mirror of https://github.com/CGAL/cgal
51 lines
1.5 KiB
TeX
51 lines
1.5 KiB
TeX
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\begin{ccRefFunctionObjectConcept}{AlgebraicStructureTraits::IsSquare}
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\ccDefinition
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\ccc{AdaptableBinaryFunction} that computes whether the first argument is a square.
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If the first argument is a square the second argument, which is taken by reference, contains the square root.
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Otherwise, the content of the second argument is undefined.
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A ring element $x$ is said to be a square iff there exists a ring element $y$ such
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that $x= y*y$. In case the ring is a \ccc{UniqueFactorizationDomain},
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$y$ is uniquely defined up to multiplication by units. \\
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%Note that this is an optional functor and not required by any algebraic structure concept.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccTypes
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\ccNestedType{result_type}
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{ Is \ccc{AlgebraicStructureTraits::Boolean}.}
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\ccGlue
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\ccNestedType{first_argument}
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{ Is \ccc{AlgebraicStructureTraits::Type}.}
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\ccGlue
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\ccNestedType{second_argument}
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{ Is \ccc{AlgebraicStructureTraits::Type&}.}
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\ccOperations
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\ccCreationVariable{is_square}
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\ccThree{xxxxxxxxxxx}{xxxxxxxxxxx}{}
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\ccMethod{result_type operator()(first_argument_type x,
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second_argument_type y);}
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{ returns {\tt true} in case $x$ is a square, i.e. $x = y*y$.
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\ccPostcond $unit\_part(y) == 1$.
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}
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\ccMethod{result_type operator()(first_argument_type x);}
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{ returns {\tt true} in case $x$ is a square.
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}
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%\ccHasModels
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\ccSeeAlso
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\ccRefIdfierPage{AlgebraicStructureTraits}
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\end{ccRefFunctionObjectConcept}
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