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

CGAL 4.8 - Modular Arithmetic

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ModularTraits Concept Reference
Concepts

## Definition

A model of `ModularTraits` is associated to a specific `Type`. In case this associated type is a model of `Modularizable`, this is indicated by the Boolean tag `ModularTraits::Is_modularizable`. The mapping into the `Residue_type` is provided by the functor `ModularTraits::Modular_image`.

Has Models:
  CGAL::Modular_traits<T>

See Also
  `CGAL::Residue`
  `Modularizable`

## Concepts
concept | ModularImage
| This `AdaptableUnaryFunction` computes the modular image of the given value with respect to a homomorphism \( \varphi\) from the `ModularTraits::Type` into the `ModularTraits::Residue_type`. More...
concept | ModularImageRepresentative
| This `AdaptableUnaryFunction` returns a representative in the original type of a given modular image. More precisely, it implements the right inverse of a proper restriction of the homomorphism \( \varphi\), which is implemented by `ModularTraits::ModularImage`. More...

## Types
A model of `ModularTraits` is supposed to provide:
typedef unspecified_type | Type
| The associated type.
typedef unspecified_type | Is_modularizable
| Tag indicating whether the associated type is modularizable. More...
typedef unspecified_type | Residue_type
| The type of the modular image. More...

## Functors
In case the associated type is a model of `Modularizable` all functors are provided. In case a functor is not provided, it is set to `CGAL::Null_functor`.
typedef unspecified_type | Modular_image
| A model of `ModularTraits::ModularImage`
typedef unspecified_type | Modular_image_representative
| A model of `ModularTraits::ModularImageRepresentative`

## Member Typedef Documentation

typedef unspecified_type ModularTraits::Is_modularizable

Tag indicating whether the associated type is modularizable.

This is either `CGAL::Tag_true` or `CGAL::Tag_false`.

typedef unspecified_type ModularTraits::Residue_type

The type of the modular image.

In case the associated type is not a model of `Modularizable` this is undefined.