regina::NLayeredLoop Class Reference
[Standard Triangulations and Subcomplexes]

Represents a layered loop component of a triangulation. More...

#include <nlayeredloop.h>

Inheritance diagram for regina::NLayeredLoop:

regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

virtual ~NLayeredLoop ()
 Destroys this layered loop.
NLayeredLoopclone () const
 Returns a newly created clone of this structure.
unsigned long getLength () const
 Returns the length of this layered loop.
unsigned long getIndex () const
 Returns the length of this layered loop.
bool isTwisted () const
 Determines if this layered loop contains a twist.
NEdgegetHinge (int which) const
 Returns the requested hinge edge of this layered loop.
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.
NAbelianGroupgetHomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented.
std::ostream & writeName (std::ostream &out) const
 Writes the name of this triangulation as a human-readable string to the given output stream.
std::ostream & writeTeXName (std::ostream &out) const
 Writes the name of this triangulation in TeX format to the given output stream.
void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream.

Static Public Member Functions

static NLayeredLoopisLayeredLoop (const NComponent *comp)
 Determines if the given triangulation component is a layered loop.


Detailed Description

Represents a layered loop component of a triangulation.

A layered loop is a layered chain of n tetrahedra whose bottom tetrahedron is layered onto its top tetrahedron to form a complete loop. See the NLayeredChain class notes for a description of a layered chain.

To make a layered chain into a layered loop, the bottom faces of the first tetrahedron will be layered upon the top faces of the last tetrahedron, completing the loop. At this stage there is a choice. The layering can be done in the usual fashion, or there may be a twist in which the upper square (the bottom faces of the first tetrahedron) is rotated 180 degrees before being layered on the lower annulus (the top faces of the last tetrahedron).

If there is a twist, the two hinge edges become identified and the entire component has a single vertex. If there is no twist, the two hinge edges remain distinct (and disjoint) and the entire component has two vertices.

The length of the layered loop is the number of tetrahedra it contains. A layered loop must contain at least one tetrahedron.

All optional NStandardTriangulation routines are implemented for this class.


Constructor & Destructor Documentation

regina::NLayeredLoop::~NLayeredLoop (  )  [inline, virtual]

Destroys this layered loop.


Member Function Documentation

NLayeredLoop* regina::NLayeredLoop::clone (  )  const

Returns a newly created clone of this structure.

Returns:
a newly created clone.

NEdge * regina::NLayeredLoop::getHinge ( int  which  )  const [inline]

Returns the requested hinge edge of this layered loop.

See the general class notes for further details. If there is only one hinge but parameter which is 1, null will be returned.

Parameters:
which specifies which hinge to return; this must be 0 or 1.
Returns:
the requested hinge edge.

NAbelianGroup* regina::NLayeredLoop::getHomologyH1 (  )  const [virtual]

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 from regina::NStandardTriangulation.

unsigned long regina::NLayeredLoop::getIndex (  )  const [inline]

Returns the length of this layered loop.

See the general class notes for further details.

Deprecated:
The preferred way of accessing the length of a layered loop is through getLength().
Returns:
the length of this layered loop.

unsigned long regina::NLayeredLoop::getLength (  )  const [inline]

Returns the length of this layered loop.

See the general class notes for further details.

Returns:
the length of this layered loop.

NManifold* regina::NLayeredLoop::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.

static NLayeredLoop* regina::NLayeredLoop::isLayeredLoop ( const NComponent comp  )  [static]

Determines if the given triangulation component is a layered loop.

Parameters:
comp the triangulation component to examine.
Returns:
a newly created structure containing details of the layered loop, or null if the given component is not a layered loop.

bool regina::NLayeredLoop::isTwisted (  )  const [inline]

Determines if this layered loop contains a twist.

See the general class notes for further details.

Returns:
true if and only if this layered loop contains a twist.

std::ostream & regina::NLayeredLoop::writeName ( std::ostream &  out  )  const [inline, 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:
out the output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

std::ostream & regina::NLayeredLoop::writeTeXName ( std::ostream &  out  )  const [inline, 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:
out the output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NStandardTriangulation.

void regina::NLayeredLoop::writeTextLong ( std::ostream &  out  )  const [inline, virtual]

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

The output should provided the user with all the information they could want. The output should end with a 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:
out the output stream to which to write.

Reimplemented from regina::ShareableObject.


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

Copyright © 1999-2008, Ben Burton
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).