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::Output< NStandardTriangulation >

Public Member Functions

NSnapPeaCensusTriclone () const
 Returns a newly created clone of this structure. More...
 
char section () const
 Returns the section of the SnapPea census to which this triangulation belongs. More...
 
REGINA_DEPRECATED char getSection () const
 Deprecated routine that returns the section of the SnapPea census to which this triangulation belongs. More...
 
unsigned long index () const
 Returns the index of this triangulation within its particular section of the SnapPea census. More...
 
REGINA_DEPRECATED unsigned long getIndex () const
 Deprecated routine that 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...
 
bool operator!= (const NSnapPeaCensusTri &compare) const
 Determines whether this and the given structure represent different triangulations from the SnapPea census. More...
 
NManifoldmanifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...
 
NAbelianGrouphomology () 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...
 
std::string name () const
 Returns the name of this specific triangulation as a human-readable string. More...
 
REGINA_DEPRECATED std::string getName () const
 Deprecated routine that returns the name of this specific triangulation as a human-readable string. More...
 
std::string TeXName () const
 Returns the name of this specific triangulation in TeX format. More...
 
REGINA_DEPRECATED std::string getTeXName () const
 Deprecated routine that returns the name of this specific triangulation in TeX format. More...
 
REGINA_DEPRECATED NManifoldgetManifold () const
 Deprecated routine that returns the 3-manifold represented by this triangulation,. More...
 
NAbelianGrouphomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
REGINA_DEPRECATED NAbelianGroupgetHomologyH1 () const
 Deprecated routine that returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes a short text representation of this object to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes a detailed text representation of this object to the given output stream. More...
 
std::string str () const
 Returns a short text representation of this object. More...
 
std::string utf8 () const
 Returns a short text representation of this object using unicode characters. More...
 
std::string detail () const
 Returns a detailed text representation of this object. More...
 
REGINA_DEPRECATED std::string toString () const
 A deprecated alias for str(). More...
 
REGINA_DEPRECATED std::string toStringLong () const
 A deprecated alias for detail(). 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 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
 

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).

Note
The modern cusped hyperbolic census now extends to nine tetrahedra, and indeed the 9-tetrahedron database is accessible through the NCensus lookup routines. However, for the time being, the scope of these NSnapPeaCensusManifold and NSnapPeaCensusTri classes is restricted to the original Callahan-Hildebrand-Weeks 7-tetrahedron census only.

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.

Member Function Documentation

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

Returns a newly created clone of this structure.

Returns
a newly created clone.
std::string regina::Output< NStandardTriangulation , false >::detail ( ) const
inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns
a detailed text representation of this object.
NAbelianGroup * regina::NStandardTriangulation::getHomologyH1 ( ) const
inlineinherited

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

Deprecated:
This routine has been renamed to homology(). See the homology() documentation for further details.
unsigned long regina::NSnapPeaCensusTri::getIndex ( ) const
inline

Deprecated routine that returns the index of this triangulation within its particular section of the SnapPea census.

Deprecated:
This routine has been renamed to index(). See the index() documentation for further details.
NManifold * regina::NStandardTriangulation::getManifold ( ) const
inlineinherited

Deprecated routine that returns the 3-manifold represented by this triangulation,.

Deprecated:
This routine has been renamed to manifold(). See the manifold() documentation for further details.
std::string regina::NStandardTriangulation::getName ( ) const
inlineinherited

Deprecated routine that returns the name of this specific triangulation as a human-readable string.

Deprecated:
This routine has been renamed to name(). See the name() documentation for further details.
char regina::NSnapPeaCensusTri::getSection ( ) const
inline

Deprecated routine that returns the section of the SnapPea census to which this triangulation belongs.

Deprecated:
This routine has been renamed to section(). See the section() documentation for further details.
std::string regina::NStandardTriangulation::getTeXName ( ) const
inlineinherited

Deprecated routine that returns the name of this specific triangulation in TeX format.

Deprecated:
This routine has been renamed to TeXName(). See the TeXName() documentation for further details.
NAbelianGroup* regina::NSnapPeaCensusTri::homology ( ) 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::homology() 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::homology() upon the associated real triangulation.

This routine can also be accessed via the alias homologyH1() (a name that is more specific, but a little longer to type).

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

Reimplemented from regina::NStandardTriangulation.

NAbelianGroup * regina::NStandardTriangulation::homologyH1 ( ) const
inlineinherited

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::homology() 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::homology() upon the associated real triangulation.

This routine can also be accessed via the alias homology() (a name that is less specific, but a little easier to type).

Returns
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.
unsigned long regina::NSnapPeaCensusTri::index ( ) 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.
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.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NComponent component)
staticinherited

Determines whether the given component represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given component must have the same corresponding boundary triangles, i.e., the component cannot have any further identifications of these boundary triangles with each other.

Note that the triangulation-based routine isStandardTriangulation(NTriangulation*) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.

Parameters
componentthe triangulation component under examination.
Returns
the details of the standard triangulation if the given component is recognised, or 0 otherwise.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NTriangulation tri)
staticinherited

Determines whether the given triangulation represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given triangulation must have the same corresponding boundary triangles, i.e., the triangulation cannot have any further identifications of these boundary triangles with each other.

This routine may recognise more triangulations than the component-based isStandardTriangulation(NComponent*), since passing an entire triangulation allows access to more information.

Parameters
trithe triangulation under examination.
Returns
the details of the standard triangualation if the given triangulation is recognised, or 0 otherwise.
NManifold* regina::NSnapPeaCensusTri::manifold ( ) 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.

std::string regina::NStandardTriangulation::name ( ) const
inherited

Returns the name of this specific triangulation as a human-readable string.

Returns
the name of this triangulation.
bool regina::NSnapPeaCensusTri::operator!= ( const NSnapPeaCensusTri compare) const
inline

Determines whether this and the given structure represent different triangulations 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 different SnapPea census triangulations.
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.
char regina::NSnapPeaCensusTri::section ( ) 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.
std::string regina::Output< NStandardTriangulation , false >::str ( ) const
inherited

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python:
In addition to str(), this is also used as the Python "stringification" function __str__().
Returns
a short text representation of this object.
std::string regina::NStandardTriangulation::TeXName ( ) const
inherited

Returns the name of this specific triangulation in TeX format.

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.
Returns
the name of this triangulation in TeX format.
REGINA_DEPRECATED std::string regina::Output< NStandardTriangulation , false >::toString ( ) const
inherited

A deprecated alias for str().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.
REGINA_DEPRECATED std::string regina::Output< NStandardTriangulation , false >::toStringLong ( ) const
inherited

A deprecated alias for detail().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.
std::string regina::Output< NStandardTriangulation , false >::utf8 ( ) const
inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.
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.

void regina::NStandardTriangulation::writeTextLong ( std::ostream &  out) const
inlinevirtualinherited

Writes a detailed text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent NStandardTriangulation class offers a reasonable default implementation based on writeName().

Python:
Not present.
Parameters
outthe output stream to which to write.

Reimplemented in regina::NLayeredSolidTorus, regina::NAugTriSolidTorus, regina::NLayeredChain, regina::NTriSolidTorus, regina::NSpiralSolidTorus, regina::NPlugTriSolidTorus, regina::NLayeredTorusBundle, regina::NBlockedSFSTriple, regina::NPluggedTorusBundle, regina::NSnappedBall, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NL31Pillow, regina::NBlockedSFSLoop, regina::NBlockedSFSPair, regina::NTrivialTri, regina::NLayeredChainPair, and regina::NBlockedSFS.

void regina::NStandardTriangulation::writeTextShort ( std::ostream &  out) const
inlinevirtualinherited

Writes a short text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent NStandardTriangulation class offers a reasonable default implementation based on writeName().

Python:
Not present.
Parameters
outthe output stream to which to write.

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 © 1999-2016, 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).