mirror of https://github.com/CGAL/cgal
67 lines
1.7 KiB
TeX
67 lines
1.7 KiB
TeX
\begin{ccRefConcept}{Field}
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\ccDefinition
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A model of \ccc{Field} is an \ccc{IntegralDomain} in which every non-zero element
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has a multiplicative inverse.
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Thus, one can divide by any non-zero element.
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Hence division is defined for any divisor != 0.
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For a Field, we require this division operation to be available through
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operators / and /=.
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Moreover, \ccc{CGAL::Algebraic_structure_traits< Field >} is a model of
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\ccc{AlgebraicStructureTraits} providing:\\
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- \ccc{CGAL::Algebraic_structure_traits< Field >::Algebraic_type} derived from \ccc{Field_tag} \\
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- \ccc{CGAL::Algebraic_structure_traits< FieldWithSqrt >::Inverse} a model of \ccc{AlgebraicStructureTraits::Inverse}\\
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\ccRefines
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\ccc{IntegralDomain}
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\ccOperations
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\ccCreationVariable{a}
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\ccFunction{Field operator/(const Field &a, const Field &b);}{}
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\ccGlue
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\ccMethod{Field operator/=(const Field &b);}{}
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\ccSeeAlso
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\ccRefIdfierPage{IntegralDomainWithoutDivision}\\
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\ccRefIdfierPage{IntegralDomain}\\
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\ccRefIdfierPage{UniqueFactorizationDomain}\\
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\ccRefIdfierPage{EuclideanRing}\\
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\ccRefIdfierPage{Field}\\
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\ccRefIdfierPage{FieldWithSqrt}\\
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\ccRefIdfierPage{FieldWithKthRoot}\\
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\ccRefIdfierPage{FieldWithRootOf}\\
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\ccRefIdfierPage{AlgebraicStructureTraits}\\
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%\ccHasModels
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%\ccc{float}\\
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%\ccc{double}\\
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%\ccc{long_double}\\
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%\ccc{CGAL::Gmpq} \\
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%\ccc{mpq_class} \\
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%%\ccc{mpf_class} \\
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%\ccc{leda_rational} \\
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%\ccc{leda_bigfloat} \\
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%\ccc{leda_real} \\
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%\ccc{CORE::BigRat} \\
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%%\ccc{CORE::BigFloat} \\
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%\ccc{CORE::Expr} \\
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%%\ccc{CGAL::Interval_nt} \\
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%%\ccc{CGAL::Interval_nt_advanced} \\
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%\ccc{CGAL::MP_Float} (inexact version)\\
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%\ccc{CGAL::Lazy_exact_nt< NT >} (depends on NT) \\
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%\ccc{CGAL::Quotient< NT >} \\
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%\ccc{CGAL::Sqrt_extension< NT, Root >} (depends on NT) \\
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\end{ccRefConcept} |