Triangulations

Triangulations of manifolds in all supported dimensions. More...

Classes
class	regina::Cut
	A cut that separates a triangulation, facet pairing or link diagram into two pieces. More...
class	regina::HomologicalData
	A specialised class that computes a large amount of detailed homological information for a 3-manifold triangulation. More...
class	regina::Example< int >
	This class offers static routines for constructing a variety of sample dim-dimensional triangulations. More...
class	regina::Example< 2 >
	Offers routines for constructing a variety of sample 2-dimensional triangulations. More...
class	regina::Example< 3 >
	Offers routines for constructing a variety of sample 3-dimensional triangulations. More...
class	regina::Example< 4 >
	Offers routines for constructing a variety of sample 4-dimensional triangulations. More...
class	regina::FaceNumbering< int, int >
	Specifies how subdim-faces are numbered within a dim-dimensional simplex. More...
class	regina::FacePair
	Represents a pair of tetrahedron face numbers. More...
class	regina::FacetPairing< 3 >
	Represents the dual graph of a 3-manifold triangulation. More...
struct	regina::FacetSpec< dim >
	A lightweight class used to refer to a particular facet of a particular top-dimensional simplex in a dim-dimensional triangulation. More...
class	regina::IsoSigPrintable< dim, supportLocks >
	The default encoding to use for isomorphism signatures. More...
class	regina::IsoSigClassic< dim >
	The default signature type to use for isomorphism signatures. More...
class	regina::IsoSigDegrees< dim, subdim >
	Defines an alternate type of isomorphism signature based on degree sequences of subdim-faces. More...

Typedefs
template<int dim>
using	regina::IsoSigPrintableLockFree = IsoSigPrintable<dim, false>
	An encoding for isomorphism signatures that ignores simplex and/or facet locks.
template<int dim>
using	regina::IsoSigEdgeDegrees = IsoSigDegrees<dim, 1>
	Defines an alternate type of isomorphism signature based on edge degree sequences.
template<int dim>
using	regina::IsoSigRidgeDegrees = IsoSigDegrees<dim, dim - 2>
	Defines an alternate type of isomorphism signature based on degree sequences of (dim-2)-faces.

Enumerations
enum class	regina::TriangleType {   regina::TriangleType::Unknown = 0 , regina::TriangleType::Triangle = 1 , regina::TriangleType::Scarf = 2 , regina::TriangleType::Parachute = 3 ,   regina::TriangleType::Cone = 4 , regina::TriangleType::Mobius = 5 , regina::TriangleType::Horn = 6 , regina::TriangleType::DunceHat = 7 ,   regina::TriangleType::L31 = 8 }
	The combinatorial type of a triangle, which indicates how the vertices and edges of the triangle are identified together. More...

Functions
void	regina::swap (Cut &a, Cut &b) noexcept
	Swaps the contents of the given cuts.
void	regina::swap (HomologicalData &a, HomologicalData &b) noexcept
	Swaps the contents of the two given HomologicalData objects.
template<int dim>
constexpr int	regina::faceOppositeEdge (int i, int j)
	Returns the (dim-2)-face number that is opposite the edge joining vertices i and j in a dim-dimensional simplex.
std::ostream &	regina::operator<< (std::ostream &out, const FacePair &pair)
	Writes the given face pair to the given output stream.
template<int dim>
std::ostream &	regina::operator<< (std::ostream &out, const FacetSpec< dim > &spec)
	Writes the given facet specifier to the given output stream.

Detailed Description

Triangulations of manifolds in all supported dimensions.

Typedef Documentation

IsoSigEdgeDegrees

template<int dim>

using regina::IsoSigEdgeDegrees = IsoSigDegrees<dim, 1>

Defines an alternate type of isomorphism signature based on edge degree sequences.

Python

Python does not support templates. You can access these classes by appending the appending the dimension as a suffix (e.g., use IsoSigEdgeDegrees3 to use edge degrees in 3-manifold triangulations).

IsoSigPrintableLockFree

template<int dim>

using regina::IsoSigPrintableLockFree = IsoSigPrintable<dim, false>

An encoding for isomorphism signatures that ignores simplex and/or facet locks.

This is exactly the same as the printable encoding that was used with Regina 7.3.x and earlier, before locks were implemented. Like IsoSigPrintable, this encoding represents an isomorphism signature as a std::string using only printable characters from the 7-bit ASCII range.

This class is designed to be used as a template parameter for Triangulation<dim>::isoSig() and Triangulation<dim>::isoSigDetail(). Typical users would have no need to create objects of this class or call any of its functions directly.

Python

Python does not support templates. Instead this class can be used by appending the dimension as a suffix (e.g., IsoSigPrintableLockFree2 and IsoSigPrintableLockFree3 for dimensions 2 and 3).

IsoSigRidgeDegrees

template<int dim>

using regina::IsoSigRidgeDegrees = IsoSigDegrees<dim, dim - 2>

Defines an alternate type of isomorphism signature based on degree sequences of (dim-2)-faces.

Python

Python does not support templates. You can access these classes by appending the appending the dimension as a suffix (e.g., use IsoSigRidgeDegrees4 to use triangle degrees in 4-manifold triangulations).

Enumeration Type Documentation

TriangleType

enum class regina::TriangleType

strong

The combinatorial type of a triangle, which indicates how the vertices and edges of the triangle are identified together.

Here the vertices of the triangle are considered unlabelled (so a relabelling will not change the combinatorial type).

This is the result of calling f.triangleType(), where f is a 2-face within a triangulation of any dimension ≥ 3.

Enumerator
Unknown	Indicates that the triangle type has not yet been determined.
Triangle	Specifies a triangle with no identified vertices or edges.
Scarf	Specifies a triangle with two identified vertices, and no other edge or vertex identifications.
Parachute	Specifies a triangle with three identified vertices, but no edge identifications.
Cone	Specifies a triangle with two edges identified to form a cone. The apex of the cone is not identified with the other two vertices, and the base of the cone is not identified with the other two edges.
Mobius	Specifies a triangle with two edges identified to form a Möbius band. The boundary of the Möbius band is not identified with the other two edges.
Horn	Specifies a triangle with two edges identified to form a cone, and with all three vertices identified. The base of the cone is not identified with the other two edges.
DunceHat	Specifies a triangle with all three edges identified, some via orientation-preserving and some via orientation-reversing gluings.
L31	Specifies a triangle with all three edges identified using orientation-reversing gluings. Note that this forms a spine for the lens space L(3,1).

Function Documentation

faceOppositeEdge()

template<int dim>

int regina::faceOppositeEdge ( int i, int j )

inlineconstexpr

Returns the (dim-2)-face number that is opposite the edge joining vertices i and j in a dim-dimensional simplex.

This function is offered because its implementation is faster than working through the FaceNumbering class.

The arguments i and j do not need to appear in ascending order.

Python

Python does not support templates. Instead, Python users should call this function in the form faceOppositeEdge(dim, i, j); that is, the template parameter dim becomes the first argument of the function.

Template Parameters

dim	the dimension of simplex that we are working with. This must be between 2 and 15 inclusive.

Parameters

i	the first vertex of an edge in a dim-dimensional simplex. This must be between 0 and dim inclusive.
j	the second vertex of an edge in a dim-dimensional simplex. This must be between 0 and dim inclusive, and must be different from i.

Returns

the number of the (dim-2)-face opposite the given edge.

operator<<() [1/2]

std::ostream & regina::operator<< ( std::ostream & out, const FacePair & pair )

inline

Writes the given face pair to the given output stream.

Parameters

out	the output stream to which to write.
pair	the face pair to write.

Returns

a reference to out.

operator<<() [2/2]

template<int dim>

std::ostream & regina::operator<< ( std::ostream & out, const FacetSpec< dim > & spec )

inline

Writes the given facet specifier to the given output stream.

Parameters

out	the output stream to which to write.
spec	the specifier to write.

Returns

a reference to out.

swap() [1/2]

void regina::swap ( Cut & a, Cut & b )

inlinenoexcept

Swaps the contents of the given cuts.

This global routine simply calls Cut::swap(); it is provided so that Cut meets the C++ Swappable requirements.

Parameters

a	the first cut whose contents should be swapped.
b	the second cut whose contents should be swapped.

swap() [2/2]

void regina::swap ( HomologicalData & a, HomologicalData & b )

inlinenoexcept

Swaps the contents of the two given HomologicalData objects.

This global routine simply calls HomologicalData::swap(); it is provided so that HomologicalData meets the C++ Swappable requirements.

Warning

Although this operation is constant time, the HomologicalData class contains an enormous amount of data spread across many different member variables, and so this should really be considered "expensive constant time". You should still work to avoid swapping (or moving, and certainly copying) HomologicalData objects where possible.

Parameters

a	the first object whose contents should be swapped.
b	the second object whose contents should be swapped.