Represents an augmented triangular solid torus component of a triangulation. More...

#include <subcomplex/augtrisolidtorus.h>

Inheritance diagram for regina::AugTriSolidTorus:

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

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

void	swap (AugTriSolidTorus &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< LayeredSolidTorus > &	augTorus (int annulus) const
	Returns the layered solid torus attached to the requested annulus on the boundary of the core triangular solid torus. More...

Perm< 3 >	edgeGroupRoles (int annulus) const
	Returns a permutation describing the role played by each top level edge group of the layered solid torus glued to the requested annulus of the core triangular solid torus. More...

size_t	chainLength () const
	Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus. More...

int	chainType () const
	Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus. More...

int	torusAnnulus () const
	Returns the single boundary annulus of the core triangular solid torus to which a layered solid torus is attached. More...

bool	hasLayeredChain () const
	Determines whether the core triangular solid torus has two of its boundary annuli linked by a layered chain as described in the general class notes. More...

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

bool	operator!= (const AugTriSolidTorus &other) const
	Determines whether this and the given structure represent different types of augmented 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< AugTriSolidTorus >	recognise (const Component< 3 > *comp)
	Determines if the given triangulation component is an augmented triangular solid torus. 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	CHAIN_NONE = 0
	Indicates that this augmented triangular solid torus contains no layered chain. More...

static constexpr int	CHAIN_MAJOR = 1
	Indicates that this augmented triangular solid torus contains a layered chain attached as described by TriSolidTorus::areAnnuliLinkedMajor(). More...

static constexpr int	CHAIN_AXIS = 2
	Indicates that this augmented triangular solid torus contains a layered chain attached as described by TriSolidTorus::areAnnuliLinkedAxis(). More...

Detailed Description

Represents an augmented 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 TriSolidTorus). Observe that the three axis edges divide the boundary into three annuli. Then take one of the following actions.

To each of these annuli, glue a layered solid torus. Note that the degenerate (2,1,1) layered solid torus (i.e., a one-triangle mobius strip) is allowed and corresponds to simply gluing the two triangles of the annulus together.
To one of these annuli, glue a layered solid torus as described above. Join the other two annuli with a layered chain in either the manner described by TriSolidTorus::areAnnuliLinkedMajor() or the manner described by TriSolidTorus::areAnnuliLinkedAxis().

It will be assumed that all layered solid tori other than the degenerate (2,1,1) will have (3,2,1) layered solid tori at their bases. That is, layered solid tori that begin with the degenerate (2,1,1) and layer over the boundary of the mobius strip are not considered in this class.

Note that (unless a (1,1,0) layered solid torus is used with the 0 edge glued to an axis edge) the resulting space will be a Seifert fibred space over the 2-sphere with at most three exceptional fibres.

Of the optional StandardTriangulation routines, manifold() is implemented for most augmented 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

◆ AugTriSolidTorus()

regina::AugTriSolidTorus::AugTriSolidTorus ( const AugTriSolidTorus & )

default

Creates a new copy of the given structure.

Member Function Documentation

◆ augTorus()

const std::optional< LayeredSolidTorus > & regina::AugTriSolidTorus::augTorus ( int annulus ) const

inline

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

If the layered solid torus is a degenerate (2,1,1) mobius band (i.e., the two triangles of the corresponding annulus have simply been glued together), then no value will be returned.

Parameters

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

Returns: the corresponding layered solid torus.

◆ chainLength()

size_t regina::AugTriSolidTorus::chainLength ( ) const

inline

Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus.

Note that this count does not include any of the tetrahedra actually belonging to the triangular solid torus.

Returns: the number of tetrahedra in the layered chain, or 0 if there is no layered chain linking two boundary annuli.

◆ chainType()

int regina::AugTriSolidTorus::chainType ( ) const

inline

Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus.

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

Returns: the type of layered chain, or CHAIN_NONE if there is no layered chain linking two boundary annuli.

◆ core()

const TriSolidTorus & regina::AugTriSolidTorus::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.

◆ edgeGroupRoles()

Perm< 3 > regina::AugTriSolidTorus::edgeGroupRoles ( int annulus ) const

inline

Returns a permutation describing the role played by each top level edge group of the layered solid torus glued to the requested annulus of the core triangular solid torus.

See LayeredSolidTorus::topEdge() for details regarding edge groups.

If the permutation returned is p, edge group p[0] will be glued to an axis edge, group p[1] will be glued to a major edge and group p[2] will be glued to a minor edge.

Even if the corresponding layered solid torus is a degenerate (2,1,1) mobius band (i.e., augTorus() returns null), the concept of edge groups is still meaningful and this routine will return correct results.

Parameters

annulus specifies which annulus to examine; this must be 0, 1 or 2. It is the layered solid torus glued to this annulus whose edge groups will be described.

Returns: a permutation describing the roles of the corresponding top level edge groups.

◆ hasLayeredChain()

bool regina::AugTriSolidTorus::hasLayeredChain ( ) const

inline

Determines whether the core triangular solid torus has two of its boundary annuli linked by a layered chain as described in the general class notes.

Returns: true if and only if the layered chain described in the class notes is present.

◆ 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::AugTriSolidTorus::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::AugTriSolidTorus::operator!= ( const AugTriSolidTorus & other ) const

inline

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

Specifically, two structures will compare as equal if and only if:

in both structures, the layered solid tori attached to the same numbered annuli have the same three integer parameters, and have their top level edge groups attached to the annuli in the same manner;
either both structures do not include a layered chain, or else both structures do include a layered chain of the same type and length, attached to the same numbered annulus.

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 an augmented 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 augmented triangular solid torus.

◆ operator=()

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

default

Sets this to be a copy of the given structure.

Returns: a reference to this structure.

◆ operator==()

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

inline

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

Specifically, two structures will compare as equal if and only if:

in both structures, the layered solid tori attached to the same numbered annuli have the same three integer parameters, and have their top level edge groups attached to the annuli in the same manner;
either both structures do not include a layered chain, or else both structures do include a layered chain of the same type and length, attached to the same numbered annulus.

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 an augmented 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 augmented triangular solid torus.

◆ 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< AugTriSolidTorus > regina::AugTriSolidTorus::recognise ( const Component< 3 > * comp )

static

Determines if the given triangulation component is an augmented 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 augmented triangular solid torus, or null if the given component is not an augmented triangular solid torus.

◆ 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::AugTriSolidTorus::swap ( AugTriSolidTorus & 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.

◆ torusAnnulus()

int regina::AugTriSolidTorus::torusAnnulus ( ) const

inline

Returns the single boundary annulus of the core triangular solid torus to which a layered solid torus is attached.

This routine is only meaningful if the other two annuli are linked by a layered chain.

The integer returned will be 0, 1 or 2; see the TriSolidTorus class notes for how the boundary annuli are numbered.

Returns: the single annulus to which the layered solid torus is attached, or -1 if there is no layered chain (and thus all three annuli have layered solid tori attached).

◆ 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::AugTriSolidTorus::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::AugTriSolidTorus::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::AugTriSolidTorus::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_AXIS

constexpr int regina::AugTriSolidTorus::CHAIN_AXIS = 2

staticconstexpr

Indicates that this augmented triangular solid torus contains a layered chain attached as described by TriSolidTorus::areAnnuliLinkedAxis().

◆ CHAIN_MAJOR

constexpr int regina::AugTriSolidTorus::CHAIN_MAJOR = 1

staticconstexpr

Indicates that this augmented triangular solid torus contains a layered chain attached as described by TriSolidTorus::areAnnuliLinkedMajor().

◆ CHAIN_NONE

constexpr int regina::AugTriSolidTorus::CHAIN_NONE = 0

staticconstexpr

Indicates that this augmented triangular solid torus contains no layered chain.

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

subcomplex/augtrisolidtorus.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ AugTriSolidTorus()

Member Function Documentation

◆ augTorus()

◆ chainLength()

◆ chainType()

◆ core()

◆ detail()

◆ edgeGroupRoles()

◆ hasLayeredChain()

◆ homology()

◆ manifold()

◆ name()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ recognise() [1/3]

◆ recognise() [2/3]

◆ recognise() [3/3]

◆ str()

◆ swap()

◆ texName()

◆ torusAnnulus()

◆ utf8()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()

Member Data Documentation

◆ CHAIN_AXIS

◆ CHAIN_MAJOR

◆ CHAIN_NONE