Regina Calculation Engine
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regina::TorusBundle Class Reference

Represents a torus bundle over the circle. More...

#include <manifold/torusbundle.h>

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

Public Member Functions

 TorusBundle ()
 Creates a new trivial torus bundle over the circle. More...
 
 TorusBundle (const Matrix2 &newMonodromy)
 Creates a new torus bundle over the circle using the given monodromy. More...
 
 TorusBundle (long mon00, long mon01, long mon10, long mon11)
 Creates a new torus bundle over the circle using the given monodromy. More...
 
 TorusBundle (const TorusBundle &cloneMe)
 Creates a clone of the given torus bundle. More...
 
const Matrix2monodromy () const
 Returns the monodromy describing how the upper and lower torus boundaries are identified. 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 torus bundle over the circle.

This is expressed as the product of the torus and the interval, with the two torus boundaries identified according to some specified monodromy.

The monodromy is described by a 2-by-2 matrix M as follows. Let a and b be generating curves of the upper torus boundary, and let p and q be the corresponding curves on the lower torus boundary (so that a and p are parallel and b and q are parallel). Then we identify the torus boundaries so that, in additive terms:

    [a]       [p]
    [ ] = M * [ ]
    [b]       [q]

All optional Manifold routines except for construct() are implemented for this class.

Todo:
Feature: Implement the == operator for finding conjugate and inverse matrices.

Constructor & Destructor Documentation

§ TorusBundle() [1/4]

regina::TorusBundle::TorusBundle ( )
inline

Creates a new trivial torus bundle over the circle.

In other words, this routine creates a torus bundle with the identity monodromy.

§ TorusBundle() [2/4]

regina::TorusBundle::TorusBundle ( const Matrix2 newMonodromy)
inline

Creates a new torus bundle over the circle using the given monodromy.

Precondition
The given matrix has determinant +1 or -1.
Parameters
newMonodromydescribes precisely how the upper and lower torus boundaries are identified. See the class notes for details.

§ TorusBundle() [3/4]

regina::TorusBundle::TorusBundle ( long  mon00,
long  mon01,
long  mon10,
long  mon11 
)
inline

Creates a new torus bundle over the circle using the given monodromy.

The four elements of the monodromy matrix are passed separately. They combine to give the full monodromy matrix M as follows:

          [ mon00  mon01 ]
    M  =  [              ]
          [ mon10  mon11 ]
Precondition
The monodromy matrix formed from the given parameters has determinant +1 or -1.
Parameters
mon00the (0,0) element of the monodromy matrix.
mon01the (0,1) element of the monodromy matrix.
mon10the (1,0) element of the monodromy matrix.
mon11the (1,1) element of the monodromy matrix.

§ TorusBundle() [4/4]

regina::TorusBundle::TorusBundle ( const TorusBundle cloneMe)
inline

Creates a clone of the given torus bundle.

Parameters
cloneMethe torus bundle to clone.

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::TorusBundle::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::TorusBundle::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.

§ monodromy()

const Matrix2 & regina::TorusBundle::monodromy ( ) const
inline

Returns the monodromy describing how the upper and lower torus boundaries are identified.

See the class notes for details.

Returns
the monodromy for this torus bundle.

§ 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<()

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.

§ 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::TorusBundle::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::TorusBundle::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).