mirror of https://github.com/CGAL/cgal
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
parent
bed259251c
commit
128b02abb8
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\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.
|
||||
|
||||
\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>`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\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.
|
||||
|
||||
|
|
@ -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.
|
||||
|
||||
\hasModel `CGAL::AABB_polyhedron_triangle_primitive<GeomTraits,Polyhedron>`
|
||||
\hasModel `CGAL::AABB_polyhedron_segment_primitive<GeomTraits,Polyhedron>`
|
||||
\cgalHasModel `CGAL::AABB_polyhedron_triangle_primitive<GeomTraits,Polyhedron>`
|
||||
\cgalHasModel `CGAL::AABB_polyhedron_segment_primitive<GeomTraits,Polyhedron>`
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAABB_treeConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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_tree<AABBTraits>`
|
||||
|
|
|
|||
|
|
@ -5,18 +5,18 @@
|
|||
|
||||
/*!
|
||||
\addtogroup PkgAABB_tree
|
||||
\PkgDescriptionBegin{3D Fast Intersection and Distance Computation,PkgAABB_treeSummary}
|
||||
\PkgPicture{aabb-teaser-thumb.png}
|
||||
\PkgSummaryBegin
|
||||
\PkgAuthors{Pierre Alliez, Stéphane 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.}
|
||||
\PkgManuals{Chapter_3D_Fast_Intersection_and_Distance_Computation,PkgAABB_tree}
|
||||
\PkgSummaryEnd
|
||||
\PkgShortInfoBegin
|
||||
\PkgSince{1.0}
|
||||
\PkgBib{cgal:atw-aabb}
|
||||
\PkgLicense{\ref licensesGPL "GPL"}
|
||||
\PkgDemo{AABB Tree,AABB_demo.zip}
|
||||
\PkgShortInfoEnd
|
||||
\PkgDescriptionEnd
|
||||
\cgalPkgDescriptionBegin{3D Fast Intersection and Distance Computation,PkgAABB_treeSummary}
|
||||
\cgalPkgPicture{aabb-teaser-thumb.png}
|
||||
\cgalPkgSummaryBegin
|
||||
\cgalPkgAuthors{Pierre Alliez, Stéphane Tayeb, Camille Wormser}
|
||||
\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.}
|
||||
\cgalPkgManuals{Chapter_3D_Fast_Intersection_and_Distance_Computation,PkgAABB_tree}
|
||||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{1.0}
|
||||
\cgalPkgBib{cgal:atw-aabb}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgDemo{AABB Tree,AABB_demo.zip}
|
||||
\cgalPkgShortInfoEnd
|
||||
\cgalPkgDescriptionEnd
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ namespace CGAL {
|
|||
|
||||
\mainpage 3D %Fast Intersection and Distance Computation (AABB Tree)
|
||||
\anchor Chapter_3D_Fast_Intersection_and_Distance_Computation
|
||||
\autotoc
|
||||
\cgalAutoToc
|
||||
|
||||
\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
|
||||
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.
|
||||
\cgal_figure_end
|
||||
\cgalFigureEnd
|
||||
|
||||
\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
|
||||
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
|
||||
|
||||
|
|
@ -192,7 +192,7 @@ option which maximizes speed.
|
|||
|
||||
The surface triangle mesh chosen for benchmarking the tree
|
||||
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
|
||||
well as for three denser versions subdivided through the Loop
|
||||
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 |
|
||||
|
||||
|
||||
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
|
||||
queries) against the number of input triangles for the knot triangle
|
||||
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.
|
||||
\cgal_figure_end
|
||||
\cgalFigureEnd
|
||||
|
||||
The following table measures the number of `AABB_tree::all_intersections()`
|
||||
queries per second against several kernels. We use the 14,400 triangle
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ namespace CGAL {
|
|||
\mainpage Algebraic Foundations
|
||||
\anchor Chapter_Algebraic_Foundations
|
||||
|
||||
\autotoc
|
||||
\cgalAutoToc
|
||||
\author Michael Hemmer
|
||||
|
||||
\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
|
||||
exceptional structures as <I>skew fields</I>.
|
||||
|
||||
\cgal_figure_begin{figConceptHierarchyOfAlgebraicStructures,AlgebraicConceptHierarchy.gif}
|
||||
\cgalFigureBegin{figConceptHierarchyOfAlgebraicStructures,AlgebraicConceptHierarchy.gif}
|
||||
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.
|
||||
`IntegralDomain`, `UniqueFactorizationDomain`, `EuclideanRing` and
|
||||
`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
|
||||
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
|
||||
|
||||
|
|
@ -177,7 +177,7 @@ concepts `Field` and `RealEmbeddable`, while
|
|||
`RingNumberType` combines `IntegralDomainWithoutDivision` and
|
||||
`RealEmbeddable`. Algebraically, the real number types do not form
|
||||
distinct structures and are therefore not listed in the concept
|
||||
hierarchy of \cgal_figure_ref{figConceptHierarchyOfAlgebraicStructures}.
|
||||
hierarchy of \cgalFigureRef{figConceptHierarchyOfAlgebraicStructures}.
|
||||
|
||||
\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
|
||||
`ExplicitInteroperable` types.
|
||||
|
||||
\cgalexample{Algebraic_foundations/interoperable.cpp}
|
||||
\cgalExample{Algebraic_foundations/interoperable.cpp}
|
||||
|
||||
The following example illustrates a dispatch for `ImplicitInteroperable` and
|
||||
`ExplicitInteroperable` types.
|
||||
|
|
@ -229,7 +229,7 @@ The binary function (that just multiplies its two arguments) is supposed to
|
|||
take two `ExplicitInteroperable` arguments. For `ImplicitInteroperable`
|
||||
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
|
||||
|
||||
|
|
@ -254,14 +254,14 @@ it is more general and offers dispatching functionality.
|
|||
\subsection Algebraic_foundationsExamples_1 Examples
|
||||
|
||||
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,
|
||||
i.e., the coefficient vector of a polynomial. Note that for minimizing
|
||||
coefficient growth `Fraction_traits<Type>::Common_factor` is used to
|
||||
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
|
||||
|
||||
|
|
|
|||
|
|
@ -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.
|
||||
|
||||
\models ::AlgebraicStructureTraits
|
||||
\cgalModels ::AlgebraicStructureTraits
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
|
|
@ -22,7 +22,7 @@ namespace CGAL {
|
|||
Tag indicating that a type is a model of the
|
||||
`EuclideanRing` concept.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `EuclideanRing`
|
||||
\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.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `Field`
|
||||
\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.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `FieldWithKthRoot`
|
||||
\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.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `FieldWithRootOf`
|
||||
\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.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `FieldWithSqrt`
|
||||
\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.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `IntegralDomain`
|
||||
\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.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `IntegralDomainWithoutDivision`
|
||||
|
||||
|
|
@ -133,7 +133,7 @@ class Integral_domain_without_division_tag {
|
|||
|
||||
Tag indicating that a type is a model of the `UniqueFactorizationDomain` concept.
|
||||
|
||||
\models ::DefaultConstructible
|
||||
\cgalModels ::DefaultConstructible
|
||||
|
||||
\sa `UniqueFactorizationDomain`
|
||||
\sa `AlgebraicStructureTraits`
|
||||
|
|
|
|||
|
|
@ -6,7 +6,7 @@ namespace CGAL {
|
|||
An instance of `Fraction_traits` is a model of `FractionTraits`,
|
||||
where `T` is the associated type.
|
||||
|
||||
\models ::FractionTraits
|
||||
\cgalModels ::FractionTraits
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
|
|
|
|||
|
|
@ -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.
|
||||
|
||||
\models ::RealEmbeddableTraits
|
||||
\cgalModels ::RealEmbeddableTraits
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction` computes the integral quotient of division
|
||||
with remainder.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
\sa ::AlgebraicStructureTraits::Mod
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableFunctor` computes both integral quotient and remainder
|
||||
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
|
||||
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.}
|
||||
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.
|
||||
|
|
@ -187,7 +187,7 @@ r
|
|||
|
||||
</TABLE>
|
||||
|
||||
\refines `AdaptableFunctor`
|
||||
\cgalRefines `AdaptableFunctor`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
\sa ::AlgebraicStructureTraits::Mod
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction`,
|
||||
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.
|
||||
The second operator returns \f$ c\f$ via the additional third argument.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
\sa ::AlgebraicStructureTraits::IntegralDivision
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`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$.
|
||||
Thus, \f$ 0\f$ is divided by every element of the Ring, in particular by itself.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction` providing an integral division.
|
||||
|
||||
|
|
@ -11,7 +11,7 @@ exists (i.e.\ if \f$ x\f$ is divisible by \f$ y\f$). Otherwise the effect of inv
|
|||
this operation is undefined. Since the ring represented is an integral domain,
|
||||
\f$ z\f$ is uniquely defined if it exists.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
\sa ::AlgebraicStructureTraits::Divides
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction` providing the inverse element with
|
||||
respect to multiplication of a `Field`.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction`,
|
||||
returns true in case the argument is the one of the ring.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`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.
|
||||
|
|
@ -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$. In case the ring is a `UniqueFactorizationDomain`,
|
||||
\f$ y\f$ is uniquely defined up to multiplication by units.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction`, returns true in case the argument is the zero element of the ring.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
\sa ::RealEmbeddableTraits::IsZero
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction` providing the k-th root.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::FieldWithRootOf
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction` computes the remainder of division with remainder.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
\sa ::AlgebraicStructureTraits::Div
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableFunctor` computes a real root of a square-free univariate
|
||||
polynomial.
|
||||
|
||||
\refines `AdaptableFunctor`
|
||||
\cgalRefines `AdaptableFunctor`
|
||||
|
||||
\sa ::FieldWithRootOf
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
This `AdaptableUnaryFunction` may simplify a given object.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction` providing the square root.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction`, computing the square of the argument.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
This `AdaptableUnaryFunction` computes the unit part of a given ring
|
||||
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
|
||||
associate being one. The unit part of zero is, by convention, one.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::AlgebraicStructureTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `AlgebraicStructureTraits` reflects the algebraic structure
|
||||
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_root_of_tag
|
||||
|
||||
\hasModel `CGAL::Algebraic_structure_traits<T>`
|
||||
\cgalHasModel `CGAL::Algebraic_structure_traits<T>`
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `EuclideanRing` represents an euclidean ring (or Euclidean domain).
|
||||
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
|
||||
the smallest positive remainder \f$ r\f$.
|
||||
|
||||
\refines `UniqueFactorizationDomain`
|
||||
\cgalRefines `UniqueFactorizationDomain`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsInteroperabilityConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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`,
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `Field` is an `IntegralDomain` in which every non-zero element
|
||||
has a multiplicative inverse.
|
||||
|
|
@ -17,7 +17,7 @@ Moreover, `CGAL::Algebraic_structure_traits< Field >` is a model of
|
|||
|
||||
- `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Inverse`
|
||||
|
||||
\refines `IntegralDomain`
|
||||
\cgalRefines `IntegralDomain`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,25 +1,25 @@
|
|||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsRealNumberTypesConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
The concept `FieldNumberType` combines the requirements of the concepts
|
||||
`Field` and `RealEmbeddable`.
|
||||
A model of `FieldNumberType` can be used as a template parameter
|
||||
for Cartesian kernels.
|
||||
|
||||
\refines `Field`
|
||||
\refines `RealEmbeddable`
|
||||
\cgalRefines `Field`
|
||||
\cgalRefines `RealEmbeddable`
|
||||
|
||||
\hasModel float
|
||||
\hasModel double
|
||||
\hasModel `CGAL::Gmpq`
|
||||
\hasModel `CGAL::Interval_nt`
|
||||
\hasModel \ref CGAL::Interval_nt_advanced
|
||||
\hasModel `CGAL::Lazy_exact_nt<FieldNumberType>`
|
||||
\hasModel `CGAL::Quotient<RingNumberType>`
|
||||
\hasModel `CGAL::leda_rational`
|
||||
\hasModel `CGAL::leda_bigfloat`
|
||||
\hasModel `CGAL::leda_real`
|
||||
\cgalHasModel float
|
||||
\cgalHasModel double
|
||||
\cgalHasModel `CGAL::Gmpq`
|
||||
\cgalHasModel `CGAL::Interval_nt`
|
||||
\cgalHasModel \ref CGAL::Interval_nt_advanced
|
||||
\cgalHasModel `CGAL::Lazy_exact_nt<FieldNumberType>`
|
||||
\cgalHasModel `CGAL::Quotient<RingNumberType>`
|
||||
\cgalHasModel `CGAL::leda_rational`
|
||||
\cgalHasModel `CGAL::leda_bigfloat`
|
||||
\cgalHasModel `CGAL::leda_real`
|
||||
|
||||
\sa `RingNumberType`
|
||||
\sa `Kernel`
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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`
|
||||
|
||||
\refines `FieldWithSqrt`
|
||||
\cgalRefines `FieldWithSqrt`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `FieldWithRootOf` is a `FieldWithKthRoot` with the possibility to
|
||||
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 >::Root_of` which is a model of `AlgebraicStructureTraits::RootOf`
|
||||
|
||||
\refines `FieldWithKthRoot`
|
||||
\cgalRefines `FieldWithKthRoot`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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 >::Sqrt` which is a model of `AlgebraicStructureTraits::Sqrt`
|
||||
|
||||
\refines `Field`
|
||||
\cgalRefines `Field`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsFractionsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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
|
||||
|
|
|
|||
|
|
@ -1,14 +1,14 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsFractionsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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
|
||||
as the numerator and denominator type.
|
||||
|
||||
\hasModel `CGAL::Fraction_traits<T>`
|
||||
\cgalHasModel `CGAL::Fraction_traits<T>`
|
||||
|
||||
\sa `FractionTraits::Decompose`
|
||||
\sa `FractionTraits::Compose`
|
||||
|
|
@ -56,7 +56,7 @@ typedef Hidden_type Denominator_type;
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsFractionsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Functor decomposing a `Fraction` into its numerator and denominator.
|
||||
|
||||
|
|
@ -86,11 +86,11 @@ FractionTraits::Denominator_type & d);
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsFractionsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction`, returns the fraction of its arguments.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `Fraction`
|
||||
\sa `FractionTraits`
|
||||
|
|
@ -137,7 +137,7 @@ result_type operator()(first_argument_type n, second_argument_type d);
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsFractionsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`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
|
||||
`UniqueFactorizationDomain`.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `Fraction`
|
||||
\sa `FractionTraits`
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsMiscellaneousConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of the concept `FromDoubleConstructible` is required
|
||||
to be constructible from the type `double`.
|
||||
|
|
|
|||
|
|
@ -1,14 +1,14 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsMiscellaneousConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of the concept `FromIntConstructible` is required
|
||||
to be constructible from int.
|
||||
|
||||
\hasModel int
|
||||
\hasModel long
|
||||
\hasModel double
|
||||
\cgalHasModel int
|
||||
\cgalHasModel long
|
||||
\cgalHasModel double
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsInteroperabilityConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Two types `A` and `B` are a model of the concept
|
||||
`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
|
||||
is `CGAL::Tag_true`.
|
||||
|
||||
\refines `ExplicitInteroperable`
|
||||
\cgalRefines `ExplicitInteroperable`
|
||||
|
||||
\sa `CGAL::Coercion_traits<A,B>`
|
||||
\sa `ExplicitInteroperable`
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`IntegralDomain` refines `IntegralDomainWithoutDivision` by
|
||||
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 >::Divides` which is a model of `AlgebraicStructureTraits::Divides`
|
||||
|
||||
\refines `IntegralDomainWithoutDivision`
|
||||
\cgalRefines `IntegralDomainWithoutDivision`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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 >::Unit_part` which is a model of `AlgebraicStructureTraits::UnitPart`
|
||||
|
||||
\refines `Assignable`
|
||||
\refines `CopyConstructible`
|
||||
\refines `DefaultConstructible`
|
||||
\refines `EqualityComparable`
|
||||
\refines `FromIntConstructible`
|
||||
\cgalRefines `Assignable`
|
||||
\cgalRefines `CopyConstructible`
|
||||
\cgalRefines `DefaultConstructible`
|
||||
\cgalRefines `EqualityComparable`
|
||||
\cgalRefines `FromIntConstructible`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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
|
||||
|
|
@ -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
|
||||
is a sub-ring of the real numbers and hence has characteristic zero.
|
||||
|
||||
\refines `Equality` Comparable
|
||||
\refines `LessThanComparable`
|
||||
\cgalRefines `Equality` Comparable
|
||||
\cgalRefines `LessThanComparable`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction` computes the absolute value of a number.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableBinaryFunction` compares two real embeddable numbers.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction`, returns true in case the argument is negative.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction`, returns true in case the argument is positive.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction`, returns true in case the argument is 0.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
\sa ::AlgebraicStructureTraits::IsZero
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
This `AdaptableUnaryFunction` computes the sign of a real embeddable number.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction` computes a double approximation of a real
|
||||
embeddable number.
|
||||
|
|
@ -9,7 +9,7 @@ embeddable number.
|
|||
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.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
`AdaptableUnaryFunction` computes for a given real embeddable
|
||||
number \f$ x\f$ a double interval containing \f$ x\f$.
|
||||
This interval is represented by `std::pair<double,double>`.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa ::RealEmbeddableTraits
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsRealEmbeddableConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `RealEmbeddableTraits` is associated to a number type
|
||||
`Type` and reflects the properties of this type with respect
|
||||
to the concept `RealEmbeddable`.
|
||||
|
||||
\hasModel `CGAL::Real_embeddable_traits<T>`
|
||||
\cgalHasModel `CGAL::Real_embeddable_traits<T>`
|
||||
*/
|
||||
|
||||
class RealEmbeddableTraits {
|
||||
|
|
|
|||
|
|
@ -1,29 +1,29 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsRealNumberTypesConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
The concept `RingNumberType` combines the requirements of the concepts
|
||||
`IntegralDomainWithoutDivision` and `RealEmbeddable`.
|
||||
A model of `RingNumberType` can be used as a template parameter
|
||||
for Homogeneous kernels.
|
||||
|
||||
\refines `IntegralDomainWithoutDivision`
|
||||
\refines `RealEmbeddable`
|
||||
\cgalRefines `IntegralDomainWithoutDivision`
|
||||
\cgalRefines `RealEmbeddable`
|
||||
|
||||
\hasModel \cpp built-in number types
|
||||
\hasModel `CGAL::Gmpq`
|
||||
\hasModel `CGAL::Gmpz`
|
||||
\hasModel` CGAL::Interval_nt`
|
||||
\hasModel \ref CGAL::Interval_nt_advanced
|
||||
\hasModel `CGAL::Lazy_exact_nt<RingNumberType>`
|
||||
\hasModel `CGAL::MP_Float`
|
||||
\hasModel `CGAL::Gmpzf`
|
||||
\hasModel `CGAL::Quotient<RingNumberType>`
|
||||
\hasModel `CGAL::leda_integer`
|
||||
\hasModel `CGAL::leda_rational`
|
||||
\hasModel `CGAL::leda_bigfloat`
|
||||
\hasModel `CGAL::leda_real`
|
||||
\cgalHasModel \cpp built-in number types
|
||||
\cgalHasModel `CGAL::Gmpq`
|
||||
\cgalHasModel `CGAL::Gmpz`
|
||||
\cgalHasModel` CGAL::Interval_nt`
|
||||
\cgalHasModel \ref CGAL::Interval_nt_advanced
|
||||
\cgalHasModel `CGAL::Lazy_exact_nt<RingNumberType>`
|
||||
\cgalHasModel `CGAL::MP_Float`
|
||||
\cgalHasModel `CGAL::Gmpzf`
|
||||
\cgalHasModel `CGAL::Quotient<RingNumberType>`
|
||||
\cgalHasModel `CGAL::leda_integer`
|
||||
\cgalHasModel `CGAL::leda_rational`
|
||||
\cgalHasModel `CGAL::leda_bigfloat`
|
||||
\cgalHasModel `CGAL::leda_real`
|
||||
|
||||
\sa `FieldNumberType`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `UniqueFactorizationDomain` is an `IntegralDomain` with the
|
||||
additional property
|
||||
|
|
@ -23,7 +23,7 @@ is a model of `AlgebraicStructureTraits` providing:
|
|||
derived from `CGAL::Unique_factorization_domain_tag`
|
||||
- `CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Gcd` which is a model of `AlgebraicStructureTraits::Gcd`
|
||||
|
||||
\refines `IntegralDomain`
|
||||
\cgalRefines `IntegralDomain`
|
||||
|
||||
\sa ::IntegralDomainWithoutDivision
|
||||
\sa ::IntegralDomain
|
||||
|
|
|
|||
|
|
@ -48,19 +48,19 @@
|
|||
\addtogroup PkgAlgebraicFoundations
|
||||
\todo check generated documentation
|
||||
|
||||
\PkgDescriptionBegin{Algebraic Foundations,PkgAlgebraicFoundationsSummary}
|
||||
\PkgPicture{Algebraic_foundations2.png}
|
||||
\PkgSummaryBegin
|
||||
\PkgAuthor{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).}
|
||||
\PkgManuals{Chapter_Algebraic_Foundations,PkgAlgebraicFoundations}
|
||||
\PkgSummaryEnd
|
||||
\PkgShortInfoBegin
|
||||
\PkgSince{3.3}
|
||||
\PkgBib{cgal:h-af}
|
||||
\PkgLicense{\ref licensesLGPL "LGPL"}
|
||||
\PkgShortInfoEnd
|
||||
\PkgDescriptionEnd
|
||||
\cgalPkgDescriptionBegin{Algebraic Foundations,PkgAlgebraicFoundationsSummary}
|
||||
\cgalPkgPicture{Algebraic_foundations2.png}
|
||||
\cgalPkgSummaryBegin
|
||||
\cgalPkgAuthor{Michael Hemmer}
|
||||
\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).}
|
||||
\cgalPkgManuals{Chapter_Algebraic_Foundations,PkgAlgebraicFoundations}
|
||||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.3}
|
||||
\cgalPkgBib{cgal:h-af}
|
||||
\cgalPkgLicense{\ref licensesLGPL "LGPL"}
|
||||
\cgalPkgShortInfoEnd
|
||||
\cgalPkgDescriptionEnd
|
||||
|
||||
\ref AlgebraicFoundationsClassified "Classified Reference Pages"
|
||||
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ namespace CGAL {
|
|||
\mainpage Algebraic Kernel
|
||||
\anchor Chapter_Algebraic_Kernel
|
||||
\anchor chapteralgebraickerneld
|
||||
\autotoc
|
||||
\cgalAutoToc
|
||||
\authors Eric Berberich, Michael Hemmer, Michael Kerber, Sylvain Lazard, Luis Peñaranda, and Monique Teillaud
|
||||
|
||||
\section Algebraic_kernel_dIntroduction Introduction
|
||||
|
|
@ -325,27 +325,27 @@ efficiency.
|
|||
|
||||
The following example illustrates the construction of `AlgebraicKernel_d_1::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
|
||||
|
||||
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
|
||||
|
||||
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
|
||||
|
||||
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
|
||||
|
||||
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
|
||||
|
||||
|
|
|
|||
|
|
@ -17,7 +17,7 @@ Currently, the following coefficient types are supported:
|
|||
|
||||
- `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.
|
||||
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
|
||||
method has quadratic convergence.
|
||||
|
||||
\models `AlgebraicKernel_d_1`
|
||||
\cgalModels `AlgebraicKernel_d_1`
|
||||
|
||||
\sa `AlgebraicKernel_d_1`
|
||||
\sa `Polynomial_d`
|
||||
|
|
|
|||
|
|
@ -37,12 +37,12 @@ Currently, the following coefficient types are supported:
|
|||
- `CORE::BigInt`, `CORE::BigRat`, (requires configuration with external library GMP)
|
||||
- `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
|
||||
above. `ROOT` should be one of the integer types. See also the
|
||||
documentation of `Sqrt_extension<NT,ROOT>`.
|
||||
|
||||
\models `AlgebraicKernel_d_2`
|
||||
\cgalModels `AlgebraicKernel_d_2`
|
||||
|
||||
\sa `AlgebraicKernel_d_1`
|
||||
\sa `AlgebraicKernel_d_2`
|
||||
|
|
|
|||
|
|
@ -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
|
||||
overhead of converting the polynomials to integer.
|
||||
|
||||
\models ::AlgebraicKernel_d_1
|
||||
\cgalModels ::AlgebraicKernel_d_1
|
||||
|
||||
\sa `Algebraic_kernel_rs_gmpz_d_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -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
|
||||
`AlgebraicKernel_d_1` concept.
|
||||
|
||||
\models `AlgebraicKernel_d_1`
|
||||
\cgalModels `AlgebraicKernel_d_1`
|
||||
|
||||
\sa `Algebraic_kernel_rs_gmpz_d_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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
|
||||
respect to a given absolute precision.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::ApproximateRelative_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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
|
||||
respect to a given relative precision.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes a number of type
|
||||
`AlgebraicKernel_d_1::Bound` in-between two
|
||||
`AlgebraicKernel_d_1::Algebraic_real_1` values.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Compares `AlgebraicKernel_d_1::Algebraic_real_1` values.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
*/
|
||||
class AlgebraicKernel_d_1::Compare_1 {
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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$.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::Isolate_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Constructs `AlgebraicKernel_d_1::Algebraic_real_1`.
|
||||
|
||||
\refines `AdaptableFunctor`
|
||||
\cgalRefines `AdaptableFunctor`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ConstructAlgebraicReal_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Determines whether a given pair of univariate polynomials \f$ p_1, p_2\f$ is coprime,
|
||||
namely if \f$ \deg({\rm gcd}(p_1 ,p_2)) = 0\f$.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::MakeCoprime_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes whether the given univariate polynomial is square free.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::MakeSquareFree_1`
|
||||
\sa `AlgebraicKernel_d_1::SquareFreeFactorize_1`
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes whether an `AlgebraicKernel_d_1::Polynomial_1`
|
||||
is zero at a given `AlgebraicKernel_d_1::Algebraic_real_1`.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::SignAt_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes an open isolating interval for an `AlgebraicKernel_d_1::Algebraic_real_1`
|
||||
with respect to the real roots of a given univariate polynomial.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::ComputePolynomial_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes for a given pair of univariate polynomials \f$ 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$
|
||||
|
|
@ -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.
|
||||
|
||||
\refines `AdaptableFunctor` with five arguments
|
||||
\cgalRefines `AdaptableFunctor` with five arguments
|
||||
|
||||
\sa `AlgebraicKernel_d_1::IsCoprime_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Returns a square free part of a univariate polynomial.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::IsSquareFree_1`
|
||||
\sa `AlgebraicKernel_d_1::SquareFreeFactorize_1`
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the number of real solutions of the given univariate polynomial.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::ConstructAlgebraicReal_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the sign of a univariate polynomial
|
||||
`AlgebraicKernel_d_1::Polynomial_1` at a real value of type
|
||||
`AlgebraicKernel_d_1::Algebraic_real_1`.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::IsZeroAt_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the real roots of a univariate polynomial.
|
||||
|
||||
\refines `Assignable`
|
||||
\refines `CopyConstructible`
|
||||
\cgalRefines `Assignable`
|
||||
\cgalRefines `CopyConstructible`
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes a square free factorization of an
|
||||
`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
|
||||
given output iterator. The constant factor \f$ c\f$ is not computed.
|
||||
|
||||
\refines `Assignable`
|
||||
\refines `CopyConstructible`
|
||||
\cgalRefines `Assignable`
|
||||
\cgalRefines `CopyConstructible`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::IsSquareFree_1`
|
||||
\sa `AlgebraicKernel_d_1::MakeSquareFree_1`
|
||||
|
|
|
|||
|
|
@ -1,17 +1,17 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsUni
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of the `AlgebraicKernel_d_1` concept is meant to provide the
|
||||
algebraic functionalities on univariate polynomials of general degree \f$ d\f$.
|
||||
|
||||
\refines `CopyConstructible`
|
||||
\refines `Assignable`
|
||||
A model of \refines `AlgebraicKernel_d_1` must provide:
|
||||
\cgalRefines `CopyConstructible`
|
||||
\cgalRefines `Assignable`
|
||||
A model of \cgalRefines `AlgebraicKernel_d_1` must provide:
|
||||
|
||||
\hasModel Algebraic_kernel_rs_gmpz_d_1
|
||||
\hasModel Algebraic_kernel_rs_gmpq_d_1
|
||||
\cgalHasModel Algebraic_kernel_rs_gmpz_d_1
|
||||
\cgalHasModel Algebraic_kernel_rs_gmpq_d_1
|
||||
|
||||
\sa `AlgebraicKernel_d_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `AlgebraicKernel_d_2::ApproximateAbsoluteX_2` is an `AdaptableBinaryFunction` that computes an
|
||||
approximation of the \f$ x\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
|
||||
with respect to a given absolute precision.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ApproximateRelativeX_2`
|
||||
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `AlgebraicKernel_d_2::ApproximateAbsoluteY_2` is an `AdaptableBinaryFunction` that computes an
|
||||
approximation of the \f$ y\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
|
||||
with respect to a given absolute precision.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ApproximateRelativeY_2`
|
||||
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `AlgebraicKernel_d_2::ApproximateRelativeX_2` is an `AdaptableBinaryFunction` that computes an
|
||||
approximation of the \f$ x\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
|
||||
with respect to a given relative precision.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ApproximateAbsoluteY_2`
|
||||
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
A model of `AlgebraicKernel_d_2::ApproximateRelativeY_2` is an `AdaptableBinaryFunction` that computes an
|
||||
approximation of the \f$ y\f$-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value
|
||||
with respect to a given relative precision.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ApproximateAbsoluteY_2`
|
||||
\sa `AlgebraicKernel_d_1::ApproximateAbsolute_1`
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes a number of type
|
||||
`AlgebraicKernel_d_1::Bound` in-between the first coordinates of two
|
||||
`AlgebraicKernel_d_2::AlgebraicReal_2`.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::BoundBetweenY_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes a number of type
|
||||
`AlgebraicKernel_d_1::Bound` in-between the second coordinates of two
|
||||
`AlgebraicKernel_d_2::AlgebraicReal_2`.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::BoundBetweenX_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Compares `AlgebraicKernel_d_2::Algebraic_real_2`s lexicographically.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::CompareX_2`
|
||||
\sa `AlgebraicKernel_d_2::CompareY_2`
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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::CompareXY_2`
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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::CompareXY_2`
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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$.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ComputePolynomialY_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes a univariate square free polynomial \f$ p\f$, such that the second coordinate of
|
||||
a given `AlgebraicKernel_d_2::Algebraic_real_2` is a real root of \f$ p\f$.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ComputePolynomialX_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the first coordinate of an
|
||||
`AlgebraicKernel_d_2::AlgebraicReal_2`.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ComputeY_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the second coordinate of an
|
||||
`AlgebraicKernel_d_2::AlgebraicReal_2`.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ComputeY_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Constructs an `AlgebraicKernel_d_2::Algebraic_real_2`.
|
||||
|
||||
\refines `AdaptableFunctor`
|
||||
\cgalRefines `AdaptableFunctor`
|
||||
|
||||
\sa `AlgebraicKernel_d_1::ConstructAlgebraicReal_1`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes whether a given pair of bivariate polynomials is coprime.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::MakeCoprime_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes whether the given bivariate polynomial is square free.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::MakeSquareFree_2`
|
||||
\sa `AlgebraicKernel_d_2::SquareFreeFactorize_2`
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes whether an `AlgebraicKernel_d_2::Polynomial_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_1::IsZeroAt_1`
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::IsolateY_2`
|
||||
\sa `AlgebraicKernel_d_2::ComputePolynomialX_2`
|
||||
|
|
|
|||
|
|
@ -1,12 +1,12 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::IsolateX_2`
|
||||
\sa `AlgebraicKernel_d_2::ComputePolynomialX_2`
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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::IsolateY_2`
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
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.
|
||||
|
|
@ -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$,
|
||||
such that \f$ 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`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Returns a square free part of a bivariate polynomial.
|
||||
|
||||
\refines `AdaptableUnaryFunction`
|
||||
\cgalRefines `AdaptableUnaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::IsSquareFree_2`
|
||||
\sa `AlgebraicKernel_d_2::SquareFreeFactorize_2`
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the number of real solutions of the given bivariate polynomial system.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::ConstructAlgebraicReal_2`
|
||||
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the sign of a bivariate polynomial
|
||||
`AlgebraicKernel_d_2::Polynomial_2` at a value of type
|
||||
`AlgebraicKernel_d_2::Algebraic_real_2`.
|
||||
|
||||
\refines `AdaptableBinaryFunction`
|
||||
\cgalRefines `AdaptableBinaryFunction`
|
||||
|
||||
\sa `AlgebraicKernel_d_2::IsZeroAt_2`
|
||||
\sa `AlgebraicKernel_d_1::SignAt_1`
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgAlgebraicKerneldConceptsBi
|
||||
\cgalconcept
|
||||
\cgalConcept
|
||||
|
||||
Computes the real zero-dimensional solutions of a bivariate polynomial system.
|
||||
The multiplicity stored in the output iterator is the multiplicity in the system.
|
||||
|
||||
\refines `Assignable`
|
||||
\refines `CopyConstructible`
|
||||
\cgalRefines `Assignable`
|
||||
\cgalRefines `CopyConstructible`
|
||||
*/
|
||||
class AlgebraicKernel_d_2::Solve_2 {
|
||||
public:
|
||||
|
|
|
|||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue