Regina Calculation Engine
Public Member Functions | Static Public Attributes | List of all members
regina::NSnapPeaCensusManifold Class Reference

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

#include <manifold/nsnappeacensusmfd.h>

Inheritance diagram for regina::NSnapPeaCensusManifold:
regina::NManifold regina::ShareableObject regina::boost::noncopyable

Public Member Functions

 NSnapPeaCensusManifold (char newSection, unsigned long newIndex)
 Creates a new SnapPea census manifold with the given parameters. More...
 
 NSnapPeaCensusManifold (const NSnapPeaCensusManifold &cloneMe)
 Creates a clone of the given SnapPea census manifold. More...
 
virtual ~NSnapPeaCensusManifold ()
 Destroys this structure. More...
 
char getSection () const
 Returns the section of the SnapPea census to which this manifold belongs. More...
 
unsigned long getIndex () const
 Returns the index of this manifold within its particular section of the SnapPea census. More...
 
bool operator== (const NSnapPeaCensusManifold &compare) const
 Determines whether this and the given structure represent the same 3-manifold from the SnapPea census. More...
 
NTriangulationconstruct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...
 
NAbelianGroupgetHomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool isHyperbolic () const
 Returns whether or not this is a finite-volume hyperbolic manifold. More...
 
std::ostream & writeName (std::ostream &out) const
 Writes the common name of this 3-manifold as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const
 Writes the common name of this 3-manifold in TeX format to the given output stream. More...
 
std::ostream & writeStructure (std::ostream &out) const
 Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More...
 
std::string getName () const
 Returns the common name of this 3-manifold as a human-readable string. More...
 
std::string getTeXName () const
 Returns the common name of this 3-manifold in TeX format. More...
 
std::string getStructure () const
 Returns details of the structure of this 3-manifold that might not be evident from its common name. More...
 
bool operator< (const NManifold &compare) const
 Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
Input and Output
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 Attributes

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

Detailed Description

Represents a 3-manifold 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 NSnapPeaCensusTri. In particular, the section constants defined in NSnapPeaCensusTri and NSnapPeaCensusManifold 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 NManifold routines are implemented for this class.

Constructor & Destructor Documentation

regina::NSnapPeaCensusManifold::NSnapPeaCensusManifold ( char  newSection,
unsigned long  newIndex 
)
inline

Creates a new SnapPea census manifold with the given parameters.

Parameters
newSectionthe section of the SnapPea census to which this manifold belongs. This must be one of the section constants defined in this class.
newIndexspecifies which particular manifold within the given section is represented. The indices for each section begin counting at zero, and so this index must be between 0 and k-1, where k is the total number of manifolds in the given section.
regina::NSnapPeaCensusManifold::NSnapPeaCensusManifold ( const NSnapPeaCensusManifold cloneMe)
inline

Creates a clone of the given SnapPea census manifold.

Parameters
cloneMethe census manifold to clone.
regina::NSnapPeaCensusManifold::~NSnapPeaCensusManifold ( )
inlinevirtual

Destroys this structure.

Member Function Documentation

NTriangulation* regina::NSnapPeaCensusManifold::construct ( ) const
virtual

Returns a triangulation of this 3-manifold, if such a construction has been implemented.

If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.

The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.

Returns
a triangulation of this 3-manifold, or 0 if the appropriate construction routine has not yet been implemented.

Reimplemented from regina::NManifold.

std::string regina::ShareableObject::detail ( ) const
inherited

Returns the output from writeTextLong() as a string.

Returns
a long text representation of this object.
NAbelianGroup* regina::NSnapPeaCensusManifold::getHomologyH1 ( ) const
virtual

Returns the first homology group of this 3-manifold, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.

The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.

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

Returns
the first homology group of this 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NManifold.

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

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

Note that indices for each section begin counting at zero.

Returns
the index of this manifold within its section.
std::string regina::NManifold::getName ( ) const
inherited

Returns the common name of this 3-manifold as a human-readable string.

Returns
the common name of this 3-manifold.
char regina::NSnapPeaCensusManifold::getSection ( ) const
inline

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

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

Returns
the section of the SnapPea census.
std::string regina::NManifold::getStructure ( ) const
inherited

Returns details of the structure of this 3-manifold that might not be evident from its common name.

For instance, for an orbit space S^3/G this routine might return the full Seifert structure.

This routine may return the empty string if no additional details are deemed necessary.

Returns
a string describing additional structural details.
std::string regina::NManifold::getTeXName ( ) const
inherited

Returns the common name of this 3-manifold 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 common name of this 3-manifold in TeX format.
bool regina::NSnapPeaCensusManifold::isHyperbolic ( ) const
inlinevirtual

Returns whether or not this is a finite-volume hyperbolic manifold.

Returns
true if this is a finite-volume hyperbolic manifold, or false if not.

Implements regina::NManifold.

bool regina::NManifold::operator< ( const NManifold compare) const
inherited

Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold.

The ordering imposed on 3-manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.

The ordering also depends on the particular representation of the 3-manifold that is used. As an example, different representations of the same Seifert fibred space might well be ordered differently.

All that this routine really offers is a well-defined way of ordering 3-manifold representations.

Warning
Currently this routine is only implemented in full for closed 3-manifolds. For most classes of bounded 3-manifolds, this routine simply compares the strings returned by getName().
Parameters
comparethe 3-manifold representation with which this will be compared.
Returns
true if and only if this is "smaller" than the given 3-manifold representation.
bool regina::NSnapPeaCensusManifold::operator== ( const NSnapPeaCensusManifold compare) const
inline

Determines whether this and the given structure represent the same 3-manifold 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 manifold.
std::string regina::ShareableObject::str ( ) const
inherited

Returns the output from writeTextShort() as a string.

Python:
This implements the __str__() function.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toString ( ) const
inlineinherited

A deprecated alias for str(), which returns the output from writeTextShort() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toStringLong ( ) const
inlineinherited

A deprecated alias for detail(), which returns the output from writeTextLong() as a string.

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::ostream& regina::NSnapPeaCensusManifold::writeName ( std::ostream &  out) const
virtual

Writes the common name of this 3-manifold 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::NManifold.

std::ostream& regina::NSnapPeaCensusManifold::writeStructure ( std::ostream &  out) const
virtual

Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.

For instance, for an orbit space S^3/G this routine might write the full Seifert structure.

This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.

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.

Reimplemented from regina::NManifold.

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

Writes the common name of this 3-manifold 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::NManifold.

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

Writes this object in long text format to the given output stream.

The output should provide the user with all the information they could want. The output should be human-readable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.

The default implementation of this routine merely calls writeTextShort() and adds a newline.

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

Reimplemented from regina::ShareableObject.

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

Writes this object in short text format to the given output stream.

The output should be human-readable, should fit on a single line, and should not end with a newline.

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

Implements regina::ShareableObject.

Member Data Documentation

const char regina::NSnapPeaCensusManifold::SEC_5
static

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

There are 415 manifolds in this section.

const char regina::NSnapPeaCensusManifold::SEC_6_NOR
static

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

There are 259 manifolds in this section.

const char regina::NSnapPeaCensusManifold::SEC_6_OR
static

Represents the collection of orientable manifolds formed from six tetrahedra.

There are 962 manifolds in this section.

const char regina::NSnapPeaCensusManifold::SEC_7_NOR
static

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

There are 887 manifolds in this section.

const char regina::NSnapPeaCensusManifold::SEC_7_OR
static

Represents the collection of orientable manifolds formed from seven tetrahedra.

There are 3552 manifolds in this section.


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

Copyright © 1999-2014, 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).