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

CGAL 4.8 - Algebraic Foundations

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RealEmbeddable Concept Reference
Concepts

## Definition

A model of this concepts represents numbers that are embeddable on the real axis. The type obeys the algebraic structure and compares two values according to the total order of the real numbers.

Moreover, `CGAL::Real_embeddable_traits< RealEmbeddable >` is a model of `RealEmbeddableTraits`

with:

- `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_real_embeddable` set to `Tag_true`

and functors :

- `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_zero` which is a model of `RealEmbeddableTraits_::IsZero`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::Abs` which is a model of `RealEmbeddableTraits_::Abs`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::Sgn` which is a model of `RealEmbeddableTraits_::Sgn`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_positive` which is a model of `RealEmbeddableTraits_::IsPositive`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_negative` which is a model of `RealEmbeddableTraits_::IsNegative`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::Compare` which is a model of `RealEmbeddableTraits_::Compare`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::To_double` which is a model of `RealEmbeddableTraits_::ToDouble`
- `CGAL::Real_embeddable_traits< RealEmbeddable >::To_interval` which is a model of `RealEmbeddableTraits_::ToInterval`

Remark:

If a number type is a model of both `IntegralDomainWithoutDivision` and `RealEmbeddable`, it follows that the ring represented by such a number type is a sub-ring of the real numbers and hence has characteristic zero.

Refines:

  `EqualityComparable`

  `LessThanComparable`

See Also
  `RealEmbeddableTraits`

## Operations
bool | operator== (const RealEmbeddable &a, const RealEmbeddable &b)
bool | operator!= (const RealEmbeddable &a, const RealEmbeddable &b)
bool | operator< (const RealEmbeddable &a, const RealEmbeddable &b)
bool | operator<= (const RealEmbeddable &a, const RealEmbeddable &b)
bool | operator> (const RealEmbeddable &a, const RealEmbeddable &b)
bool | operator>= (const RealEmbeddable &a, const RealEmbeddable &b)