list) );

Print ("And back to a list:\n");
Print ("   newlist := MultisetToList( mult, (Size(list) );\n");
Print ( newlist, "\n\n" );