Regina Calculation Engine

Represents a layered chain in a triangulation. More...
#include <subcomplex/nlayeredchain.h>
Public Member Functions  
NLayeredChain (NTetrahedron *tet, NPerm4 vertexRoles)  
Creates a new layered chain containing only the given tetrahedron. More...  
NLayeredChain (const NLayeredChain &cloneMe)  
Creates a new layered chain that is a clone of the given structure. More...  
virtual  ~NLayeredChain () 
Destroys this layered chain. More...  
NTetrahedron *  bottom () const 
Returns the bottom tetrahedron of this layered chain. More...  
REGINA_DEPRECATED NTetrahedron *  getBottom () const 
Deprecated routine that returns the bottom tetrahedron of this layered chain. More...  
NTetrahedron *  top () const 
Returns the top tetrahedron of this layered chain. More...  
REGINA_DEPRECATED NTetrahedron *  getTop () const 
Deprecated routine that returns the top tetrahedron of this layered chain. More...  
unsigned long  index () const 
Returns the number of tetrahedra in this layered chain. More...  
REGINA_DEPRECATED unsigned long  getIndex () const 
Deprecated routine that returns the number of tetrahedra in this layered chain. More...  
NPerm4  bottomVertexRoles () const 
Returns a permutation represeting the role that each vertex of the bottom tetrahedron plays in the layered chain. More...  
REGINA_DEPRECATED NPerm4  getBottomVertexRoles () const 
Deprecated routine that returns a permutation represeting the role that each vertex of the bottom tetrahedron plays in the layered chain. More...  
NPerm4  topVertexRoles () const 
Returns a permutation represeting the role that each vertex of the top tetrahedron plays in the layered chain. More...  
REGINA_DEPRECATED NPerm4  getTopVertexRoles () const 
Deprecated routine that returns a permutation represeting the role that each vertex of the top tetrahedron plays in the layered chain. More...  
bool  extendAbove () 
Checks to see whether this layered chain can be extended to include the tetrahedron above the top tetrahedron (and still remain a layered chain). More...  
bool  extendBelow () 
Checks to see whether this layered chain can be extended to include the tetrahedron below the bottom tetrahedron (and still remain a layered chain). More...  
bool  extendMaximal () 
Extends this layered chain to a maximal length layered chain. More...  
void  reverse () 
Reverses this layered chain so the top tetrahedron becomes the bottom and vice versa. More...  
void  invert () 
Inverts this layered chain so the upper hinge becomes the lower and vice versa. More...  
NManifold *  manifold () const 
Returns the 3manifold represented by this triangulation, if such a recognition routine has been implemented. More...  
NAbelianGroup *  homology () const 
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...  
std::ostream &  writeName (std::ostream &out) const 
Writes the name of this triangulation as a humanreadable 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 humanreadable string. More...  
REGINA_DEPRECATED std::string  getName () const 
Deprecated routine that returns the name of this specific triangulation as a humanreadable 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 NManifold *  getManifold () const 
Deprecated routine that returns the 3manifold represented by this triangulation,. More...  
NAbelianGroup *  homologyH1 () const 
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...  
REGINA_DEPRECATED NAbelianGroup *  getHomologyH1 () 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 NStandardTriangulation *  isStandardTriangulation (NComponent *component) 
Determines whether the given component represents one of the standard triangulations understood by Regina. More...  
static NStandardTriangulation *  isStandardTriangulation (NTriangulation *tri) 
Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...  
Represents a layered chain in a triangulation.
A layered chain is a set of n tetrahedra glued to each other by layerings. For each tetrahedron, select two top faces, two bottom faces and two hinge edges, so that the top faces are adjacent, the bottom faces are adjacent, the hinge edges are opposite and each hinge meets both a top and a bottom face. The tetrahedron can thus be thought of as a fattened square with the top and bottom faces above and below the square respectively, and the hinges as the top and bottom edges of the square. The left and right edges of the square are identified to form an annulus.
For each i, the top faces of tetrahedron i are glued to the bottom faces of tetrahedron i+1. This is done by layering the upper tetrahedron upon the annulus formed by the top faces of the lower tetrahedron. The layering should be done over the left or right edge of the lower square (note that these two edges are actually identified). The top hinges of each tetrahedron should be identified, as should the bottom hinges.
The bottom faces of the first tetrahedron and the top faces of the last tetrahedron form the boundary of the layered chain. If there is more than one tetrahedron, the layered chain forms a solid torus with two vertices whose axis is parallel to each hinge edge.
The index of the layered chain is the number of tetrahedra it contains. A layered chain must contain at least one tetrahedron.
Note that for the purposes of manifold() and homology(), a layered chain containing only one tetrahedron will be considered as a standalone tetrahedron that forms a 3ball (and not a solid torus).
All optional NStandardTriangulation routines are implemented for this class.

inline 
Creates a new layered chain containing only the given tetrahedron.
This new layered chain will have index 1, but may be extended using extendAbove(), extendBelow() or extendMaximal().
tet  the tetrahedron that will make up this layered chain. 
vertexRoles  a permutation describing the role each tetrahedron vertex must play in the layered chain; this must be in the same format as the permutation returned by bottomVertexRoles() and topVertexRoles(). 

inline 
Creates a new layered chain that is a clone of the given structure.
cloneMe  the layered chain to clone. 

inlinevirtual 
Destroys this layered chain.

inline 
Returns the bottom tetrahedron of this layered chain.

inline 
Returns a permutation represeting the role that each vertex of the bottom tetrahedron plays in the layered chain.
The permutation returned (call this p
) maps 0, 1, 2 and 3 to the four vertices of the bottom tetrahedron so that the edge from p[0]
to p[1]
is the top hinge, the edge from p[2]
to p[3]
is the bottom hinge, faces p[1]
and p[2]
are the (boundary) bottom faces and faces p[0]
and p[3]
are the top faces.
See the general class notes for further details.

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 humanreadable, 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.
bool regina::NLayeredChain::extendAbove  (  ) 
Checks to see whether this layered chain can be extended to include the tetrahedron above the top tetrahedron (and still remain a layered chain).
If so, this layered chain will be modified accordingly (note that its index will be increased by one and its top tetrahedron will change).
true
if and only if this layered chain was extended. bool regina::NLayeredChain::extendBelow  (  ) 
Checks to see whether this layered chain can be extended to include the tetrahedron below the bottom tetrahedron (and still remain a layered chain).
If so, this layered chain will be modified accordingly (note that its index will be increased by one and its bottom tetrahedron will change).
true
if and only if this layered chain was extended. bool regina::NLayeredChain::extendMaximal  (  ) 
Extends this layered chain to a maximal length layered chain.
Both extendAbove() and extendBelow() will be used until this layered chain can be extended no further.
true
if and only if this layered chain was extended.

inline 
Deprecated routine that returns the bottom tetrahedron of this layered chain.

inline 
Deprecated routine that returns a permutation represeting the role that each vertex of the bottom tetrahedron plays in the layered chain.

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

inline 
Deprecated routine that returns the number of tetrahedra in this layered chain.

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

inlineinherited 
Deprecated routine that returns the name of this specific triangulation as a humanreadable string.

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

inline 
Deprecated routine that returns the top tetrahedron of this layered chain.

inline 
Deprecated routine that returns a permutation represeting the role that each vertex of the top tetrahedron plays in the layered chain.

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::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).
Reimplemented from regina::NStandardTriangulation.

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).

inline 
Returns the number of tetrahedra in this layered chain.
void regina::NLayeredChain::invert  (  ) 
Inverts this layered chain so the upper hinge becomes the lower and vice versa.
The top and bottom tetrahedra will remain the top and bottom tetrahedra respectively.
Note that this operation will cause the hinge edges to point in the opposite direction around the solid torus formed by this layered chain.
Note that only the representation of the chain is altered; the underlying triangulation is not changed.

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 triangulationbased routine isStandardTriangulation(NTriangulation*) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.
component  the triangulation component under examination. 

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 componentbased isStandardTriangulation(NComponent*), since passing an entire triangulation allows access to more information.
tri  the triangulation under examination. 

virtual 
Returns the 3manifold represented by this triangulation, if such a recognition routine has been implemented.
If the 3manifold cannot be recognised then this routine will return 0.
The details of which standard triangulations have 3manifold 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 3manifolds can be recognised will grow between releases.
The 3manifold will be newly allocated and must be destroyed by the caller of this routine.
Reimplemented from regina::NStandardTriangulation.

inherited 
Returns the name of this specific triangulation as a humanreadable string.
void regina::NLayeredChain::reverse  (  ) 
Reverses this layered chain so the top tetrahedron becomes the bottom and vice versa.
The upper and lower hinges will remain the upper and lower hinges respectively.
Note that this operation will cause the hinge edges to point in the opposite direction around the solid torus formed by this layered chain.
Note that only the representation of the chain is altered; the underlying triangulation is not changed.

inherited 
Returns a short text representation of this object.
This text should be humanreadable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
__str__()
.

inherited 
Returns the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.

inline 
Returns the top tetrahedron of this layered chain.

inline 
Returns a permutation represeting the role that each vertex of the top tetrahedron plays in the layered chain.
The permutation returned (call this p
) maps 0, 1, 2 and 3 to the four vertices of the top tetrahedron so that the edge from p[0]
to p[1]
is the top hinge, the edge from p[2]
to p[3]
is the bottom hinge, faces p[1]
and p[2]
are the bottom faces and faces p[0]
and p[3]
are the (boundary) top faces.
See the general class notes for further details.

inherited 
A deprecated alias for str().

inherited 
A deprecated alias for detail().

inherited 
Returns a short text representation of this object using unicode characters.
Like str(), this text should be humanreadable, 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 UTF8.

inlinevirtual 
Writes the name of this triangulation as a humanreadable string to the given output stream.
out  the output stream to which to write. 
Implements regina::NStandardTriangulation.

inlinevirtual 
Writes the name of this triangulation in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
out  the output stream to which to write. 
Implements regina::NStandardTriangulation.

inlinevirtual 
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().
out  the output stream to which to write. 
Reimplemented from regina::NStandardTriangulation.

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().
out  the output stream to which to write. 