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.

See Also: 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_tag

Has Models:: CGAL::Algebraic_structure_traits<T>

Types
A model of `AlgebraicStructureTraits` is supposed to provide:
typedef unspecified_type	Type
	The associated type.

typedef unspecified_type	Algebraic_category
	Tag indicating the algebraic structure of the associated type. More...

typedef unspecified_type	Is_exact
	Tag indicating whether `Type` is exact. More...

typedef unspecified_type	Is_numerical_sensitive
	Tag indicating whether `Type` is numerical sensitive. More...

typedef unspecified_type	Boolean
	This type specifies the return type of the predicates provided by this traits. More...

Functors
In case a functor is not provided, it is set to `CGAL::Null_functor`.
typedef unspecified_type	Is_zero
	A model of `AlgebraicStructureTraits_::IsZero`. More...

typedef unspecified_type	Is_one
	A model of `AlgebraicStructureTraits_::IsOne`. More...

typedef unspecified_type	Square
	A model of `AlgebraicStructureTraits_::Square`. More...

typedef unspecified_type	Simplify
	A model of `AlgebraicStructureTraits_::Simplify`. More...

typedef unspecified_type	Unit_part
	A model of `AlgebraicStructureTraits_::UnitPart`. More...

typedef unspecified_type	Integral_division
	A model of `AlgebraicStructureTraits_::IntegralDivision`. More...

typedef unspecified_type	Divides
	A model of `AlgebraicStructureTraits_::Divides`. More...

typedef unspecified_type	Is_square
	A model of `AlgebraicStructureTraits_::IsSquare`. More...

typedef unspecified_type	Gcd
	A model of `AlgebraicStructureTraits_::Gcd`. More...

typedef unspecified_type	Mod
	A model of `AlgebraicStructureTraits_::Mod`. More...

typedef unspecified_type	Div
	A model of `AlgebraicStructureTraits_::Div`. More...

typedef unspecified_type	Div_mod
	A model of `AlgebraicStructureTraits_::DivMod`. More...

typedef unspecified_type	Inverse
	A model of `AlgebraicStructureTraits_::Inverse`. More...

typedef unspecified_type	Sqrt
	A model of `AlgebraicStructureTraits_::Sqrt`. More...

typedef unspecified_type	Kth_root
	A model of `AlgebraicStructureTraits_::KthRoot`. More...

typedef unspecified_type	Root_of
	A model of `AlgebraicStructureTraits_::RootOf`. More...

Member Typedef Documentation

typedef unspecified_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`

typedef unspecified_type 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.

typedef unspecified_type AlgebraicStructureTraits::Div

A model of AlgebraicStructureTraits_::Div.

Required by the concept EuclideanRing.

typedef unspecified_type AlgebraicStructureTraits::Div_mod

A model of AlgebraicStructureTraits_::DivMod.

Required by the concept EuclideanRing.

typedef unspecified_type AlgebraicStructureTraits::Divides

A model of AlgebraicStructureTraits_::Divides.

Required by the concept IntegralDomain.

typedef unspecified_type AlgebraicStructureTraits::Gcd

A model of AlgebraicStructureTraits_::Gcd.

Required by the concept UniqueFactorizationDomain.

typedef unspecified_type AlgebraicStructureTraits::Integral_division

A model of AlgebraicStructureTraits_::IntegralDivision.

Required by the concept IntegralDomain.

typedef unspecified_type AlgebraicStructureTraits::Inverse

A model of AlgebraicStructureTraits_::Inverse.

Required by the concept Field.

typedef unspecified_type 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.

typedef unspecified_type 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.

typedef unspecified_type AlgebraicStructureTraits::Is_one

A model of AlgebraicStructureTraits_::IsOne.

Required by the concept IntegralDomainWithoutDivision.

typedef unspecified_type AlgebraicStructureTraits::Is_square

A model of AlgebraicStructureTraits_::IsSquare.

Required by the concept IntegralDomainWithoutDivision.

typedef unspecified_type AlgebraicStructureTraits::Is_zero