cgal/Algebraic_foundations/doc_tex/Algebraic_foundations_ref/AlgebraicStructureTraits_Is...

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\begin{ccRefFunctionObjectConcept}{AlgebraicStructureTraits::IsSquare}
\ccDefinition
\ccc{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 \ccc{UniqueFactorizationDomain},
$y$ is uniquely defined up to multiplication by units. \\
%Note that this is an optional functor and not required by any algebraic structure concept.
\ccRefines
\ccc{AdaptableBinaryFunction}
\ccTypes
\ccNestedType{result_type}
{ Is \ccc{AlgebraicStructureTraits::Boolean}.}
\ccGlue
\ccNestedType{first_argument}
{ Is \ccc{AlgebraicStructureTraits::Type}.}
\ccGlue
\ccNestedType{second_argument}
{ Is \ccc{AlgebraicStructureTraits::Type&}.}
\ccOperations
\ccCreationVariable{is_square}
\ccThree{xxxxxxxxxxx}{xxxxxxxxxxx}{}
\ccMethod{result_type operator()(first_argument_type x,
second_argument_type y);}
{ returns {\tt true} in case $x$ is a square, i.e. $x = y*y$.
\ccPostcond $unit\_part(y) == 1$.
}
\ccMethod{result_type operator()(first_argument_type x);}
{ returns {\tt true} in case $x$ is a square.
}
%\ccHasModels
\ccSeeAlso
\ccRefIdfierPage{AlgebraicStructureTraits}
\end{ccRefFunctionObjectConcept}