Regina Calculation Engine
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Represents a layered lens space component of a triangulation. More...
#include <subcomplex/nlayeredlensspace.h>
Public Member Functions | |
virtual | ~NLayeredLensSpace () |
Destroys this lens space; note that the corresponding layered solid torus will also be destroyed. More... | |
NLayeredLensSpace * | clone () const |
Returns a newly created clone of this structure. More... | |
unsigned long | p () const |
Returns the first parameter p of this lens space L(p,q). More... | |
REGINA_DEPRECATED unsigned long | getP () const |
Deprecated routine that returns the first parameter p of this lens space L(p,q). More... | |
unsigned long | q () const |
Returns the second parameter q of this lens space L(p,q). More... | |
REGINA_DEPRECATED unsigned long | getQ () const |
Deprecated routine that returns the second parameter q of this lens space L(p,q). More... | |
const NLayeredSolidTorus & | torus () const |
Returns the layered solid torus to which the mobius strip is glued. More... | |
REGINA_DEPRECATED const NLayeredSolidTorus & | getTorus () const |
Deprecated routine that returns the layered solid torus to which the mobius strip is glued. More... | |
int | mobiusBoundaryGroup () const |
Determines which edge of the layered solid torus is glued to the boundary of the mobius strip (i.e., the weight 2 edge of the degenerate (2,1,1) layered solid torus). More... | |
REGINA_DEPRECATED int | getMobiusBoundaryGroup () const |
Deprecated routine that retermines which edge of the layered solid torus is glued to the boundary of the mobius strip. More... | |
bool | isSnapped () const |
Determines if the layered solid torus that forms the basis for this lens space is snapped shut (folded closed without a twist). More... | |
bool | isTwisted () const |
Determines if the layered solid torus that forms the basis for this lens space is twisted shut (folded closed with a twist). 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 NLayeredLensSpace * | isLayeredLensSpace (const NComponent *comp) |
Determines if the given triangulation component is a layered lens space. 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 lens space component of a triangulation.
A layered lens space is considered to be any layered solid torus glued to a degenerate (2,1,1) layered solid torus (i.e., a one-triangle mobius strip). Note that the three possible gluing options represent the three possible ways of closing the initial torus - either twisting it shut (in one of two possible ways) or snapping it shut without any twist.
A layered lens space must contain at least one tetrahedron.
All optional NStandardTriangulation routines are implemented for this class.
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inlinevirtual |
Destroys this lens space; note that the corresponding layered solid torus will also be destroyed.
NLayeredLensSpace* regina::NLayeredLensSpace::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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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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inline |
Deprecated routine that retermines which edge of the layered solid torus is glued to the boundary of the mobius strip.
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inlineinherited |
Deprecated routine that returns the name of this specific triangulation as a human-readable string.
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inline |
Deprecated routine that returns the first parameter p of this lens space L(p,q).
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inline |
Deprecated routine that returns the second parameter q of this lens space L(p,q).
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inlineinherited |
Deprecated routine that returns the name of this specific triangulation in TeX format.
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inline |
Deprecated routine that returns the layered solid torus to which the mobius strip is glued.
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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 lens space.
comp | the triangulation component to examine. |
null
if the given component is not a layered lens space.
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inline |
Determines if the layered solid torus that forms the basis for this lens space is snapped shut (folded closed without a twist).
true
if and only if the torus is snapped shut.
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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 if the layered solid torus that forms the basis for this lens space is twisted shut (folded closed with a twist).
true
if and only if the torus is twisted shut.
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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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inline |
Determines which edge of the layered solid torus is glued to the boundary of the mobius strip (i.e., the weight 2 edge of the degenerate (2,1,1) layered solid torus).
The return value will be one of the three top level tetrahedron edge groups in the layered solid torus; see NLayeredSolidTorus::topEdge() for further details about edge groups.
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inherited |
Returns the name of this specific triangulation as a human-readable string.
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inline |
Returns the first parameter p of this lens space L(p,q).
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inline |
Returns the second parameter q of this lens space L(p,q).
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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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inline |
Returns the layered solid torus to which the mobius strip is glued.
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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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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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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. |