Triangulations of 3-manifolds. More...

Namespaces
	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

§ NComponent

typedef Component< 3 > regina::NComponent

A convenience typedef for Component<3>.

§ NEdgeEmbedding

typedef FaceEmbedding<3, 1> regina::NEdgeEmbedding

A convenience typedef for FaceEmbedding<3, 1>.

§ NFacePairing

typedef FacetPairing<3> regina::NFacePairing

A convenience typedef for FacetPairing<3>.

§ NIsomorphism

typedef Isomorphism< 3 > regina::NIsomorphism

A convenience typedef for Isomorphism<3>.

§ NTetrahedron

typedef Simplex< 3 > regina::NTetrahedron

A convenience typedef for Simplex<3>.

§ NTriangle

typedef Face< 3, 2 > regina::NTriangle

A convenience typedef for Face<3, 2>.

§ NTriangleEmbedding

typedef FaceEmbedding<3, 2> regina::NTriangleEmbedding

A convenience typedef for FaceEmbedding<3, 2>.

§ NVertexEmbedding

typedef FaceEmbedding<3, 0> regina::NVertexEmbedding

A convenience typedef for FaceEmbedding<3, 0>.

§ NXMLTriangulationReader

typedef XMLTriangulationReader<3> regina::NXMLTriangulationReader

A convenience typedef for XMLTriangulationReader<3>.

Enumeration Type Documentation

§ TuraevViroAlg

enum regina::TuraevViroAlg

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

§ NFacePairingIsoList

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.

§ UseFacePairing

REGINA_DEPRECATED typedef void(* regina::UseFacePairing) (const FacetPairing< 3 > *, const NFacePairingIsoList *, void *)