Regina Calculation Engine
Public Member Functions | Static Public Attributes
regina::NSnapPeaCensusManifold Class Reference

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

#include <nsnappeacensusmfd.h>

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

List of all members.

Public Member Functions

 NSnapPeaCensusManifold (char newSection, unsigned long newIndex)
 Creates a new SnapPea census manifold with the given parameters.
 NSnapPeaCensusManifold (const NSnapPeaCensusManifold &cloneMe)
 Creates a clone of the given SnapPea census manifold.
virtual ~NSnapPeaCensusManifold ()
 Destroys this structure.
char getSection () const
 Returns the section of the SnapPea census to which this manifold belongs.
unsigned long getIndex () const
 Returns the index of this manifold within its particular section of the SnapPea census.
bool operator== (const NSnapPeaCensusManifold &compare) const
 Determines whether this and the given structure represent the same 3-manifold from the SnapPea census.
NTriangulationconstruct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented.
NAbelianGroupgetHomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented.
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.
std::ostream & writeTeXName (std::ostream &out) const
 Writes the common name of this 3-manifold in TeX format to the given output stream.
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.

Static Public Attributes

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

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).

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 except for construct() are implemented for this class, though construct() and getHomologyH1() only return solutions for the very smallest SnapPea census manifolds (for which the homology groups have been hard-coded).

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

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 ( ) [inline, virtual]

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.

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.
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.
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::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.


Member Data Documentation

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

There are 415 manifolds in this section.

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

There are 259 manifolds in this section.

Represents the collection of orientable manifolds formed from six tetrahedra.

There are 962 manifolds in this section.

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

There are 887 manifolds in this section.

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 © 1999-2009, 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).