Regina Calculation Engine
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regina::GraphPair Class Reference

Represents a closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus. More...

#include <manifold/graphpair.h>

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

Public Member Functions

 GraphPair (SFSpace *sfs0, SFSpace *sfs1, long mat00, long mat01, long mat10, long mat11)
 
Creates a new graph manifold as a pair of joined Seifert fibred spaces. More...
 
 GraphPair (SFSpace *sfs0, SFSpace *sfs1, const Matrix2 &matchingReln)
 
Creates a new graph manifold as a pair of joined Seifert fibred spaces. More...
 
 GraphPair (const GraphPair &cloneMe)
 Creates a clone of the given graph manifold. More...
 
 ~GraphPair ()
 Destroys this structure along with the component Seifert fibred spaces and the matching matrix. More...
 
const SFSpacesfs (unsigned which) const
 Returns a reference to one of the two bounded Seifert fibred spaces that are joined together. More...
 
const Matrix2 & matchingReln () const
 Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces are joined together. More...
 
bool operator< (const GraphPair &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...
 
GraphPairoperator= (const GraphPair &cloneMe)
 Sets this to be a clone of the given graph manifold. More...
 
AbelianGrouphomology () const override
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool isHyperbolic () const override
 Returns whether or not this is a finite-volume hyperbolic manifold. More...
 
std::ostream & writeName (std::ostream &out) const override
 
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 override
 
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 two bounded Seifert fibred spaces along a common torus.

Each Seifert fibred space must have just one boundary component, corresponding to a puncture in the base orbifold (with no fibre-reversing twist as one travels around this boundary).

The way in which the two spaces are joined is specified by a 2-by-2 matrix M. This matrix expresses the locations of the fibres and base orbifold of the second Seifert fibred space in terms of the first.

More specifically, suppose that f0 and o0 are generators of the common torus, where f0 represents a directed fibre in the first Seifert fibred space and o0 represents the oriented boundary of the corresponding base orbifold. Likewise, let f1 and o1 be generators of the common torus representing a directed fibre and the base orbifold of the second Seifert fibred space. Then the curves f0, o0, f1 and o1 are 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

◆ GraphPair() [1/3]

regina::GraphPair::GraphPair ( SFSpace sfs0,
SFSpace sfs1,
long  mat00,
long  mat01,
long  mat10,
long  mat11 
)
inline


Creates a new graph manifold as a pair of joined Seifert fibred spaces.

The two bounded Seifert fibred spaces 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 two given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.

Precondition
Each Seifert fibred space has a single torus boundary, corresponding to a single untwisted puncture in the base orbifold.
The given matching matrix has determinant +1 or -1.
Python
In Python, this constructor clones its SFSpace arguments instead of claiming ownership of them.
Parameters
sfs0the first Seifert fibred space.
sfs1the second 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.

◆ GraphPair() [2/3]

regina::GraphPair::GraphPair ( SFSpace sfs0,
SFSpace sfs1,
const Matrix2 &  matchingReln 
)
inline


Creates a new graph manifold as a pair of joined Seifert fibred spaces.

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

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

Precondition
Each Seifert fibred space has a single torus boundary, corresponding to a single untwisted puncture in the base orbifold.
The given matching matrix has determinant +1 or -1.
Python
In Python, this constructor clones its SFSpace arguments instead of claiming ownership of them.
Parameters
sfs0the first Seifert fibred space.
sfs1the second Seifert fibred space.
matchingRelnthe 2-by-2 matching matrix.

◆ GraphPair() [3/3]

regina::GraphPair::GraphPair ( const GraphPair cloneMe)
inline

Creates a clone of the given graph manifold.

Parameters
cloneMethe manifold to clone.

◆ ~GraphPair()

regina::GraphPair::~GraphPair ( )

Destroys this structure along with the component Seifert fibred spaces 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::GraphPair::homology ( ) const
overridevirtual

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::GraphPair::isHyperbolic ( ) const
inlineoverridevirtual

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::GraphPair::matchingReln ( ) const
inline

Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces 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::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.

◆ operator<() [2/2]

bool regina::GraphPair::operator< ( const GraphPair 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=()

GraphPair & regina::GraphPair::operator= ( const GraphPair cloneMe)
inline

Sets this to be a clone of the given graph manifold.

Parameters
cloneMethe manifold to clone.

◆ sfs()

const SFSpace & regina::GraphPair::sfs ( unsigned  which) const
inline

Returns a reference to one of the two bounded Seifert fibred spaces that are joined together.

Parameters
which0 if the first Seifert fibred space is to be returned, or 1 if the second space is to be returned.
Returns
a reference to the requested 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::GraphPair::writeName ( std::ostream &  out) const
overridevirtual


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::GraphPair::writeTeXName ( std::ostream &  out) const
overridevirtual


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 © 1999-2021, 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).