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update CGAL custom doxygen macros 

corresponds to a run of the script Documentation/conversion_tools/rename_macros.sh
+manual edit of doxyassist.xml and pkglist_filter.py
This commit is contained in:
Sébastien Loriot 2012-11-14 00:31:05 +01:00
parent bed259251c
commit 128b02abb8
1197 changed files with 5595 additions and 5595 deletions
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4
AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAABB_treeConcepts \ingroup PkgAABB_treeConcepts
\cgalconcept \cgalConcept
The concept `AABBGeomTraits` defines the requirements for the first template parameter of the class `CGAL::AABB_traits<AABBGeomTraits, AABBPrimitive>`. It provides predicates and constructors to detect and compute intersections between query objects and the primitives stored in the AABB tree. In addition, it contains predicates and constructors to compute distances between a point query and the primitives stored in the AABB tree. The concept `AABBGeomTraits` defines the requirements for the first template parameter of the class `CGAL::AABB_traits<AABBGeomTraits, AABBPrimitive>`. It provides predicates and constructors to detect and compute intersections between query objects and the primitives stored in the AABB tree. In addition, it contains predicates and constructors to compute distances between a point query and the primitives stored in the AABB tree.
\hasModel Any Kernel is a model of this traits concept. \cgalHasModel Any Kernel is a model of this traits concept.
\sa `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>` \sa `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>`

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AABB_tree/doc/AABB_tree/Concepts/AABBPrimitive.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAABB_treeConcepts \ingroup PkgAABB_treeConcepts
\cgalconcept \cgalConcept
The concept `AABBPrimitive` describes the requirements for the primitives stored in the AABB tree data structure. The concept encapsulates a type for the input datum (a geometric object) and an identifier (id) type through which those primitives are referred to. The concept `AABBPrimitive` also refines the concepts DefaultConstructible and Assignable. The concept `AABBPrimitive` describes the requirements for the primitives stored in the AABB tree data structure. The concept encapsulates a type for the input datum (a geometric object) and an identifier (id) type through which those primitives are referred to. The concept `AABBPrimitive` also refines the concepts DefaultConstructible and Assignable.
@ -11,8 +11,8 @@ The concept `AABBPrimitive` describes the requirements for the primitives stored
The `Primitive` type can be, e.g., a wrapper around a `Handle`. Assume for instance that the input objects are the triangle faces of a mesh stored as a `CGAL::Polyhedron_3`. The `Datum` would be a `Triangle_3` and the `Id` would be a polyhedron `Face_handle`. Method `datum()` can return either a `Triangle_3` constructed on the fly from the face handle or a `Triangle_3` stored internally. This provides a way for the user to trade memory for efficiency. The `Primitive` type can be, e.g., a wrapper around a `Handle`. Assume for instance that the input objects are the triangle faces of a mesh stored as a `CGAL::Polyhedron_3`. The `Datum` would be a `Triangle_3` and the `Id` would be a polyhedron `Face_handle`. Method `datum()` can return either a `Triangle_3` constructed on the fly from the face handle or a `Triangle_3` stored internally. This provides a way for the user to trade memory for efficiency.
\hasModel `CGAL::AABB_polyhedron_triangle_primitive<GeomTraits,Polyhedron>` \cgalHasModel `CGAL::AABB_polyhedron_triangle_primitive<GeomTraits,Polyhedron>`
\hasModel `CGAL::AABB_polyhedron_segment_primitive<GeomTraits,Polyhedron>` \cgalHasModel `CGAL::AABB_polyhedron_segment_primitive<GeomTraits,Polyhedron>`
*/ */

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AABB_tree/doc/AABB_tree/Concepts/AABBTraits.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAABB_treeConcepts \ingroup PkgAABB_treeConcepts
\cgalconcept \cgalConcept
The concept `AABBTraits` provides the geometric primitive types and methods for the class `CGAL::AABB_tree<AABBTraits>`. The concept `AABBTraits` provides the geometric primitive types and methods for the class `CGAL::AABB_tree<AABBTraits>`.
\hasModel `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>` \cgalHasModel `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>`
\sa `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>` \sa `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>`
\sa `CGAL::AABB_tree<AABBTraits>` \sa `CGAL::AABB_tree<AABBTraits>`

28
AABB_tree/doc/AABB_tree/PackageDescription.txt
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@ -5,18 +5,18 @@
/*! /*!
\addtogroup PkgAABB_tree \addtogroup PkgAABB_tree
\PkgDescriptionBegin{3D Fast Intersection and Distance Computation,PkgAABB_treeSummary} \cgalPkgDescriptionBegin{3D Fast Intersection and Distance Computation,PkgAABB_treeSummary}
\PkgPicture{aabb-teaser-thumb.png} \cgalPkgPicture{aabb-teaser-thumb.png}
\PkgSummaryBegin \cgalPkgSummaryBegin
\PkgAuthors{Pierre Alliez, St&eacute;phane Tayeb, Camille Wormser} \cgalPkgAuthors{Pierre Alliez, St&eacute;phane Tayeb, Camille Wormser}
\PkgDesc{The AABB (axis-aligned bounding box) tree component offers a static data structure and algorithms to perform efficient intersection and distance queries on sets of finite 3D geometric objects.} \cgalPkgDesc{The AABB (axis-aligned bounding box) tree component offers a static data structure and algorithms to perform efficient intersection and distance queries on sets of finite 3D geometric objects.}
\PkgManuals{Chapter_3D_Fast_Intersection_and_Distance_Computation,PkgAABB_tree} \cgalPkgManuals{Chapter_3D_Fast_Intersection_and_Distance_Computation,PkgAABB_tree}
\PkgSummaryEnd \cgalPkgSummaryEnd
\PkgShortInfoBegin \cgalPkgShortInfoBegin
\PkgSince{1.0} \cgalPkgSince{1.0}
\PkgBib{cgal:atw-aabb} \cgalPkgBib{cgal:atw-aabb}
\PkgLicense{\ref licensesGPL "GPL"} \cgalPkgLicense{\ref licensesGPL "GPL"}
\PkgDemo{AABB Tree,AABB_demo.zip} \cgalPkgDemo{AABB Tree,AABB_demo.zip}
\PkgShortInfoEnd \cgalPkgShortInfoEnd
\PkgDescriptionEnd \cgalPkgDescriptionEnd
*/ */

16
AABB_tree/doc/AABB_tree/aabb_tree.txt
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@ -4,7 +4,7 @@ namespace CGAL {
\mainpage 3D %Fast Intersection and Distance Computation (AABB Tree) \mainpage 3D %Fast Intersection and Distance Computation (AABB Tree)
\anchor Chapter_3D_Fast_Intersection_and_Distance_Computation \anchor Chapter_3D_Fast_Intersection_and_Distance_Computation
\autotoc \cgalAutoToc
\authors Pierre Alliez, Stephane Tayeb, and Camille Wormser \authors Pierre Alliez, Stephane Tayeb, and Camille Wormser
@ -41,9 +41,9 @@ well the as id (here the face handle) of the intersected
primitives. Similarly, each distance query can return the closest primitives. Similarly, each distance query can return the closest
point from the point query as well as the id of the closest primitive. point from the point query as well as the id of the closest primitive.
\cgal_figure_begin{aabbtree_meca,anchor.png} \cgalFigureBegin{aabbtree_meca,anchor.png}
Left: surface triangle mesh of a mechanical part. Right AABB tree constructed. Left: surface triangle mesh of a mechanical part. Right AABB tree constructed.
\cgal_figure_end \cgalFigureEnd
\section aabb_tree_interface Interface \section aabb_tree_interface Interface
@ -107,7 +107,7 @@ iterator in the list as `id`. We compute the number of input
triangles intersected by a ray query, as well as the closest point and triangles intersected by a ray query, as well as the closest point and
the squared distance from a point query. the squared distance from a point query.
\cgalexample{AABB_tree/AABB_triangle_3_example.cpp} \cgalExample{AABB_tree/AABB_triangle_3_example.cpp}
\subsection aabb_tree_examples_2 Tree of Polyhedron Triangle Facets for Intersection Queries \subsection aabb_tree_examples_2 Tree of Polyhedron Triangle Facets for Intersection Queries
@ -192,7 +192,7 @@ option which maximizes speed.
The surface triangle mesh chosen for benchmarking the tree The surface triangle mesh chosen for benchmarking the tree
construction is the knot model (14,400 triangles) depicted by construction is the knot model (14,400 triangles) depicted by
\cgal_figure_ref{figAABB-tree-bench}. We measure the tree construction time (both \cgalFigureRef{figAABB-tree-bench}. We measure the tree construction time (both
AABB tree alone and AABB tree with internal KD-tree) for this model as AABB tree alone and AABB tree with internal KD-tree) for this model as
well as for three denser versions subdivided through the Loop well as for three denser versions subdivided through the Loop
subdivision scheme which multiplies the number of triangles by four. subdivision scheme which multiplies the number of triangles by four.
@ -260,15 +260,15 @@ the intersection functions which enumerate all intersections.
| AABB_tree::all_intersections() | 46,507 | 38,471 | 36,374 | 2,644 | | AABB_tree::all_intersections() | 46,507 | 38,471 | 36,374 | 2,644 |
Curve of \cgal_figure_ref{figAABB-tree-bench} plots the number of queries per second Curve of \cgalFigureRef{figAABB-tree-bench} plots the number of queries per second
(here the `AABB_tree::all_intersections()` function with random segment (here the `AABB_tree::all_intersections()` function with random segment
queries) against the number of input triangles for the knot triangle queries) against the number of input triangles for the knot triangle
surface mesh. surface mesh.
\cgal_figure_begin{figAABB-tree-bench,bench.png} \cgalFigureBegin{figAABB-tree-bench,bench.png}
Number of queries per second against number of triangles for the knot model with 14K (shown), 57K, 230K and 921K triangles. We call the `all_intersections` function with segment queries randomly chosen within the bounding box. Number of queries per second against number of triangles for the knot model with 14K (shown), 57K, 230K and 921K triangles. We call the `all_intersections` function with segment queries randomly chosen within the bounding box.
\cgal_figure_end \cgalFigureEnd
The following table measures the number of `AABB_tree::all_intersections()` The following table measures the number of `AABB_tree::all_intersections()`
queries per second against several kernels. We use the 14,400 triangle queries per second against several kernels. We use the 14,400 triangle

20
Algebraic_foundations/doc/Algebraic_foundations/Algebraic_foundations.txt
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@ -4,7 +4,7 @@ namespace CGAL {
\mainpage Algebraic Foundations \mainpage Algebraic Foundations
\anchor Chapter_Algebraic_Foundations \anchor Chapter_Algebraic_Foundations
\autotoc \cgalAutoToc
\author Michael Hemmer \author Michael Hemmer
\section Algebraic_foundationsIntroduction Introduction \section Algebraic_foundationsIntroduction Introduction
@ -31,11 +31,11 @@ it was not desirable to cover all known algebraic structures,
e.g., we did not introduce concepts for such basic structures as <I>groups</I> or e.g., we did not introduce concepts for such basic structures as <I>groups</I> or
exceptional structures as <I>skew fields</I>. exceptional structures as <I>skew fields</I>.
\cgal_figure_begin{figConceptHierarchyOfAlgebraicStructures,AlgebraicConceptHierarchy.gif} \cgalFigureBegin{figConceptHierarchyOfAlgebraicStructures,AlgebraicConceptHierarchy.gif}
Concept Hierarchy of Algebraic Structures Concept Hierarchy of Algebraic Structures
\cgal_figure_end \cgalFigureEnd
\cgal_figure_ref{figConceptHierarchyOfAlgebraicStructures} shows the refinement \cgalFigureRef{figConceptHierarchyOfAlgebraicStructures} shows the refinement
relationship of the algebraic structure concepts. relationship of the algebraic structure concepts.
`IntegralDomain`, `UniqueFactorizationDomain`, `EuclideanRing` and `IntegralDomain`, `UniqueFactorizationDomain`, `EuclideanRing` and
`Field` correspond to the algebraic structures with the `Field` correspond to the algebraic structures with the
@ -126,7 +126,7 @@ The following example illustrates a dispatch for `Field`s using overloaded
functions. The example only needs two overloads since the algebraic functions. The example only needs two overloads since the algebraic
category tags reflect the algebraic structure hierarchy. category tags reflect the algebraic structure hierarchy.
\cgalexample{Algebraic_foundations/algebraic_structure_dispatch.cpp} \cgalExample{Algebraic_foundations/algebraic_structure_dispatch.cpp}
\section Algebraic_foundationsRealE Real Embeddable \section Algebraic_foundationsRealE Real Embeddable
@ -177,7 +177,7 @@ concepts `Field` and `RealEmbeddable`, while
`RingNumberType` combines `IntegralDomainWithoutDivision` and `RingNumberType` combines `IntegralDomainWithoutDivision` and
`RealEmbeddable`. Algebraically, the real number types do not form `RealEmbeddable`. Algebraically, the real number types do not form
distinct structures and are therefore not listed in the concept distinct structures and are therefore not listed in the concept
hierarchy of \cgal_figure_ref{figConceptHierarchyOfAlgebraicStructures}. hierarchy of \cgalFigureRef{figConceptHierarchyOfAlgebraicStructures}.
\section Algebraic_foundationsInteroperability Interoperability \section Algebraic_foundationsInteroperability Interoperability
@ -221,7 +221,7 @@ provided by `Algebraic_structure_traits` and `Real_embeddable_traits` of
The following example illustrates how two write code for The following example illustrates how two write code for
`ExplicitInteroperable` types. `ExplicitInteroperable` types.
\cgalexample{Algebraic_foundations/interoperable.cpp} \cgalExample{Algebraic_foundations/interoperable.cpp}
The following example illustrates a dispatch for `ImplicitInteroperable` and The following example illustrates a dispatch for `ImplicitInteroperable` and
`ExplicitInteroperable` types. `ExplicitInteroperable` types.
@ -229,7 +229,7 @@ The binary function (that just multiplies its two arguments) is supposed to
take two `ExplicitInteroperable` arguments. For `ImplicitInteroperable` take two `ExplicitInteroperable` arguments. For `ImplicitInteroperable`
types a variant that avoids the explicit cast is selected. types a variant that avoids the explicit cast is selected.
\cgalexample{Algebraic_foundations/implicit_interoperable_dispatch.cpp} \cgalExample{Algebraic_foundations/implicit_interoperable_dispatch.cpp}
\section Algebraic_foundationsFractions Fractions \section Algebraic_foundationsFractions Fractions
@ -254,14 +254,14 @@ it is more general and offers dispatching functionality.
\subsection Algebraic_foundationsExamples_1 Examples \subsection Algebraic_foundationsExamples_1 Examples
The following example show a simple use of `Fraction_traits`: The following example show a simple use of `Fraction_traits`:
\cgalexample{Algebraic_foundations/fraction_traits.cpp} \cgalExample{Algebraic_foundations/fraction_traits.cpp}
The following example illustrates the integralization of a vector, The following example illustrates the integralization of a vector,
i.e., the coefficient vector of a polynomial. Note that for minimizing i.e., the coefficient vector of a polynomial. Note that for minimizing
coefficient growth `Fraction_traits<Type>::Common_factor` is used to coefficient growth `Fraction_traits<Type>::Common_factor` is used to
compute the 'least' common multiple of the denominators. compute the 'least' common multiple of the denominators.
\cgalexample{Algebraic_foundations/integralize.cpp} \cgalExample{Algebraic_foundations/integralize.cpp}
\section Algebraic_foundationsDesign Design and Implementation History \section Algebraic_foundationsDesign Design and Implementation History

18
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Algebraic_structure_traits.h
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@ -5,7 +5,7 @@ namespace CGAL {
An instance of `Algebraic_structure_traits` is a model of `AlgebraicStructureTraits`, where <span class="textsc">T</span> is the associated type. An instance of `Algebraic_structure_traits` is a model of `AlgebraicStructureTraits`, where <span class="textsc">T</span> is the associated type.
\models ::AlgebraicStructureTraits \cgalModels ::AlgebraicStructureTraits
*/ */
template< typename T > template< typename T >
@ -22,7 +22,7 @@ namespace CGAL {
Tag indicating that a type is a model of the Tag indicating that a type is a model of the
`EuclideanRing` concept. `EuclideanRing` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `EuclideanRing` \sa `EuclideanRing`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`
@ -38,7 +38,7 @@ class Euclidean_ring_tag : public Unique_factorization_domain_tag {
Tag indicating that a type is a model of the `Field` concept. Tag indicating that a type is a model of the `Field` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `Field` \sa `Field`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`
@ -54,7 +54,7 @@ class Field_tag : public Integral_domain_tag {
Tag indicating that a type is a model of the `FieldWithKthRoot` concept. Tag indicating that a type is a model of the `FieldWithKthRoot` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `FieldWithKthRoot` \sa `FieldWithKthRoot`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`
@ -70,7 +70,7 @@ class Field_with_kth_root_tag : public Field_with_sqrt_tag {
Tag indicating that a type is a model of the `FieldWithRootOf` concept. Tag indicating that a type is a model of the `FieldWithRootOf` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `FieldWithRootOf` \sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`
@ -86,7 +86,7 @@ class Field_with_root_of_tag : public Field_with_kth_root_tag {
Tag indicating that a type is a model of the `FieldWithSqrt` concept. Tag indicating that a type is a model of the `FieldWithSqrt` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `FieldWithSqrt` \sa `FieldWithSqrt`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`
@ -102,7 +102,7 @@ class Field_with_sqrt_tag : public Field_tag {
Tag indicating that a type is a model of the `IntegralDomain` concept. Tag indicating that a type is a model of the `IntegralDomain` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `IntegralDomain` \sa `IntegralDomain`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`
@ -118,7 +118,7 @@ class Integral_domain_tag : public Integral_domain_without_division_tag {
Tag indicating that a type is a model of the `IntegralDomainWithoutDivision` concept. Tag indicating that a type is a model of the `IntegralDomainWithoutDivision` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `IntegralDomainWithoutDivision` \sa `IntegralDomainWithoutDivision`
@ -133,7 +133,7 @@ class Integral_domain_without_division_tag {
Tag indicating that a type is a model of the `UniqueFactorizationDomain` concept. Tag indicating that a type is a model of the `UniqueFactorizationDomain` concept.
\models ::DefaultConstructible \cgalModels ::DefaultConstructible
\sa `UniqueFactorizationDomain` \sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits` \sa `AlgebraicStructureTraits`

2
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Fraction_traits.h
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@ -6,7 +6,7 @@ namespace CGAL {
An instance of `Fraction_traits` is a model of `FractionTraits`, An instance of `Fraction_traits` is a model of `FractionTraits`,
where `T` is the associated type. where `T` is the associated type.
\models ::FractionTraits \cgalModels ::FractionTraits
*/ */
template< typename T > template< typename T >

2
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Real_embeddable_traits.h
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@ -6,7 +6,7 @@ namespace CGAL {
An instance of `Real_embeddable_traits` is a model of `RealEmbeddableTraits`, where <span class="textsc">T</span> is the associated type. An instance of `Real_embeddable_traits` is a model of `RealEmbeddableTraits`, where <span class="textsc">T</span> is the associated type.
\models ::RealEmbeddableTraits \cgalModels ::RealEmbeddableTraits
*/ */
template< typename T > template< typename T >

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Div.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` computes the integral quotient of division `AdaptableBinaryFunction` computes the integral quotient of division
with remainder. with remainder.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits
\sa ::AlgebraicStructureTraits::Mod \sa ::AlgebraicStructureTraits::Mod

6
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--DivMod.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableFunctor` computes both integral quotient and remainder `AdaptableFunctor` computes both integral quotient and remainder
of division with remainder. The quotient \f$ q\f$ and remainder \f$ r\f$ are computed of division with remainder. The quotient \f$ q\f$ and remainder \f$ r\f$ are computed
such that \f$ x = q*y + r\f$ and \f$ |r| < |y|\f$ with respect to the proper integer norm of such that \f$ x = q*y + r\f$ and \f$ |r| < |y|\f$ with respect to the proper integer norm of
the represented ring. the represented ring.
\footnote{For integers this norm is the absolute value. \cgalFootnote{For integers this norm is the absolute value.
For univariate polynomials this norm is the degree.} For univariate polynomials this norm is the degree.}
In particular, \f$ r\f$ is chosen to be \f$ 0\f$ if possible. In particular, \f$ r\f$ is chosen to be \f$ 0\f$ if possible.
Moreover, we require \f$ q\f$ to be minimized with respect to the proper integer norm. Moreover, we require \f$ q\f$ to be minimized with respect to the proper integer norm.
@ -187,7 +187,7 @@ r
</TABLE> </TABLE>
\refines `AdaptableFunctor` \cgalRefines `AdaptableFunctor`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits
\sa ::AlgebraicStructureTraits::Mod \sa ::AlgebraicStructureTraits::Mod

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Divides.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction`, `AdaptableBinaryFunction`,
returns true if the first argument divides the second argument. returns true if the first argument divides the second argument.
@ -14,7 +14,7 @@ This functor is required to provide two operators. The first operator takes two
arguments and returns true if the first argument divides the second argument. arguments and returns true if the first argument divides the second argument.
The second operator returns \f$ c\f$ via the additional third argument. The second operator returns \f$ c\f$ via the additional third argument.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits
\sa ::AlgebraicStructureTraits::IntegralDivision \sa ::AlgebraicStructureTraits::IntegralDivision

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Gcd.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` providing the gcd. `AdaptableBinaryFunction` providing the gcd.
@ -15,7 +15,7 @@ unit-normal (i.e.\ have unit part 1).
to the partial order of divisibility. This is because an element \f$ a \in R\f$ is said to divide \f$ b \in R\f$, iff \f$ \exists r \in R\f$ such that \f$ a \cdot r = b\f$. to the partial order of divisibility. This is because an element \f$ a \in R\f$ is said to divide \f$ b \in R\f$, iff \f$ \exists r \in R\f$ such that \f$ a \cdot r = b\f$.
Thus, \f$ 0\f$ is divided by every element of the Ring, in particular by itself. Thus, \f$ 0\f$ is divided by every element of the Ring, in particular by itself.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IntegralDivision.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` providing an integral division. `AdaptableBinaryFunction` providing an integral division.
@ -11,7 +11,7 @@ exists (i.e.\ if \f$ x\f$ is divisible by \f$ y\f$). Otherwise the effect of inv
this operation is undefined. Since the ring represented is an integral domain, this operation is undefined. Since the ring represented is an integral domain,
\f$ z\f$ is uniquely defined if it exists. \f$ z\f$ is uniquely defined if it exists.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits
\sa ::AlgebraicStructureTraits::Divides \sa ::AlgebraicStructureTraits::Divides

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Inverse.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction` providing the inverse element with `AdaptableUnaryFunction` providing the inverse element with
respect to multiplication of a `Field`. respect to multiplication of a `Field`.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IsOne.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction`, `AdaptableUnaryFunction`,
returns true in case the argument is the one of the ring. returns true in case the argument is the one of the ring.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IsSquare.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` that computes whether the first argument is a square. `AdaptableBinaryFunction` that computes whether the first argument is a square.
If the first argument is a square the second argument, which is taken by reference, contains the square root. If the first argument is a square the second argument, which is taken by reference, contains the square root.
@ -11,7 +11,7 @@ A ring element \f$ x\f$ is said to be a square iff there exists a ring element \
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`, that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units. \f$ y\f$ is uniquely defined up to multiplication by units.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IsZero.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is the zero element of the ring. `AdaptableUnaryFunction`, returns true in case the argument is the zero element of the ring.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits
\sa ::RealEmbeddableTraits::IsZero \sa ::RealEmbeddableTraits::IsZero

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--KthRoot.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` providing the k-th root. `AdaptableBinaryFunction` providing the k-th root.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::FieldWithRootOf \sa ::FieldWithRootOf
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Mod.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` computes the remainder of division with remainder. `AdaptableBinaryFunction` computes the remainder of division with remainder.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits
\sa ::AlgebraicStructureTraits::Div \sa ::AlgebraicStructureTraits::Div

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--RootOf.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableFunctor` computes a real root of a square-free univariate `AdaptableFunctor` computes a real root of a square-free univariate
polynomial. polynomial.
\refines `AdaptableFunctor` \cgalRefines `AdaptableFunctor`
\sa ::FieldWithRootOf \sa ::FieldWithRootOf
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Simplify.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
This `AdaptableUnaryFunction` may simplify a given object. This `AdaptableUnaryFunction` may simplify a given object.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Sqrt.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction` providing the square root. `AdaptableUnaryFunction` providing the square root.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Square.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction`, computing the square of the argument. `AdaptableUnaryFunction`, computing the square of the argument.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--UnitPart.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
This `AdaptableUnaryFunction` computes the unit part of a given ring This `AdaptableUnaryFunction` computes the unit part of a given ring
element. element.
@ -19,7 +19,7 @@ hence the unit-part of a non-zero integer is its sign. For a `Field`, every
non-zero element is a unit and is its own unit part, its unit normal non-zero element is a unit and is its own unit part, its unit normal
associate being one. The unit part of zero is, by convention, one. associate being one. The unit part of zero is, by convention, one.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::AlgebraicStructureTraits \sa ::AlgebraicStructureTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `AlgebraicStructureTraits` reflects the algebraic structure A model of `AlgebraicStructureTraits` reflects the algebraic structure
of an associated type `Type`. of an associated type `Type`.
@ -28,7 +28,7 @@ algebraic operations within that structure.
\sa ::CGAL::Field_with_kth_root_tag \sa ::CGAL::Field_with_kth_root_tag
\sa ::CGAL::Field_with_root_of_tag \sa ::CGAL::Field_with_root_of_tag
\hasModel `CGAL::Algebraic_structure_traits<T>` \cgalHasModel `CGAL::Algebraic_structure_traits<T>`
*/ */

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/EuclideanRing.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `EuclideanRing` represents an euclidean ring (or Euclidean domain). A model of `EuclideanRing` represents an euclidean ring (or Euclidean domain).
It is an `UniqueFactorizationDomain` that affords a suitable notion of minimality of remainders It is an `UniqueFactorizationDomain` that affords a suitable notion of minimality of remainders
@ -23,7 +23,7 @@ The most prominent example of a Euclidean ring are the integers.
Whenever both \f$ x\f$ and \f$ y\f$ are positive, then it is conventional to choose Whenever both \f$ x\f$ and \f$ y\f$ are positive, then it is conventional to choose
the smallest positive remainder \f$ r\f$. the smallest positive remainder \f$ r\f$.
\refines `UniqueFactorizationDomain` \cgalRefines `UniqueFactorizationDomain`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

2
Algebraic_foundations/doc/Algebraic_foundations/Concepts/ExplicitInteroperable.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsInteroperabilityConcepts \ingroup PkgAlgebraicFoundationsInteroperabilityConcepts
\cgalconcept \cgalConcept
Two types `A` and `B` are a model of the `ExplicitInteroperable` Two types `A` and `B` are a model of the `ExplicitInteroperable`
concept, if it is possible to derive a superior type for `A` and `B`, concept, if it is possible to derive a superior type for `A` and `B`,

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/Field.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `Field` is an `IntegralDomain` in which every non-zero element A model of `Field` is an `IntegralDomain` in which every non-zero element
has a multiplicative inverse. has a multiplicative inverse.
@ -17,7 +17,7 @@ Moreover, `CGAL::Algebraic_structure_traits< Field >` is a model of
- `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Inverse` - `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Inverse`
\refines `IntegralDomain` \cgalRefines `IntegralDomain`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

26
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldNumberType.h
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@ -1,25 +1,25 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsRealNumberTypesConcepts \ingroup PkgAlgebraicFoundationsRealNumberTypesConcepts
\cgalconcept \cgalConcept
The concept `FieldNumberType` combines the requirements of the concepts The concept `FieldNumberType` combines the requirements of the concepts
`Field` and `RealEmbeddable`. `Field` and `RealEmbeddable`.
A model of `FieldNumberType` can be used as a template parameter A model of `FieldNumberType` can be used as a template parameter
for Cartesian kernels. for Cartesian kernels.
\refines `Field` \cgalRefines `Field`
\refines `RealEmbeddable` \cgalRefines `RealEmbeddable`
\hasModel float \cgalHasModel float
\hasModel double \cgalHasModel double
\hasModel `CGAL::Gmpq` \cgalHasModel `CGAL::Gmpq`
\hasModel `CGAL::Interval_nt` \cgalHasModel `CGAL::Interval_nt`
\hasModel \ref CGAL::Interval_nt_advanced \cgalHasModel \ref CGAL::Interval_nt_advanced
\hasModel `CGAL::Lazy_exact_nt<FieldNumberType>` \cgalHasModel `CGAL::Lazy_exact_nt<FieldNumberType>`
\hasModel `CGAL::Quotient<RingNumberType>` \cgalHasModel `CGAL::Quotient<RingNumberType>`
\hasModel `CGAL::leda_rational` \cgalHasModel `CGAL::leda_rational`
\hasModel `CGAL::leda_bigfloat` \cgalHasModel `CGAL::leda_bigfloat`
\hasModel `CGAL::leda_real` \cgalHasModel `CGAL::leda_real`
\sa `RingNumberType` \sa `RingNumberType`
\sa `Kernel` \sa `Kernel`

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldWithKthRoot.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `FieldWithKthRoot` is a `FieldWithSqrt` that has operations to take k-th roots. A model of `FieldWithKthRoot` is a `FieldWithSqrt` that has operations to take k-th roots.
@ -11,7 +11,7 @@ Moreover, `CGAL::Algebraic_structure_traits< FieldWithKthRoot >` is a model of `
- `CGAL::Algebraic_structure_traits< FieldWithKthRoot >::Kth_root` - `CGAL::Algebraic_structure_traits< FieldWithKthRoot >::Kth_root`
\refines `FieldWithSqrt` \cgalRefines `FieldWithSqrt`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldWithRootOf.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `FieldWithRootOf` is a `FieldWithKthRoot` with the possibility to A model of `FieldWithRootOf` is a `FieldWithKthRoot` with the possibility to
construct it as the root of a univariate polynomial. construct it as the root of a univariate polynomial.
@ -11,7 +11,7 @@ Moreover, `CGAL::Algebraic_structure_traits< FieldWithRootOf >` is a model of `A
- `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Algebraic_type` derived from `CGAL::Field_with_kth_root_tag` - `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Algebraic_type` derived from `CGAL::Field_with_kth_root_tag`
- `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Root_of` which is a model of `AlgebraicStructureTraits::RootOf` - `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Root_of` which is a model of `AlgebraicStructureTraits::RootOf`
\refines `FieldWithKthRoot` \cgalRefines `FieldWithKthRoot`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldWithSqrt.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `FieldWithSqrt` is a `Field` that has operations to take square roots. A model of `FieldWithSqrt` is a `Field` that has operations to take square roots.
@ -10,7 +10,7 @@ Moreover, `CGAL::Algebraic_structure_traits< FieldWithSqrt >` is a model of `Alg
- `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Algebraic_type` derived from `CGAL::Field_with_sqrt_tag` - `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Algebraic_type` derived from `CGAL::Field_with_sqrt_tag`
- `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Sqrt` which is a model of `AlgebraicStructureTraits::Sqrt` - `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Sqrt` which is a model of `AlgebraicStructureTraits::Sqrt`
\refines `Field` \cgalRefines `Field`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

2
Algebraic_foundations/doc/Algebraic_foundations/Concepts/Fraction.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsFractionsConcepts \ingroup PkgAlgebraicFoundationsFractionsConcepts
\cgalconcept \cgalConcept
A type is considered as a `Fraction`, if there is a reasonable way to A type is considered as a `Fraction`, if there is a reasonable way to
decompose it into a numerator and denominator. In this case the relevant decompose it into a numerator and denominator. In this case the relevant

14
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FractionTraits.h
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@ -1,14 +1,14 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsFractionsConcepts \ingroup PkgAlgebraicFoundationsFractionsConcepts
\cgalconcept \cgalConcept
A model of `FractionTraits` is associated with a type `Type`. A model of `FractionTraits` is associated with a type `Type`.
In case the associated type is a `Fraction`, a model of `FractionTraits` provides the relevant functionality for decomposing and re-composing as well In case the associated type is a `Fraction`, a model of `FractionTraits` provides the relevant functionality for decomposing and re-composing as well
as the numerator and denominator type. as the numerator and denominator type.
\hasModel `CGAL::Fraction_traits<T>` \cgalHasModel `CGAL::Fraction_traits<T>`
\sa `FractionTraits::Decompose` \sa `FractionTraits::Decompose`
\sa `FractionTraits::Compose` \sa `FractionTraits::Compose`
@ -56,7 +56,7 @@ typedef Hidden_type Denominator_type;
/*! /*!
\ingroup PkgAlgebraicFoundationsFractionsConcepts \ingroup PkgAlgebraicFoundationsFractionsConcepts
\cgalconcept \cgalConcept
Functor decomposing a `Fraction` into its numerator and denominator. Functor decomposing a `Fraction` into its numerator and denominator.
@ -86,11 +86,11 @@ FractionTraits::Denominator_type & d);
/*! /*!
\ingroup PkgAlgebraicFoundationsFractionsConcepts \ingroup PkgAlgebraicFoundationsFractionsConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction`, returns the fraction of its arguments. `AdaptableBinaryFunction`, returns the fraction of its arguments.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `Fraction` \sa `Fraction`
\sa `FractionTraits` \sa `FractionTraits`
@ -137,7 +137,7 @@ result_type operator()(first_argument_type n, second_argument_type d);
/*! /*!
\ingroup PkgAlgebraicFoundationsFractionsConcepts \ingroup PkgAlgebraicFoundationsFractionsConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction`, finds great common factor of denominators. `AdaptableBinaryFunction`, finds great common factor of denominators.
@ -145,7 +145,7 @@ This can be considered as a relaxed version of `AlgebraicStructureTraits::Gcd`,
this is needed because it is not guaranteed that `FractionTraits::Denominator_type` is a model of this is needed because it is not guaranteed that `FractionTraits::Denominator_type` is a model of
`UniqueFactorizationDomain`. `UniqueFactorizationDomain`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `Fraction` \sa `Fraction`
\sa `FractionTraits` \sa `FractionTraits`

2
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FromDoubleConstructible.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsMiscellaneousConcepts \ingroup PkgAlgebraicFoundationsMiscellaneousConcepts
\cgalconcept \cgalConcept
A model of the concept `FromDoubleConstructible` is required A model of the concept `FromDoubleConstructible` is required
to be constructible from the type `double`. to be constructible from the type `double`.

8
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FromIntConstructible.h
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@ -1,14 +1,14 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsMiscellaneousConcepts \ingroup PkgAlgebraicFoundationsMiscellaneousConcepts
\cgalconcept \cgalConcept
A model of the concept `FromIntConstructible` is required A model of the concept `FromIntConstructible` is required
to be constructible from int. to be constructible from int.
\hasModel int \cgalHasModel int
\hasModel long \cgalHasModel long
\hasModel double \cgalHasModel double
*/ */

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/ImplicitInteroperable.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsInteroperabilityConcepts \ingroup PkgAlgebraicFoundationsInteroperabilityConcepts
\cgalconcept \cgalConcept
Two types `A` and `B` are a model of the concept Two types `A` and `B` are a model of the concept
`ImplicitInteroperable`, if there is a superior type, such that `ImplicitInteroperable`, if there is a superior type, such that
@ -15,7 +15,7 @@ In this case
\link CGAL::Coercion_traits::Are_implicit_interoperable `CGAL::Coercion_traits<A,B>::Are_implicit_interoperable`\endlink \link CGAL::Coercion_traits::Are_implicit_interoperable `CGAL::Coercion_traits<A,B>::Are_implicit_interoperable`\endlink
is `CGAL::Tag_true`. is `CGAL::Tag_true`.
\refines `ExplicitInteroperable` \cgalRefines `ExplicitInteroperable`
\sa `CGAL::Coercion_traits<A,B>` \sa `CGAL::Coercion_traits<A,B>`
\sa `ExplicitInteroperable` \sa `ExplicitInteroperable`

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/IntegralDomain.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
`IntegralDomain` refines `IntegralDomainWithoutDivision` by `IntegralDomain` refines `IntegralDomainWithoutDivision` by
providing an integral division. providing an integral division.
@ -16,7 +16,7 @@ Moreover, `CGAL::Algebraic_structure_traits< IntegralDomain >` is a model of
- `CGAL::Algebraic_structure_traits< IntegralDomain >::Integral_division` which is a model of `AlgebraicStructureTraits::IntegralDivision` - `CGAL::Algebraic_structure_traits< IntegralDomain >::Integral_division` which is a model of `AlgebraicStructureTraits::IntegralDivision`
- `CGAL::Algebraic_structure_traits< IntegralDomain >::Divides` which is a model of `AlgebraicStructureTraits::Divides` - `CGAL::Algebraic_structure_traits< IntegralDomain >::Divides` which is a model of `AlgebraicStructureTraits::Divides`
\refines `IntegralDomainWithoutDivision` \cgalRefines `IntegralDomainWithoutDivision`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

12
Algebraic_foundations/doc/Algebraic_foundations/Concepts/IntegralDomainWithoutDivision.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
This is the most basic concept for algebraic structures considered within CGAL. This is the most basic concept for algebraic structures considered within CGAL.
@ -30,11 +30,11 @@ Moreover, `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >` is
- `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Simplify` which is a model of `AlgebraicStructureTraits::Simplify` - `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Simplify` which is a model of `AlgebraicStructureTraits::Simplify`
- `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Unit_part` which is a model of `AlgebraicStructureTraits::UnitPart` - `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Unit_part` which is a model of `AlgebraicStructureTraits::UnitPart`
\refines `Assignable` \cgalRefines `Assignable`
\refines `CopyConstructible` \cgalRefines `CopyConstructible`
\refines `DefaultConstructible` \cgalRefines `DefaultConstructible`
\refines `EqualityComparable` \cgalRefines `EqualityComparable`
\refines `FromIntConstructible` \cgalRefines `FromIntConstructible`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

6
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddable.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts \ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts
\cgalconcept \cgalConcept
A model of this concepts represents numbers that are embeddable on the real A model of this concepts represents numbers that are embeddable on the real
axis. The type obeys the algebraic structure and compares two values according axis. The type obeys the algebraic structure and compares two values according
@ -38,8 +38,8 @@ If a number type is a model of both `IntegralDomainWithoutDivision` and
`RealEmbeddable`, it follows that the ring represented by such a number type `RealEmbeddable`, it follows that the ring represented by such a number type
is a sub-ring of the real numbers and hence has characteristic zero. is a sub-ring of the real numbers and hence has characteristic zero.
\refines `Equality` Comparable \cgalRefines `Equality` Comparable
\refines `LessThanComparable` \cgalRefines `LessThanComparable`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--Abs.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts \ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction` computes the absolute value of a number. `AdaptableUnaryFunction` computes the absolute value of a number.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--Compare.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
`AdaptableBinaryFunction` compares two real embeddable numbers. `AdaptableBinaryFunction` compares two real embeddable numbers.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--IsNegative.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is negative. `AdaptableUnaryFunction`, returns true in case the argument is negative.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--IsPositive.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is positive. `AdaptableUnaryFunction`, returns true in case the argument is positive.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--IsZero.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is 0. `AdaptableUnaryFunction`, returns true in case the argument is 0.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits
\sa ::AlgebraicStructureTraits::IsZero \sa ::AlgebraicStructureTraits::IsZero

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--Sgn.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
This `AdaptableUnaryFunction` computes the sign of a real embeddable number. This `AdaptableUnaryFunction` computes the sign of a real embeddable number.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--ToDouble.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction` computes a double approximation of a real `AdaptableUnaryFunction` computes a double approximation of a real
embeddable number. embeddable number.
@ -9,7 +9,7 @@ embeddable number.
Remark: In order to control the quality of approximation one has to resort Remark: In order to control the quality of approximation one has to resort
to methods that are specific to NT. There are no general guarantees whatsoever. to methods that are specific to NT. There are no general guarantees whatsoever.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--ToInterval.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsConcepts \ingroup PkgAlgebraicFoundationsConcepts
\cgalconcept \cgalConcept
`AdaptableUnaryFunction` computes for a given real embeddable `AdaptableUnaryFunction` computes for a given real embeddable
number \f$ x\f$ a double interval containing \f$ x\f$. number \f$ x\f$ a double interval containing \f$ x\f$.
This interval is represented by `std::pair<double,double>`. This interval is represented by `std::pair<double,double>`.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa ::RealEmbeddableTraits \sa ::RealEmbeddableTraits

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts \ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts
\cgalconcept \cgalConcept
A model of `RealEmbeddableTraits` is associated to a number type A model of `RealEmbeddableTraits` is associated to a number type
`Type` and reflects the properties of this type with respect `Type` and reflects the properties of this type with respect
to the concept `RealEmbeddable`. to the concept `RealEmbeddable`.
\hasModel `CGAL::Real_embeddable_traits<T>` \cgalHasModel `CGAL::Real_embeddable_traits<T>`
*/ */
class RealEmbeddableTraits { class RealEmbeddableTraits {

32
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RingNumberType.h
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@ -1,29 +1,29 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsRealNumberTypesConcepts \ingroup PkgAlgebraicFoundationsRealNumberTypesConcepts
\cgalconcept \cgalConcept
The concept `RingNumberType` combines the requirements of the concepts The concept `RingNumberType` combines the requirements of the concepts
`IntegralDomainWithoutDivision` and `RealEmbeddable`. `IntegralDomainWithoutDivision` and `RealEmbeddable`.
A model of `RingNumberType` can be used as a template parameter A model of `RingNumberType` can be used as a template parameter
for Homogeneous kernels. for Homogeneous kernels.
\refines `IntegralDomainWithoutDivision` \cgalRefines `IntegralDomainWithoutDivision`
\refines `RealEmbeddable` \cgalRefines `RealEmbeddable`
\hasModel \cpp built-in number types \cgalHasModel \cpp built-in number types
\hasModel `CGAL::Gmpq` \cgalHasModel `CGAL::Gmpq`
\hasModel `CGAL::Gmpz` \cgalHasModel `CGAL::Gmpz`
\hasModel` CGAL::Interval_nt` \cgalHasModel` CGAL::Interval_nt`
\hasModel \ref CGAL::Interval_nt_advanced \cgalHasModel \ref CGAL::Interval_nt_advanced
\hasModel `CGAL::Lazy_exact_nt<RingNumberType>` \cgalHasModel `CGAL::Lazy_exact_nt<RingNumberType>`
\hasModel `CGAL::MP_Float` \cgalHasModel `CGAL::MP_Float`
\hasModel `CGAL::Gmpzf` \cgalHasModel `CGAL::Gmpzf`
\hasModel `CGAL::Quotient<RingNumberType>` \cgalHasModel `CGAL::Quotient<RingNumberType>`
\hasModel `CGAL::leda_integer` \cgalHasModel `CGAL::leda_integer`
\hasModel `CGAL::leda_rational` \cgalHasModel `CGAL::leda_rational`
\hasModel `CGAL::leda_bigfloat` \cgalHasModel `CGAL::leda_bigfloat`
\hasModel `CGAL::leda_real` \cgalHasModel `CGAL::leda_real`
\sa `FieldNumberType` \sa `FieldNumberType`

4
Algebraic_foundations/doc/Algebraic_foundations/Concepts/UniqueFactorizationDomain.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts \ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalconcept \cgalConcept
A model of `UniqueFactorizationDomain` is an `IntegralDomain` with the A model of `UniqueFactorizationDomain` is an `IntegralDomain` with the
additional property additional property
@ -23,7 +23,7 @@ is a model of `AlgebraicStructureTraits` providing:
derived from `CGAL::Unique_factorization_domain_tag` derived from `CGAL::Unique_factorization_domain_tag`
- `CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Gcd` which is a model of `AlgebraicStructureTraits::Gcd` - `CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Gcd` which is a model of `AlgebraicStructureTraits::Gcd`
\refines `IntegralDomain` \cgalRefines `IntegralDomain`
\sa ::IntegralDomainWithoutDivision \sa ::IntegralDomainWithoutDivision
\sa ::IntegralDomain \sa ::IntegralDomain

26
Algebraic_foundations/doc/Algebraic_foundations/PackageDescription.txt
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@ -48,19 +48,19 @@
\addtogroup PkgAlgebraicFoundations \addtogroup PkgAlgebraicFoundations
\todo check generated documentation \todo check generated documentation
\PkgDescriptionBegin{Algebraic Foundations,PkgAlgebraicFoundationsSummary} \cgalPkgDescriptionBegin{Algebraic Foundations,PkgAlgebraicFoundationsSummary}
\PkgPicture{Algebraic_foundations2.png} \cgalPkgPicture{Algebraic_foundations2.png}
\PkgSummaryBegin \cgalPkgSummaryBegin
\PkgAuthor{Michael Hemmer} \cgalPkgAuthor{Michael Hemmer}
\PkgDesc{This package defines what algebra means for \cgal, in terms of concepts, classes and functions. The main features are: (i) explicit concepts for interoperability of types (ii) separation between algebraic types (not necessarily embeddable into the reals), and number types (embeddable into the reals).} \cgalPkgDesc{This package defines what algebra means for \cgal, in terms of concepts, classes and functions. The main features are: (i) explicit concepts for interoperability of types (ii) separation between algebraic types (not necessarily embeddable into the reals), and number types (embeddable into the reals).}
\PkgManuals{Chapter_Algebraic_Foundations,PkgAlgebraicFoundations} \cgalPkgManuals{Chapter_Algebraic_Foundations,PkgAlgebraicFoundations}
\PkgSummaryEnd \cgalPkgSummaryEnd
\PkgShortInfoBegin \cgalPkgShortInfoBegin
\PkgSince{3.3} \cgalPkgSince{3.3}
\PkgBib{cgal:h-af} \cgalPkgBib{cgal:h-af}
\PkgLicense{\ref licensesLGPL "LGPL"} \cgalPkgLicense{\ref licensesLGPL "LGPL"}
\PkgShortInfoEnd \cgalPkgShortInfoEnd
\PkgDescriptionEnd \cgalPkgDescriptionEnd
\ref AlgebraicFoundationsClassified "Classified Reference Pages" \ref AlgebraicFoundationsClassified "Classified Reference Pages"

12
Algebraic_kernel_d/doc/Algebraic_kernel_d/Algebraic_kernel_d.txt
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@ -4,7 +4,7 @@ namespace CGAL {
\mainpage Algebraic Kernel \mainpage Algebraic Kernel
\anchor Chapter_Algebraic_Kernel \anchor Chapter_Algebraic_Kernel
\anchor chapteralgebraickerneld \anchor chapteralgebraickerneld
\autotoc \cgalAutoToc
\authors Eric Berberich, Michael Hemmer, Michael Kerber, Sylvain Lazard, Luis Pe&ntilde;aranda, and Monique Teillaud \authors Eric Berberich, Michael Hemmer, Michael Kerber, Sylvain Lazard, Luis Pe&ntilde;aranda, and Monique Teillaud
\section Algebraic_kernel_dIntroduction Introduction \section Algebraic_kernel_dIntroduction Introduction
@ -325,27 +325,27 @@ efficiency.
The following example illustrates the construction of `AlgebraicKernel_d_1::Algebraic_real_1` The following example illustrates the construction of `AlgebraicKernel_d_1::Algebraic_real_1`
using `AlgebraicKernel_d_1::Construct_algebraic_real_1`: using `AlgebraicKernel_d_1::Construct_algebraic_real_1`:
<SMALL>\cgalexample{Algebraic_kernel_d/Construct_algebraic_real_1.cpp}</SMALL> <SMALL>\cgalExample{Algebraic_kernel_d/Construct_algebraic_real_1.cpp}</SMALL>
\subsection CGALAK1Solving Solving Univariate Polynomials \subsection CGALAK1Solving Solving Univariate Polynomials
The following example illustrates the construction of `AlgebraicKernel_d_1::Algebraic_real_1` The following example illustrates the construction of `AlgebraicKernel_d_1::Algebraic_real_1`
using `AlgebraicKernel_d_1::Solve_1`: <SMALL>\cgalexample{Algebraic_kernel_d/Solve_1.cpp} </SMALL> using `AlgebraicKernel_d_1::Solve_1`: <SMALL>\cgalExample{Algebraic_kernel_d/Solve_1.cpp} </SMALL>
\subsection CGALAK1EGCompare_1 Comparison and Approximation of Algebraic Real Numbers \subsection CGALAK1EGCompare_1 Comparison and Approximation of Algebraic Real Numbers
The following example illustrates the comparison of `AlgebraicKernel_d_1::Algebraic_real_1` numbers: The following example illustrates the comparison of `AlgebraicKernel_d_1::Algebraic_real_1` numbers:
<SMALL>\cgalexample{Algebraic_kernel_d/Compare_1.cpp}</SMALL> <SMALL>\cgalExample{Algebraic_kernel_d/Compare_1.cpp}</SMALL>
\subsection CGALAK1EGIsolate_1 Isolation of Algebraic Real Numbers with respect to roots of other polynomials \subsection CGALAK1EGIsolate_1 Isolation of Algebraic Real Numbers with respect to roots of other polynomials
The following example illustrates the isolation of `AlgebraicKernel_d_1::Algebraic_real_1` numbers: The following example illustrates the isolation of `AlgebraicKernel_d_1::Algebraic_real_1` numbers:
<SMALL>\cgalexample{Algebraic_kernel_d/Isolate_1.cpp}</SMALL> <SMALL>\cgalExample{Algebraic_kernel_d/Isolate_1.cpp}</SMALL>
\subsection CGALAK1EGSign_at_1 Interplay with Polynomials \subsection CGALAK1EGSign_at_1 Interplay with Polynomials
The following example illustrates the sign evaluation of `AlgebraicKernel_d_1::Algebraic_real_1` numbers in polynomials: The following example illustrates the sign evaluation of `AlgebraicKernel_d_1::Algebraic_real_1` numbers in polynomials:
<SMALL>\cgalexample{Algebraic_kernel_d/Sign_at_1.cpp}</SMALL> <SMALL>\cgalExample{Algebraic_kernel_d/Sign_at_1.cpp}</SMALL>
\section Algebraic_kernel_dDesign Design and Implementation History \section Algebraic_kernel_dDesign Design and Implementation History

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_d_1.h
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@ -17,7 +17,7 @@ Currently, the following coefficient types are supported:
- `leda_integer`, `leda_rational`. (requires configuration with external library LEDA) - `leda_integer`, `leda_rational`. (requires configuration with external library LEDA)
\advanced The template argument type can also be set to `Sqrt_extension<NT,ROOT>`, where `NT` is \cgalAdvanced The template argument type can also be set to `Sqrt_extension<NT,ROOT>`, where `NT` is
one of the types listed above. `ROOT` should be one of the integer types. one of the types listed above. `ROOT` should be one of the integer types.
See also the documentation of `Sqrt_extension<NT,ROOT>`. See also the documentation of `Sqrt_extension<NT,ROOT>`.
@ -27,7 +27,7 @@ approximation of an algebraic real root is a slightly modified
(filtered) version of the one presented in \cite abbott-qir-06. The (filtered) version of the one presented in \cite abbott-qir-06. The
method has quadratic convergence. method has quadratic convergence.
\models `AlgebraicKernel_d_1` \cgalModels `AlgebraicKernel_d_1`
\sa `AlgebraicKernel_d_1` \sa `AlgebraicKernel_d_1`
\sa `Polynomial_d` \sa `Polynomial_d`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_d_2.h
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@ -37,12 +37,12 @@ Currently, the following coefficient types are supported:
- `CORE::BigInt`, `CORE::BigRat`, (requires configuration with external library GMP) - `CORE::BigInt`, `CORE::BigRat`, (requires configuration with external library GMP)
- `leda_integer`, `leda_rational`. (requires configuration with external library LEDA) - `leda_integer`, `leda_rational`. (requires configuration with external library LEDA)
\advanced The template argument type can also be set to \cgalAdvanced The template argument type can also be set to
`Sqrt_extension<NT,ROOT>`, where `NT` is one of the types listed `Sqrt_extension<NT,ROOT>`, where `NT` is one of the types listed
above. `ROOT` should be one of the integer types. See also the above. `ROOT` should be one of the integer types. See also the
documentation of `Sqrt_extension<NT,ROOT>`. documentation of `Sqrt_extension<NT,ROOT>`.
\models `AlgebraicKernel_d_2` \cgalModels `AlgebraicKernel_d_2`
\sa `AlgebraicKernel_d_1` \sa `AlgebraicKernel_d_1`
\sa `AlgebraicKernel_d_2` \sa `AlgebraicKernel_d_2`

2
Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_rs_gmpq_d_1.h
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@ -12,7 +12,7 @@ rational univariate polynomial root isolation. It is a model of the
isolate integer polynomials, the operations of this kernel have the isolate integer polynomials, the operations of this kernel have the
overhead of converting the polynomials to integer. overhead of converting the polynomials to integer.
\models ::AlgebraicKernel_d_1 \cgalModels ::AlgebraicKernel_d_1
\sa `Algebraic_kernel_rs_gmpz_d_1` \sa `Algebraic_kernel_rs_gmpz_d_1`

2
Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_rs_gmpz_d_1.h
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@ -10,7 +10,7 @@ This univariate algebraic kernel uses the Rs library to perform
integer univariate polynomial root isolation. It is a model of the integer univariate polynomial root isolation. It is a model of the
`AlgebraicKernel_d_1` concept. `AlgebraicKernel_d_1` concept.
\models `AlgebraicKernel_d_1` \cgalModels `AlgebraicKernel_d_1`
\sa `Algebraic_kernel_rs_gmpz_d_1` \sa `Algebraic_kernel_rs_gmpz_d_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--ApproximateAbsolute_1.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
A model of `AlgebraicKernel_d_1::ApproximateAbsolute_1` is an `AdaptableBinaryFunction` that computes an A model of `AlgebraicKernel_d_1::ApproximateAbsolute_1` is an `AdaptableBinaryFunction` that computes an
approximation of an `AlgebraicKernel_d_1::Algebraic_real_1` value with approximation of an `AlgebraicKernel_d_1::Algebraic_real_1` value with
respect to a given absolute precision. respect to a given absolute precision.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_1::ApproximateRelative_1` \sa `AlgebraicKernel_d_1::ApproximateRelative_1`

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--ApproximateRelative_1.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
A model of `AlgebraicKernel_d_1::ApproximateRelative_1` is an `AdaptableBinaryFunction` that computes an A model of `AlgebraicKernel_d_1::ApproximateRelative_1` is an `AdaptableBinaryFunction` that computes an
approximation of an `AlgebraicKernel_d_1::Algebraic_real_1` value with approximation of an `AlgebraicKernel_d_1::Algebraic_real_1` value with
respect to a given relative precision. respect to a given relative precision.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1` \sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--BoundBetween_1.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes a number of type Computes a number of type
`AlgebraicKernel_d_1::Bound` in-between two `AlgebraicKernel_d_1::Bound` in-between two
`AlgebraicKernel_d_1::Algebraic_real_1` values. `AlgebraicKernel_d_1::Algebraic_real_1` values.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
*/ */

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--Compare_1.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Compares `AlgebraicKernel_d_1::Algebraic_real_1` values. Compares `AlgebraicKernel_d_1::Algebraic_real_1` values.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
*/ */
class AlgebraicKernel_d_1::Compare_1 { class AlgebraicKernel_d_1::Compare_1 {

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--ComputePolynomial_1.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes a square free univariate polynomial \f$ p\f$, such that the given Computes a square free univariate polynomial \f$ p\f$, such that the given
`AlgebraicKernel_d_1::Algebraic_real_1` is a root of \f$ p\f$. `AlgebraicKernel_d_1::Algebraic_real_1` is a root of \f$ p\f$.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_1::Isolate_1` \sa `AlgebraicKernel_d_1::Isolate_1`

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--ConstructAlgebraicReal_1.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Constructs `AlgebraicKernel_d_1::Algebraic_real_1`. Constructs `AlgebraicKernel_d_1::Algebraic_real_1`.
\refines `AdaptableFunctor` \cgalRefines `AdaptableFunctor`
\sa `AlgebraicKernel_d_2::ConstructAlgebraicReal_2` \sa `AlgebraicKernel_d_2::ConstructAlgebraicReal_2`

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--IsCoprime_1.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Determines whether a given pair of univariate polynomials \f$ p_1, p_2\f$ is coprime, Determines whether a given pair of univariate polynomials \f$ p_1, p_2\f$ is coprime,
namely if \f$ \deg({\rm gcd}(p_1 ,p_2)) = 0\f$. namely if \f$ \deg({\rm gcd}(p_1 ,p_2)) = 0\f$.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_1::MakeCoprime_1` \sa `AlgebraicKernel_d_1::MakeCoprime_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--IsSquareFree_1.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes whether the given univariate polynomial is square free. Computes whether the given univariate polynomial is square free.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_1::MakeSquareFree_1` \sa `AlgebraicKernel_d_1::MakeSquareFree_1`
\sa `AlgebraicKernel_d_1::SquareFreeFactorize_1` \sa `AlgebraicKernel_d_1::SquareFreeFactorize_1`

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--IsZeroAt_1.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes whether an `AlgebraicKernel_d_1::Polynomial_1` Computes whether an `AlgebraicKernel_d_1::Polynomial_1`
is zero at a given `AlgebraicKernel_d_1::Algebraic_real_1`. is zero at a given `AlgebraicKernel_d_1::Algebraic_real_1`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_1::SignAt_1` \sa `AlgebraicKernel_d_1::SignAt_1`

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Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--Isolate_1.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes an open isolating interval for an `AlgebraicKernel_d_1::Algebraic_real_1` Computes an open isolating interval for an `AlgebraicKernel_d_1::Algebraic_real_1`
with respect to the real roots of a given univariate polynomial. with respect to the real roots of a given univariate polynomial.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_1::ComputePolynomial_1` \sa `AlgebraicKernel_d_1::ComputePolynomial_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--MakeCoprime_1.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes for a given pair of univariate polynomials \f$ p_1\f$, \f$ p_2\f$ their Computes for a given pair of univariate polynomials \f$ p_1\f$, \f$ p_2\f$ their
common part \f$ g\f$ up to a constant factor and coprime parts \f$ q_1\f$, \f$ q_2\f$ common part \f$ g\f$ up to a constant factor and coprime parts \f$ q_1\f$, \f$ q_2\f$
@ -16,7 +16,7 @@ such that \f$ q_1\f$ and \f$ q_2\f$ are coprime.
It returns true if \f$ p_1\f$ and \f$ p_2\f$ are already coprime. It returns true if \f$ p_1\f$ and \f$ p_2\f$ are already coprime.
\refines `AdaptableFunctor` with five arguments \cgalRefines `AdaptableFunctor` with five arguments
\sa `AlgebraicKernel_d_1::IsCoprime_1` \sa `AlgebraicKernel_d_1::IsCoprime_1`

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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Returns a square free part of a univariate polynomial. Returns a square free part of a univariate polynomial.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_1::IsSquareFree_1` \sa `AlgebraicKernel_d_1::IsSquareFree_1`
\sa `AlgebraicKernel_d_1::SquareFreeFactorize_1` \sa `AlgebraicKernel_d_1::SquareFreeFactorize_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--NumberOfSolutions_1.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes the number of real solutions of the given univariate polynomial. Computes the number of real solutions of the given univariate polynomial.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_1::ConstructAlgebraicReal_1` \sa `AlgebraicKernel_d_1::ConstructAlgebraicReal_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--SignAt_1.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes the sign of a univariate polynomial Computes the sign of a univariate polynomial
`AlgebraicKernel_d_1::Polynomial_1` at a real value of type `AlgebraicKernel_d_1::Polynomial_1` at a real value of type
`AlgebraicKernel_d_1::Algebraic_real_1`. `AlgebraicKernel_d_1::Algebraic_real_1`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_1::IsZeroAt_1` \sa `AlgebraicKernel_d_1::IsZeroAt_1`

6
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--Solve_1.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes the real roots of a univariate polynomial. Computes the real roots of a univariate polynomial.
\refines `Assignable` \cgalRefines `Assignable`
\refines `CopyConstructible` \cgalRefines `CopyConstructible`
*/ */

6
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1--SquareFreeFactorize_1.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
Computes a square free factorization of an Computes a square free factorization of an
`AlgebraicKernel_d_1::Polynomial_1`. `AlgebraicKernel_d_1::Polynomial_1`.
@ -14,8 +14,8 @@ and a constant factor \f$ c\f$, such that
The factor multiplicity pairs \f$ <q_i,m_i>\f$ are written to the The factor multiplicity pairs \f$ <q_i,m_i>\f$ are written to the
given output iterator. The constant factor \f$ c\f$ is not computed. given output iterator. The constant factor \f$ c\f$ is not computed.
\refines `Assignable` \cgalRefines `Assignable`
\refines `CopyConstructible` \cgalRefines `CopyConstructible`
\sa `AlgebraicKernel_d_1::IsSquareFree_1` \sa `AlgebraicKernel_d_1::IsSquareFree_1`
\sa `AlgebraicKernel_d_1::MakeSquareFree_1` \sa `AlgebraicKernel_d_1::MakeSquareFree_1`

12
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_1.h
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@ -1,17 +1,17 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsUni \ingroup PkgAlgebraicKerneldConceptsUni
\cgalconcept \cgalConcept
A model of the `AlgebraicKernel_d_1` concept is meant to provide the A model of the `AlgebraicKernel_d_1` concept is meant to provide the
algebraic functionalities on univariate polynomials of general degree \f$ d\f$. algebraic functionalities on univariate polynomials of general degree \f$ d\f$.
\refines `CopyConstructible` \cgalRefines `CopyConstructible`
\refines `Assignable` \cgalRefines `Assignable`
A model of \refines `AlgebraicKernel_d_1` must provide: A model of \cgalRefines `AlgebraicKernel_d_1` must provide:
\hasModel Algebraic_kernel_rs_gmpz_d_1 \cgalHasModel Algebraic_kernel_rs_gmpz_d_1
\hasModel Algebraic_kernel_rs_gmpq_d_1 \cgalHasModel Algebraic_kernel_rs_gmpq_d_1
\sa `AlgebraicKernel_d_2` \sa `AlgebraicKernel_d_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ApproximateAbsoluteX_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
A model of `AlgebraicKernel_d_2::ApproximateAbsoluteX_2` is an `AdaptableBinaryFunction` that computes an A model of `AlgebraicKernel_d_2::ApproximateAbsoluteX_2` is an `AdaptableBinaryFunction` that computes an
approximation of the \f$ x\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value approximation of the \f$ x\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
with respect to a given absolute precision. with respect to a given absolute precision.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::ApproximateRelativeX_2` \sa `AlgebraicKernel_d_2::ApproximateRelativeX_2`
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1` \sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ApproximateAbsoluteY_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
A model of `AlgebraicKernel_d_2::ApproximateAbsoluteY_2` is an `AdaptableBinaryFunction` that computes an A model of `AlgebraicKernel_d_2::ApproximateAbsoluteY_2` is an `AdaptableBinaryFunction` that computes an
approximation of the \f$ y\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value approximation of the \f$ y\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
with respect to a given absolute precision. with respect to a given absolute precision.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::ApproximateRelativeY_2` \sa `AlgebraicKernel_d_2::ApproximateRelativeY_2`
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1` \sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ApproximateRelativeX_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
A model of `AlgebraicKernel_d_2::ApproximateRelativeX_2` is an `AdaptableBinaryFunction` that computes an A model of `AlgebraicKernel_d_2::ApproximateRelativeX_2` is an `AdaptableBinaryFunction` that computes an
approximation of the \f$ x\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value approximation of the \f$ x\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
with respect to a given relative precision. with respect to a given relative precision.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::ApproximateAbsoluteY_2` \sa `AlgebraicKernel_d_2::ApproximateAbsoluteY_2`
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1` \sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ApproximateRelativeY_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
A model of `AlgebraicKernel_d_2::ApproximateRelativeY_2` is an `AdaptableBinaryFunction` that computes an A model of `AlgebraicKernel_d_2::ApproximateRelativeY_2` is an `AdaptableBinaryFunction` that computes an
approximation of the \f$ y\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value approximation of the \f$ y\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
with respect to a given relative precision. with respect to a given relative precision.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::ApproximateAbsoluteY_2` \sa `AlgebraicKernel_d_2::ApproximateAbsoluteY_2`
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1` \sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--BoundBetweenX_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes a number of type Computes a number of type
`AlgebraicKernel_d_1::Bound` in-between the first coordinates of two `AlgebraicKernel_d_1::Bound` in-between the first coordinates of two
`AlgebraicKernel_d_2::AlgebraicReal_2`. `AlgebraicKernel_d_2::AlgebraicReal_2`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::BoundBetweenY_2` \sa `AlgebraicKernel_d_2::BoundBetweenY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--BoundBetweenY_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes a number of type Computes a number of type
`AlgebraicKernel_d_1::Bound` in-between the second coordinates of two `AlgebraicKernel_d_1::Bound` in-between the second coordinates of two
`AlgebraicKernel_d_2::AlgebraicReal_2`. `AlgebraicKernel_d_2::AlgebraicReal_2`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::BoundBetweenX_2` \sa `AlgebraicKernel_d_2::BoundBetweenX_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--CompareXY_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Compares `AlgebraicKernel_d_2::Algebraic_real_2`s lexicographically. Compares `AlgebraicKernel_d_2::Algebraic_real_2`s lexicographically.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::CompareX_2` \sa `AlgebraicKernel_d_2::CompareX_2`
\sa `AlgebraicKernel_d_2::CompareY_2` \sa `AlgebraicKernel_d_2::CompareY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--CompareX_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Compares the first coordinates of `AlgebraicKernel_d_2::Algebraic_real_2`s. Compares the first coordinates of `AlgebraicKernel_d_2::Algebraic_real_2`s.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::CompareY_2` \sa `AlgebraicKernel_d_2::CompareY_2`
\sa `AlgebraicKernel_d_2::CompareXY_2` \sa `AlgebraicKernel_d_2::CompareXY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--CompareY_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Compares the second coordinated of `AlgebraicKernel_d_2::Algebraic_real_2`s. Compares the second coordinated of `AlgebraicKernel_d_2::Algebraic_real_2`s.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::CompareX_2` \sa `AlgebraicKernel_d_2::CompareX_2`
\sa `AlgebraicKernel_d_2::CompareXY_2` \sa `AlgebraicKernel_d_2::CompareXY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ComputePolynomialX_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes a univariate square free polynomial \f$ p\f$, such that the first coordinate of Computes a univariate square free polynomial \f$ p\f$, such that the first coordinate of
a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \f$ p\f$. a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \f$ p\f$.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_2::ComputePolynomialY_2` \sa `AlgebraicKernel_d_2::ComputePolynomialY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ComputePolynomialY_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes a univariate square free polynomial \f$ p\f$, such that the second coordinate of Computes a univariate square free polynomial \f$ p\f$, such that the second coordinate of
a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \f$ p\f$. a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \f$ p\f$.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_2::ComputePolynomialX_2` \sa `AlgebraicKernel_d_2::ComputePolynomialX_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ComputeX_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes the first coordinate of an Computes the first coordinate of an
`AlgebraicKernel_d_2::AlgebraicReal_2`. `AlgebraicKernel_d_2::AlgebraicReal_2`.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_2::ComputeY_2` \sa `AlgebraicKernel_d_2::ComputeY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ComputeY_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes the second coordinate of an Computes the second coordinate of an
`AlgebraicKernel_d_2::AlgebraicReal_2`. `AlgebraicKernel_d_2::AlgebraicReal_2`.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_2::ComputeY_2` \sa `AlgebraicKernel_d_2::ComputeY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--ConstructAlgebraicReal_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Constructs an `AlgebraicKernel_d_2::Algebraic_real_2`. Constructs an `AlgebraicKernel_d_2::Algebraic_real_2`.
\refines `AdaptableFunctor` \cgalRefines `AdaptableFunctor`
\sa `AlgebraicKernel_d_1::ConstructAlgebraicReal_1` \sa `AlgebraicKernel_d_1::ConstructAlgebraicReal_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--IsCoprime_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes whether a given pair of bivariate polynomials is coprime. Computes whether a given pair of bivariate polynomials is coprime.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::MakeCoprime_2` \sa `AlgebraicKernel_d_2::MakeCoprime_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--IsSquareFree_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes whether the given bivariate polynomial is square free. Computes whether the given bivariate polynomial is square free.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_2::MakeSquareFree_2` \sa `AlgebraicKernel_d_2::MakeSquareFree_2`
\sa `AlgebraicKernel_d_2::SquareFreeFactorize_2` \sa `AlgebraicKernel_d_2::SquareFreeFactorize_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--IsZeroAt_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes whether an `AlgebraicKernel_d_2::Polynomial_2` Computes whether an `AlgebraicKernel_d_2::Polynomial_2`
is zero at a given `AlgebraicKernel_d_2::Algebraic_real_2`. is zero at a given `AlgebraicKernel_d_2::Algebraic_real_2`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::SignAt_2` \sa `AlgebraicKernel_d_2::SignAt_2`
\sa `AlgebraicKernel_d_1::IsZeroAt_1` \sa `AlgebraicKernel_d_1::IsZeroAt_1`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--IsolateX_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes an isolating interval for the first coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` Computes an isolating interval for the first coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2`
with respect to the real roots of a univariate polynomial. with respect to the real roots of a univariate polynomial.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::IsolateY_2` \sa `AlgebraicKernel_d_2::IsolateY_2`
\sa `AlgebraicKernel_d_2::ComputePolynomialX_2` \sa `AlgebraicKernel_d_2::ComputePolynomialX_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--IsolateY_2.h
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@ -1,12 +1,12 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes an isolating interval for the second coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` Computes an isolating interval for the second coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2`
with respect to the real roots of a univariate polynomial. with respect to the real roots of a univariate polynomial.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::IsolateX_2` \sa `AlgebraicKernel_d_2::IsolateX_2`
\sa `AlgebraicKernel_d_2::ComputePolynomialX_2` \sa `AlgebraicKernel_d_2::ComputePolynomialX_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--Isolate_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes an isolating box for a given `AlgebraicKernel_d_2::Algebraic_real_2`. Computes an isolating box for a given `AlgebraicKernel_d_2::Algebraic_real_2`.
\refines `AdaptableFunctor` \cgalRefines `AdaptableFunctor`
\sa `AlgebraicKernel_d_2::IsolateX_2` \sa `AlgebraicKernel_d_2::IsolateX_2`
\sa `AlgebraicKernel_d_2::IsolateY_2` \sa `AlgebraicKernel_d_2::IsolateY_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--MakeCoprime_2.h
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@ -1,7 +1,7 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes for a given pair of bivariate polynomials \f$ p_1\f$, \f$ p_2\f$ their Computes for a given pair of bivariate polynomials \f$ p_1\f$, \f$ p_2\f$ their
common part \f$ g\f$ and coprime parts \f$ q_1\f$, \f$ q_2\f$ respectively. common part \f$ g\f$ and coprime parts \f$ q_1\f$, \f$ q_2\f$ respectively.
@ -13,7 +13,7 @@ That is, it computes \f$ g, q_1, q_2\f$ such that:
\f$ c_2 \cdot p_2 = g \cdot q_2\f$ for some constant \f$ c_2\f$, \f$ c_2 \cdot p_2 = g \cdot q_2\f$ for some constant \f$ c_2\f$,
such that \f$ q_1\f$ and \f$ q_2\f$ are coprime. such that \f$ q_1\f$ and \f$ q_2\f$ are coprime.
\refines `AdaptableFunctor` with five arguments \cgalRefines `AdaptableFunctor` with five arguments
\sa `AlgebraicKernel_d_2::IsCoprime_2` \sa `AlgebraicKernel_d_2::IsCoprime_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--MakeSquareFree_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Returns a square free part of a bivariate polynomial. Returns a square free part of a bivariate polynomial.
\refines `AdaptableUnaryFunction` \cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicKernel_d_2::IsSquareFree_2` \sa `AlgebraicKernel_d_2::IsSquareFree_2`
\sa `AlgebraicKernel_d_2::SquareFreeFactorize_2` \sa `AlgebraicKernel_d_2::SquareFreeFactorize_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--NumberOfSolutions_2.h
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@ -1,11 +1,11 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes the number of real solutions of the given bivariate polynomial system. Computes the number of real solutions of the given bivariate polynomial system.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::ConstructAlgebraicReal_2` \sa `AlgebraicKernel_d_2::ConstructAlgebraicReal_2`

4
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--SignAt_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes the sign of a bivariate polynomial Computes the sign of a bivariate polynomial
`AlgebraicKernel_d_2::Polynomial_2` at a value of type `AlgebraicKernel_d_2::Polynomial_2` at a value of type
`AlgebraicKernel_d_2::Algebraic_real_2`. `AlgebraicKernel_d_2::Algebraic_real_2`.
\refines `AdaptableBinaryFunction` \cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicKernel_d_2::IsZeroAt_2` \sa `AlgebraicKernel_d_2::IsZeroAt_2`
\sa `AlgebraicKernel_d_1::SignAt_1` \sa `AlgebraicKernel_d_1::SignAt_1`

6
Algebraic_kernel_d/doc/Algebraic_kernel_d/Concepts/AlgebraicKernel_d_2--Solve_2.h
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@ -1,13 +1,13 @@
/*! /*!
\ingroup PkgAlgebraicKerneldConceptsBi \ingroup PkgAlgebraicKerneldConceptsBi
\cgalconcept \cgalConcept
Computes the real zero-dimensional solutions of a bivariate polynomial system. Computes the real zero-dimensional solutions of a bivariate polynomial system.
The multiplicity stored in the output iterator is the multiplicity in the system. The multiplicity stored in the output iterator is the multiplicity in the system.
\refines `Assignable` \cgalRefines `Assignable`
\refines `CopyConstructible` \cgalRefines `CopyConstructible`
*/ */
class AlgebraicKernel_d_2::Solve_2 { class AlgebraicKernel_d_2::Solve_2 {
public: public:

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