CGAL 6.2 - Algebraic Foundations: AlgebraicStructureTraits_::IsSquare Concept Reference

CGAL 6.2 - Algebraic Foundations

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AlgebraicStructureTraits_::IsSquare Concept Reference
Reference Manual » Concepts

## 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. \( x = y*y\).
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
  \( unit\_part(y) == 1\).