Regina Calculation Engine
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regina::GraphLoop Class Reference

Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus. More...

#include <manifold/graphloop.h>

Inheritance diagram for regina::GraphLoop:
regina::Manifold regina::Output< Manifold >

Public Member Functions

 GraphLoop (SFSpace *sfs, long mat00, long mat01, long mat10, long mat11)
 Creates a new graph manifold as a self-identified Seifert fibred space. More...
 
 GraphLoop (SFSpace *sfs, const Matrix2 &matchingReln)
 Creates a new graph manifold as a self-identified Seifert fibred space. More...
 
 ~GraphLoop ()
 Destroys this structure along with the bounded Seifert fibred space and the matching matrix. More...
 
const SFSpacesfs () const
 Returns a reference to the bounded Seifert fibred space that is joined to itself. More...
 
const Matrix2matchingReln () const
 Returns a reference to the 2-by-2 matrix describing how the two boundary tori of the Seifert fibred space are joined together. More...
 
bool operator< (const GraphLoop &compare) const
 Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More...
 
AbelianGrouphomology () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool isHyperbolic () const
 Returns whether or not this is a finite-volume hyperbolic manifold. More...
 
std::ostream & writeName (std::ostream &out) const
 Writes the common name of this 3-manifold as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const
 Writes the common name of this 3-manifold in TeX format to the given output stream. More...
 
std::string name () const
 Returns the common name of this 3-manifold as a human-readable string. More...
 
std::string TeXName () const
 Returns the common name of this 3-manifold in TeX format. More...
 
std::string structure () const
 Returns details of the structure of this 3-manifold that might not be evident from its common name. More...
 
virtual Triangulation< 3 > * construct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...
 
AbelianGrouphomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool operator< (const Manifold &compare) const
 Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold. More...
 
virtual std::ostream & writeStructure (std::ostream &out) const
 Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More...
 
void writeTextShort (std::ostream &out) const
 Writes a short text representation of this object 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 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...
 

Detailed Description

Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus.

The Seifert fibred space must have two boundary components, each a torus corresponding to a puncture in the base orbifold (with no fibre-reversing twist as one travels around the boundary).

The way in which the two torus boundaries are joined together is specified by a 2-by-2 matrix M. This matrix relates the locations of the fibres and base orbifold on the two boundary tori.

More specifically, suppose that f0 and o0 are generators of the first boundary torus, where f0 represents a directed fibre in the Seifert fibred space and o0 represents the oriented boundary of the base orbifold. Likewise, let f1 and o1 be generators of the second boundary torus representing a directed fibre and the oriented boundary of the base orbifold. Then the tori are joined together so that the curves f0, o0, f1 and o1 become related as follows:

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

See the page on Notation for Seifert fibred spaces for details on some of the terminology used above.

The optional Manifold routine homology() is implemented, but the optional routine construct() is not.

Todo:
Optimise: Speed up homology calculations involving orientable base spaces by adding rank afterwards, instead of adding generators for genus into the presentation matrix.

Constructor & Destructor Documentation

◆ GraphLoop() [1/2]

regina::GraphLoop::GraphLoop ( SFSpace sfs,
long  mat00,
long  mat01,
long  mat10,
long  mat11 
)
inline

Creates a new graph manifold as a self-identified Seifert fibred space.

The bounded Seifert fibred space and the four elements of the 2-by-2 matching matrix are all passed separately. The elements of the matching matrix combine to give the full matrix M as follows:

          [ mat00  mat01 ]
    M  =  [              ]
          [ mat10  mat11 ]

Note that the new object will take ownership of the given Seifert fibred space, and when this object is destroyed the Seifert fibred space will be destroyed also.

Precondition
The given Seifert fibred space has precisely two torus boundaries, corresponding to two untwisted punctures in the base orbifold.
The given matching matrix has determinant +1 or -1.
Python:
In Python, this constructor clones its SFSpace argument instead of claiming ownership of it.
Parameters
sfsthe bounded Seifert fibred space.
mat00the (0,0) element of the matching matrix.
mat01the (0,1) element of the matching matrix.
mat10the (1,0) element of the matching matrix.
mat11the (1,1) element of the matching matrix.

◆ GraphLoop() [2/2]

regina::GraphLoop::GraphLoop ( SFSpace sfs,
const Matrix2 matchingReln 
)
inline

Creates a new graph manifold as a self-identified Seifert fibred space.

The bounded Seifert fibred space and the entire 2-by-2 matching matrix are each passed separately.

Note that the new object will take ownership of the given Seifert fibred space, and when this object is destroyed the Seifert fibred space will be destroyed also.

Precondition
The given Seifert fibred space has precisely two torus boundaries, corresponding to two punctures in the base orbifold.
The given matching matrix has determinant +1 or -1.
Python:
In Python, this constructor clones its SFSpace argument instead of claiming ownership of it.
Parameters
sfsthe bounded Seifert fibred space.
matchingRelnthe 2-by-2 matching matrix.

◆ ~GraphLoop()

regina::GraphLoop::~GraphLoop ( )

Destroys this structure along with the bounded Seifert fibred space and the matching matrix.

Member Function Documentation

◆ construct()

Triangulation< 3 > * regina::Manifold::construct ( ) const
inlinevirtualinherited

Returns a triangulation of this 3-manifold, if such a construction has been implemented.

If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.

The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.

Returns
a triangulation of this 3-manifold, or 0 if the appropriate construction routine has not yet been implemented.

Reimplemented in regina::SFSpace, regina::SnapPeaCensusManifold, regina::LensSpace, and regina::SimpleSurfaceBundle.

◆ detail()

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

◆ homology()

AbelianGroup* regina::GraphLoop::homology ( ) const
virtual

Returns the first homology group of this 3-manifold, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.

The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.

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

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 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::Manifold.

◆ homologyH1()

AbelianGroup * regina::Manifold::homologyH1 ( ) const
inlineinherited

Returns the first homology group of this 3-manifold, if such a routine has been implemented.

If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.

The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.

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

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 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

◆ isHyperbolic()

bool regina::GraphLoop::isHyperbolic ( ) const
inlinevirtual

Returns whether or not this is a finite-volume hyperbolic manifold.

Returns
true if this is a finite-volume hyperbolic manifold, or false if not.

Implements regina::Manifold.

◆ matchingReln()

const Matrix2 & regina::GraphLoop::matchingReln ( ) const
inline

Returns a reference to the 2-by-2 matrix describing how the two boundary tori of the Seifert fibred space are joined together.

See the class notes for details on precisely how this matrix is represented.

Returns
a reference to the matching matrix.

◆ name()

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

Returns the common name of this 3-manifold as a human-readable string.

Returns
the common name of this 3-manifold.

◆ operator<() [1/2]

bool regina::GraphLoop::operator< ( const GraphLoop compare) const

Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space.

The ordering imposed on graph manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.

All that this routine really offers is a well-defined way of ordering graph manifold representations.

Parameters
comparethe representation with which this will be compared.
Returns
true if and only if this is "smaller" than the given graph manifold representation.

◆ operator<() [2/2]

bool regina::Manifold::operator< ( const Manifold compare) const
inherited

Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold.

The ordering imposed on 3-manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.

The ordering also depends on the particular representation of the 3-manifold that is used. As an example, different representations of the same Seifert fibred space might well be ordered differently.

All that this routine really offers is a well-defined way of ordering 3-manifold representations.

Warning
Currently this routine is only implemented in full for closed 3-manifolds. For most classes of bounded 3-manifolds, this routine simply compares the strings returned by name().
Parameters
comparethe 3-manifold representation with which this will be compared.
Returns
true if and only if this is "smaller" than the given 3-manifold representation.

◆ sfs()

const SFSpace & regina::GraphLoop::sfs ( ) const
inline

Returns a reference to the bounded Seifert fibred space that is joined to itself.

Returns
a reference to the bounded Seifert fibred space.

◆ str()

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

◆ structure()

std::string regina::Manifold::structure ( ) const
inherited

Returns details of the structure of this 3-manifold that might not be evident from its common name.

For instance, for an orbit space S^3/G this routine might return the full Seifert structure.

This routine may return the empty string if no additional details are deemed necessary.

Returns
a string describing additional structural details.

◆ TeXName()

std::string regina::Manifold::TeXName ( ) const
inherited

Returns the common name of this 3-manifold 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 common name of this 3-manifold in TeX format.

◆ utf8()

std::string regina::Output< Manifold , 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::GraphLoop::writeName ( std::ostream &  out) const
virtual

Writes the common name of this 3-manifold as a human-readable string to the given output stream.

Python:
The parameter out does not exist; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::Manifold.

◆ writeStructure()

std::ostream & regina::Manifold::writeStructure ( std::ostream &  out) const
inlinevirtualinherited

Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.

For instance, for an orbit space S^3/G this routine might write the full Seifert structure.

This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.

Python:
The parameter out does not exist; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Reimplemented in regina::SFSpace, and regina::SnapPeaCensusManifold.

◆ writeTeXName()

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

Writes the common name of this 3-manifold 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; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::Manifold.

◆ writeTextLong()

void regina::Manifold::writeTextLong ( std::ostream &  out) const
inlineinherited

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

Subclasses must not override this routine. They should override writeName() and writeStructure() instead.

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

◆ writeTextShort()

void regina::Manifold::writeTextShort ( std::ostream &  out) const
inlineinherited

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

Subclasses must not override this routine. They should override writeName() instead.

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).