\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 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.