Regina Calculation Engine
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Describes a triangulation or subcomplex of a triangulation whose structure is well-understood. More...
#include <subcomplex/standardtri.h>
Public Member Functions | |
virtual | ~StandardTriangulation () |
A destructor that does nothing. More... | |
std::string | name () const |
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... | |
virtual Manifold * | manifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More... | |
virtual AbelianGroup * | homology () const |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More... | |
AbelianGroup * | homologyH1 () const |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More... | |
virtual std::ostream & | writeName (std::ostream &out) const =0 |
Writes the name of this triangulation as a human-readable string to the given output stream. More... | |
virtual std::ostream & | writeTeXName (std::ostream &out) const =0 |
Writes the name of this triangulation in TeX format to the given output stream. More... | |
virtual void | writeTextShort (std::ostream &out) const |
Writes a short text representation of this object to the given output stream. More... | |
virtual void | writeTextLong (std::ostream &out) const |
Writes a detailed text representation of this object to the given output stream. More... | |
StandardTriangulation & | operator= (const StandardTriangulation &)=delete |
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... | |
Static Public Member Functions | |
static StandardTriangulation * | isStandardTriangulation (Component< 3 > *component) |
Determines whether the given component represents one of the standard triangulations understood by Regina. More... | |
static StandardTriangulation * | isStandardTriangulation (Triangulation< 3 > *tri) |
Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More... | |
Protected Member Functions | |
StandardTriangulation ()=default | |
Default constructor. More... | |
StandardTriangulation (const StandardTriangulation &)=default | |
Do-nothing copy constructor. More... | |
Describes a triangulation or subcomplex of a triangulation whose structure is well-understood.
A StandardTriangulation is generally connected with a real triangulation, i.e., a Triangulation<3> object, which it describes some portion of.
In general StandardTriangulation objects cannot be constructed directly, but are instead created through static identification routines such as StandardTriangulation::isStandardTriangulation(Triangulation<3>*).
Subclasses corresponding to different families of triangulations may, but not need to, override the output routines writeTextShort() and writeTextLong(). This class offers sensible default implementations of both routines, which call the pure virtual function writeName() (which every subclass must override).
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inlinevirtual |
A destructor that does nothing.
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protecteddefault |
Default constructor.
This is needed for subclasses to implicitly call from their own constructors.
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protecteddefault |
Do-nothing copy constructor.
This is needed for subclasses to implicitly call from their own default copy constructors.
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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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inlinevirtual |
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 Triangulation<3>::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 StandardTriangulation. 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 StandardTriangulation describes an entire Triangulation<3> (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling Triangulation<3>::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 in regina::LayeredSolidTorus, regina::TriSolidTorus, regina::LayeredChain, regina::SpiralSolidTorus, regina::LayeredTorusBundle, regina::SnapPeaCensusTri, regina::LayeredLensSpace, regina::SnappedBall, regina::LayeredLoop, regina::TrivialTri, regina::L31Pillow, and regina::LayeredChainPair.
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inline |
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 Triangulation<3>::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 StandardTriangulation. 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 StandardTriangulation describes an entire Triangulation<3> (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling Triangulation<3>::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 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(Triangulation<3>*) 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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static |
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(Component<3>*), since passing an entire triangulation allows access to more information.
tri | the triangulation under examination. |
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inlinevirtual |
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 StandardTriangulation. 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 in regina::LayeredSolidTorus, regina::TriSolidTorus, regina::LayeredChain, regina::AugTriSolidTorus, regina::SpiralSolidTorus, regina::LayeredTorusBundle, regina::PlugTriSolidTorus, regina::BlockedSFSTriple, regina::PluggedTorusBundle, regina::SnapPeaCensusTri, regina::LayeredLensSpace, regina::BlockedSFSLoop, regina::SnappedBall, regina::BlockedSFSPair, regina::LayeredLoop, regina::TrivialTri, regina::L31Pillow, regina::LayeredChainPair, and regina::BlockedSFS.
std::string regina::StandardTriangulation::name | ( | ) | const |
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__()
.std::string regina::StandardTriangulation::TeXName | ( | ) | const |
Returns the name of this specific triangulation in TeX format.
No leading or trailing dollar signs will be included.
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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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pure 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. |
Implemented in regina::LayeredSolidTorus, regina::TriSolidTorus, regina::LayeredChain, regina::AugTriSolidTorus, regina::SpiralSolidTorus, regina::LayeredTorusBundle, regina::PlugTriSolidTorus, regina::BlockedSFSTriple, regina::PluggedTorusBundle, regina::SnapPeaCensusTri, regina::LayeredLensSpace, regina::BlockedSFSLoop, regina::SnappedBall, regina::LayeredLoop, regina::BlockedSFSPair, regina::TrivialTri, regina::L31Pillow, regina::LayeredChainPair, and regina::BlockedSFS.
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pure 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. |
Implemented in regina::LayeredSolidTorus, regina::TriSolidTorus, regina::LayeredChain, regina::AugTriSolidTorus, regina::SpiralSolidTorus, regina::LayeredTorusBundle, regina::PlugTriSolidTorus, regina::BlockedSFSTriple, regina::PluggedTorusBundle, regina::SnapPeaCensusTri, regina::LayeredLensSpace, regina::BlockedSFSLoop, regina::SnappedBall, regina::LayeredLoop, regina::BlockedSFSPair, regina::TrivialTri, regina::L31Pillow, regina::LayeredChainPair, and regina::BlockedSFS.
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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 StandardTriangulation class offers a reasonable default implementation based on writeName().
out | the output stream to which to write. |
Reimplemented in regina::LayeredSolidTorus, regina::TriSolidTorus, regina::LayeredChain, regina::AugTriSolidTorus, regina::SpiralSolidTorus, regina::LayeredTorusBundle, regina::PlugTriSolidTorus, regina::BlockedSFSTriple, regina::PluggedTorusBundle, regina::LayeredLensSpace, regina::BlockedSFSLoop, regina::SnappedBall, regina::LayeredLoop, regina::BlockedSFSPair, regina::TrivialTri, regina::L31Pillow, regina::LayeredChainPair, and regina::BlockedSFS.
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inlinevirtual |
Writes a short text representation of this object to the given output stream.
This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeName().
out | the output stream to which to write. |