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

Represents a blocked Seifert fibred space with two boundary tori that are joined together. More...

#include <subcomplex/nblockedsfsloop.h>

Inheritance diagram for regina::NBlockedSFSLoop:
regina::NStandardTriangulation regina::Output< NStandardTriangulation >

Public Member Functions

 ~NBlockedSFSLoop ()
 Destroys this structure and its constituent components. More...
 
const NSatRegionregion () const
 Returns details of the saturated region from which this triangulation is formed. More...
 
const NMatrix2matchingReln () const
 Returns the matrix describing how the two torus boundaries of the saturated region are joined. More...
 
NManifoldmanifold () 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 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...
 
REGINA_DEPRECATED std::string getName () const
 Deprecated routine that 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...
 
REGINA_DEPRECATED std::string getTeXName () const
 Deprecated routine that returns the name of this specific triangulation in TeX format. More...
 
REGINA_DEPRECATED NManifoldgetManifold () const
 Deprecated routine that returns the 3-manifold represented by this triangulation,. More...
 
virtual NAbelianGrouphomology () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
NAbelianGrouphomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
REGINA_DEPRECATED NAbelianGroupgetHomologyH1 () const
 Deprecated routine that 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...
 
REGINA_DEPRECATED std::string toString () const
 A deprecated alias for str(). More...
 
REGINA_DEPRECATED std::string toStringLong () const
 A deprecated alias for detail(). More...
 

Static Public Member Functions

static NBlockedSFSLoopisBlockedSFSLoop (NTriangulation *tri)
 Determines if the given triangulation is a blocked Seifert fibred space with identified boundaries, as described by this class. 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...
 

Detailed Description

Represents a blocked Seifert fibred space with two boundary tori that are joined together.

This is a particular type of triangulation of a graph manifold, formed from a single saturated region whose two torus boundaries are identified. An optional layering may be placed between the two torus boundaries to allow for a more interesting relationship between the two sets of boundary curves. For more detail on saturated regions and their constituent saturated blocks, see the NSatRegion class; for more detail on layerings, see the NLayering class.

The saturated region may have two boundary components formed from one saturated annulus each. Alternatively, it may have one boundary formed from two saturated annuli, where this boundary is pinched together so that each annulus becomes a two-sided torus (both of which are later joined together). None of the boundary components (or the two-sided tori discussed above) may be twisted (i.e., they must be tori, not Klein bottles).

The way in which the two torus boundaries are identified is specified by a 2-by-2 matrix, which expresses curves representing the fibres and base orbifold on the second boundary in terms of such curves on the first boundary (see the page on Notation for Seifert fibred spaces for terminology).

More specifically, suppose that f0 and o0 are directed curves on the first boundary torus and f1 and o1 are directed curves on the second boundary torus, where f0 and f1 represent the fibres of the region and o0 and o1 represent the base orbifold. Then the boundaries are joined according to the following relation:

    [f1]       [f0]
    [  ] = M * [  ]
    [o1]       [o0]

If a layering is present between the two torus boundaries, then the corresponding boundary curves are not identified directly. In this case, the matrix M shows how the layering relates the curves on each boundary.

Note that the routines writeName() and writeTeXName() do not offer enough information to uniquely identify the triangulation, since this essentially requires 2-dimensional assemblings of saturated blocks. For full details, writeTextLong() may be used instead.

The optional NStandardTriangulation routine manifold() is implemented for this class, but homology() is not.

Constructor & Destructor Documentation

§ ~NBlockedSFSLoop()

regina::NBlockedSFSLoop::~NBlockedSFSLoop ( )

Destroys this structure and its constituent components.

Member Function Documentation

§ detail()

std::string regina::Output< NStandardTriangulation , 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.

§ getHomologyH1()

NAbelianGroup * regina::NStandardTriangulation::getHomologyH1 ( ) const
inlineinherited

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

Deprecated:
This routine has been renamed to homology(). See the homology() documentation for further details.

§ getManifold()

NManifold * regina::NStandardTriangulation::getManifold ( ) const
inlineinherited

Deprecated routine that returns the 3-manifold represented by this triangulation,.

Deprecated:
This routine has been renamed to manifold(). See the manifold() documentation for further details.

§ getName()

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

Deprecated routine that returns the name of this specific triangulation as a human-readable string.

Deprecated:
This routine has been renamed to name(). See the name() documentation for further details.

§ getTeXName()

std::string regina::NStandardTriangulation::getTeXName ( ) const
inlineinherited

Deprecated routine that returns the name of this specific triangulation in TeX format.

Deprecated:
This routine has been renamed to TeXName(). See the TeXName() documentation for further details.

§ homology()

NAbelianGroup * regina::NStandardTriangulation::homology ( ) 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::homology() 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::homology() upon the associated real triangulation.

This routine can also be accessed via the alias homologyH1() (a name that is more specific, but a little longer to type).

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

§ homologyH1()

NAbelianGroup * regina::NStandardTriangulation::homologyH1 ( ) const
inlineinherited

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::homology() 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::homology() upon the associated real triangulation.

This routine can also be accessed via the alias homology() (a name that is less specific, but a little easier to type).

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

§ isBlockedSFSLoop()

static NBlockedSFSLoop* regina::NBlockedSFSLoop::isBlockedSFSLoop ( NTriangulation tri)
static

Determines if the given triangulation is a blocked Seifert fibred space with identified boundaries, as described by this class.

Parameters
trithe triangulation to examine.
Returns
a newly created structure containing details of the blocked self-identified Seifert fibred space, or null if the given triangulation is not of this form.

§ isStandardTriangulation() [1/2]

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.

§ isStandardTriangulation() [2/2]

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.

§ manifold()

NManifold* regina::NBlockedSFSLoop::manifold ( ) 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.

§ matchingReln()

const NMatrix2 & regina::NBlockedSFSLoop::matchingReln ( ) const
inline

Returns the matrix describing how the two torus boundaries of the saturated region are joined.

Note that if a layering is placed between the two boundary tori, then any changes to the boundary relationships caused by the layering are included in this matrix.

See the class notes above for precise information on how this matrix is presented.

Returns
the matrix describing how the boundaries of the region are joined.

§ name()

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

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

Returns
the name of this triangulation.

§ region()

const NSatRegion & regina::NBlockedSFSLoop::region ( ) const
inline

Returns details of the saturated region from which this triangulation is formed.

See the class notes above for further information.

Returns
details of the saturated region.

§ str()

std::string regina::Output< NStandardTriangulation , false >::str ( ) const
inherited

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python:
In addition to str(), this is also used as the Python "stringification" function __str__().
Returns
a short text representation of this object.

§ TeXName()

std::string regina::NStandardTriangulation::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.

§ toString()

REGINA_DEPRECATED std::string regina::Output< NStandardTriangulation , false >::toString ( ) const
inherited

A deprecated alias for str().

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

§ toStringLong()

REGINA_DEPRECATED std::string regina::Output< NStandardTriangulation , false >::toStringLong ( ) const
inherited

A deprecated alias for detail().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.

§ utf8()

std::string regina::Output< NStandardTriangulation , false >::utf8 ( ) const
inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.

§ writeName()

std::ostream& regina::NBlockedSFSLoop::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.

§ writeTeXName()

std::ostream& regina::NBlockedSFSLoop::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.

§ writeTextLong()

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

Writes a detailed text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent NStandardTriangulation class offers a reasonable default implementation based on writeName().

Python:
Not present.
Parameters
outthe output stream to which to write.

Reimplemented from regina::NStandardTriangulation.

§ writeTextShort()

void regina::NStandardTriangulation::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 NStandardTriangulation class offers a reasonable default implementation based on writeName().

Python:
Not present.
Parameters
outthe output stream to which to write.

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

Copyright © 1999-2016, 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@maths.uq.edu.au).