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

CGAL 4.8 - Algebraic Foundations

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IntegralDomain Concept Reference
Concepts

## Definition

`IntegralDomain` refines `IntegralDomainWithoutDivision` by providing an integral division.

Note: The concept does not require the operator / for this operation. We intend to reserve the operator syntax for use with a `Field`.

Moreover, `CGAL::Algebraic_structure_traits< IntegralDomain >` is a model of `AlgebraicStructureTraits` providing:

- `CGAL::Algebraic_structure_traits< IntegralDomain >::Algebraic_category` derived from `CGAL::Integral_domain_tag`
- `CGAL::Algebraic_structure_traits< IntegralDomain >::Integral_division` which is a model of `AlgebraicStructureTraits_::IntegralDivision`
- `CGAL::Algebraic_structure_traits< IntegralDomain >::Divides` which is a model of `AlgebraicStructureTraits_::Divides`

Refines:
  `IntegralDomainWithoutDivision`

See Also
  `IntegralDomainWithoutDivision`
  `IntegralDomain`
  `UniqueFactorizationDomain`
  `EuclideanRing`
  `Field`
  `FieldWithSqrt`
  `FieldWithKthRoot`
  `FieldWithRootOf`
  `AlgebraicStructureTraits`