Regina Calculation Engine
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Represents one of a few particular hard-coded trivial triangulations that do not belong to any of the other larger families. More...
#include <subcomplex/trivialtri.h>
Public Member Functions | |
TrivialTri * | clone () const |
Returns a newly created clone of this structure. More... | |
int | type () const |
Returns the specific trivial triangulation being represented. More... | |
Manifold * | manifold () const override |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More... | |
AbelianGroup * | homology () const override |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More... | |
std::ostream & | writeName (std::ostream &out) const override |
Writes the name of this triangulation as a human-readable string to the given output stream. More... | |
std::ostream & | writeTeXName (std::ostream &out) const override |
Writes the name of this triangulation in TeX format to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const override |
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... | |
std::string | TeXName () const |
Returns the name of this specific triangulation in TeX format. More... | |
AbelianGroup * | homologyH1 () 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 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... | |
Static Public Member Functions | |
static TrivialTri * | isTrivialTriangulation (const Component< 3 > *comp) |
Determines if the given triangulation component is one of the trivial triangulations recognised by this class. More... | |
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... | |
Static Public Attributes | |
static const int | SPHERE_4_VERTEX |
Represents the two-tetrahedron four-vertex triangulation of the 3-sphere. More... | |
static const int | BALL_3_VERTEX |
Represents the one-tetrahedron three-vertex triangulation of the ball. More... | |
static const int | BALL_4_VERTEX |
Represents the one-tetrahedron four-vertex triangulation of the ball. More... | |
static const int | N2 |
Represents the two-tetrahedron triangulation N(2) of the twisted 2-sphere bundle over the circle. More... | |
static const int | N3_1 |
Represents the three-tetrahedron triangulation N(3,1) of the projective plane bundle over the circle. More... | |
static const int | N3_2 |
Represents the three-tetrahedron triangulation N(3,2) of the projective plane bundle over the circle. More... | |
Represents one of a few particular hard-coded trivial triangulations that do not belong to any of the other larger families.
All optional StandardTriangulation 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 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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overridevirtual |
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 from regina::StandardTriangulation.
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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 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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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(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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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(Component<3>*), since passing an entire triangulation allows access to more information.
tri | the triangulation under examination. |
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static |
Determines if the given triangulation component is one of the trivial triangulations recognised by this class.
comp | the triangulation component to examine. |
null
if the given component is not one of the triangulations recognised by this class.
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overridevirtual |
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 from regina::StandardTriangulation.
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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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inline |
Returns the specific trivial triangulation being represented.
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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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overridevirtual |
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::StandardTriangulation.
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overridevirtual |
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::StandardTriangulation.
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overridevirtual |
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 from regina::StandardTriangulation.
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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 StandardTriangulation class offers a reasonable default implementation based on writeName().
out | the output stream to which to write. |
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static |
Represents the one-tetrahedron three-vertex triangulation of the ball.
This is a single tetrahedron with two faces as boundary and the other two faces folded together.
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static |
Represents the one-tetrahedron four-vertex triangulation of the ball.
This is a single tetrahedron with all four faces as boundary.
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static |
Represents the two-tetrahedron triangulation N(2) of the twisted 2-sphere bundle over the circle.
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static |
Represents the three-tetrahedron triangulation N(3,1) of the projective plane bundle over the circle.
This particular triangulation has no Mobius band triangles.
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static |
Represents the three-tetrahedron triangulation N(3,2) of the projective plane bundle over the circle.
This particular triangulation has two Mobius band triangles.
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static |
Represents the two-tetrahedron four-vertex triangulation of the 3-sphere.