ring_concept.h

// Description: Ring concept
// Documentation: algebra.txt

#ifndef PASTELSYS_RING_CONCEPT_H
#define PASTELSYS_RING_CONCEPT_H

#include "pastel/sys/algebra/group_concept.h"
#include "pastel/sys/algebra/monoid_concept.h"

namespace Pastel
{

    //! A ring.
    /*!
   A ring is a triple (X, +, 0, *, 1) such that
       
   1) (X, +, 0) is a commutative group,

   2) (X, *, 1) is a monoid,
       
   3) 
       (x + y) * z = x * z + y * z
       z * (x + y) = z * x + z * y
       
   for all x, y, z in X, and
   */
    struct Ring_Concept
    : Refines<
        Additive_Group_Concept,
        Multiplicative_Monoid_Concept>
    {
        template <typename Type>
        auto requires_(Type&& t) -> decltype
        (
            conceptCheck(
                //! Adds 1 to the element, returns itself.
                Concept::hasType<Type&>(++t),
                //! Adds 1 to the element, returns the previous value.
                Concept::convertsTo<Type>(t++),
                //! Subtracts 1 from the element, returns itself.
                Concept::hasType<Type&>(--t),
                //! Subtracts 1 from the element, returns the previous value.
                Concept::convertsTo<Type>(t--)
            )
        );
    };

}

#endif