\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.4 - Algebraic Foundations
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RealEmbeddableTraits Concept Reference
Concepts

Definition

A model of RealEmbeddableTraits is associated to a number type Type and reflects the properties of this type with respect to the concept RealEmbeddable.

Has Models:
CGAL::Real_embeddable_traits<T>

Types

A model of RealEmbeddableTraits is supposed to provide:

typedef unspecified_type Type
 The associated number type.
 
typedef unspecified_type Is_real_embeddable
 Tag indicating whether the associated type is real embeddable. More...
 
typedef unspecified_type Boolean
 This type specifies the return type of the predicates provided by this traits. More...
 
typedef unspecified_type Sign
 This type specifies the return type of the Sgn functor. More...
 
typedef unspecified_type Comparison_result
 This type specifies the return type of the Compare functor. More...
 

Functors

In case the associated type is RealEmbeddable all functors are provided.

In case a functor is not provided, it is set to CGAL::Null_functor.

typedef unspecified_type Is_zero
 A model of RealEmbeddableTraits_::IsZero In case Type is also model of IntegralDomainWithoutDivision this is a model of AlgebraicStructureTraits_::IsZero.
 
typedef unspecified_type Abs
 A model of RealEmbeddableTraits_::Abs
 
typedef unspecified_type Sgn
 A model of RealEmbeddableTraits_::Sgn
 
typedef unspecified_type Is_positive
 A model of RealEmbeddableTraits_::IsPositive
 
typedef unspecified_type Is_negative
 A model of RealEmbeddableTraits_::IsNegative
 
typedef unspecified_type Compare
 A model of RealEmbeddableTraits_::Compare
 
typedef unspecified_type To_double
 A model of RealEmbeddableTraits_::ToDouble
 
typedef unspecified_type To_interval
 A model of RealEmbeddableTraits_::ToInterval
 

Member Typedef Documentation

typedef unspecified_type RealEmbeddableTraits::Boolean

This type specifies the return type of the predicates provided by this traits.

The type must be convertible to bool and typically the type indeed maps to bool. However, there are also cases such as interval arithmetic, in which it is Uncertain<bool> or some similar type.

typedef unspecified_type RealEmbeddableTraits::Comparison_result

This type specifies the return type of the Compare functor.

The type must be convertible to CGAL::Comparison_result and typically the type indeed maps to CGAL::Comparison_result. However, there are also cases such as interval arithmetic, in which it is Uncertain<CGAL::Comparison_result> or some similar type.

typedef unspecified_type RealEmbeddableTraits::Is_real_embeddable

Tag indicating whether the associated type is real embeddable.

This is either Tag_true or Tag_false.

typedef unspecified_type RealEmbeddableTraits::Sign

This type specifies the return type of the Sgn functor.

The type must be convertible to CGAL::Sign and typically the type indeed maps to CGAL::Sign. However, there are also cases such as interval arithmetic, in which it is Uncertain<CGAL::Sign> or some similar type.