CGAL 4.7 - Modular Arithmetic: ModularTraits Concept Reference

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CGAL 4.7 - 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.