mirror of https://github.com/CGAL/cgal
62 lines
1.8 KiB
TeX
62 lines
1.8 KiB
TeX
\begin{ccRefConcept}{UniqueFactorizationDomain}
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\ccDefinition
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A model of \ccc{UniqueFactorizationDomain} is an \ccc{IntegralDomain} with the
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additional property
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that the ring it represents is a unique factorization domain
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(a.k.a. UFD or factorial ring), meaning that every non-zero non-unit
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element has a factorization into irreducible elements that is unique
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up to order and up to multiplication by invertible elements (units).
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(An irreducible element is a non-unit ring element that cannot be factored
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further into two non-unit elements. In a UFD, the irreducible elements
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are precisely the prime elements.)
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In a UFD, any two elements, not both zero, possess a greatest common
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divisor (gcd).
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Moreover, \ccc{CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >}
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is a model of \ccc{AlgebraicStructureTraits} providing:\\
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- \ccc{CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Algebraic_type}
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derived from \ccc{Unique_factorization_domain_tag} \\
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- \ccc{CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Gcd} a model of \ccc{AlgebraicStructureTraits::Gcd}\\
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\ccRefines
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\ccc{IntegralDomain}
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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{int}\\
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%\ccc{long}\\
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%\ccc{CGAL::Gmpz} \\
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%\ccc{CGAL::Gmpzf} \\
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%\ccc{mpz_class} \\
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%\ccc{leda_integer} \\
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%\ccc{CORE::BigInt} \\
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%\ccc{CGAL::MP_Float} ( exact version )\\
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%\ccc{CGAL::Lazy_exact_nt< NT > } (depends on NT) \\
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%\ccc{CGAL::Polynomial< T >} \\
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\end{ccRefConcept} |