Regina Calculation Engine
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Represents a 3-manifold triangulation from the SnapPea cusped census. More...
#include <subcomplex/nsnappeacensustri.h>
Public Member Functions | |
NSnapPeaCensusTri * | clone () const |
Returns a newly created clone of this structure. More... | |
char | getSection () const |
Returns the section of the SnapPea census to which this triangulation belongs. More... | |
unsigned long | getIndex () const |
Returns the index of this triangulation within its particular section of the SnapPea census. More... | |
bool | operator== (const NSnapPeaCensusTri &compare) const |
Determines whether this and the given structure represent the same triangulation from the SnapPea census. More... | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More... | |
NAbelianGroup * | getHomologyH1 () 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... | |
std::string | getName () const |
Returns the name of this specific triangulation as a human-readable string. More... | |
std::string | getTeXName () const |
Returns the name of this specific triangulation in TeX format. More... | |
virtual void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. More... | |
Input and Output | |
virtual void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. More... | |
std::string | str () const |
Returns the output from writeTextShort() as a string. More... | |
std::string | toString () const |
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More... | |
std::string | detail () const |
Returns the output from writeTextLong() as a string. More... | |
std::string | toStringLong () const |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More... | |
Static Public Member Functions | |
static NSnapPeaCensusTri * | isSmallSnapPeaCensusTri (const NComponent *comp) |
Determines if the given triangulation component is one of the smallest SnapPea census triangulations. 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... | |
Static Public Attributes | |
static const char | SEC_5 |
Represents the collection of triangulations formed from five or fewer tetrahedra (both orientable and non-orientable). More... | |
static const char | SEC_6_OR |
Represents the collection of orientable triangulations formed from six tetrahedra. More... | |
static const char | SEC_6_NOR |
Represents the collection of non-orientable triangulations formed from six tetrahedra. More... | |
static const char | SEC_7_OR |
Represents the collection of orientable triangulations formed from seven tetrahedra. More... | |
static const char | SEC_7_NOR |
Represents the collection of non-orientable triangulations formed from seven tetrahedra. More... | |
Friends | |
class | NSnapPeaCensusManifold |
Represents a 3-manifold triangulation from the SnapPea cusped census.
The SnapPea cusped census is the census of cusped hyperbolic 3-manifolds formed from up to seven tetrahedra. This census was tabulated by Callahan, Hildebrand and Weeks, and is shipped with SnapPea 3.0d3 (and also with Regina).
The census is split into five different sections according to number of tetrahedra and orientability. Each of these sections corresponds to one of the section constants defined in this class.
For further details regarding the SnapPea census, see "A census of cusped hyperbolic 3-manifolds", Patrick J. Callahan, Martin V. Hildebrand and Jeffrey R. Weeks, Math. Comp. 68 (1999), no. 225, pp. 321–332.
Note that this class is closely tied to NSnapPeaCensusManifold. In particular, the section constants defined in NSnapPeaCensusManifold and NSnapPeaCensusTri are identical, and so may be freely mixed. Furthermore, the section and index parameters of an NSnapPeaCensusTri are identical to those of its corresponding NSnapPeaCensusManifold.
All of the optional NStandardTriangulation routines are implemented for this class.
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inline |
Returns a newly created clone of this structure.
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inherited |
Returns the output from writeTextLong() as a string.
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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::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.
Reimplemented from regina::NStandardTriangulation.
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inline |
Returns the index of this triangulation within its particular section of the SnapPea census.
Note that indices for each section begin counting at zero.
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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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inline |
Returns the section of the SnapPea census to which this triangulation belongs.
This will be one of the section constants defined in this class.
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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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static |
Determines if the given triangulation component is one of the smallest SnapPea census triangulations.
This routine is able to recognise a small selection of triangulations from the beginning of the SnapPea census, by way of hard-coding their structures and properties. Most triangulations from the census however will not be recognised by this routine.
comp | the triangulation component to examine. |
null
if the given component is not one of the few SnapPea census triangulations recognised by this routine.
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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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inline |
Determines whether this and the given structure represent the same triangulation from the SnapPea census.
compare | the structure with which this will be compared. |
true
if and only if this and the given structure represent the same SnapPea census triangulation.
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inherited |
Returns the output from writeTextShort() as a string.
__str__()
function.
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inlineinherited |
A deprecated alias for str(), which returns the output from writeTextShort() as a string.
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inlineinherited |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
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virtual |
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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virtual |
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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inlinevirtualinherited |
Writes this object in long text format to the given output stream.
The output should provide the user with all the information they could want. The output should be human-readable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out | the output stream to which to write. |
Reimplemented in regina::NSnapPeaTriangulation, regina::NGroupPresentation, regina::NHomMarkedAbelianGroup, regina::NNormalSurfaceList, regina::NTetrahedron, regina::NSatRegion, regina::NVertex, regina::NEdge, regina::Dim2Triangle, regina::NTriangle, regina::NLayeredSolidTorus, regina::NHomGroupPresentation, regina::NGenericIsomorphism< dim >, regina::NGenericIsomorphism< 2 >, regina::NGenericIsomorphism< 3 >, regina::NTriangulation, regina::NComponent, regina::NTxICore, regina::NTriSolidTorus, regina::NAngleStructureList, regina::Dim2Edge, regina::NBoundaryComponent, regina::NLayeredChain, regina::Dim2Vertex, regina::Dim2Component, regina::NScript, regina::NAugTriSolidTorus, regina::NSpiralSolidTorus, regina::NSurfaceFilterProperties, regina::NLayeredTorusBundle, regina::NManifold, regina::NPlugTriSolidTorus, regina::NMatrixInt, regina::NBlockedSFSTriple, regina::NPluggedTorusBundle, regina::Dim2Triangulation, regina::NSurfaceSubset, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NFileInfo, regina::NBlockedSFSLoop, regina::NSnappedBall, regina::NBlockedSFSPair, regina::Dim2BoundaryComponent, regina::NTrivialTri, regina::NL31Pillow, regina::NLayeredChainPair, regina::NText, regina::NSurfaceFilterCombination, and regina::NBlockedSFS.
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inlinevirtualinherited |
Writes this object in short text format to the given output stream.
The output should be human-readable, should fit on a single line, and should not end with a newline.
out | the output stream to which to write. |
Implements regina::ShareableObject.
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static |
Represents the collection of triangulations formed from five or fewer tetrahedra (both orientable and non-orientable).
There are 415 triangulations in this section.
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static |
Represents the collection of non-orientable triangulations formed from six tetrahedra.
There are 259 triangulations in this section.
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Represents the collection of orientable triangulations formed from six tetrahedra.
There are 962 triangulations in this section.
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static |
Represents the collection of non-orientable triangulations formed from seven tetrahedra.
There are 887 triangulations in this section.
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static |
Represents the collection of orientable triangulations formed from seven tetrahedra.
There are 3552 triangulations in this section.