Regina Calculation Engine
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regina::NSnapPeaCensusTri Class Reference

Represents a 3-manifold triangulation from the SnapPea cusped census. More...

#include <subcomplex/nsnappeacensustri.h>

Inheritance diagram for regina::NSnapPeaCensusTri:
regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

Public Member Functions

NSnapPeaCensusTriclone () const
 Returns a newly created clone of this structure. More...
 
char getSection () const
 Returns the section of the SnapPea census to which this triangulation belongs. More...
 
unsigned long getIndex () const
 Returns the index of this triangulation within its particular section of the SnapPea census. More...
 
bool operator== (const NSnapPeaCensusTri &compare) const
 Determines whether this and the given structure represent the same triangulation from the SnapPea census. More...
 
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...
 
NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream. More...
 
- Public Member Functions inherited from regina::NStandardTriangulation
virtual ~NStandardTriangulation ()
 A destructor that does nothing. More...
 
std::string getName () const
 Returns the name of this specific triangulation as a human-readable string. More...
 
std::string getTeXName () const
 Returns the name of this specific triangulation in TeX format. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream. More...
 
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing. More...
 
virtual ~ShareableObject ()
 Default destructor that does nothing. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
std::string str () const
 Returns the output from writeTextShort() as a string. More...
 
std::string toString () const
 A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...
 
std::string detail () const
 Returns the output from writeTextLong() as a string. More...
 
std::string toStringLong () const
 A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...
 

Static Public Member Functions

static NSnapPeaCensusTriisSmallSnapPeaCensusTri (const NComponent *comp)
 Determines if the given triangulation component is one of the smallest SnapPea census triangulations. More...
 
- Static Public Member Functions inherited from regina::NStandardTriangulation
static NStandardTriangulationisStandardTriangulation (NComponent *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina. More...
 
static NStandardTriangulationisStandardTriangulation (NTriangulation *tri)
 Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...
 

Static Public Attributes

static const char SEC_5
 Represents the collection of triangulations formed from five or fewer tetrahedra (both orientable and non-orientable). More...
 
static const char SEC_6_OR
 Represents the collection of orientable triangulations formed from six tetrahedra. More...
 
static const char SEC_6_NOR
 Represents the collection of non-orientable triangulations formed from six tetrahedra. More...
 
static const char SEC_7_OR
 Represents the collection of orientable triangulations formed from seven tetrahedra. More...
 
static const char SEC_7_NOR
 Represents the collection of non-orientable triangulations formed from seven tetrahedra. More...
 

Friends

class NSnapPeaCensusManifold
 

Additional Inherited Members

- Protected Member Functions inherited from regina::boost::noncopyable
 noncopyable ()
 A constructor which does nothing. More...
 
 ~noncopyable ()
 A destructor which does nothing. More...
 

Detailed Description

Represents a 3-manifold triangulation from the SnapPea cusped census.

The SnapPea cusped census is the census of cusped hyperbolic 3-manifolds formed from up to seven tetrahedra. This census was tabulated by Callahan, Hildebrand and Weeks, and is shipped with SnapPea 3.0d3 (and also with Regina).

The census is split into five different sections according to number of tetrahedra and orientability. Each of these sections corresponds to one of the section constants defined in this class.

For further details regarding the SnapPea census, see "A census of cusped hyperbolic 3-manifolds", Patrick J. Callahan, Martin V. Hildebrand and Jeffrey R. Weeks, Math. Comp. 68 (1999), no. 225, pp. 321–332.

Note that this class is closely tied to NSnapPeaCensusManifold. In particular, the section constants defined in NSnapPeaCensusManifold and NSnapPeaCensusTri are identical, and so may be freely mixed. Furthermore, the section and index parameters of an NSnapPeaCensusTri are identical to those of its corresponding NSnapPeaCensusManifold.

All of the optional NStandardTriangulation routines are implemented for this class.

Test:
Included in the test suite.

Member Function Documentation

NSnapPeaCensusTri * regina::NSnapPeaCensusTri::clone ( ) const
inline

Returns a newly created clone of this structure.

Returns
a newly created clone.
NAbelianGroup* regina::NSnapPeaCensusTri::getHomologyH1 ( ) const
virtual

Returns the expected first homology group of this triangulation, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this triangulation then this routine will return 0.

This routine does not work by calling NTriangulation::getHomologyH1() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.

The details of which standard triangulations have homology calculation routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

The homology group will be newly allocated and must be destroyed by the caller of this routine.

If this NStandardTriangulation describes an entire NTriangulation (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling NTriangulation::getHomologyH1() upon the associated real triangulation.

Returns
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NStandardTriangulation.

unsigned long regina::NSnapPeaCensusTri::getIndex ( ) const
inline

Returns the index of this triangulation within its particular section of the SnapPea census.

Note that indices for each section begin counting at zero.

Returns
the index of this triangulation within its section.
NManifold* regina::NSnapPeaCensusTri::getManifold ( ) const
virtual

Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.

If the 3-manifold cannot be recognised then this routine will return 0.

The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.

The 3-manifold will be newly allocated and must be destroyed by the caller of this routine.

Returns
the underlying 3-manifold.

Reimplemented from regina::NStandardTriangulation.

char regina::NSnapPeaCensusTri::getSection ( ) const
inline

Returns the section of the SnapPea census to which this triangulation belongs.

This will be one of the section constants defined in this class.

Returns
the section of the SnapPea census.
static NSnapPeaCensusTri* regina::NSnapPeaCensusTri::isSmallSnapPeaCensusTri ( const NComponent comp)
static

Determines if the given triangulation component is one of the smallest SnapPea census triangulations.

This routine is able to recognise a small selection of triangulations from the beginning of the SnapPea census, by way of hard-coding their structures and properties. Most triangulations from the census however will not be recognised by this routine.

Parameters
compthe triangulation component to examine.
Returns
a newly created structure representing the small SnapPea census triangulation, or null if the given component is not one of the few SnapPea census triangulations recognised by this routine.
bool regina::NSnapPeaCensusTri::operator== ( const NSnapPeaCensusTri compare) const
inline

Determines whether this and the given structure represent the same triangulation from the SnapPea census.

Parameters
comparethe structure with which this will be compared.
Returns
true if and only if this and the given structure represent the same SnapPea census triangulation.
std::ostream& regina::NSnapPeaCensusTri::writeName ( std::ostream &  out) const
virtual

Writes the name of this triangulation as a human-readable string to the given output stream.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NStandardTriangulation.

std::ostream& regina::NSnapPeaCensusTri::writeTeXName ( std::ostream &  out) const
virtual

Writes the name of this triangulation in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Warning
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NStandardTriangulation.

Member Data Documentation

const char regina::NSnapPeaCensusTri::SEC_5
static

Represents the collection of triangulations formed from five or fewer tetrahedra (both orientable and non-orientable).

There are 415 triangulations in this section.

const char regina::NSnapPeaCensusTri::SEC_6_NOR
static

Represents the collection of non-orientable triangulations formed from six tetrahedra.

There are 259 triangulations in this section.

const char regina::NSnapPeaCensusTri::SEC_6_OR
static

Represents the collection of orientable triangulations formed from six tetrahedra.

There are 962 triangulations in this section.

const char regina::NSnapPeaCensusTri::SEC_7_NOR
static

Represents the collection of non-orientable triangulations formed from seven tetrahedra.

There are 887 triangulations in this section.

const char regina::NSnapPeaCensusTri::SEC_7_OR
static

Represents the collection of orientable triangulations formed from seven tetrahedra.

There are 3552 triangulations in this section.


The documentation for this class was generated from the following file:

Copyright © 1999-2013, 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@debian.org).