regina::NTrivialTri Class Reference
[Standard Triangulations and Subcomplexes]

Represents one of a few particular trivial triangulations that do not belong to any of the other larger families. More...

#include <ntrivialtri.h>

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

List of all members.

Public Member Functions

NTrivialTriclone () const
 Returns a newly created clone of this structure.
int getType () const
 Returns the specific trivial triangulation being represented.
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 NTrivialTriisTrivialTriangulation (const NComponent *comp)
 Determines if the given triangulation component is one of the trivial triangulations recognised by this class.

Static Public Attributes

static const int SPHERE_4_VERTEX
 Represents the two-tetrahedron four-vertex triangulation of the 3-sphere.
static const int BALL_3_VERTEX
 Represents the one-tetrahedron three-vertex triangulation of the ball.
static const int BALL_4_VERTEX
 Represents the one-tetrahedron four-vertex triangulation of the ball.
static const int N2
 Represents the two-tetrahedron triangulation N(2) of the twisted 2-sphere bundle over the circle.
static const int N3_1
 Represents the three-tetrahedron triangulation N(3,1) of the projective plane bundle over the circle.
static const int N3_2
 Represents the three-tetrahedron triangulation N(3,2) of the projective plane bundle over the circle.

Detailed Description

Represents one of a few particular trivial triangulations that do not belong to any of the other larger families.

All optional NStandardTriangulation routines are implemented for this class.

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

Member Function Documentation

NTrivialTri * regina::NTrivialTri::clone (  )  const [inline]

Returns a newly created clone of this structure.

Returns:
a newly created clone.
NAbelianGroup* regina::NTrivialTri::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.

NManifold* regina::NTrivialTri::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.

int regina::NTrivialTri::getType (  )  const [inline]

Returns the specific trivial triangulation being represented.

Returns:
the specific triangulation. This will be one of the triangulation constants defined in this class.
static NTrivialTri* regina::NTrivialTri::isTrivialTriangulation ( const NComponent comp  )  [static]

Determines if the given triangulation component is one of the trivial triangulations recognised by this class.

Parameters:
comp the triangulation component to examine.
Returns:
a newly created structure representing the trivial triangulation, or null if the given component is not one of the triangulations recognised by this class.
std::ostream& regina::NTrivialTri::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:
out the output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

std::ostream& regina::NTrivialTri::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:
out the output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

void regina::NTrivialTri::writeTextLong ( std::ostream &  out  )  const [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:
out the output stream to which to write.

Reimplemented from regina::ShareableObject.


Member Data Documentation

Represents the one-tetrahedron three-vertex triangulation of the ball.

This is a single tetrahedron with two faces as boundary and the other two faces folded together.

Represents the one-tetrahedron four-vertex triangulation of the ball.

This is a single tetrahedron with all four faces as boundary.

const int regina::NTrivialTri::N2 [static]

Represents the two-tetrahedron triangulation N(2) of the twisted 2-sphere bundle over the circle.

const int regina::NTrivialTri::N3_1 [static]

Represents the three-tetrahedron triangulation N(3,1) of the projective plane bundle over the circle.

This particular triangulation has no Mobius band faces.

const int regina::NTrivialTri::N3_2 [static]

Represents the three-tetrahedron triangulation N(3,2) of the projective plane bundle over the circle.

This particular triangulation has two Mobius band faces.

Represents the two-tetrahedron four-vertex triangulation of the 3-sphere.


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).