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

#include <DGtal/kernel/CCommutativeRing.h>

Inheritance diagram for DGtal::concepts::CCommutativeRing< T >:

Public Member Functions
	BOOST_CONCEPT_USAGE (CCommutativeRing)

Public Member Functions inherited from DGtal::concepts::CSignedNumber< T >
	BOOST_CONCEPT_USAGE (CSignedNumber)

Private Attributes
T	a

T	b

T	c

Detailed Description

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

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

Description of concept 'CCommutativeRing'

Refinement of

CSignedNumber<T>

Associated types

Notation

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

Definitions

Valid expressions and semantics

Name	Expression	Return type	Semantics
Construction from basic integer type	X( i )		X represents the integer i
Should have a 0	X(0)		Neutral element for addition
Should have a 1	X(1)		Neutral element for multiplication
Addition	x + y	X	addition of two numbers
Substraction	x - y	X	substraction of two numbers
Multiplication	x * y	X	multiplication of two numbers
Addition	x + y	X	addition of two numbers
Opposite operator	- x	X	opposite of a number

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 100 of file CCommutativeRing.h.

Member Function Documentation

◆ BOOST_CONCEPT_USAGE()

template<typename T >

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

inline

The 0 and 1 neutral elements should be tested.

Definition at line 105 of file CCommutativeRing.h.

    {
      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 ) );
 
    }