#include <CCommutativeRing.h>

Inheritance diagram for DGtal::CCommutativeRing< T >:

Collaboration diagram for DGtal::CCommutativeRing< T >:

Public Member Functions
	BOOST_CONCEPT_USAGE (CCommutativeRing)

Private Attributes
T	a
T	b
T	c

Detailed Description

template<typename T>
struct DGtal::CCommutativeRing< T >

Aim: Defines the mathematical concept equivalent to a unitary commutative ring.

Description of concept 'CCommutativeRing'

Refinement of boost::Assignable<T>,

boost::EqualityComparable<T>, boost::LessThanComparable<T>

Associated types :

Notation

X : A type that is a model of CCommutativeRing
x, y : Object of type Integer

Definitions

Valid expressions and

Name	Expression	Type requirements	Return type	Precondition	Semantics	Postcondition	Complexity
Construction from basic integer type	X( i )				X represents the integer i
Addition	x + y		X		addition of two numbers
Subtraction	x - y		X		subtraction of two numbers
Multiplication	x - y		X		subtraction of two numbers
Opposite operator	- x		X		defines the opposite of x ( x + -x = 0)
X should have a 0 (neutral element for addition)	X( 0 )		X		the value 0
X should have a 1 (neutral element for multiplication)	X ( 1 )		X		the value 1

Invariants

Models

DGtal::int32_t, DGtal::int64_t, DGtal::int8_t, float, double, long double, DGtal::BigInteger

Notes

Template Parameters:

T	the type that should be a model of commutative ring.

Definition at line 171 of file CCommutativeRing.h.

Member Function Documentation

template<typename T >

DGtal::CCommutativeRing< T >::BOOST_CONCEPT_USAGE ( CCommutativeRing< T > )

inline

The 0 and 1 neutral elements should be tested.

Definition at line 177 of file CCommutativeRing.h.

References DGtal::ConceptUtils::sameType().

    {
      ConceptUtils::sameType( c, T( 25 ) );
      ConceptUtils::sameType( c, T( -25 ) );
      ConceptUtils::sameType( c, T( a+b ) );
      ConceptUtils::sameType( c, T( -a ) );
      ConceptUtils::sameType( c, T( a-b ) );
      ConceptUtils::sameType( c, T( a*b ) );
      ConceptUtils::sameType( c, T( 0 ) );
      ConceptUtils::sameType( c, T( 1 ) );
    }