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.

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.

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`.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Member Typedef Documentation

◆ Algebraic_category

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`

◆ Boolean

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 CGAL::Uncertain<bool> or some similar type.

◆ Div

typedef unspecified_type AlgebraicStructureTraits::Div

A model of AlgebraicStructureTraits_::Div.

Required by the concept EuclideanRing.

◆ Div_mod

typedef unspecified_type AlgebraicStructureTraits::Div_mod

A model of AlgebraicStructureTraits_::DivMod.

Required by the concept EuclideanRing.

◆ Divides

typedef unspecified_type AlgebraicStructureTraits::Divides

A model of AlgebraicStructureTraits_::Divides.

Required by the concept IntegralDomain.

◆ Gcd

typedef unspecified_type AlgebraicStructureTraits::Gcd

A model of AlgebraicStructureTraits_::Gcd.

Required by the concept UniqueFactorizationDomain.

◆ Integral_division

typedef unspecified_type AlgebraicStructureTraits::Integral_division

A model of AlgebraicStructureTraits_::IntegralDivision.

Required by the concept IntegralDomain.

◆ Inverse

typedef unspecified_type AlgebraicStructureTraits::Inverse

A model of AlgebraicStructureTraits_::Inverse.

Required by the concept Field.

◆ Is_exact

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.