Represents a plugged triangular solid torus component of a triangulation. More...

#include <subcomplex/plugtrisolidtorus.h>

Inheritance diagram for regina::PlugTriSolidTorus:

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

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

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

const TriSolidTorus &	core () const
	Returns the triangular solid torus at the core of this triangulation. More...

const std::optional< LayeredChain > &	chain (int annulus) const
	Returns the layered chain attached to the requested annulus on the boundary of the core triangular solid torus. More...

int	chainType (int annulus) const
	Returns the way in which a layered chain is attached to the requested annulus on the boundary of the core triangular solid torus. More...

int	equatorType () const
	Returns which types of edges form the equator of the plug. More...

bool	operator== (const PlugTriSolidTorus &other) const
	Determines whether this and the given structure represent the same type of plugged triangular solid torus. More...

bool	operator!= (const PlugTriSolidTorus &other) const
	Determines whether this and the given structure represent different types of plugged triangular solid torus. 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...

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 AbelianGroup	homology () 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 std::unique_ptr< PlugTriSolidTorus >	recognise (Component< 3 > *comp)
	Determines if the given triangulation component is a plugged triangular solid torus. 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	CHAIN_NONE = 0
	Indicates an annulus on the triangular solid torus boundary with no attached layered chain. More...

static constexpr int	CHAIN_MAJOR = 1
	Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the major edge of the annulus. More...

static constexpr int	CHAIN_MINOR = 3
	Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the minor edge of the annulus. More...

static constexpr int	EQUATOR_MAJOR = 1
	Indicates that, if no layered chains were present, the equator of the plug would consist of major edges of the core triangular solid torus. More...

static constexpr int	EQUATOR_MINOR = 3
	Indicates that, if no layered chains were present, the equator of the plug would consist of minor edges of the core triangular solid torus. More...

Detailed Description

Represents a plugged triangular solid torus component of a triangulation.

Such a component is obtained as follows.

Begin with a three-tetrahedron triangular solid torus (as described by class TriSolidTorus). Observe that the three axis edges divide the boundary into three annuli.

To each of these annuli a layered chain may be optionally attached. If present, the chain should be attached so its hinge edges are identified with the axis edges of the corresonding annulus and its bottom tetrahedron is layered over either the major edge or minor edge of the corresponding annulus. The top two triangular faces of the layered chain should remain free.

Thus we now have three annuli on the boundary, each represented as a square two of whose (opposite) edges are axis edges of the original triangular solid torus (and possibly also hinge edges of a layered chain).

Create a plug by gluing two tetrahedra together along a single triangle. The six edges that do not run along this common triangle split the plug boundary into three squares. These three squares must be glued to the three boundary annuli previously described. Each axis edge meets two of the annuli; the two corresponding edges of the plug must be non-adjacent (have no common vertex) on the plug. In this way each of the six edges of the plug not running along its interior triangle corresponds to precisely one of the two instances of precisely one of the three axis edges.

If the axis edges are directed so that they all point the same way around the triangular solid torus, these axis edges when drawn on the plug must all point from one common tip of the plug to the other (where the tips of the plug are the vertices not meeting the interior triangle). The gluings must also be made so that the resulting triangulation component is orientable.

Of the optional StandardTriangulation routines, manifold() is implemented for most plugged triangular solid tori and homology() is not implemented at all.

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

◆ PlugTriSolidTorus()

regina::PlugTriSolidTorus::PlugTriSolidTorus ( const PlugTriSolidTorus & )

default

Creates a new copy of the given structure.

Member Function Documentation

◆ chain()

const std::optional< LayeredChain > & regina::PlugTriSolidTorus::chain ( int annulus ) const

inline

Returns the layered chain attached to the requested annulus on the boundary of the core triangular solid torus.

If there is no attached layered chain, no value will be returned.

Note that the core triangular solid torus will be attached to the bottom (as opposed to the top) of the layered chain.

Parameters

annulus specifies which annulus to examine; this must be 0, 1 or 2.

Returns: the corresponding layered chain.

◆ chainType()

int regina::PlugTriSolidTorus::chainType ( int annulus ) const

inline

Returns the way in which a layered chain is attached to the requested annulus on the boundary of the core triangular solid torus.

This will be one of the chain type constants defined in this class.

Parameters

annulus specifies which annulus to examine; this must be 0, 1 or 2.

Returns: the type of layered chain, or CHAIN_NONE if there is no layered chain attached to the requested annulus.

◆ core()

const TriSolidTorus & regina::PlugTriSolidTorus::core ( ) const

inline

Returns the triangular solid torus at the core of this triangulation.

Returns: the core triangular solid torus.

◆ 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.

◆ equatorType()

int regina::PlugTriSolidTorus::equatorType ( ) const

inline

Returns which types of edges form the equator of the plug.

In the absence of layered chains these will either all be major edges or all be minor edges.

Layered chains complicate matters, but the roles that the major and minor edges play on the boundary annuli of the triangular solid torus can be carried up to the annuli at the top of each layered chain; the edges filling the corresponding major or minor roles will then form the equator of the plug.

Returns: the types of edges that form the equator of the plug; this will be one of the equator type constants defined in this class.

◆ homology()

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

virtualinherited

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::PlugTriSolidTorus::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::PlugTriSolidTorus::operator!= ( const PlugTriSolidTorus & other ) const

inline

Determines whether this and the given structure represent different types of plugged triangular solid torus.

Specifically, two structures will compare as equal if and only if their equators are of the same (major/minor) type, and the same numbered annuli either both have no chains attached or both have chains of the same length attached in the same (major/minor) manner.

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 is more specific than combinatorial isomorphism, since this test does not account for the many symmetries in a plugged triangular solid torus).

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 plugged triangular solid torus.

◆ operator=()

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

default

Sets this to be a copy of the given structure.

Returns: a reference to this structure.

◆ operator==()

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

inline

Determines whether this and the given structure represent the same type of plugged triangular solid torus.

Specifically, two structures will compare as equal if and only if their equators are of the same (major/minor) type, and the same numbered annuli either both have no chains attached or both have chains of the same length attached in the same (major/minor) manner.

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 is more specific than combinatorial isomorphism, since this test does not account for the many symmetries in a plugged triangular solid torus).

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 plugged triangular solid torus.

◆ recognise() [1/2]

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

static

Determines if the given triangulation component is a plugged triangular solid torus.

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 containing details of the plugged triangular solid torus, or null if the given component is not a plugged triangular solid torus.

◆ recognise() [2/2]

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::PlugTriSolidTorus::swap ( PlugTriSolidTorus & 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.

◆ 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::PlugTriSolidTorus::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::PlugTriSolidTorus::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::PlugTriSolidTorus::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

◆ CHAIN_MAJOR

constexpr int regina::PlugTriSolidTorus::CHAIN_MAJOR = 1

staticconstexpr

Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the major edge of the annulus.

◆ CHAIN_MINOR

constexpr int regina::PlugTriSolidTorus::CHAIN_MINOR = 3

staticconstexpr

Indicates an annulus on the triangular solid torus boundary with an attached layered chain layered over the minor edge of the annulus.

◆ CHAIN_NONE

constexpr int regina::PlugTriSolidTorus::CHAIN_NONE = 0

staticconstexpr

Indicates an annulus on the triangular solid torus boundary with no attached layered chain.

◆ EQUATOR_MAJOR

constexpr int regina::PlugTriSolidTorus::EQUATOR_MAJOR = 1

staticconstexpr

Indicates that, if no layered chains were present, the equator of the plug would consist of major edges of the core triangular solid torus.

◆ EQUATOR_MINOR

constexpr int regina::PlugTriSolidTorus::EQUATOR_MINOR = 3

staticconstexpr

Indicates that, if no layered chains were present, the equator of the plug would consist of minor edges of the core triangular solid torus.

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

subcomplex/plugtrisolidtorus.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PlugTriSolidTorus()

Member Function Documentation

◆ chain()

◆ chainType()

◆ core()

◆ detail()

◆ equatorType()

◆ homology()

◆ manifold()

◆ name()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ recognise() [1/2]

◆ recognise() [2/2]

◆ str()

◆ swap()

◆ texName()

◆ utf8()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()

Member Data Documentation

◆ CHAIN_MAJOR

◆ CHAIN_MINOR

◆ CHAIN_NONE

◆ EQUATOR_MAJOR

◆ EQUATOR_MINOR