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

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

#include <manifold/snappeacensusmfd.h>

Inheritance diagram for regina::SnapPeaCensusManifold:
regina::Manifold regina::Output< Manifold >

Public Member Functions

 SnapPeaCensusManifold (char newSection, unsigned long newIndex)
 Creates a new SnapPea census manifold with the given parameters. More...
 
 SnapPeaCensusManifold (const SnapPeaCensusManifold &cloneMe)
 Creates a clone of the given SnapPea census manifold. More...
 
virtual ~SnapPeaCensusManifold ()
 Destroys this structure. More...
 
char section () const
 Returns the section of the SnapPea census to which this manifold belongs. More...
 
unsigned long index () const
 Returns the index of this manifold within its particular section of the SnapPea census. More...
 
bool operator== (const SnapPeaCensusManifold &compare) const
 Determines whether this and the given structure represent the same 3-manifold from the SnapPea census. More...
 
bool operator!= (const SnapPeaCensusManifold &compare) const
 Determines whether this and the given structure represent different 3-manifolds from the SnapPea census. More...
 
Triangulation< 3 > * construct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...
 
AbelianGrouphomology () 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 name () const
 Returns the common name of this 3-manifold as a human-readable string. More...
 
std::string TeXName () const
 Returns the common name of this 3-manifold in TeX format. More...
 
std::string structure () const
 Returns details of the structure of this 3-manifold that might not be evident from its common name. More...
 
AbelianGrouphomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool operator< (const Manifold &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...
 
void writeTextShort (std::ostream &out) const
 Writes a short text representation of this object to the given output stream. More...
 
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...
 

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 Census lookup routines. However, for the time being, the scope of these SnapPeaCensusManifold and SnapPeaCensusTri 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 SnapPeaCensusTri. In particular, the section constants defined in SnapPeaCensusTri and SnapPeaCensusManifold are identical, and so may be freely mixed. Furthermore, the section and index parameters of a SnapPeaCensusTri are identical to those of its corresponding SnapPeaCensusManifold.

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

Constructor & Destructor Documentation

◆ SnapPeaCensusManifold() [1/2]

regina::SnapPeaCensusManifold::SnapPeaCensusManifold ( 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.

◆ SnapPeaCensusManifold() [2/2]

regina::SnapPeaCensusManifold::SnapPeaCensusManifold ( const SnapPeaCensusManifold cloneMe)
inline

Creates a clone of the given SnapPea census manifold.

Parameters
cloneMethe census manifold to clone.

◆ ~SnapPeaCensusManifold()

regina::SnapPeaCensusManifold::~SnapPeaCensusManifold ( )
inlinevirtual

Destroys this structure.

Member Function Documentation

◆ construct()

Triangulation<3>* regina::SnapPeaCensusManifold::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 Manifold. 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::Manifold.

◆ detail()

std::string regina::Output< Manifold , 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.

◆ homology()

AbelianGroup* regina::SnapPeaCensusManifold::homology ( ) 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 Manifold. 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.

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 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::Manifold.

◆ homologyH1()

AbelianGroup * regina::Manifold::homologyH1 ( ) const
inlineinherited

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 Manifold. 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.

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 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

◆ index()

unsigned long regina::SnapPeaCensusManifold::index ( ) 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.

◆ isHyperbolic()

bool regina::SnapPeaCensusManifold::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::Manifold.

◆ name()

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

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

Returns
the common name of this 3-manifold.

◆ operator!=()

bool regina::SnapPeaCensusManifold::operator!= ( const SnapPeaCensusManifold compare) const
inline

Determines whether this and the given structure represent different 3-manifolds from the SnapPea census.

As of Regina 5.0, this test respects the recent discovery that the manifolds x101 and x103 are homeomorphic. For details, see B.B., A duplicate pair in the SnapPea census, Experimental Mathematics, 23:170-173, 2014.

Parameters
comparethe structure with which this will be compared.
Returns
true if and only if this and the given structure represent different SnapPea census manifolds.

◆ operator<()

bool regina::Manifold::operator< ( const Manifold 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 name().
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.

◆ operator==()

bool regina::SnapPeaCensusManifold::operator== ( const SnapPeaCensusManifold compare) const
inline

Determines whether this and the given structure represent the same 3-manifold from the SnapPea census.

As of Regina 5.0, this test respects the recent discovery that the manifolds x101 and x103 are homeomorphic. For details, see B.B., A duplicate pair in the SnapPea census, Experimental Mathematics, 23:170-173, 2014.

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.

◆ section()

char regina::SnapPeaCensusManifold::section ( ) 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.

◆ str()

std::string regina::Output< Manifold , 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.

◆ structure()

std::string regina::Manifold::structure ( ) 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.

◆ TeXName()

std::string regina::Manifold::TeXName ( ) 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.

◆ utf8()

std::string regina::Output< Manifold , 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.

◆ writeName()

std::ostream& regina::SnapPeaCensusManifold::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; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::Manifold.

◆ writeStructure()

std::ostream& regina::SnapPeaCensusManifold::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; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Reimplemented from regina::Manifold.

◆ writeTeXName()

std::ostream& regina::SnapPeaCensusManifold::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; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::Manifold.

◆ writeTextLong()

void regina::Manifold::writeTextLong ( std::ostream &  out) const
inlineinherited

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

Subclasses must not override this routine. They should override writeName() and writeStructure() instead.

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

◆ writeTextShort()

void regina::Manifold::writeTextShort ( std::ostream &  out) const
inlineinherited

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

Subclasses must not override this routine. They should override writeName() instead.

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

Member Data Documentation

◆ SEC_5

const char regina::SnapPeaCensusManifold::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.

◆ SEC_6_NOR

const char regina::SnapPeaCensusManifold::SEC_6_NOR
static

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

There are 259 manifolds in this section.

◆ SEC_6_OR

const char regina::SnapPeaCensusManifold::SEC_6_OR
static

Represents the collection of orientable manifolds formed from six tetrahedra.

There are 962 manifolds in this section.

◆ SEC_7_NOR

const char regina::SnapPeaCensusManifold::SEC_7_NOR
static

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

There are 887 manifolds in this section.

◆ SEC_7_OR

const char regina::SnapPeaCensusManifold::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 © 1999-2016, 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).