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CGAL 6.0 - Algebraic Foundations
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A model of AlgebraicStructureTraits reflects the algebraic structure of an associated type Type.
Depending on the concepts that Type fulfills, it contains various functors and descriptive tags. Moreover it gives access to the several possible algebraic operations within that structure.
IntegralDomainWithoutDivision IntegralDomain UniqueFactorizationDomain EuclideanRing Field FieldWithSqrt FieldWithKthRoot FieldWithRootOf CGAL::Integral_domain_without_division_tag CGAL::Integral_domain_tag CGAL::Unique_factorization_domain_tag CGAL::Euclidean_ring_tag CGAL::Field_tag CGAL::Field_with_sqrt_tag CGAL::Field_with_kth_root_tag CGAL::Field_with_root_of_tagCGAL::Algebraic_structure_traits<T> Types | |
A model of | |
| typedef unspecified_type | Type |
| The associated type. | |
| typedef unspecified_type | Algebraic_category |
| Tag indicating the algebraic structure of the associated type. | |
| typedef unspecified_type | Is_exact |
Tag indicating whether Type is exact. | |
| typedef unspecified_type | Is_numerical_sensitive |
Tag indicating whether Type is numerical sensitive. | |
| typedef unspecified_type | Boolean |
| This type specifies the return type of the predicates provided by this traits. | |
Tag indicating the algebraic structure of the associated type.
This type specifies the return type of the predicates provided by this traits.
The type must be convertible to bool and typically the type indeed maps to bool. However, there are also cases such as interval arithmetic, in which it is CGAL::Uncertain<bool> or some similar type.
A model of AlgebraicStructureTraits_::Div.
Required by the concept EuclideanRing.
A model of AlgebraicStructureTraits_::DivMod.
Required by the concept EuclideanRing.
A model of AlgebraicStructureTraits_::Divides.
Required by the concept IntegralDomain.
A model of AlgebraicStructureTraits_::Gcd.
Required by the concept UniqueFactorizationDomain.
A model of AlgebraicStructureTraits_::IntegralDivision.
Required by the concept IntegralDomain.
A model of AlgebraicStructureTraits_::Inverse.
Required by the concept Field.
Tag indicating whether Type is exact.
This is either CGAL::Tag_true or CGAL::Tag_false.
An algebraic structure is considered exact, if all operations required by its concept are computed such that a comparison of two algebraic expressions is always correct. The exactness covers only those operations that are required by the algebraic structure concept.
e.g. an exact Field may have a Sqrt functor that is not exact.
Tag indicating whether Type is numerical sensitive.
This is either CGAL::Tag_true or CGAL::Tag_false.
An algebraic structure is considered as numerically sensitive, if the performance of the type is sensitive to the condition number of an algorithm.
A model of AlgebraicStructureTraits_::IsOne.
Required by the concept IntegralDomainWithoutDivision.
A model of AlgebraicStructureTraits_::IsSquare.
Required by the concept IntegralDomainWithoutDivision.
A model of AlgebraicStructureTraits_::IsZero.
Required by the concept IntegralDomainWithoutDivision. In case Type is also model of RealEmbeddable this is a model of RealEmbeddableTraits_::IsZero.
A model of AlgebraicStructureTraits_::KthRoot.
Required by the concept FieldWithKthRoot.
A model of AlgebraicStructureTraits_::Mod.
Required by the concept EuclideanRing.
A model of AlgebraicStructureTraits_::RootOf.
Required by the concept FieldWithRootOf.
A model of AlgebraicStructureTraits_::Simplify.
Required by the concept IntegralDomainWithoutDivision.
A model of AlgebraicStructureTraits_::Sqrt.
Required by the concept FieldWithSqrt.
A model of AlgebraicStructureTraits_::Square.
Required by the concept IntegralDomainWithoutDivision.
A model of AlgebraicStructureTraits_::UnitPart.
Required by the concept IntegralDomainWithoutDivision.