Describes a triangulation or subcomplex of a triangulation whose structure is well-understood. More...

#include <subcomplex/standardtri.h>

Inheritance diagram for regina::StandardTriangulation:

Public Member Functions
virtual	~StandardTriangulation ()=default
	A destructor that does nothing. 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...

virtual std::unique_ptr< Manifold >	manifold () const
	Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...

virtual AbelianGroup	homology () const
	Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...

virtual std::ostream &	writeName (std::ostream &out) const =0
	Writes the name of this triangulation as a human-readable string to the given output stream. More...

virtual std::ostream &	writeTeXName (std::ostream &out) const =0
	Writes the name of this triangulation in TeX format to the given output stream. More...

virtual void	writeTextShort (std::ostream &out) const
	Writes a short text representation of this object to the given output stream. More...

virtual void	writeTextLong (std::ostream &out) const
	Writes a detailed 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 std::unique_ptr< StandardTriangulation >	recognise (Component< 3 > *component)
	Determines whether the given component represents one of the standard triangulations understood by Regina. More...

static std::unique_ptr< StandardTriangulation >	recognise (const Triangulation< 3 > &tri)
	Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...

Protected Member Functions
	StandardTriangulation ()=default
	Default constructor. More...

	StandardTriangulation (const StandardTriangulation &)=default
	Do-nothing copy constructor. More...

StandardTriangulation &	operator= (const StandardTriangulation &)=default
	Do-nothing assignment operator. More...

Detailed Description

Describes a triangulation or subcomplex of a triangulation whose structure is well-understood.

This is an abstract base class: its subclasses correspond to different combinatorial constructions (typically parameterised families of triangulations or subcomplexes).

A StandardTriangulation is generally identified with a concrete triangulation, i.e., a Triangulation<3> object, which it describes some portion of (or possibly all of).

In general StandardTriangulation objects cannot be constructed directly, but are instead created through static identification routines such as StandardTriangulation::recognise(const Triangulation<3>&).

Each subclass of StandardTriangulation:

must override all pure virtual functions (of course);
may optionally override manifold() and/or homology(), if they are able to provide this functionality;
may optionally override writeTextShort() and writeTextLong(), though this class provides sensible default implementations which use writeName() (which subclasses always override because writeName() is pure virtual);
provide value semantics (including at least a copy constructor and assignment operator);
provide member and global swap functions, for consistency across all StandardTriangulation subclasses.

Constructor & Destructor Documentation

◆ ~StandardTriangulation()

virtual regina::StandardTriangulation::~StandardTriangulation ( )

virtualdefault

A destructor that does nothing.

◆ StandardTriangulation() [1/2]

regina::StandardTriangulation::StandardTriangulation ( )

protecteddefault

Default constructor.

This is here for subclasses to implicitly call from their own constructors.

◆ StandardTriangulation() [2/2]

regina::StandardTriangulation::StandardTriangulation ( const StandardTriangulation & )

protecteddefault

Do-nothing copy constructor.

This is here for subclasses to implicitly call from their own copy constructors.

Member Function Documentation

◆ 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()

virtual AbelianGroup regina::StandardTriangulation::homology ( ) const

virtual

Returns the expected first homology group of this triangulation, if such a routine has been implemented.

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.

This means that homology() needs to be implemented separately for each class of standard triangulation. See the class notes for each subclass of StandardTriangulation for details on whether homology has been implemented for that particular subclass. The default implementation of this routine just throws a NotImplemented exception.

Most users will not need this routine, since presumably you already have an explicit Triangulation<3> available and so you can just call Triangulation<3>::homology() instead (which, unlike this routine, is always implemented). This StandardTriangulation::homology() routine should be seen as more of a verification/validation tool for the Regina developers.

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.

Exceptions

NotImplemented	Homology calculation has not yet been implemented for this particular type of standard triangulation.
FileError	The homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusTri, which reads its results from the SnapPea census databases that are installed with Regina.

Returns: the first homology group of this triangulation, if this functionality has been implemented.

Reimplemented in regina::LayeredChain, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredSolidTorus, regina::LayeredTorusBundle, regina::SnapPeaCensusTri, regina::SnappedBall, regina::SpiralSolidTorus, regina::TriSolidTorus, and regina::TrivialTri.

◆ manifold()

std::unique_ptr< Manifold > regina::StandardTriangulation::manifold ( ) const

inlinevirtual

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 null.

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 null.

It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.

Returns: the underlying 3-manifold.

Reimplemented in regina::AugTriSolidTorus, regina::BlockedSFS, regina::BlockedSFSLoop, regina::BlockedSFSPair, regina::BlockedSFSTriple, regina::LayeredChain, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredSolidTorus, regina::LayeredTorusBundle, regina::PluggedTorusBundle, regina::PlugTriSolidTorus, regina::SnapPeaCensusTri, regina::SnappedBall, regina::SpiralSolidTorus, regina::TriSolidTorus, and regina::TrivialTri.

◆ name()

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

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

Returns: the name of this triangulation.

◆ operator=()

StandardTriangulation & regina::StandardTriangulation::operator= ( const StandardTriangulation & )

protecteddefault

Do-nothing assignment operator.

This is here for subclasses to implicitly call from their own assignment operators.

◆ recognise() [1/2]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( Component< 3 > * component )

static

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 recognise(const Triangulation<3>&) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.

Parameters

component the triangulation component under examination.

Returns: the details of the standard triangulation if the given component is recognised, or null otherwise.

◆ recognise() [2/2]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( const Triangulation< 3 > & tri )

static

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 recognise(Component<3>*), since passing an entire triangulation allows access to more information.

Parameters

tri	the triangulation under examination.

Returns: the details of the standard triangualation if the given triangulation is recognised, or null otherwise.

◆ 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 use plain ASCII characters where possible, and should not contain any newlines.

Within these limits, this short text ouptut should be as information-rich as possible, since in most cases this forms the basis for the Python __str__() and __repr__() functions.

Python: The Python "stringification" function __str__() will use precisely this function, and for most classes the Python __repr__() function will incorporate this into its output.

Returns: a short text representation of this object.

◆ texName()

std::string regina::StandardTriangulation::texName ( ) const

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.

◆ 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 not contain any newlines, and (within these constraints) should be as information-rich as is reasonable.

Unlike str(), this function may use unicode characters to make the output more pleasant to read. The string that is returned will be encoded in UTF-8.

Returns: a short text representation of this object.

◆ writeName()

virtual std::ostream & regina::StandardTriangulation::writeName ( std::ostream & out ) const

pure virtual

Writes the name of this triangulation as a human-readable string to the given output stream.

Python: Not present. Instead use the variant name() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implemented in regina::AugTriSolidTorus, regina::BlockedSFS, regina::BlockedSFSLoop, regina::BlockedSFSPair, regina::BlockedSFSTriple, regina::LayeredChain, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredSolidTorus, regina::LayeredTorusBundle, regina::PluggedTorusBundle, regina::PlugTriSolidTorus, regina::SnapPeaCensusTri, regina::SnappedBall, regina::SpiralSolidTorus, regina::TriSolidTorus, and regina::TrivialTri.

◆ writeTeXName()

virtual std::ostream & regina::StandardTriangulation::writeTeXName ( std::ostream & out ) const

pure 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: Not present. Instead use the variant texName() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implemented in regina::AugTriSolidTorus, regina::BlockedSFS, regina::BlockedSFSLoop, regina::BlockedSFSPair, regina::BlockedSFSTriple, regina::LayeredChain, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredSolidTorus, regina::LayeredTorusBundle, regina::PluggedTorusBundle, regina::PlugTriSolidTorus, regina::SnapPeaCensusTri, regina::SnappedBall, regina::SpiralSolidTorus, regina::TriSolidTorus, and regina::TrivialTri.

◆ writeTextLong()

void regina::StandardTriangulation::writeTextLong ( std::ostream & out ) const

inlinevirtual

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 writeTextShort().

Python: Not present. Use detail() instead.

Parameters

out	the output stream to which to write.

Reimplemented in regina::AugTriSolidTorus, regina::BlockedSFS, regina::BlockedSFSLoop, regina::BlockedSFSPair, regina::BlockedSFSTriple, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredTorusBundle, regina::PluggedTorusBundle, regina::PlugTriSolidTorus, and regina::TrivialTri.

◆ writeTextShort()

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

inlinevirtual

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. Use str() instead.

Parameters

out	the output stream to which to write.

Reimplemented in regina::LayeredChain, regina::LayeredSolidTorus, regina::SnappedBall, regina::SpiralSolidTorus, and regina::TriSolidTorus.

The documentation for this class was generated from the following file:

subcomplex/standardtri.h

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ~StandardTriangulation()

◆ StandardTriangulation() [1/2]

◆ StandardTriangulation() [2/2]

Member Function Documentation

◆ detail()

◆ homology()

◆ manifold()

◆ name()

◆ operator=()

◆ recognise() [1/2]

◆ recognise() [2/2]

◆ str()

◆ texName()

◆ utf8()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()