AlgebraicStructureTraits_::IsSquare Class Reference

#include <Concepts/AlgebraicStructureTraits--IsSquare.h>

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. More...
typedef unspecified_type	first_argument
	Is AlgebraicStructureTraits::Type. More...
typedef unspecified_type	second_argument
	Is AlgebraicStructureTraits::Type&. More...

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. More...

Member Typedef Documentation

first_argument

typedef unspecified_type AlgebraicStructureTraits_::IsSquare::first_argument

Is AlgebraicStructureTraits::Type.

result_type

typedef unspecified_type AlgebraicStructureTraits_::IsSquare::result_type

Is AlgebraicStructureTraits::Boolean.

second_argument

typedef unspecified_type AlgebraicStructureTraits_::IsSquare::second_argument

Is AlgebraicStructureTraits::Type&.

Member Function Documentation

operator()() [1/2]

result_type AlgebraicStructureTraits_::IsSquare::operator()

(

first_argument_type

x

)

returns true in case \( x\) is a square.

operator()() [2/2]

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

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