ReadMeadditional.txt				Shean T. McMahon	
						P231, Final Project
New Developments

To compile this program just compile Main.cpp with g++.  No switches
or options need to be selected.  Compiling will also implement 
the "test" program.

Updates to NumberTheory Class

  *  Added virtual functions and polymorphism to handle I/O for
     most functions.
		
     Previously, all I/O was done using cin and cout statements. 
     Currently, virtual	functions and polymorphism is used for I/O 
     on all but operations which require multiple ( >2 ) inputs
     or outputs.

  *  Removed Congruences and other functions classes

     These classes were removed to ease modifications to the main
     and header files.  Reinstating them is not particularly 
     difficult, although there is nothing really c++ about them, 
     so they don't add anything which has not already been done.

  *  Redesigned Is_Prime function to eliminate bug

     Previously, the Is_Prime function had two bugs.  It would 
     always report that	3 was a composite number, and all multiples
     of 2 were reported to be prime. 

     This had devestating consequences in all methods which used 
     Is_Prime.  The initial workaround was to have the function just
     eliminate three, and start testing for primality at 5.  This
     worked, but was very ugly.  This approach did not work for the
     problem with multiples of 2 however.  

     The function was redisigned using a switch statement to 
     eliminate cases such as 0, 1, 2, and 3.  Testing is then 
     started at 5.  This is a far cleaner approach, than was used 
     before.  Additionally, this method is far easier to expand, 
     such as to add values for it to skip, thus reducing processor
     requirements.
    
  *  Redesigned Twin_Prime function

     The twin prime function had a bug which popped up on multiples
     of two.  Specifically, it reported that 2 was not prime.  This
     was not related to the problems with Is_Prime(), but instead 
     fell out of the data display method used.  The function was
     redesigned to address this issue.

  *  Modified inheritance structure.

     Previously, all inheritance was public; class 2 was derived 
     from class 1, class 3 derived from class 2 and so on.  This 
     worked, but was clunky.  Additionally, it was really not a 
     correct approach to inheritance in this problem.

     The new inheritance structure breaks with this approach.  
     Instead, only operations which are intimatly related are 
     grouped in the same class.  Classes and Functions which are
     similar, and possess an "is-a" relation share a public 
     inheritance.

  *  Calculation of greatest common divisor made a global function.
	
     The GCD is needed for several calculations in the class.  
     Unfortunatly, these functions do not share a close enough 
     relation to justify an inheritance structure between their 
     respective classes.  The best solution to this problem was to 
     make the GCD function global.  Note that this does not 
     invalidate the GCD class, as this class still deals with I/O, 
     and the GCD for multiple inputs.

  *  Main Menu moved to main function

     Previously, the main menu function was called from the main 
     function.  The main menu has been coded directly into the main
     function in the current version.