IntegralDomain corresponds to a commutative ring, where a mod b picks a canonical element of the equivalence class of a in the ideal generated by b. div and mod satisfy the laws

                         a * b === b * a
 (a `div` b) * b + (a `mod` b) === a
               (a+k*b) `mod` b === a `mod` b
                     0 `mod` b === 0

Typical examples of IntegralDomain include integers and polynomials over a field. Note that for a field, there is a canonical instance defined by the above rules; e.g.,

 instance IntegralDomain.C Rational where
     divMod a b =
        if isZero b
          then (undefined,a)
          else (a\/b,0)

It shall be noted, that div, mod, divMod have a parameter order which is unfortunate for partial application. But it is adapted to mathematical conventions, where the operators are used in infix notation.

Minimal definition: divMod or (div and mod)