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
   */
    template <typename T>
    concept Ring_Concept_ = 
        Additive_Group_Concept<T> && 
        Multiplicative_Monoid_Concept<T> && 
        requires(T t) {
        //! Adds 1 to the element, returns itself.
        {++t} -> std::convertible_to<T>;
        //! Adds 1 to the element, returns the previous value.
        {t++} -> std::convertible_to<T>;
        //! Subtracts 1 from the element, returns itself.
        {--t} -> std::convertible_to<T>;
        //! Subtracts 1 from the element, returns the previous value.
        {t--} -> std::convertible_to<T>;
    };

    template <typename T>
    concept Ring_Concept = 
        Ring_Concept_<RemoveCvRef<T>>;

}

#endif