Regina Calculation Engine
Public Member Functions | Static Public Member Functions | Static Public Attributes | List of all members
regina::TrivialTri 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/trivialtri.h>

Inheritance diagram for regina::TrivialTri:
regina::StandardTriangulation regina::Output< StandardTriangulation >

Public Member Functions

TrivialTriclone () const
 Returns a newly created clone of this structure. More...
 
int type () const
 Returns the specific trivial triangulation being represented. More...
 
Manifoldmanifold () const override
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...
 
AbelianGrouphomology () const override
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
std::ostream & writeName (std::ostream &out) const override
 
Writes the name of this triangulation as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const override
 
Writes the name of this triangulation in TeX format to the given output stream. More...
 
void writeTextLong (std::ostream &out) const override
 
Writes a detailed text representation of this object to the given output stream. More...
 
std::string name () const
 Returns the name of this specific triangulation as a human-readable string. More...
 
std::string TeXName () const
 Returns the name of this specific triangulation in TeX format. More...
 
AbelianGrouphomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
virtual void writeTextShort (std::ostream &out) const
 
Writes a short 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 Member Functions

static TrivialTriisTrivialTriangulation (const Component< 3 > *comp)
 Determines if the given triangulation component is one of the trivial triangulations recognised by this class. More...
 
static StandardTriangulationisStandardTriangulation (Component< 3 > *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina. More...
 
static StandardTriangulationisStandardTriangulation (Triangulation< 3 > *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 StandardTriangulation routines are implemented for this class.

Member Function Documentation

◆ clone()

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

Returns a newly created clone of this structure.

Returns
a newly created clone.

◆ detail()

std::string regina::Output< StandardTriangulation , 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::TrivialTri::homology ( ) const
overridevirtual

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 Triangulation<3>::homology() 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 StandardTriangulation. 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 StandardTriangulation describes an entire Triangulation<3> (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling Triangulation<3>::homology() upon the associated real triangulation.

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 triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::StandardTriangulation.

◆ homologyH1()

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

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 Triangulation<3>::homology() 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 StandardTriangulation. 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 StandardTriangulation describes an entire Triangulation<3> (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling Triangulation<3>::homology() upon the associated real triangulation.

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 triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

◆ isStandardTriangulation() [1/2]

static StandardTriangulation* regina::StandardTriangulation::isStandardTriangulation ( Component< 3 > *  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(Triangulation<3>*) 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.

◆ isStandardTriangulation() [2/2]

static StandardTriangulation* regina::StandardTriangulation::isStandardTriangulation ( Triangulation< 3 > *  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(Component<3>*), 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.

◆ isTrivialTriangulation()

static TrivialTri* regina::TrivialTri::isTrivialTriangulation ( const Component< 3 > *  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.

◆ manifold()

Manifold* regina::TrivialTri::manifold ( ) const
overridevirtual

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 StandardTriangulation. 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::StandardTriangulation.

◆ name()

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

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

Returns
the name of this triangulation.

◆ str()

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

◆ TeXName()

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

◆ type()

int regina::TrivialTri::type ( ) 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.

◆ utf8()

std::string regina::Output< StandardTriangulation , 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::TrivialTri::writeName ( std::ostream &  out) const
overridevirtual


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::StandardTriangulation.

◆ writeTeXName()

std::ostream& regina::TrivialTri::writeTeXName ( std::ostream &  out) const
overridevirtual


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::StandardTriangulation.

◆ writeTextLong()

void regina::TrivialTri::writeTextLong ( std::ostream &  out) const
overridevirtual


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

This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeName().

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

Reimplemented from regina::StandardTriangulation.

◆ writeTextShort()

void regina::StandardTriangulation::writeTextShort ( std::ostream &  out) const
inlinevirtualinherited


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

This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeName().

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

Member Data Documentation

◆ BALL_3_VERTEX

const int regina::TrivialTri::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.

◆ BALL_4_VERTEX

const int regina::TrivialTri::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.

◆ N2

const int regina::TrivialTri::N2
static

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

◆ N3_1

const int regina::TrivialTri::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.

◆ N3_2

const int regina::TrivialTri::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.

◆ SPHERE_4_VERTEX

const int regina::TrivialTri::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 © 1999-2021, 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).