AlgebraicStructureTraits_::Divides Concept Reference

Definition

AdaptableBinaryFunction, returns true if the first argument divides the second argument.

Integral division (a.k.a. exact division or division without remainder) maps ring elements \( (n,d)\) to ring element \( c\) such that \( n = dc\) if such a \( c\) exists. In this case it is said that \( d\) divides \( n\).

This functor is required to provide two operators. The first operator takes two arguments and returns true if the first argument divides the second argument. The second operator returns \( c\) via the additional third argument.

Refines

AdaptableBinaryFunction

See also

AlgebraicStructureTraits

AlgebraicStructureTraits_::IntegralDivision

Types
typedef unspecified_type	result_type
	Is AlgebraicStructureTraits::Boolean.
typedef unspecified_type	first_argument
	Is AlgebraicStructureTraits::Type.
typedef unspecified_type	second_argument
	Is AlgebraicStructureTraits::Type.

Operations
result_type	operator() (first_argument_type d, second_argument_type n)
	Computes whether \( d\) divides \( n\).
result_type	operator() (first_argument_type d, second_argument_type n, AlgebraicStructureTraits::Type &c)
	Computes whether \( d\) divides \( n\).

Member Function Documentation

operator()()

result_type AlgebraicStructureTraits_::Divides::operator()	(	first_argument_type	d,
		second_argument_type	n,
		AlgebraicStructureTraits::Type &	c
	)

Computes whether \( d\) divides \( n\).

Moreover it computes \( c\) if \( d\) divides \( n\), otherwise the value of \( c\) is undefined.