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:

Public Member Functions
	TrivialTri (const TrivialTri &)=default
	Creates a new copy of the given structure. More...

TrivialTri &	operator= (const TrivialTri &)=default
	Sets this to be a copy of the given structure. More...

void	swap (TrivialTri &other) noexcept
	Swaps the contents of this and the given structure. More...

int	type () const
	Returns the specific trivial triangulation being represented. More...

bool	operator== (const TrivialTri &other) const
	Determines whether this and the given structure represent the same type of trivial triangulation. More...

bool	operator!= (const TrivialTri &other) const
	Determines whether this and the given structure represent different types of trivial triangulation. More...

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

AbelianGroup	homology () 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...

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 std::unique_ptr< TrivialTri >	recognise (const Component< 3 > *comp)
	Determines if the given triangulation component is one of the trivial triangulations recognised by this class. More...

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...

Static Public Attributes
static constexpr int	SPHERE_4_VERTEX = 5000
	Represents the two-tetrahedron four-vertex triangulation of the 3-sphere. More...

static constexpr int	BALL_3_VERTEX = 5100
	Represents the one-tetrahedron three-vertex triangulation of the ball. More...

static constexpr int	BALL_4_VERTEX = 5101
	Represents the one-tetrahedron four-vertex triangulation of the ball. More...

static constexpr int	L31_PILLOW = 5200
	Represents the two-tetrahedron two-vertex triangulation of the lens space L(3,1), formed by identifying the two boundary faces of a triangular pillow with a one-third twist. More...

static constexpr int	N2 = 200
	Represents the two-tetrahedron triangulation N(2) of the twisted 2-sphere bundle over the circle. More...

static constexpr int	N3_1 = 301
	Represents the three-tetrahedron triangulation N(3,1) of the projective plane bundle over the circle. More...

static constexpr int	N3_2 = 302
	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.

This class supports copying but does not implement separate move operations, since its internal data is so small that copying is just as efficient. It implements the C++ Swappable requirement via its own member and global swap() functions, for consistency with the other StandardTriangulation subclasses. Note that the only way to create these objects (aside from copying or moving) is via the static member function recognise().

Constructor & Destructor Documentation

◆ TrivialTri()

regina::TrivialTri::TrivialTri ( const TrivialTri & )

default

Creates a new copy of the given structure.

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()

AbelianGroup regina::TrivialTri::homology ( ) const

overridevirtual

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 from regina::StandardTriangulation.

◆ manifold()

std::unique_ptr< 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 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 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.

◆ operator!=()

bool regina::TrivialTri::operator!= ( const TrivialTri & other ) const

inline

Determines whether this and the given structure represent different types of trivial triangulation.

This is the same as testing whether type() returns different values for this and the given triangulation.

This test follows the general rule for most subclasses of StandardTriangulation (excluding fixed structures such as SnappedBall and TriSolidTorus): two objects compare as equal if and only if they have the same combinatorial parameters (which for this subclass means they describe isomorphic structures).

Parameters

other the structure with which this will be compared.

Returns: true if and only if this and the given structure represent different types of trivial triangulation.

◆ operator=()

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

default

Sets this to be a copy of the given structure.

Returns: a reference to this structure.

◆ operator==()

bool regina::TrivialTri::operator== ( const TrivialTri & other ) const

inline

Determines whether this and the given structure represent the same type of trivial triangulation.

This is the same as testing whether type() returns the same value for this and the given triangulation.

This test follows the general rule for most subclasses of StandardTriangulation (excluding fixed structures such as SnappedBall and TriSolidTorus): two objects compare as equal if and only if they have the same combinatorial parameters (which for this subclass means they describe isomorphic structures).

Parameters

other the structure with which this will be compared.

Returns: true if and only if this and the given structure represent the same type of trivial triangulation.

◆ recognise() [1/3]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( 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 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() [2/3]

static std::unique_ptr< TrivialTri > regina::TrivialTri::recognise ( const Component< 3 > * comp )

static

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

This function returns by (smart) pointer for consistency with StandardTriangulation::recognise(), which makes use of the polymorphic nature of the StandardTriangulation class hierarchy.

Parameters

comp	the triangulation component to examine.

Returns: a structure representing the trivial triangulation, or null if the given component is not one of the triangulations recognised by this class.

◆ recognise() [3/3]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( const 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 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.

◆ swap()

void regina::TrivialTri::swap ( TrivialTri & other )

inlinenoexcept

Swaps the contents of this and the given structure.

Parameters

other the structure whose contents should be swapped with this.

◆ 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 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()

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: 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.

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: 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.

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 writeTextShort().

Python: Not present. Use detail() instead.

Parameters

out	the 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. 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.

Member Data Documentation

◆ BALL_3_VERTEX

constexpr int regina::TrivialTri::BALL_3_VERTEX = 5100

staticconstexpr

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

constexpr int regina::TrivialTri::BALL_4_VERTEX = 5101

staticconstexpr

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

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

◆ L31_PILLOW

constexpr int regina::TrivialTri::L31_PILLOW = 5200

staticconstexpr

Represents the two-tetrahedron two-vertex triangulation of the lens space L(3,1), formed by identifying the two boundary faces of a triangular pillow with a one-third twist.

◆ N2

constexpr int regina::TrivialTri::N2 = 200

staticconstexpr

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

◆ N3_1

constexpr int regina::TrivialTri::N3_1 = 301

staticconstexpr

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

constexpr int regina::TrivialTri::N3_2 = 302

staticconstexpr

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

constexpr int regina::TrivialTri::SPHERE_4_VERTEX = 5000

staticconstexpr

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

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

subcomplex/trivialtri.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TrivialTri()

Member Function Documentation

◆ detail()

◆ homology()

◆ manifold()

◆ name()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ recognise() [1/3]

◆ recognise() [2/3]

◆ recognise() [3/3]

◆ str()

◆ swap()

◆ texName()

◆ type()

◆ utf8()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()

Member Data Documentation

◆ BALL_3_VERTEX

◆ BALL_4_VERTEX

◆ L31_PILLOW

◆ N2

◆ N3_1

◆ N3_2

◆ SPHERE_4_VERTEX