Represents a layered solid torus in a triangulation. More...

#include <subcomplex/layeredsolidtorus.h>

Inheritance diagram for regina::LayeredSolidTorus:

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

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

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

size_t	size () const
	Returns the number of tetrahedra in this layered solid torus. More...

const Tetrahedron< 3 > *	base () const
	Returns the tetrahedron that is glued to itself at the base of this layered solid torus. More...

int	baseEdge (int group, int index) const
	Returns the requested edge of the base tetrahedron belonging to the given group. More...

int	baseEdgeGroup (int edge) const
	Returns the group that the given edge of the base tetrahedron belongs to. More...

int	baseFace (int index) const
	Returns one of the two faces of the base tetrahedron that are glued to each other. More...

const Tetrahedron< 3 > *	topLevel () const
	Returns the top level tetrahedron in this layered solid torus. More...

unsigned long	meridinalCuts (int group) const
	Returns the number of times the meridinal disc of the torus cuts the top level tetrahedron edges in the given group. More...

int	topEdge (int group, int index) const
	Returns the requested edge of the top level tetrahedron belonging to the given group. More...

int	topEdgeGroup (int edge) const
	Returns the group that the given edge of the top level tetrahedron belongs to. More...

int	topFace (int index) const
	Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus. More...

bool	operator== (const LayeredSolidTorus &other) const
	Determines whether this and the given object represent the same type of layered solid torus. More...

bool	operator!= (const LayeredSolidTorus &other) const
	Determines whether this and the given object do not represent the same type of layered solid torus. More...

Triangulation< 3 >	flatten (int mobiusBandBdry) const
	Flattens this layered solid torus to a Mobius band. More...

void	transform (const Triangulation< 3 > &originalTri, const Isomorphism< 3 > &iso, const Triangulation< 3 > &newTri)
	Adjusts the details of this layered solid torus according to the given isomorphism between triangulations. 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	writeTextShort (std::ostream &out) const override
	Writes a short 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	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< LayeredSolidTorus >	recogniseFromBase (const Tetrahedron< 3 > *tet)
	Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation. More...

static std::unique_ptr< LayeredSolidTorus >	recogniseFromTop (const Tetrahedron< 3 > *tet, unsigned topFace1, unsigned topFace2)
	Determines if the given tetrahedron forms the top level tetrahedron of a layered solid torus, with the two given faces of this tetrahedron representing the boundary of the layered solid torus. More...

static std::unique_ptr< LayeredSolidTorus >	recognise (Component< 3 > *comp)
	Determines if the given triangulation component forms a layered solid torus in its entirity. 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...

Detailed Description

Represents a layered solid torus in a triangulation.

A layered solid torus must contain at least one tetrahedron.

Note that this class only represents layered solid tori with a (3,2,1) at their base. Thus triangulations that begin with a degenerate (2,1,1) mobius strip and layer over the mobius strip boundary (including the minimal (1,1,0) triangulation) are not described by this class.

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

◆ LayeredSolidTorus()

regina::LayeredSolidTorus::LayeredSolidTorus ( const LayeredSolidTorus & )

default

Creates a new copy of the given structure.

Member Function Documentation

◆ base()

const Tetrahedron< 3 > * regina::LayeredSolidTorus::base ( ) const

inline

Returns the tetrahedron that is glued to itself at the base of this layered solid torus.

Returns: the base tetrahedron.

◆ baseEdge()

int regina::LayeredSolidTorus::baseEdge	(	int	group,
		int	index
	)		const

inline

Returns the requested edge of the base tetrahedron belonging to the given group.

The layering identifies the six edges of the base tetrahedron into a group of three, a group of two and a single unidentified edge; these are referred to as groups 3, 2 and 1 respectively.

Note that baseEdgeGroup(baseEdge(group, index)) == group for all values of group and index.

Edges baseEdge(2,0) and baseEdge(3,0) will both belong to face baseFace(0). Edges baseEdge(2,1) and baseEdge(3,2) will both belong to face baseFace(1).

Parameters

group	the group that the requested edge should belong to; this must be 1, 2 or 3.
index	the index within the given group of the requested edge; this must be between 0 and group-1 inclusive. Note that in group 3 the edge at index 1 is adjacent to both the edges at indexes 0 and 2.

Returns: the edge number in the base tetrahedron of the requested edge; this will be between 0 and 5 inclusive.

◆ baseEdgeGroup()

int regina::LayeredSolidTorus::baseEdgeGroup ( int edge ) const

inline

Returns the group that the given edge of the base tetrahedron belongs to.

See baseEdge() for further details about groups.

Note that baseEdgeGroup(baseEdge(group, index)) == group for all values of group and index.

Parameters

edge	the edge number in the base tetrahedron of the given edge; this must be between 0 and 5 inclusive.

Returns: the group to which the given edge belongs; this will be 1, 2 or 3.

◆ baseFace()

int regina::LayeredSolidTorus::baseFace ( int index ) const

inline

Returns one of the two faces of the base tetrahedron that are glued to each other.

Parameters

index specifies which of the two faces to return; this must be 0 or 1.

Returns: the requested face number in the base tetrahedron; this will be between 0 and 3 inclusive.

◆ 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.

◆ flatten()

Triangulation< 3 > regina::LayeredSolidTorus::flatten ( int mobiusBandBdry ) const

Flattens this layered solid torus to a Mobius band.

A new modified triangulation is returned; the original triangulation that contains this layered solid torus will be left unchanged.

Note that there are three different ways in which this layered solid torus can be flattened, corresponding to the three different edges of the boundary torus that could become the boundary edge of the new Mobius band.

Parameters

mobiusBandBdry the edge group on the boundary of this layered solid torus that will become the boundary of the new Mobius band (the remaining edge groups will become internal edges of the new Mobius band). This must be 0, 1 or 2. See topEdge() for further details about edge groups.

Returns: a new triangulation in which this layered solid torus has been flattened to a Mobius band.

◆ homology()

AbelianGroup regina::LayeredSolidTorus::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::LayeredSolidTorus::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.

◆ meridinalCuts()

unsigned long regina::LayeredSolidTorus::meridinalCuts ( int group ) const

inline

Returns the number of times the meridinal disc of the torus cuts the top level tetrahedron edges in the given group.

See topEdge() for further details about groups.

Parameters

group the given edge group; this must be 0, 1 or 2.

Returns: the number of times the meridinal disc cuts the edges in the given group.

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

inline

Determines whether this and the given object do not represent the same type of layered solid torus.

Specifically, two layered solid tori will compare as equal if and only if each has the same ordered triple of integer parameters (describing how many times the three top-level edge groups cut the meridinal disc).

Note that it is possible for two non-isomorphic layered solid tori to compare as equal, since these integer parameters do not detect the presence of redundant layerings (i.e., consecutive layerings that topologically cancel each other out).

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, as noted above, is weaker than combinatorial isomorphism).

Parameters

other the layered solid torus to compare with this.

Returns: true if and only if this and the given object do not represent the same type of layered solid torus.

◆ operator=()

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

default

Sets this to be a copy of the given structure.

Returns: a reference to this structure.

◆ operator==()

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

inline

Determines whether this and the given object represent the same type of layered solid torus.

Specifically, two layered solid tori will compare as equal if and only if each has the same ordered triple of integer parameters (describing how many times the three top-level edge groups cut the meridinal disc).

Note that it is possible for two non-isomorphic layered solid tori to compare as equal, since these integer parameters do not detect the presence of redundant layerings (i.e., consecutive layerings that topologically cancel each other out).

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, as noted above, is weaker than combinatorial isomorphism).

Parameters

other the layered solid torus to compare with this.

Returns: true if and only if this and the given object represent the same type of layered solid torus.

◆ recognise() [1/2]

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

static

Determines if the given triangulation component forms a layered solid torus in its entirity.

Note that, unlike recogniseFromBase(), this routine tests for a component that is a layered solid torus with no additional tetrahedra or gluings. That is, the two boundary triangles of the layered solid torus must in fact be boundary triangles of the component.

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 layered solid torus, or null if the given component is not a layered 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.

◆ recogniseFromBase()

static std::unique_ptr< LayeredSolidTorus > regina::LayeredSolidTorus::recogniseFromBase ( const Tetrahedron< 3 > * tet )

static

Determines if the given tetrahedron forms the base of a layered solid torus within a triangulation.

The torus need not be the entire triangulation; the top level tetrahedron of the torus may be glued to something else (or to itself).

Note that the base tetrahedron of a layered solid torus is the tetrahedron furthest from the boundary of the torus, i.e. the tetrahedron glued to itself with a twist.

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

Parameters

tet	the tetrahedron to examine as a potential base.

Returns: a structure containing details of the layered solid torus, or null if the given tetrahedron is not the base of a layered solid torus.

◆ recogniseFromTop()

static std::unique_ptr< LayeredSolidTorus > regina::LayeredSolidTorus::recogniseFromTop	(	const Tetrahedron< 3 > *	tet,
		unsigned	topFace1,
		unsigned	topFace2
	)

static

Determines if the given tetrahedron forms the top level tetrahedron of a layered solid torus, with the two given faces of this tetrahedron representing the boundary of the layered solid torus.

Note that the two given faces need not be boundary triangles in the overall triangulation. That is, the layered solid torus may be a subcomplex of some larger triangulation. For example, the two given faces may be joined to some other tetrahedra outside the layered solid torus or they may be joined to each other. In fact, they may even extend this smaller layered solid torus to a larger layered 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

tet	the tetrahedron to examine as a potential top level of a layered solid torus.
topFace1	the face number of the given tetrahedron that should represent the first boundary triangle of the layered solid torus. This should be between 0 and 3 inclusive.
topFace2	the face number of the given tetrahedron that should represent the second boundary triangle of the layered solid torus. This should be between 0 and 3 inclusive, and should not be equal to topFace1.

Returns: a structure containing details of the layered solid torus, or null if the given tetrahedron with its two faces do not form the top level of a layered solid torus.

◆ size()

size_t regina::LayeredSolidTorus::size ( ) const

inline

Returns the number of tetrahedra in this layered solid torus.

Returns: the number of tetrahedra.

◆ 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::LayeredSolidTorus::swap ( LayeredSolidTorus & 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.

◆ topEdge()

int regina::LayeredSolidTorus::topEdge	(	int	group,
		int	index
	)		const

inline

Returns the requested edge of the top level tetrahedron belonging to the given group.

The layering reduces five of the top level tetrahedron edges to three boundary edges of the solid torus; this divides the five initial edges into groups of size two, two and one.

Group 0 represents the boundary edge that the meridinal disc cuts fewest times. Group 2 represents the boundary edge that the meridinal disc cuts most times. Group 1 is in the middle.

Note that topEdgeGroup(topEdge(group, index)) == group for all values of group and index that actually correspond to an edge.

Edges topEdge(group, 0) will all belong to face topFace(0). Edges topEdge(group, 1) (if they exist) will all belong to face topFace(1).

Parameters

group	the group that the requested edge should belong to; this must be 0, 1 or 2.
index	the index within the given group of the requested edge; this must be 0 or 1. Note that one of the groups only contains one tetrahedron edge, in which case this edge will be stored at index 0.

Returns: the edge number in the top level tetrahedron of the requested edge (between 0 and 5 inclusive), or -1 if there is no such edge (only possible if the given group was the group of size one and the given index was 1).

◆ topEdgeGroup()

int regina::LayeredSolidTorus::topEdgeGroup ( int edge ) const

inline

Returns the group that the given edge of the top level tetrahedron belongs to.

See topEdge() for further details about groups.

Note that topEdgeGroup(topEdge(group, index)) == group for all values of group and index that actually correspond to an edge.

Parameters

edge	the edge number in the top level tetrahedron of the given edge; this must be between 0 and 5 inclusive.

Returns: the group to which the given edge belongs (0, 1 or 2), or -1 if this edge does not belong to any group (only possible if this is the unique edge in the top tetrahedron not on the torus boundary).

◆ topFace()

int regina::LayeredSolidTorus::topFace ( int index ) const

inline

Returns one of the two faces of the top level tetrahedron that form the boundary of this layered solid torus.

Parameters

index specifies which of the two faces to return; this must be 0 or 1.

Returns: the requested face number in the top level tetrahedron; this will be between 0 and 3 inclusive.

◆ topLevel()

const Tetrahedron< 3 > * regina::LayeredSolidTorus::topLevel ( ) const

inline

Returns the top level tetrahedron in this layered solid torus.

This is the tetrahedron that would be on the boundary of the torus if the torus were the entire manifold.

Returns: the top level tetrahedron.

◆ transform()

void regina::LayeredSolidTorus::transform	(	const Triangulation< 3 > &	originalTri,
		const Isomorphism< 3 > &	iso,
		const Triangulation< 3 > &	newTri
	)

Adjusts the details of this layered solid torus according to the given isomorphism between triangulations.

The given isomorphism must describe a mapping from originalTri to newTri, and this layered solid torus must currently refer to tetrahedra in originalTri. After this routine is called this structure will instead refer to the corresponding tetrahedra in newTri (with changes in vertex/face numbering also accounted for).

Precondition: This layered solid torus currently refers to tetrahedra in originalTri, and iso describes a mapping from originalTri to newTri.

Parameters

originalTri	the triangulation currently referenced by this layered solid torus.
iso	the mapping from originalTri to newTri.
newTri	the triangulation to be referenced by the updated layered solid torus.

◆ 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::LayeredSolidTorus::writeName ( std::ostream & out ) const

inlineoverridevirtual

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::LayeredSolidTorus::writeTeXName ( std::ostream & out ) const

inlineoverridevirtual

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

inlinevirtualinherited

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::LayeredSolidTorus::writeTextShort ( std::ostream & out ) const

overridevirtual

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 from regina::StandardTriangulation.

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

subcomplex/layeredsolidtorus.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LayeredSolidTorus()

Member Function Documentation

◆ base()

◆ baseEdge()

◆ baseEdgeGroup()

◆ baseFace()

◆ detail()

◆ flatten()

◆ homology()

◆ manifold()

◆ meridinalCuts()

◆ name()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ recognise() [1/2]

◆ recognise() [2/2]

◆ recogniseFromBase()

◆ recogniseFromTop()

◆ size()

◆ str()

◆ swap()

◆ texName()

◆ topEdge()

◆ topEdgeGroup()

◆ topFace()

◆ topLevel()

◆ transform()

◆ utf8()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()