AlgebraicStructureTraits

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AlgebraicStructureTraits

Definition

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.

Types

A model of AlgebraicStructureTraits is supposed to provide:

AlgebraicStructureTraits::Type

The associated type.

AlgebraicStructureTraits::Algebraic_category

Tag indicating the algebraic structure of the associated type.


Tag is:	Type is model of:

CGAL::Null_tag	no algebraic concept
CGAL::Integral_domain_without_division_tag	IntegralDomainWithoutDivision
CGAL::Integral_domain_tag	IntegralDomain
CGAL::Unique_factorization_domain_tag	UniqueFactorizationDomain
CGAL::Euclidean_ring_tag	EuclideanRing
CGAL::Field_tag	Field
CGAL::Field_with_sqrt_tag	FieldWithSqrt
CGAL::Field_with_kth_root_tag	FieldWithKthRoot
CGAL::Field_with_root_of_tag	FieldWithRootOf

AlgebraicStructureTraits::Is_exact

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.

AlgebraicStructureTraits::Is_numerical_sensitive

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.

AlgebraicStructureTraits::Boolean

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 Uncertain<bool> or some similar type.

Functors

In case a functor is not provided, it is set to CGAL::Null_functor.

AlgebraicStructureTraits::Is_zero
	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.

AlgebraicStructureTraits::Is_one
	A model of AlgebraicStructureTraits::IsOne. Required by the concept IntegralDomainWithoutDivision.

AlgebraicStructureTraits::Square
	A model of AlgebraicStructureTraits::Square. Required by the concept IntegralDomainWithoutDivision.

AlgebraicStructureTraits::Simplify
	A model of AlgebraicStructureTraits::Simplify. Required by the concept IntegralDomainWithoutDivision.

AlgebraicStructureTraits::Unit_part
	A model of AlgebraicStructureTraits::UnitPart. Required by the concept IntegralDomainWithoutDivision.

AlgebraicStructureTraits::Integral_division
	A model of AlgebraicStructureTraits::IntegralDivision. Required by the concept IntegralDomain.

AlgebraicStructureTraits::Divides
	A model of AlgebraicStructureTraits::Divides. Required by the concept IntegralDomain.

AlgebraicStructureTraits::Is_square
	A model of AlgebraicStructureTraits::IsSquare. Required by the concept IntegralDomainWithoutDivision.

AlgebraicStructureTraits::Gcd
	A model of AlgebraicStructureTraits::Gcd. Required by the concept UniqueFactorizationDomain.

AlgebraicStructureTraits::Mod
	A model of AlgebraicStructureTraits::Mod. Required by the concept EuclideanRing.

AlgebraicStructureTraits::Div
	A model of AlgebraicStructureTraits::Div. Required by the concept EuclideanRing.

AlgebraicStructureTraits::Div_mod
	A model of AlgebraicStructureTraits::DivMod. Required by the concept EuclideanRing.

AlgebraicStructureTraits::Sqrt
	A model of AlgebraicStructureTraits::Sqrt. Required by the concept FieldWithSqrt.

AlgebraicStructureTraits::Kth_root
	A model of AlgebraicStructureTraits::KthRoot. Required by the concept FieldWithKthRoot.

AlgebraicStructureTraits::Root_of
	A model of AlgebraicStructureTraits::RootOf. Required by the concept FieldWithRootOf.

Has Models

CGAL::Algebraic_structure_traits<T>

Next: AlgebraicStructureTraits::IsZero

Navigation: Up Table of Contents Package Overview Bibliography Index Title Acknowledging CGAL

CGAL Open Source Project. Release 3.5. 1 October 2009.