Regina Calculation Engine
Public Member Functions | Static Public Member Functions
regina::NL31Pillow Class Reference

Represents a triangular pillow L(3,1) component of a triangulation. More...

#include <nl31pillow.h>

Inheritance diagram for regina::NL31Pillow:
regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

virtual ~NL31Pillow ()
 Destroys this structure.
NL31Pillowclone () const
 Returns a newly created clone of this structure.
NTetrahedrongetTetrahedron (int whichTet) const
 Returns one of the two tetrahedra involved in this structure.
unsigned getInteriorVertex (int whichTet) const
 Returns the vertex number of the given tetrahedron corresponding to the degree three vertex in the interior of the triangular pillow.
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.
void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream.

Static Public Member Functions

static NL31PillowisL31Pillow (const NComponent *comp)
 Determines if the given triangulation component is a triangular pillow L(3,1).

Detailed Description

Represents a triangular pillow L(3,1) component of a triangulation.

A triangular pillow L(3,1) is a two-tetrahedron two-vertex triangulation of the lens space L(3,1) formed as follows.

A triangular pillow is formed from two tetrahedra with a single degree three vertex in the interior of the pillow. The two boundary faces of this pillow are then identified with a one-third twist.

All optional NStandardTriangulation routines are implemented for this class.

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

Constructor & Destructor Documentation

regina::NL31Pillow::~NL31Pillow ( ) [inline, virtual]

Destroys this structure.


Member Function Documentation

NL31Pillow* regina::NL31Pillow::clone ( ) const

Returns a newly created clone of this structure.

Returns:
a newly created clone.
NAbelianGroup* regina::NL31Pillow::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 regina::NL31Pillow::getInteriorVertex ( int  whichTet) const [inline]

Returns the vertex number of the given tetrahedron corresponding to the degree three vertex in the interior of the triangular pillow.

See the general class notes for further details.

The specific tetrahedron to examine is determined by the argument whichTet; this will be the tetrahedron getTetrahedron(whichTet).

Parameters:
whichTetspecifies which tetrahedron to examine; this must be either 0 or 1.
Returns:
the vertex of tetrahedron whichTet corresponding to the vertex in the interior of the triangular pillow; this will be between 0 and 3 inclusive.
NManifold* regina::NL31Pillow::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.

NTetrahedron * regina::NL31Pillow::getTetrahedron ( int  whichTet) const [inline]

Returns one of the two tetrahedra involved in this structure.

Parameters:
whichTetspecifies which tetrahedron to return; this must be either 0 or 1.
Returns:
the requested tetrahedron.
static NL31Pillow* regina::NL31Pillow::isL31Pillow ( const NComponent comp) [static]

Determines if the given triangulation component is a triangular pillow L(3,1).

Parameters:
compthe triangulation component to examine.
Returns:
a newly created structure containing details of the triangular pillow L(3,1), or null if the given component is not a triangular pillow L(3,1).
std::ostream & regina::NL31Pillow::writeName ( std::ostream &  out) const [inline, 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::NL31Pillow::writeTeXName ( std::ostream &  out) const [inline, 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::NL31Pillow::writeTextLong ( std::ostream &  out) const [inline, virtual]

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

The output should provided the user with all the information they could want. The output should end with a 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.


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).