Regina Calculation Engine
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Represents a layered chain pair component of a triangulation. More...
#include <subcomplex/nlayeredchainpair.h>
Public Member Functions | |
virtual | ~NLayeredChainPair () |
Destroys this layered chain pair. More... | |
NLayeredChainPair * | clone () const |
Returns a newly created clone of this structure. More... | |
const NLayeredChain * | chain (int which) const |
Returns the requested layered chain used to form this structure. More... | |
REGINA_DEPRECATED const NLayeredChain * | getChain (int which) const |
Deprecated routine that returns the requested layered chain used to form this structure. More... | |
NManifold * | manifold () const |
Returns the 3-manifold 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 human-readable 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 human-readable string. More... | |
REGINA_DEPRECATED std::string | getName () const |
Deprecated routine that returns the name of this specific triangulation as a human-readable 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 3-manifold 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 NLayeredChainPair * | isLayeredChainPair (const NComponent *comp) |
Determines if the given triangulation component is a layered chain pair. More... | |
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 pair component of a triangulation.
A layered chain pair consists of two layered chains (as described by class NLayeredChain) glued together in a particular way.
Orient the hinge edges and diagonals of each chain so they all point in the same direction around the solid tori formed by each layered chain (a diagonal is an edge between the two top triangular faces or an edge between the two bottom triangular faces of a layered chain).
The two top faces of the first chain are glued to a top and bottom face of the second chain, and the two bottom faces of the first chain are glued to a top and bottom face of the second chain.
The four oriented diagonals are all identified as a single edge. Of the remaining unglued edges (two hinge edges and two non-hinge edges per chain), each hinge edge of one chain must be identified to a non-hinge edge of the other chain and vice versa. From here the face identifications are uniquely determined.
Note that a layered chain pair in which one of the chains contains only one tetrahedron is in fact a layered loop with a twist (see class NLayeredLoop).
All optional NStandardTriangulation routines are implemented for this class.
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inlinevirtual |
Destroys this layered chain pair.
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inline |
Returns the requested layered chain used to form this structure.
If the two chains have different lengths, the shorter chain will be chain 0 and the longer chain will be chain 1.
which | specifies which chain to return; this must be 0 or 1. |
NLayeredChainPair* regina::NLayeredChainPair::clone | ( | ) | const |
Returns a newly created clone of this structure.
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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.
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inline |
Deprecated routine that returns the requested layered chain used to form this structure.
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inlineinherited |
Deprecated routine that returns the expected first homology group of this triangulation, if such a routine has been implemented.
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inlineinherited |
Deprecated routine that returns the 3-manifold represented by this triangulation,.
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inlineinherited |
Deprecated routine that returns the name of this specific triangulation as a human-readable string.
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inlineinherited |
Deprecated routine that returns the name of this specific triangulation in TeX format.
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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.
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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).
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static |
Determines if the given triangulation component is a layered chain pair.
comp | the triangulation component to examine. |
null
if the given component is not a layered chain pair.
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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 triangulation-based 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. |
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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 component-based isStandardTriangulation(NComponent*), since passing an entire triangulation allows access to more information.
tri | the triangulation under examination. |
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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.
Reimplemented from regina::NStandardTriangulation.
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inherited |
Returns the name of this specific triangulation as a human-readable string.
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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.
__str__()
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inherited |
Returns the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.
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inherited |
A deprecated alias for str().
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inherited |
A deprecated alias for detail().
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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.
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inlinevirtual |
Writes the name of this triangulation as a human-readable string to the given output stream.
out | the output stream to which to write. |
Implements regina::NStandardTriangulation.
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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.
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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.
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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. |