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

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

#include <subcomplex/ntrivialtri.h>

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

Public Member Functions

NTrivialTriclone () const
 Returns a newly created clone of this structure. More...
 
int getType () const
 Returns the specific trivial triangulation being represented. More...
 
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...
 
NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream. More...
 
void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
std::string getName () const
 Returns the name of this specific triangulation as a human-readable string. More...
 
std::string getTeXName () const
 Returns the name of this specific triangulation in TeX format. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short 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 Member Functions

static NTrivialTriisTrivialTriangulation (const NComponent *comp)
 Determines if the given triangulation component is one of the trivial triangulations recognised by this class. More...
 
static NStandardTriangulationisStandardTriangulation (NComponent *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina. More...
 
static NStandardTriangulationisStandardTriangulation (NTriangulation *tri)
 Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...
 

Static Public Attributes

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

Detailed Description

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

All optional NStandardTriangulation routines are implemented for this class.

Member Function Documentation

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

Returns a newly created clone of this structure.

Returns
a newly created clone.
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::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.

std::string regina::NStandardTriangulation::getName ( ) const
inherited

Returns the name of this specific triangulation as a human-readable string.

Returns
the name of this triangulation.
std::string regina::NStandardTriangulation::getTeXName ( ) const
inherited

Returns the name of this specific triangulation 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 name of this triangulation in TeX format.
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 NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NComponent component)
staticinherited

Determines whether the given component represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given component must have the same corresponding boundary triangles, i.e., the component cannot have any further identifications of these boundary triangles with each other.

Note that the triangulation-based routine isStandardTriangulation(NTriangulation*) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.

Parameters
componentthe triangulation component under examination.
Returns
the details of the standard triangulation if the given component is recognised, or 0 otherwise.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NTriangulation tri)
staticinherited

Determines whether the given triangulation represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given triangulation must have the same corresponding boundary triangles, i.e., the triangulation cannot have any further identifications of these boundary triangles with each other.

This routine may recognise more triangulations than the component-based isStandardTriangulation(NComponent*), since passing an entire triangulation allows access to more information.

Parameters
trithe triangulation under examination.
Returns
the details of the standard triangualation if the given triangulation is recognised, or 0 otherwise.
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
compthe 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::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::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
outthe 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
outthe 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 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::NStandardTriangulation::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 int regina::NTrivialTri::BALL_3_VERTEX
static

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.

const int regina::NTrivialTri::BALL_4_VERTEX
static

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 triangles.

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 triangles.

const int regina::NTrivialTri::SPHERE_4_VERTEX
static

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


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).