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

CGAL 4.8 - Algebraic Foundations

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AlgebraicStructureTraits_::IntegralDivision Concept Reference
Concepts

## Definition

`AdaptableBinaryFunction` providing an integral division.

Integral division (a.k.a. exact division or division without remainder) maps ring elements \( (x,y)\) to ring element \( z\) such that \( x = yz\) if such a \( z\) exists (i.e. if \( x\) is divisible by \( y\)). Otherwise the effect of invoking this operation is undefined. Since the ring represented is an integral domain, \( z\) is uniquely defined if it exists.

Refines:
  `AdaptableBinaryFunction`

See Also
  `AlgebraicStructureTraits`
  `AlgebraicStructureTraits_::Divides`

## Types
typedef unspecified_type | result_type
| Is `AlgebraicStructureTraits::Type`.
typedef unspecified_type | first_argument
| Is `AlgebraicStructureTraits::Type`.
typedef unspecified_type | second_argument
| Is `AlgebraicStructureTraits::Type`.

## Operations
result_type | operator() (first_argument_type x, second_argument_type y)
| returns \( x/y\), this is an integral division.
template<class NT1 , class NT2 >
result_type | operator() (NT1 x, NT2 y)
| This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable` with coercion type `AlgebraicStructureTraits::Type`.