AlgebraicStructureTraits_::IsSquare Concept Reference

Definition

AdaptableBinaryFunction that computes whether the first argument is a square. If the first argument is a square the second argument, which is taken by reference, contains the square root. Otherwise, the content of the second argument is undefined.

A ring element $x$ is said to be a square iff there exists a ring element $y$ such that $x= y*y$. In case the ring is a UniqueFactorizationDomain, $y$ is uniquely defined up to multiplication by units.

Refines:

AdaptableBinaryFunction

See also

AlgebraicStructureTraits

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 x, second_argument_type y)
	returns true in case $x$ is a square, i.e. $x = y*y$. More...
result_type	operator() (first_argument_type x)
	returns true in case $x$ is a square.

Member Function Documentation

operator()()

result_type AlgebraicStructureTraits_::IsSquare::operator()	(	first_argument_type	x,
		second_argument_type	y
	)

returns true in case $x$ is a square, i.e. $x = y*y$.

Postcondition

$unit\_part(y) == 1$.