Re: Number/Algebraic concepts (was RE: [boost] RE: rational.hpp)

From: Doug Gregor (gregod_at_[hidden])
Date: 2001-01-13 20:45:46

On Friday 12 January 2001 07:00, you wrote:
> Paris (U.E;), le 13/01/2001
>
> 	I would absolutely welcome algebraic classes!

These are algebraic concept classes, not general algebraic classes. The idea 
behind them is that they can be used to determine algebraic properties of a 
given type. For instance, given the following integer exponentiation 
algorithm (borrowed from some class notes at 
http://www.cs.rpi.edu/~schupp/entries/COURSES/pl/notes/gp.html):

template<class SemigroupElement, class Integer>
SemigroupElement 
exponentiate2(SemigroupElement x, Integer n) {
 while (even(n)) {
    x = x * x;
    n = n/2;
  }
  SemigroupElement P=x;
  n = integral_part(n/2);
  while (n>0) {
   x=x*x;
   if (odd(n))
      P = P*x;
   n = integral_part(n/2);
  }
  return P;
}

We should be checking that the type bound to SemigroupElement does indeed 
form a semigroup with the operation *. The algebraic concept classes allow us 
to do this check statically, so compilation will fail if the user does not 
assert the associativity of * for the type bound to SemigroupElement.

        Doug Gregor
        gregod_at_[hidden]