regina::NSnapPeaCensusTri Class Reference
[Standard Triangulations and Subcomplexes]

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

#include <nsnappeacensustri.h>

Inheritance diagram for regina::NSnapPeaCensusTri:

regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

NSnapPeaCensusTriclone () const
 Returns a newly created clone of this structure.
char getSection () const
 Returns the section of the SnapPea census to which this triangulation belongs.
unsigned long getIndex () const
 Returns the index of this triangulation within its particular section of the SnapPea census.
bool operator== (const NSnapPeaCensusTri &compare) const
 Determines whether this and the given structure represent the same triangulation from the SnapPea census.
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.
NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented.
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream.
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream.

Static Public Member Functions

static NSnapPeaCensusTriisSmallSnapPeaCensusTri (const NComponent *comp)
 Determines if the given triangulation component is one of the smallest SnapPea census triangulations.

Static Public Attributes

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

Friends

class NSnapPeaCensusManifold


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, though getHomologyH1() only returns a solution for the very smallest SnapPea triangulations (for which the homology groups have been hard-coded).

Test:
Tested in the test suite, though not exhaustively.

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:
comp the 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:
compare the 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:
out the 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:
out the 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.

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

There are 259 triangulations in this section.

Represents the collection of orientable triangulations formed from six tetrahedra.

There are 962 triangulations in this section.

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

There are 887 triangulations in this section.

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 © 1999-2009, Ben Burton
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).