Census of Triangulations

Census lookup and enumeration for triangulations of various dimensions. More...

Classes
class	regina::CensusDB
	Stores the location and description of one of Regina's in-built census databases. More...
class	regina::CensusHit
	Stores a single "hit" indicating that some given triangulation has been located in one of Regina's in-built census databases. More...
class	regina::Census
	A utility class used to search for triangulations across one or more 3-manifold census databases. More...
class	regina::GluingPerms< dim >
	Represents a specific set of gluing permutations to complement a particular pairwise matching of simplex facets. More...
class	regina::GluingPermSearcher< dim >
	A utility class used to build a census of triangulations, by searching through all possible sets of gluing permutations to match a given facet pairing. More...
class	regina::GluingPermSearcher< 2 >
	A utility class for searching through all possible gluing permutation sets that correspond to a given triangle edge pairing. More...
class	regina::GluingPermSearcher< 3 >
	A utility class for searching through all possible gluing permutation sets that correspond to a given tetrahedron face pairing. More...
class	regina::EulerSearcher
	A gluing permutation search class that offers a specialised search algorithm for when all vertex links must all have a given fixed Euler characteristic. More...
class	regina::CompactSearcher
	A gluing permutation search class that offers a specialised search algorithm for when only compact (finite) 3-manifold triangulations are required. More...
class	regina::ClosedPrimeMinSearcher
	A gluing permutation search class that offers a specialised search algorithm for when (i) only closed prime minimal P2-irreducible triangulations are required, and (ii) the given face pairing has order at least three. More...
class	regina::HyperbolicMinSearcher
	A gluing permutation search class that offers a specialised search algorithm for when only minimal ideal triangulations of cusped finite-volume hyperbolic 3-manifolds are required. More...
class	regina::GluingPermSearcher< 4 >
	A utility class for searching through all possible gluing permutation sets that correspond to a given pentachoron facet pairing. More...

Macros
#define	PRUNE_HIGH_DEG_EDGE_SET   1
	Specifies whether the ClosedPrimeMinSearcher census generation code should prune on high-degree edges. More...

Typedefs
using	regina::CensusPurge = regina::Flags< CensusPurgeFlags >
	A combination of flags for census generation. More...

Enumerations
enum	regina::CensusPurgeFlags {   regina::PURGE_NONE = 0x00 , regina::PURGE_NON_MINIMAL = 0x01 , regina::PURGE_NON_PRIME = 0x02 , regina::PURGE_NON_MINIMAL_PRIME = 0x03 ,   regina::PURGE_NON_MINIMAL_HYP = 0x09 , regina::PURGE_P2_REDUCIBLE = 0x04 }
	Represents different classes of triangulations that may be ignored by census generation algorithms. More...

Functions
void	regina::swap (CensusDB &a, CensusDB &b) noexcept
	Swaps the contents of the given database references. More...
void	regina::swap (CensusHit &a, CensusHit &b) noexcept
	Swaps the contents of the given census hits. More...
template<int dim>
void	regina::swap (GluingPerms< dim > &a, GluingPerms< dim > &b) noexcept
	Swaps the contents of the given gluing permutation sets. More...
CensusPurge	regina::operator| (CensusPurgeFlags lhs, CensusPurgeFlags rhs)
	Returns the bitwise OR of the two given flags. More...

Detailed Description

Census lookup and enumeration for triangulations of various dimensions.

Macro Definition Documentation

PRUNE_HIGH_DEG_EDGE_SET

#define PRUNE_HIGH_DEG_EDGE_SET   1

Specifies whether the ClosedPrimeMinSearcher census generation code should prune on high-degree edges.

It is well known that a closed prime minimal P²-irreducible triangulation formed from at least three tetrahedra can never have an edge of degree one or two. Combining this with the fact that such a triangulation must always have one vertex, a simple Euler characteristic calculation shows that there must be precisely n+1 edges, where n is the number of tetrahedra.

A little arithmetic then shows that, for any k edges, the sum of their edge degrees can be no more than 3(n+k-1); otherwise one of the remaining edges will be forced to have degree one or two. This observation is the basis behind the high-degree edge pruning that this option controls.

To enable pruning on high-degree edges, set this macro to 1 (the default for Regina's main source distribution); to disable it, set it to 0.

Typedef Documentation

CensusPurge

using regina::CensusPurge = typedef regina::Flags<CensusPurgeFlags>

A combination of flags for census generation.

If a function requires a CensusPurge object as an argument, you can pass a single CensusPurgeFlags constant, or a combination of such constants using the bitwise OR operator, or empty braces {} to indicate no flags at all.

Enumeration Type Documentation

CensusPurgeFlags

enum regina::CensusPurgeFlags

Represents different classes of triangulations that may be ignored by census generation algorithms.

Excluding a triangulation from a census is not a promise: for example, a census that uses the flag PURGE_NON_MINIMAL might include some non-minimal triangulations and exclude others.

However, including a triangulation is a promise: for example, a census that uses the flag PURGE_NON_MINIMAL will promise to include every minimal triangulations.

These flags can be combined using the bitwise OR operator. See (for example) the GluingPermSearcher<3> constructor documentation for further details on how these flags are used.

Enumerator
PURGE_NONE	Indicates that no triangulations should be ignored.
PURGE_NON_MINIMAL	Indicates that non-minimal triangulations may be ignored.
PURGE_NON_PRIME	Indicates that any triangulation that is not prime (i.e., can be written as a non-trivial connected sum) and any bounded triangulation that is reducible over a disc may be ignored.
PURGE_NON_MINIMAL_PRIME	Indicates that any triangulation that is not prime (i.e., can be written as a non-trivial connected sum), any bounded triangulation that is reducible over a disc and any triangulation that is non-minimal may be ignored. Note that this is simply a combination of the constants PURGE_NON_MINIMAL and PURGE_NON_PRIME.
PURGE_NON_MINIMAL_HYP	Indicates that any triangulation that is not a minimal ideal triangulation of a cusped finite-volume hyperbolic 3-manifold may be ignored.
PURGE_P2_REDUCIBLE	Indicates that any triangulation containing an embedded two-sided projective plane may be ignored.

Function Documentation

operator|()

CensusPurge regina::operator| ( CensusPurgeFlags  lhs, CensusPurgeFlags  rhs  )

inline

Returns the bitwise OR of the two given flags.

Parameters

lhs	the first flag to combine.
rhs	the second flag to combine.

Returns

the combination of both flags.

swap() [1/3]

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

inlinenoexcept

Swaps the contents of the given database references.

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

Parameters

a	the first database reference whose contents should be swapped.
b	the second database reference whose contents should be swapped.

swap() [2/3]

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

inlinenoexcept

Swaps the contents of the given census hits.

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

Parameters

a	the first census hit whose contents should be swapped.
b	the second census hit whose contents should be swapped.

swap() [3/3]

template<int dim>

void regina::swap ( GluingPerms< dim > &  a, GluingPerms< dim > &  b  )

inlinenoexcept

Swaps the contents of the given gluing permutation sets.

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

Parameters

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