Regina Calculation Engine
Public Member Functions | Static Public Member Functions | Static Public Attributes | List of all members
regina::NAugTriSolidTorus Class Reference

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

#include <subcomplex/naugtrisolidtorus.h>

Inheritance diagram for regina::NAugTriSolidTorus:
regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

Public Member Functions

virtual ~NAugTriSolidTorus ()
 Destroys this augmented solid torus; note that the corresponding triangular and layered solid tori will also be destroyed. More...
 
NAugTriSolidTorusclone () const
 Returns a newly created clone of this structure. More...
 
const NTriSolidTorusgetCore () const
 Returns the triangular solid torus at the core of this triangulation. More...
 
const NLayeredSolidTorusgetAugTorus (int annulus) const
 Returns the layered solid torus attached to the requested annulus on the boundary of the core triangular solid torus. More...
 
NPerm4 getEdgeGroupRoles (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...
 
unsigned long getChainLength () const
 Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus. More...
 
int getChainType () const
 Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus. More...
 
int getTorusAnnulus () 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...
 
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...
 
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream. More...
 
void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
std::string getName () const
 Returns the name of this specific triangulation as a human-readable string. More...
 
std::string getTeXName () const
 Returns the name of this specific triangulation in TeX format. More...
 
virtual NAbelianGroupgetHomologyH1 () 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 this object in short text format to the given output stream. More...
 
Input and Output
std::string str () const
 Returns the output from writeTextShort() as a string. More...
 
std::string toString () const
 A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...
 
std::string detail () const
 Returns the output from writeTextLong() as a string. More...
 
std::string toStringLong () const
 A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...
 

Static Public Member Functions

static NAugTriSolidTorusisAugTriSolidTorus (const NComponent *comp)
 Determines if the given triangulation component is an augmented triangular solid torus. More...
 
static NStandardTriangulationisStandardTriangulation (NComponent *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina. More...
 
static NStandardTriangulationisStandardTriangulation (NTriangulation *tri)
 Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...
 

Static Public Attributes

static const int CHAIN_NONE
 Indicates that this augmented triangular solid torus contains no layered chain. More...
 
static const int CHAIN_MAJOR
 Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedMajor(). More...
 
static const int CHAIN_AXIS
 Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::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 NTriSolidTorus). Observe that the three axis edges divide the boundary into three annuli. Then take one of the following actions.

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 NStandardTriangulation routines, getManifold() is implemented for most augmented triangular solid tori and getHomologyH1() is not implemented at all.

Constructor & Destructor Documentation

virtual regina::NAugTriSolidTorus::~NAugTriSolidTorus ( )
virtual

Destroys this augmented solid torus; note that the corresponding triangular and layered solid tori will also be destroyed.

Member Function Documentation

NAugTriSolidTorus* regina::NAugTriSolidTorus::clone ( ) const

Returns a newly created clone of this structure.

Returns
a newly created clone.
std::string regina::ShareableObject::detail ( ) const
inherited

Returns the output from writeTextLong() as a string.

Returns
a long text representation of this object.
const NLayeredSolidTorus * regina::NAugTriSolidTorus::getAugTorus ( 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), null will be returned.

Parameters
annulusspecifies which annulus to examine; this must be 0, 1 or 2.
Returns
the corresponding layered solid torus.
unsigned long regina::NAugTriSolidTorus::getChainLength ( ) 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.
int regina::NAugTriSolidTorus::getChainType ( ) 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.
const NTriSolidTorus & regina::NAugTriSolidTorus::getCore ( ) const
inline

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

Returns
the core triangular solid torus.
NPerm4 regina::NAugTriSolidTorus::getEdgeGroupRoles ( 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 NLayeredSolidTorus::getTopEdge() 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. p[3] will always be 3.

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

Parameters
annulusspecifies 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.
NAbelianGroup * regina::NStandardTriangulation::getHomologyH1 ( ) const
inlinevirtualinherited

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

If the calculation of homology has not yet been implemented for this triangulation then this routine will return 0.

This routine does not work by calling NTriangulation::getHomologyH1() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.

The details of which standard triangulations have homology calculation routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

The homology group will be newly allocated and must be destroyed by the caller of this routine.

If this NStandardTriangulation describes an entire NTriangulation (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling NTriangulation::getHomologyH1() upon the associated real triangulation.

Returns
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented in regina::NLayeredSolidTorus, regina::NTriSolidTorus, regina::NLayeredChain, regina::NSpiralSolidTorus, regina::NLayeredTorusBundle, regina::NSnapPeaCensusTri, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NSnappedBall, regina::NTrivialTri, regina::NL31Pillow, and regina::NLayeredChainPair.

NManifold* regina::NAugTriSolidTorus::getManifold ( ) const
virtual

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 0.

The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.

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

The 3-manifold will be newly allocated and must be destroyed by the caller of this routine.

Returns
the underlying 3-manifold.

Reimplemented from regina::NStandardTriangulation.

std::string regina::NStandardTriangulation::getName ( ) const
inherited

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

Returns
the name of this triangulation.
std::string regina::NStandardTriangulation::getTeXName ( ) 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.
int regina::NAugTriSolidTorus::getTorusAnnulus ( ) 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 NTriSolidTorus 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).
bool regina::NAugTriSolidTorus::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.
static NAugTriSolidTorus* regina::NAugTriSolidTorus::isAugTriSolidTorus ( const NComponent comp)
static

Determines if the given triangulation component is an augmented triangular solid torus.

Parameters
compthe triangulation component to examine.
Returns
a newly created structure containing details of the augmented triangular solid torus, or null if the given component is not an augmented triangular solid torus.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NComponent 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 isStandardTriangulation(NTriangulation*) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.

Parameters
componentthe triangulation component under examination.
Returns
the details of the standard triangulation if the given component is recognised, or 0 otherwise.
static NStandardTriangulation* regina::NStandardTriangulation::isStandardTriangulation ( NTriangulation 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 isStandardTriangulation(NComponent*), since passing an entire triangulation allows access to more information.

Parameters
trithe triangulation under examination.
Returns
the details of the standard triangualation if the given triangulation is recognised, or 0 otherwise.
std::string regina::ShareableObject::str ( ) const
inherited

Returns the output from writeTextShort() as a string.

Python:
This implements the __str__() function.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toString ( ) const
inlineinherited

A deprecated alias for str(), which returns the output from writeTextShort() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.
std::string regina::ShareableObject::toStringLong ( ) const
inlineinherited

A deprecated alias for detail(), which returns the output from writeTextLong() as a string.

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.
std::ostream& regina::NAugTriSolidTorus::writeName ( std::ostream &  out) const
virtual

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

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NStandardTriangulation.

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

Writes the name of this triangulation in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Warning
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NStandardTriangulation.

void regina::NAugTriSolidTorus::writeTextLong ( std::ostream &  out) const
virtual

Writes this object in long text format to the given output stream.

The output should provide the user with all the information they could want. The output should be human-readable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.

The default implementation of this routine merely calls writeTextShort() and adds a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Reimplemented from regina::ShareableObject.

void regina::NStandardTriangulation::writeTextShort ( std::ostream &  out) const
inlinevirtualinherited

Writes this object in short text format to the given output stream.

The output should be human-readable, should fit on a single line, and should not end with a newline.

Python:
The parameter out does not exist; standard output will be used.
Parameters
outthe output stream to which to write.

Implements regina::ShareableObject.

Member Data Documentation

const int regina::NAugTriSolidTorus::CHAIN_AXIS
static

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

const int regina::NAugTriSolidTorus::CHAIN_MAJOR
static

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

const int regina::NAugTriSolidTorus::CHAIN_NONE
static

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


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

Copyright © 1999-2014, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).