Regina Calculation Engine
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Represents an augmented triangular solid torus component of a triangulation. More...
#include <subcomplex/naugtrisolidtorus.h>
Public Member Functions | |
virtual | ~NAugTriSolidTorus () |
Destroys this augmented solid torus; note that the corresponding triangular and layered solid tori will also be destroyed. More... | |
NAugTriSolidTorus * | clone () const |
Returns a newly created clone of this structure. More... | |
const NTriSolidTorus & | getCore () const |
Returns the triangular solid torus at the core of this triangulation. More... | |
const NLayeredSolidTorus * | getAugTorus (int annulus) const |
Returns the layered solid torus attached to the requested annulus on the boundary of the core triangular solid torus. More... | |
NPerm4 | getEdgeGroupRoles (int annulus) const |
Returns a permutation describing the role played by each top level edge group of the layered solid torus glued to the requested annulus of the core triangular solid torus. More... | |
unsigned long | getChainLength () const |
Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus. More... | |
int | getChainType () const |
Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus. More... | |
int | getTorusAnnulus () const |
Returns the single boundary annulus of the core triangular solid torus to which a layered solid torus is attached. More... | |
bool | hasLayeredChain () const |
Determines whether the core triangular solid torus has two of its boundary annuli linked by a layered chain as described in the general class notes. More... | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition 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 this object in long text 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 NAbelianGroup * | getHomologyH1 () const |
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 this object in short text format to the given output stream. More... | |
Input and Output | |
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 NAugTriSolidTorus * | isAugTriSolidTorus (const NComponent *comp) |
Determines if the given triangulation component is an augmented triangular solid torus. 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 int | CHAIN_NONE |
Indicates that this augmented triangular solid torus contains no layered chain. More... | |
static const int | CHAIN_MAJOR |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedMajor(). More... | |
static const int | CHAIN_AXIS |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedAxis(). More... | |
Represents an augmented triangular solid torus component of a triangulation.
Such a component is obtained as follows. Begin with a three-tetrahedron triangular solid torus (as described by NTriSolidTorus). Observe that the three axis edges divide the boundary into three annuli. Then take one of the following actions.
It will be assumed that all layered solid tori other than the degenerate (2,1,1) will have (3,2,1) layered solid tori at their bases. That is, layered solid tori that begin with the degenerate (2,1,1) and layer over the boundary of the mobius strip are not considered in this class.
Note that (unless a (1,1,0) layered solid torus is used with the 0 edge glued to an axis edge) the resulting space will be a Seifert fibred space over the 2-sphere with at most three exceptional fibres.
Of the optional NStandardTriangulation routines, getManifold() is implemented for most augmented triangular solid tori and getHomologyH1() is not implemented at all.
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virtual |
Destroys this augmented solid torus; note that the corresponding triangular and layered solid tori will also be destroyed.
NAugTriSolidTorus* regina::NAugTriSolidTorus::clone | ( | ) | const |
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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inline |
Returns the layered solid torus attached to the requested annulus on the boundary of the core triangular solid torus.
If the layered solid torus is a degenerate (2,1,1) mobius band (i.e., the two triangles of the corresponding annulus have simply been glued together), null
will be returned.
annulus | specifies which annulus to examine; this must be 0, 1 or 2. |
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inline |
Returns the number of tetrahedra in the layered chain linking two of the boundary annuli of the core triangular solid torus.
Note that this count does not include any of the tetrahedra actually belonging to the triangular solid torus.
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inline |
Returns the way in which a layered chain links two of the boundary annuli of the core triangular solid torus.
This will be one of the chain type constants defined in this class.
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inline |
Returns the triangular solid torus at the core of this triangulation.
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inline |
Returns a permutation describing the role played by each top level edge group of the layered solid torus glued to the requested annulus of the core triangular solid torus.
See NLayeredSolidTorus::getTopEdge() for details regarding edge groups.
If the permutation returned is p
, edge group p[0]
will be glued to an axis edge, group p[1]
will be glued to a major edge and group p[2]
will be glued to a minor edge. p[3]
will always be 3.
Even if the corresponding layered solid torus is a degenerate (2,1,1) mobius band (i.e., getAugTorus() returns null
), the concept of edge groups is still meaningful and this routine will return correct results.
annulus | specifies which annulus to examine; this must be 0, 1 or 2. It is the layered solid torus glued to this annulus whose edge groups will be described. |
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inlinevirtualinherited |
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 in regina::NLayeredSolidTorus, regina::NTriSolidTorus, regina::NLayeredChain, regina::NSpiralSolidTorus, regina::NLayeredTorusBundle, regina::NSnapPeaCensusTri, regina::NLayeredLensSpace, regina::NLayeredLoop, regina::NSnappedBall, regina::NTrivialTri, regina::NL31Pillow, and regina::NLayeredChainPair.
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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 the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.
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inline |
Returns the single boundary annulus of the core triangular solid torus to which a layered solid torus is attached.
This routine is only meaningful if the other two annuli are linked by a layered chain.
The integer returned will be 0, 1 or 2; see the NTriSolidTorus class notes for how the boundary annuli are numbered.
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inline |
Determines whether the core triangular solid torus has two of its boundary annuli linked by a layered chain as described in the general class notes.
true
if and only if the layered chain described in the class notes is present.
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static |
Determines if the given triangulation component is an augmented triangular solid torus.
comp | the triangulation component to examine. |
null
if the given component is not an augmented triangular solid torus.
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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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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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virtual |
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 from regina::ShareableObject.
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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 |
Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedAxis().
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Indicates that this augmented triangular solid torus contains a layered chain attached as described by NTriSolidTorus::areAnnuliLinkedMajor().
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Indicates that this augmented triangular solid torus contains no layered chain.