Regina Calculation Engine
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Represents a blocked Seifert fibred space (possibly with boundary). More...
#include <subcomplex/blockedsfs.h>
Public Member Functions | |
~BlockedSFS () | |
Destroys this structure and its constituent components. More... | |
const SatRegion & | region () const |
Returns details of the single saturated region that fills this triangulation. More... | |
bool | isPluggedIBundle (std::string &name) const |
Determines whether this triangulation is a plugged thin I-bundle or a plugged thick I-bundle. More... | |
Manifold * | manifold () const override |
Returns the 3-manifold represented by this triangulation, if such a recognition 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... | |
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 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 BlockedSFS * | isBlockedSFS (Triangulation< 3 > *tri) |
Determines if the given triangulation is a blocked Seifert fibred space. 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... | |
Represents a blocked Seifert fibred space (possibly with boundary).
This is a particular type of triangulation of a Seifert fibred space, where this triangulation is formed from a single saturated region. A saturated region is in turn formed from saturated blocks by identifying their boundary annuli in pairs; see the SatRegion class for details.
Note that the routines writeName() and writeTeXName() do not offer enough information to uniquely identify the triangulation, since this essentially requires a 2-dimensional assembling of saturated blocks. For full detail, writeTextLong() may be used instead.
The optional StandardTriangulation routine manifold() is implemented for this class, but homology() is not.
regina::BlockedSFS::~BlockedSFS | ( | ) |
Destroys this structure and its constituent components.
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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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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 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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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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static |
Determines if the given triangulation is a blocked Seifert fibred space.
tri | the triangulation to examine. |
null
if the given triangulation is not a blocked Seifert fibred space. bool regina::BlockedSFS::isPluggedIBundle | ( | std::string & | name | ) | const |
Determines whether this triangulation is a plugged thin I-bundle or a plugged thick I-bundle.
These structures are described in "Structures of small closed non-orientable 3-manifold triangulations", Benjamin A. Burton, J. Knot Theory Ramifications 16 (2007), 545–574.
name | used to return the name of the plugged thin/thick I-bundle, if the triangulation is of this form. If the triangulation is not of this form, this string is not touched. |
true
if this triangulation is indeed a plugged thin I-bundle or a plugged thick I-bundle.
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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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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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inline |
Returns details of the single saturated region that fills this triangulation.
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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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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. |