Regina Calculation Engine
Namespaces | Classes | Typedefs | Enumerations | Variables
3-Manifold Triangulations

Triangulations of 3-manifolds. More...

Namespaces

namespace  regina::detail
 Contains implementation details and common functionality for Regina's dimension-agnostic classes.
 

Classes

class  regina::Dim2ExampleTriangulation
 This class offers routines for constructing sample 2-manifold triangulations of various types. More...
 
class  regina::NBoundaryComponent
 Represents a component of the boundary of a triangulation. More...
 
class  regina::Component< 3 >
 Represents a connected component of a 3-manifold triangulation. More...
 
class  regina::Face< 3, 1 >
 Represents an edge in the skeleton of a 3-manifold triangulation. More...
 
class  regina::NExampleTriangulation
 This class offers routines for constructing sample 3-manifold triangulations of various types. More...
 
class  regina::NFacePair
 Represents a pair of tetrahedron face numbers. More...
 
class  regina::FacetPairing< 3 >
 Represents the dual graph of a 3-manifold triangulation. More...
 
class  regina::Isomorphism< 3 >
 Represents a combinatorial isomorphism from one 3-manifold triangulation into another. More...
 
class  regina::NPermItS4
 An iterator class that runs through all 24 permutations of four elements. More...
 
class  regina::Simplex< 3 >
 Represents a tetrahedron within a 3-manifold triangulation. More...
 
class  regina::Face< 3, 2 >
 Represents a triangle in the skeleton of a 3-manifold triangulation. More...
 
class  regina::Triangulation< 3 >
 Represents a 3-dimensional triangulation, typically of a 3-manifold. More...
 
class  regina::Face< 3, 0 >
 Represents a vertex in the skeleton of a 3-manifold triangulation. More...
 
class  regina::XMLTriangulationReader< 3 >
 An XML packet reader that reads a single 3-dimensional triangulation. More...
 

Typedefs

typedef Component< 3 > regina::NComponent
 A convenience typedef for Component<3>. More...
 
typedef FaceEmbedding< 3, 1 > regina::NEdgeEmbedding
 A convenience typedef for FaceEmbedding<3, 1>. More...
 
typedef FacetPairing< 3 > regina::NFacePairing
 A convenience typedef for FacetPairing<3>. More...
 
typedef Isomorphism< 3 > regina::NIsomorphism
 A convenience typedef for Isomorphism<3>. More...
 
typedef Simplex< 3 > regina::NTetrahedron
 A convenience typedef for Simplex<3>. More...
 
typedef FaceEmbedding< 3, 2 > regina::NTriangleEmbedding
 A convenience typedef for FaceEmbedding<3, 2>. More...
 
typedef Face< 3, 2 > regina::NTriangle
 A convenience typedef for Face<3, 2>. More...
 
typedef FaceEmbedding< 3, 0 > regina::NVertexEmbedding
 A convenience typedef for FaceEmbedding<3, 0>. More...
 
typedef XMLTriangulationReader< 3 > regina::NXMLTriangulationReader
 A convenience typedef for XMLTriangulationReader<3>. More...
 

Enumerations

enum  regina::TuraevViroAlg { regina::TV_DEFAULT = 0, regina::TV_BACKTRACK = 1, regina::TV_TREEWIDTH = 2, regina::TV_NAIVE = 3 }
 Represents the various algorithms available for computing Turaev-Viro invariants. More...
 

Variables

REGINA_DEPRECATED typedef
std::list< NIsomorphism * > 
regina::NFacePairingIsoList
 A deprecated typedef provided for backward compatibility only. More...
 
REGINA_DEPRECATED typedef void(* regina::UseFacePairing )(const FacetPairing< 3 > *, const NFacePairingIsoList *, void *)
 A deprecated typedef provided for backward compatibility only. More...
 

Detailed Description

Triangulations of 3-manifolds.

Typedef Documentation

typedef Component< 3 > regina::NComponent

A convenience typedef for Component<3>.

typedef FaceEmbedding<3, 1> regina::NEdgeEmbedding

A convenience typedef for FaceEmbedding<3, 1>.

typedef FacetPairing<3> regina::NFacePairing

A convenience typedef for FacetPairing<3>.

typedef Isomorphism< 3 > regina::NIsomorphism

A convenience typedef for Isomorphism<3>.

typedef Simplex< 3 > regina::NTetrahedron

A convenience typedef for Simplex<3>.

typedef Face< 3, 2 > regina::NTriangle

A convenience typedef for Face<3, 2>.

typedef FaceEmbedding<3, 2> regina::NTriangleEmbedding

A convenience typedef for FaceEmbedding<3, 2>.

typedef FaceEmbedding<3, 0> regina::NVertexEmbedding

A convenience typedef for FaceEmbedding<3, 0>.

typedef XMLTriangulationReader<3> regina::NXMLTriangulationReader

A convenience typedef for XMLTriangulationReader<3>.

Enumeration Type Documentation

Represents the various algorithms available for computing Turaev-Viro invariants.

Enumerator
TV_DEFAULT 

The default algorithm.

Here Regina will choose whichever algorithm it thinks (rightly or wrongly) is most appropriate.

TV_BACKTRACK 

An optimised backtracking algorithm.

This enumerates edge colourings and sums their corresponding weights. This can be slow in general (since there could be exponentially many edge colourings), but it has very small memory usage.

TV_TREEWIDTH 

A treewidth-based algorithm.

This uses dynamic programming over a tree decomposition of the face pairing graph. This can be fast for triangulations whose face pairing graphs have small treewidth, but it may require extremely large amounts of memory.

TV_NAIVE 

An unoptimised backtracking algorithm.

Like TV_BACKTRACK, this enumerates edge colourings and sums weights. However, the implementation is more naive.

Warning
This algorithm should only be used for comparison and experimentation. Due to its slow performance, it is not suitable for "real" applications.

Variable Documentation

REGINA_DEPRECATED typedef std::list<NIsomorphism*> regina::NFacePairingIsoList

A deprecated typedef provided for backward compatibility only.

Deprecated:
As of Regina 4.94, this typedef is now available as NFacePairing::IsoList. The old typedef NFacePairingIsoList is provided for backward compatibility, but will be removed in some future version of Regina.
REGINA_DEPRECATED typedef void(* regina::UseFacePairing)(const FacetPairing< 3 > *, const NFacePairingIsoList *, void *)

A deprecated typedef provided for backward compatibility only.

Deprecated:
As of Regina 4.94, this typedef is now available as NFacePairing::Use. The old typedef UseFacePairing is provided for backward compatibility, but will be removed in some future version of Regina.

Copyright © 1999-2016, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).