IntegralDomainWithoutDivision Class Reference

#include <Concepts/IntegralDomainWithoutDivision.h>

Definition

This is the most basic concept for algebraic structures considered within CGAL.

A model IntegralDomainWithoutDivision represents an integral domain, i.e. commutative ring with 0, 1, +, * and unity free of zero divisors.

Note: A model is not required to offer the always well defined integral division.

It refines Assignable, CopyConstructible, DefaultConstructible and FromIntConstructible.

It refines EqualityComparable, where equality is defined w.r.t. the ring element being represented.

The operators unary and binary plus +, unary and binary minus -, multiplication * and their compound forms +=, -=, *= are required and implement the respective ring operations.

Moreover, CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision > is a model of AlgebraicStructureTraits providing:

• CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Algebraic_category derived from CGAL::Integral_domain_without_division_tag
• CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Is_zero which is a model of AlgebraicStructureTraits_::IsZero
• CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Is_one which is a model of AlgebraicStructureTraits_::IsOne
• CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Square which is a model of AlgebraicStructureTraits_::Square
• CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Simplify which is a model of AlgebraicStructureTraits_::Simplify

• CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Unit_part which is a model of AlgebraicStructureTraits_::UnitPart

  Refines:

  Assignable

  CopyConstructible

  DefaultConstructible

  EqualityComparable

  FromIntConstructible

See also

IntegralDomainWithoutDivision

IntegralDomain

UniqueFactorizationDomain

EuclideanRing

Field

FieldWithSqrt

FieldWithKthRoot

FieldWithRootOf

AlgebraicStructureTraits

Operations
IntegralDomainWithoutDivision	operator+ (const IntegralDomainWithoutDivision &a)
	unary plus More...
IntegralDomainWithoutDivision	operator- (const IntegralDomainWithoutDivision &a)
	unary minus More...
IntegralDomainWithoutDivision	operator+ (const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b)
IntegralDomainWithoutDivision	operator- (const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b)
IntegralDomainWithoutDivision	operator* (const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b)
IntegralDomainWithoutDivision	operator+= (const IntegralDomainWithoutDivision &b)
IntegralDomainWithoutDivision	operator-= (const IntegralDomainWithoutDivision &b)
IntegralDomainWithoutDivision	operator*= (const IntegralDomainWithoutDivision &b)
result_type	operator== (const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b)
	The result_type is convertible to bool. More...
result_type	operator!= (const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b)
	The result_type is convertible to bool. More...

Member Function Documentation

operator!=()

result_type IntegralDomainWithoutDivision::operator!=	(	const IntegralDomainWithoutDivision &	a,
		const IntegralDomainWithoutDivision &	b
	)

The result_type is convertible to bool.

operator*()

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator*	(	const IntegralDomainWithoutDivision &	a,
		const IntegralDomainWithoutDivision &	b
	)

operator*=()

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator*=

(

const IntegralDomainWithoutDivision &

b

)

operator+() [1/2]

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator+

(

const IntegralDomainWithoutDivision &

a

)

unary plus

operator+() [2/2]

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator+	(	const IntegralDomainWithoutDivision &	a,
		const IntegralDomainWithoutDivision &	b
	)

operator+=()

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator+=

(

const IntegralDomainWithoutDivision &

b

)

operator-() [1/2]

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator-

(

const IntegralDomainWithoutDivision &

a

)

unary minus

operator-() [2/2]

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator-	(	const IntegralDomainWithoutDivision &	a,
		const IntegralDomainWithoutDivision &	b
	)

operator-=()

IntegralDomainWithoutDivision IntegralDomainWithoutDivision::operator-=

(

const IntegralDomainWithoutDivision &

b

)

operator==()

result_type IntegralDomainWithoutDivision::operator==	(	const IntegralDomainWithoutDivision &	a,
		const IntegralDomainWithoutDivision &	b
	)

The result_type is convertible to bool.