To all:

After some careful reading,  it became obvious to me that I was going to 
have to implement a slew of two parameter functions that took a const 
object as the first member, in order to deal with the const problem.

One person writes:

Adding the keyword const to the end of a member function's prototype 
tells the compiler:

    I promise not to modify the object which calls me (directly or
    indirectly), and therefore I may be called by const objects. 

And adding this const to the member functions which contained a class 
reference fixed the other problems.

I have to say that the class file has grown enormously and I still 
haven't finished with the arithmetic functions yet.

I can see why writing overload operators is such a tedious task.

Randall

P.S. So consider the problem now solved.

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