Regina Calculation Engine
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Classes | |
class | regina::GraphLoop |
Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus. More... | |
class | regina::GraphPair |
Represents a closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus. More... | |
class | regina::GraphTriple |
Represents a closed graph manifold formed by joining three bounded Seifert fibred spaces along their torus boundaries. More... | |
class | regina::Handlebody |
Represents an arbitrary handlebody. More... | |
class | regina::LensSpace |
Represents a general lens space. More... | |
class | regina::Manifold |
Represents a particular 3-manifold. More... | |
struct | regina::SFSFibre |
Represents an exceptional (alpha, beta) fibre in a Seifert fibred space. More... | |
class | regina::SFSpace |
Represents a general Seifert fibred space, which may be orientable or non-orientable. More... | |
class | regina::SFSAltSet |
Provides a variety of alternative representations of a single bounded Seifert fibred space. More... | |
class | regina::SimpleSurfaceBundle |
Represents a particularly simple closed surface bundle over the circle. More... | |
class | regina::SnapPeaCensusManifold |
Represents a 3-manifold from the SnapPea cusped census. More... | |
class | regina::TorusBundle |
Represents a torus bundle over the circle. More... | |
Typedefs | |
typedef GraphLoop | regina::NGraphLoop |
Deprecated typedef for backward compatibility. More... | |
typedef GraphPair | regina::NGraphPair |
Deprecated typedef for backward compatibility. More... | |
typedef GraphTriple | regina::NGraphTriple |
Deprecated typedef for backward compatibility. More... | |
typedef Handlebody | regina::NHandlebody |
Deprecated typedef for backward compatibility. More... | |
typedef LensSpace | regina::NLensSpace |
Deprecated typedef for backward compatibility. More... | |
typedef Manifold | regina::NManifold |
Deprecated typedef for backward compatibility. More... | |
typedef SFSFibre | regina::NSFSFibre |
Deprecated typedef for backward compatibility. More... | |
typedef SFSpace | regina::NSFSpace |
Deprecated typedef for backward compatibility. More... | |
typedef SFSAltSet | regina::NSFSAltSet |
Deprecated typedef for backward compatibility. More... | |
typedef SimpleSurfaceBundle | regina::NSimpleSurfaceBundle |
Deprecated typedef for backward compatibility. More... | |
typedef SnapPeaCensusManifold | regina::NSnapPeaCensusManifold |
Deprecated typedef for backward compatibility. More... | |
typedef TorusBundle | regina::NTorusBundle |
Deprecated typedef for backward compatibility. More... | |
Enumerations | |
enum | regina::SFSpace::classType { regina::SFSpace::o1 = 101, regina::SFSpace::o2 = 102, regina::SFSpace::n1 = 201, regina::SFSpace::n2 = 202, regina::SFSpace::n3 = 203, regina::SFSpace::n4 = 204, regina::SFSpace::bo1 = 301, regina::SFSpace::bo2 = 302, regina::SFSpace::bn1 = 401, regina::SFSpace::bn2 = 402, regina::SFSpace::bn3 = 403 } |
Lists the six classes o1 , o2 , n1 , n2 , n3 , n4 for base orbifolds without boundaries, plus five classes bo1 , b02 , bn1 , bn2 , bn3 for base orbifolds with boundaries. More... | |
Functions | |
regina::GraphLoop::GraphLoop (SFSpace *sfs, long mat00, long mat01, long mat10, long mat11) | |
Creates a new graph manifold as a self-identified Seifert fibred space. More... | |
regina::GraphLoop::GraphLoop (SFSpace *sfs, const Matrix2 &matchingReln) | |
Creates a new graph manifold as a self-identified Seifert fibred space. More... | |
regina::GraphLoop::~GraphLoop () | |
Destroys this structure along with the bounded Seifert fibred space and the matching matrix. More... | |
const SFSpace & | regina::GraphLoop::sfs () const |
Returns a reference to the bounded Seifert fibred space that is joined to itself. More... | |
const Matrix2 & | regina::GraphLoop::matchingReln () const |
Returns a reference to the 2-by-2 matrix describing how the two boundary tori of the Seifert fibred space are joined together. More... | |
bool | regina::GraphLoop::operator< (const GraphLoop &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More... | |
AbelianGroup * | regina::GraphLoop::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::GraphLoop::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::GraphLoop::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::GraphLoop::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
regina::GraphPair::GraphPair (SFSpace *sfs0, SFSpace *sfs1, long mat00, long mat01, long mat10, long mat11) | |
Creates a new graph manifold as a pair of joined Seifert fibred spaces. More... | |
regina::GraphPair::GraphPair (SFSpace *sfs0, SFSpace *sfs1, const Matrix2 &matchingReln) | |
Creates a new graph manifold as a pair of joined Seifert fibred spaces. More... | |
regina::GraphPair::~GraphPair () | |
Destroys this structure along with the component Seifert fibred spaces and the matching matrix. More... | |
const SFSpace & | regina::GraphPair::sfs (unsigned which) const |
Returns a reference to one of the two bounded Seifert fibred spaces that are joined together. More... | |
const Matrix2 & | regina::GraphPair::matchingReln () const |
Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces are joined together. More... | |
bool | regina::GraphPair::operator< (const GraphPair &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More... | |
AbelianGroup * | regina::GraphPair::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::GraphPair::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::GraphPair::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::GraphPair::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
regina::GraphTriple::GraphTriple (SFSpace *end0, SFSpace *centre, SFSpace *end1, const Matrix2 &matchingReln0, const Matrix2 &matchingReln1) | |
Creates a new graph manifold from three bounded Seifert fibred spaces, as described in the class notes. More... | |
regina::GraphTriple::~GraphTriple () | |
Destroys this structure along with the component Seifert fibred spaces and matching matrices. More... | |
const SFSpace & | regina::GraphTriple::end (unsigned which) const |
Returns a reference to one of the two end spaces. More... | |
const SFSpace & | regina::GraphTriple::centre () const |
Returns a reference to the central space. More... | |
const Matrix2 & | regina::GraphTriple::matchingReln (unsigned which) const |
Returns a reference to the 2-by-2 matrix describing how the two requested bounded Seifert fibred spaces are joined together. More... | |
bool | regina::GraphTriple::operator< (const GraphTriple &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More... | |
AbelianGroup * | regina::GraphTriple::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::GraphTriple::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::GraphTriple::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::GraphTriple::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
regina::Handlebody::Handlebody (unsigned long newHandles, bool newOrientable) | |
Creates a new handlebody with the given parameters. More... | |
regina::Handlebody::Handlebody (const Handlebody &cloneMe) | |
Creates a clone of the given handlebody. More... | |
virtual | regina::Handlebody::~Handlebody () |
Destroys this handlebody. More... | |
unsigned long | regina::Handlebody::handles () const |
Returns the number of handles of this handlebody. More... | |
bool | regina::Handlebody::isOrientable () const |
Returns whether this handlebody is orientable. More... | |
bool | regina::Handlebody::operator== (const Handlebody &compare) const |
Determines whether this and the given handlebody represent the same 3-manifold. More... | |
bool | regina::Handlebody::operator!= (const Handlebody &compare) const |
Determines whether this and the given handlebody represent different 3-manifolds. More... | |
AbelianGroup * | regina::Handlebody::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::Handlebody::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::Handlebody::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::Handlebody::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
regina::LensSpace::LensSpace (unsigned long newP, unsigned long newQ) | |
Creates a new lens space with the given parameters. More... | |
regina::LensSpace::LensSpace (const LensSpace &cloneMe) | |
Creates a clone of the given lens space. More... | |
virtual | regina::LensSpace::~LensSpace () |
Destroys this lens space. More... | |
unsigned long | regina::LensSpace::p () const |
Returns the first parameter p of this lens space L(p,q). More... | |
unsigned long | regina::LensSpace::q () const |
Returns the second parameter q of this lens space L(p,q). More... | |
bool | regina::LensSpace::operator== (const LensSpace &compare) const |
Determines whether this and the given lens space are homeomorphic 3-manifolds. More... | |
bool | regina::LensSpace::operator!= (const LensSpace &compare) const |
Determines whether this and the given lens space are non-homeomorphic 3-manifolds. More... | |
Triangulation< 3 > * | regina::LensSpace::construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
AbelianGroup * | regina::LensSpace::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::LensSpace::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::LensSpace::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::LensSpace::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
virtual | regina::Manifold::~Manifold () |
A destructor that does nothing. More... | |
std::string | regina::Manifold::name () const |
Returns the common name of this 3-manifold as a human-readable string. More... | |
std::string | regina::Manifold::TeXName () const |
Returns the common name of this 3-manifold in TeX format. More... | |
std::string | regina::Manifold::structure () const |
Returns details of the structure of this 3-manifold that might not be evident from its common name. More... | |
virtual Triangulation< 3 > * | regina::Manifold::construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
virtual AbelianGroup * | regina::Manifold::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
AbelianGroup * | regina::Manifold::homologyH1 () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
virtual bool | regina::Manifold::isHyperbolic () const =0 |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
bool | regina::Manifold::operator< (const Manifold &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold. More... | |
virtual std::ostream & | regina::Manifold::writeName (std::ostream &out) const =0 |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
virtual std::ostream & | regina::Manifold::writeTeXName (std::ostream &out) const =0 |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
virtual std::ostream & | regina::Manifold::writeStructure (std::ostream &out) const |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More... | |
void | regina::Manifold::writeTextShort (std::ostream &out) const |
Writes a short text representation of this object to the given output stream. More... | |
void | regina::Manifold::writeTextLong (std::ostream &out) const |
Writes a detailed text representation of this object to the given output stream. More... | |
regina::SFSFibre::SFSFibre () | |
Creates a new uninitialised exceptional fibre. More... | |
regina::SFSFibre::SFSFibre (long newAlpha, long newBeta) | |
Creates a new exceptional fibre with the given parameters. More... | |
regina::SFSFibre::SFSFibre (const SFSFibre &cloneMe) | |
Creates a new exceptional fibre that is a clone of the given fibre. More... | |
void | regina::SFSFibre::operator= (const SFSFibre &cloneMe) |
Makes this exceptional fibre a clone of the given fibre. More... | |
bool | regina::SFSFibre::operator== (const SFSFibre &compare) const |
Determines if this and the given exceptional fibre are identical. More... | |
bool | regina::SFSFibre::operator!= (const SFSFibre &compare) const |
Determines if this and the given exceptional fibre are different. More... | |
bool | regina::SFSFibre::operator< (const SFSFibre &compare) const |
Determines if this exceptional fibre is smaller than the given fibre. More... | |
std::ostream & | regina::operator<< (std::ostream &out, const SFSFibre &f) |
Writes the given fibre in human-readable format to the given output stream. More... | |
regina::SFSpace::SFSpace () | |
Creates a new Seifert fibred space with base orbifold the 2-sphere and no exceptional fibres. More... | |
regina::SFSpace::SFSpace (classType useClass, unsigned long genus, unsigned long punctures=0, unsigned long puncturesTwisted=0, unsigned long reflectors=0, unsigned long reflectorsTwisted=0) | |
Creates a new Seifert fibred space of the given class with the given base orbifold and no exceptional fibres. More... | |
regina::SFSpace::SFSpace (const SFSpace &cloneMe) | |
Creates a new Seifert fibred space that is a clone of the given space. More... | |
virtual | regina::SFSpace::~SFSpace () |
Destroys this Seifert fibred space. More... | |
void | regina::SFSpace::operator= (const SFSpace &cloneMe) |
Modifies this Seifert fibred space to be a clone of the given space. More... | |
classType | regina::SFSpace::baseClass () const |
Returns which of the eleven predefined classes this space belongs to. More... | |
unsigned long | regina::SFSpace::baseGenus () const |
Returns the genus of the base orbifold. More... | |
bool | regina::SFSpace::baseOrientable () const |
Returns whether or not the base surface is orientable. More... | |
bool | regina::SFSpace::fibreReversing () const |
Returns whether or not this space contains any fibre-reversing paths. More... | |
bool | regina::SFSpace::fibreNegating () const |
Returns whether or not we can negate an exceptional fibre by passing it around the interior of the base orbifold. More... | |
unsigned long | regina::SFSpace::punctures () const |
Returns the total number of punctures in the base orbifold. More... | |
unsigned long | regina::SFSpace::punctures (bool twisted) const |
Returns the number of punctures of the given type in the base orbifold. More... | |
unsigned long | regina::SFSpace::reflectors () const |
Returns the total number of reflector boundary components of the base orbifold. More... | |
unsigned long | regina::SFSpace::reflectors (bool twisted) const |
Returns the number of reflector boundary components of the given type in the base orbifold. More... | |
unsigned long | regina::SFSpace::fibreCount () const |
Returns the number of exceptional fibres in this Seifert fibred space. More... | |
SFSFibre | regina::SFSpace::fibre (unsigned long which) const |
Returns the requested exceptional fibre. More... | |
long | regina::SFSpace::obstruction () const |
Returns the obstruction constant b for this Seifert fibred space. More... | |
void | regina::SFSpace::addHandle (bool fibreReversing=false) |
Inserts a new handle into the base orbifold. More... | |
void | regina::SFSpace::addCrosscap (bool fibreReversing=false) |
Inserts a new crosscap into the base orbifold. More... | |
void | regina::SFSpace::addPuncture (bool twisted=false, unsigned long nPunctures=1) |
Inserts one or more new punctures into the base orbifold. More... | |
void | regina::SFSpace::addReflector (bool twisted=false, unsigned long nReflectors=1) |
Adds one or more new reflector boundary components to the base orbifold. More... | |
void | regina::SFSpace::insertFibre (const SFSFibre &fibre) |
Adds the given fibre to this Seifert fibred space. More... | |
void | regina::SFSpace::insertFibre (long alpha, long beta) |
Adds the given fibre to this Seifert fibred space. More... | |
void | regina::SFSpace::reflect () |
Replaces this space with its mirror image. More... | |
void | regina::SFSpace::complementAllFibres () |
Replaces each exceptional fibre of the form (alpha, beta) with a fibre of the form (alpha, alpha - beta). More... | |
void | regina::SFSpace::reduce (bool mayReflect=true) |
Reduces the parameters of this Seifert fibred space to a simpler form if possible, without changing the underlying fibration. More... | |
LensSpace * | regina::SFSpace::isLensSpace () const |
Determines if this Seifert fibred space is a Lens space. More... | |
bool | regina::SFSpace::operator== (const SFSpace &compare) const |
Determines whether this and the given structure contain precisely the same representations of precisely the same Seifert fibred spaces. More... | |
bool | regina::SFSpace::operator!= (const SFSpace &compare) const |
Determines whether this and the given structure do not contain precisely the same representations of precisely the same Seifert fibred spaces. More... | |
bool | regina::SFSpace::operator< (const SFSpace &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More... | |
Triangulation< 3 > * | regina::SFSpace::construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
AbelianGroup * | regina::SFSpace::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::SFSpace::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::SFSpace::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::SFSpace::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
std::ostream & | regina::SFSpace::writeStructure (std::ostream &out) const |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More... | |
regina::SFSAltSet::SFSAltSet (const SFSpace *sfs) | |
Creates a new set of alternatives for the given Seifert fibred space. More... | |
void | regina::SFSAltSet::deleteAll () |
Destroys all of the alternative representations in this set. More... | |
void | regina::SFSAltSet::deleteAll (SFSpace *exception) |
Destroys all of the alternative representations in this set, except for the given exception. More... | |
void | regina::SFSAltSet::deleteAll (SFSpace *exception1, SFSpace *exception2) |
Destroys all of the alternative representations in this set, except for the two given exceptions. More... | |
unsigned | regina::SFSAltSet::size () const |
Returns the number of alternative spaces in this set. More... | |
SFSpace * | regina::SFSAltSet::operator[] (unsigned which) const |
Returns the requested alternative space. More... | |
const Matrix2 & | regina::SFSAltSet::conversion (unsigned which) const |
Returns the conversion matrix for the requested alternative space. More... | |
bool | regina::SFSAltSet::reflected (unsigned which) const |
Returns whether or not a reflection was used when creating the requested alternative space. More... | |
regina::SimpleSurfaceBundle::SimpleSurfaceBundle (int newType) | |
Creates a new surface bundle of the given type. More... | |
regina::SimpleSurfaceBundle::SimpleSurfaceBundle (const SimpleSurfaceBundle &cloneMe) | |
Creates a clone of the given surface bundle. More... | |
int | regina::SimpleSurfaceBundle::type () const |
Returns the specific type of surface bundle being represented. More... | |
bool | regina::SimpleSurfaceBundle::operator== (const SimpleSurfaceBundle &compare) const |
Determines whether this and the given surface bundle represent the same 3-manifold. More... | |
bool | regina::SimpleSurfaceBundle::operator!= (const SimpleSurfaceBundle &compare) const |
Determines whether this and the given surface bundle represent different 3-manifolds. More... | |
virtual Triangulation< 3 > * | regina::SimpleSurfaceBundle::construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
AbelianGroup * | regina::SimpleSurfaceBundle::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::SimpleSurfaceBundle::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::SimpleSurfaceBundle::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::SimpleSurfaceBundle::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
regina::SnapPeaCensusManifold::SnapPeaCensusManifold (char newSection, unsigned long newIndex) | |
Creates a new SnapPea census manifold with the given parameters. More... | |
regina::SnapPeaCensusManifold::SnapPeaCensusManifold (const SnapPeaCensusManifold &cloneMe) | |
Creates a clone of the given SnapPea census manifold. More... | |
virtual | regina::SnapPeaCensusManifold::~SnapPeaCensusManifold () |
Destroys this structure. More... | |
char | regina::SnapPeaCensusManifold::section () const |
Returns the section of the SnapPea census to which this manifold belongs. More... | |
unsigned long | regina::SnapPeaCensusManifold::index () const |
Returns the index of this manifold within its particular section of the SnapPea census. More... | |
bool | regina::SnapPeaCensusManifold::operator== (const SnapPeaCensusManifold &compare) const |
Determines whether this and the given structure represent the same 3-manifold from the SnapPea census. More... | |
bool | regina::SnapPeaCensusManifold::operator!= (const SnapPeaCensusManifold &compare) const |
Determines whether this and the given structure represent different 3-manifolds from the SnapPea census. More... | |
Triangulation< 3 > * | regina::SnapPeaCensusManifold::construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
AbelianGroup * | regina::SnapPeaCensusManifold::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::SnapPeaCensusManifold::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::SnapPeaCensusManifold::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::SnapPeaCensusManifold::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
std::ostream & | regina::SnapPeaCensusManifold::writeStructure (std::ostream &out) const |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More... | |
regina::TorusBundle::TorusBundle () | |
Creates a new trivial torus bundle over the circle. More... | |
regina::TorusBundle::TorusBundle (const Matrix2 &newMonodromy) | |
Creates a new torus bundle over the circle using the given monodromy. More... | |
regina::TorusBundle::TorusBundle (long mon00, long mon01, long mon10, long mon11) | |
Creates a new torus bundle over the circle using the given monodromy. More... | |
regina::TorusBundle::TorusBundle (const TorusBundle &cloneMe) | |
Creates a clone of the given torus bundle. More... | |
const Matrix2 & | regina::TorusBundle::monodromy () const |
Returns the monodromy describing how the upper and lower torus boundaries are identified. More... | |
AbelianGroup * | regina::TorusBundle::homology () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | regina::TorusBundle::isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | regina::TorusBundle::writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | regina::TorusBundle::writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
Variables | |
long | regina::SFSFibre::alpha |
The first parameter of this (alpha, beta) fibre. More... | |
long | regina::SFSFibre::beta |
The second parameter of this (alpha, beta) fibre. More... | |
static const int | regina::SimpleSurfaceBundle::S2xS1 |
Represents the orientable 2-sphere bundle over the circle. More... | |
static const int | regina::SimpleSurfaceBundle::S2xS1_TWISTED |
Represents the non-orientable twisted 2-sphere bundle over the circle. More... | |
static const int | regina::SimpleSurfaceBundle::RP2xS1 |
Represents the projective plane bundle over the circle. More... | |
static const char | regina::SnapPeaCensusManifold::SEC_5 |
Represents the collection of manifolds formed from five or fewer tetrahedra (both orientable and non-orientable). More... | |
static const char | regina::SnapPeaCensusManifold::SEC_6_OR |
Represents the collection of orientable manifolds formed from six tetrahedra. More... | |
static const char | regina::SnapPeaCensusManifold::SEC_6_NOR |
Represents the collection of non-orientable manifolds formed from six tetrahedra. More... | |
static const char | regina::SnapPeaCensusManifold::SEC_7_OR |
Represents the collection of orientable manifolds formed from seven tetrahedra. More... | |
static const char | regina::SnapPeaCensusManifold::SEC_7_NOR |
Represents the collection of non-orientable manifolds formed from seven tetrahedra. More... | |
Standard 3-manifolds whose structures are well-understood.
typedef GraphLoop regina::NGraphLoop |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef GraphPair regina::NGraphPair |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef GraphTriple regina::NGraphTriple |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef Handlebody regina::NHandlebody |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef LensSpace regina::NLensSpace |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef Manifold regina::NManifold |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef SFSAltSet regina::NSFSAltSet |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef SFSFibre regina::NSFSFibre |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef SFSpace regina::NSFSpace |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
typedef TorusBundle regina::NTorusBundle |
Deprecated typedef for backward compatibility.
This typedef will be removed in a future release of Regina.
Lists the six classes o1
, o2
, n1
, n2
, n3
, n4
for base orbifolds without boundaries, plus five classes bo1
, b02
, bn1
, bn2
, bn3
for base orbifolds with boundaries.
void regina::SFSpace::addCrosscap | ( | bool | fibreReversing = false | ) |
Inserts a new crosscap into the base orbifold.
This makes the base orbifold non-orientable, and increases its non-orientable genus by one. It is equivalent to removing a disc from the base orbifold and replacing it with a Mobius band.
Note that this operation may alter which of the classes described by classType this space belongs to.
The exceptional fibres and the obstruction constant b are not modified by this routine.
fibreReversing | true if the generator of the new crosscap should give a fibre-reversing curve in the overall 3-manifold, or false (the default) if it should preserve the directions of the fibres. |
void regina::SFSpace::addHandle | ( | bool | fibreReversing = false | ) |
Inserts a new handle into the base orbifold.
This increases the orientable genus of the base orbifold by one, or the non-orientable genus by two. It is equivalent to removing a disc from the base orbifold and replacing it with a punctured torus.
Note that this operation may alter which of the classes described by classType this space belongs to.
The exceptional fibres and the obstruction constant b are not modified by this routine.
fibreReversing | true if one or both generators of the new handle should give fibre-reversing curves in the overall 3-manifold, or false (the default) if both generators should preserve the directions of the fibres. |
void regina::SFSpace::addPuncture | ( | bool | twisted = false , |
unsigned long | nPunctures = 1 |
||
) |
Inserts one or more new punctures into the base orbifold.
The punctures may be twisted or untwisted.
Each puncture insertion is equivalent to removing a disc from the base orbifold. In the untwisted case this results in a new torus boundary for the 3-manifold, and in the twisted case it results in a new Klein bottle boundary.
The exceptional fibres and the obstruction constant b are not modified by this routine.
twisted | true if the new punctures should be twisted (i.e., their boundaries should be fibre-reversing), or false if the new punctures should be untwisted. |
nPunctures | the number of new punctures to insert. |
void regina::SFSpace::addReflector | ( | bool | twisted = false , |
unsigned long | nReflectors = 1 |
||
) |
Adds one or more new reflector boundary components to the base orbifold.
The new reflector boundaries may be twisted or untwisted.
Each addition of a reflector boundary component is equivalent to removing a disc from the base orbifold and replacing it with an annulus with one reflector boundary.
In the untwisted case, it has the effect of removing a trivially fibred solid torus from the overall 3-manifold and replacing it with an appropriately fibred twisted I-bundle over the torus.
The exceptional fibres and the obstruction constant b are not modified by this routine.
twisted | true if the new reflector boundaries should be twisted (i.e., the boundaries should be fibre-reversing), or false if the new reflector boundaries should be untwisted. |
nReflectors | the number of new reflector boundaries to add. |
|
inline |
Returns which of the eleven predefined classes this space belongs to.
The specific class indicates whether the base orbifold has punctures and/or reflector boundaries, whether the base orbifold is orientable, and gives information on fibre-reversing paths.
The class can be (indirectly) modified by calling addHandle(), addCrosscap(), addPuncture() or addReflector().
For more information on the eleven predefined classes, see the SFSpace class notes or the classType enumeration notes.
|
inline |
Returns the genus of the base orbifold.
All punctures and reflector boundaries in the base orbifold are ignored (i.e., they are treated as though they had been replaced with ordinary filled discs).
The genus is the number of tori or projective planes that the base surface is formed from. In particular, if the base surface is non-orientable then this is the non-orientable genus.
|
inline |
Returns whether or not the base surface is orientable.
Reflector boundary components of the base orbifold are not considered here.
The orientability of the base surface can be (indirectly) modified by calling addCrosscap().
true
if and only if the base surface is orientable.
|
inline |
Returns a reference to the central space.
This is the Seifert fibred space with two boundary components, to which the two end spaces are joined. See the class notes for further discussion.
void regina::SFSpace::complementAllFibres | ( | ) |
Replaces each exceptional fibre of the form (alpha, beta) with a fibre of the form (alpha, alpha - beta).
The obstruction constant b is not touched.
|
inlinevirtual |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
Reimplemented in regina::SFSpace, regina::SnapPeaCensusManifold, regina::LensSpace, and regina::SimpleSurfaceBundle.
|
virtual |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
Reimplemented from regina::Manifold.
|
virtual |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
Reimplemented from regina::Manifold.
|
virtual |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
Reimplemented from regina::Manifold.
|
virtual |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
Reimplemented from regina::Manifold.
|
inline |
Returns the conversion matrix for the requested alternative space.
This matrix describes the fibre and base curves of the alternative space on the first boundary torus in terms of the fibre and base curves of the original space (which was passed to the SFSAltSet constructor). See the class notes above for details.
Note that this conversion matrix applies only to the first boundary torus! If there is more than one boundary, the remaining boundary conversions are simpler and depend only on whether a reflection has been used or not. See reflected() or the class notes for details.
which | indicates which of the alternatives we should return the conversion matrix for; this must be between 0 and size()-1 inclusive. |
void regina::SFSAltSet::deleteAll | ( | ) |
Destroys all of the alternative representations in this set.
This routine is for situations where none of the alternatives here are appropriate for keeping and using elsewhere.
void regina::SFSAltSet::deleteAll | ( | SFSpace * | exception | ) |
Destroys all of the alternative representations in this set, except for the given exception.
If the given exception is null or is not one of the alternatives in this set, every alternative will be destroyed.
This routine is for situations where one of the alternatives has been kept for later use, and the rest are to be discarded.
exception | the one alternative that should not be destroyed. |
Destroys all of the alternative representations in this set, except for the two given exceptions.
If either exception is null or is not one of the alternatives in this set, it will be ignored (and this routine will behave like the one-exception or no-exceptions variant). Likewise, if both exceptions are the same then this routine will behave like the one-exception variant.
This routine is for situations where one of the alternatives has been kept for later use, but due to other operations that may have taken place (such as space swapping) it is only known that the alternative we kept is one of two possibilities.
exception1 | the first alternative that should not be destroyed. |
exception2 | the second alternative that should not be destroyed. |
|
inline |
Returns a reference to one of the two end spaces.
These are the Seifert fibred spaces with just one boundary component, to be joined to the central space. See the class notes for further discussion.
which | 0 if the first end space is to be returned, or 1 if the second end space is to be returned. |
SFSFibre regina::SFSpace::fibre | ( | unsigned long | which | ) | const |
Returns the requested exceptional fibre.
Fibres are stored in sorted order by alpha (the index) and then by beta. See the SFSpace class notes for details.
which | determines which fibre to return; this must be between 0 and getFibreCount()-1 inclusive. |
|
inline |
Returns the number of exceptional fibres in this Seifert fibred space.
Note that the obstruction parameter b is not included in this count. That is, any (1,k) fibres are ignored.
|
inline |
Returns whether or not we can negate an exceptional fibre by passing it around the interior of the base orbifold.
That is, this routine determines whether a (p, q) exceptional fibre can become a (p, -q) exceptional fibre simply by sliding it around.
This is possible if either
Note that reflector boundary components, whilst making the overall 3-manifold non-orientable, have no bearing on the outcome of this routine.
true
if and only an exceptional fibre can be reflected as described above.
|
inline |
Returns whether or not this space contains any fibre-reversing paths.
true
if and only if a fibre-reversing path exists. Creates a new graph manifold as a self-identified Seifert fibred space.
The bounded Seifert fibred space and the entire 2-by-2 matching matrix are each passed separately.
Note that the new object will take ownership of the given Seifert fibred space, and when this object is destroyed the Seifert fibred space will be destroyed also.
sfs | the bounded Seifert fibred space. |
matchingReln | the 2-by-2 matching matrix. |
|
inline |
Creates a new graph manifold as a self-identified Seifert fibred space.
The bounded Seifert fibred space and the four elements of the 2-by-2 matching matrix are all passed separately. The elements of the matching matrix combine to give the full matrix M as follows:
[ mat00 mat01 ] M = [ ] [ mat10 mat11 ]
Note that the new object will take ownership of the given Seifert fibred space, and when this object is destroyed the Seifert fibred space will be destroyed also.
sfs | the bounded Seifert fibred space. |
mat00 | the (0,0) element of the matching matrix. |
mat01 | the (0,1) element of the matching matrix. |
mat10 | the (1,0) element of the matching matrix. |
mat11 | the (1,1) element of the matching matrix. |
|
inline |
Creates a new graph manifold as a pair of joined Seifert fibred spaces.
The two bounded Seifert fibred spaces and the entire 2-by-2 matching matrix are each passed separately.
Note that the new object will take ownership of the two given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.
sfs0 | the first Seifert fibred space. |
sfs1 | the second Seifert fibred space. |
matchingReln | the 2-by-2 matching matrix. |
|
inline |
Creates a new graph manifold as a pair of joined Seifert fibred spaces.
The two bounded Seifert fibred spaces and the four elements of the 2-by-2 matching matrix are all passed separately. The elements of the matching matrix combine to give the full matrix M as follows:
[ mat00 mat01 ] M = [ ] [ mat10 mat11 ]
Note that the new object will take ownership of the two given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.
sfs0 | the first Seifert fibred space. |
sfs1 | the second Seifert fibred space. |
mat00 | the (0,0) element of the matching matrix. |
mat01 | the (0,1) element of the matching matrix. |
mat10 | the (1,0) element of the matching matrix. |
mat11 | the (1,1) element of the matching matrix. |
|
inline |
Creates a new graph manifold from three bounded Seifert fibred spaces, as described in the class notes.
The three Seifert fibred spaces and both 2-by-2 matching matrices are passed separately.
Note that the new object will take ownership of the three given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.
end0 | the first end space, as described in the class notes. |
centre | the central space, as described in the class notes. |
end1 | the second end space, as described in the class notes. |
matchingReln0 | the 2-by-2 matching matrix that specifies how spaces end0 and centre are joined. |
matchingReln1 | the 2-by-2 matching matrix that specifies how spaces end1 and centre are joined. |
|
inline |
Creates a clone of the given handlebody.
cloneMe | the handlebody to clone. |
|
inline |
Creates a new handlebody with the given parameters.
newHandles | the number of handles of the handlebody. |
newOrientable | true if the handlebody is to be orientable or false if the handlebody is to be non-orientable. This must be true if the handlebody has no handles. |
|
inline |
Returns the number of handles of this handlebody.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
inlinevirtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::SFSpace, regina::GraphTriple, regina::GraphPair, regina::GraphLoop, regina::SnapPeaCensusManifold, regina::TorusBundle, regina::LensSpace, regina::SimpleSurfaceBundle, and regina::Handlebody.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
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::Manifold.
|
inline |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of Manifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
This routine can also be accessed via the alias homology() (a name that is less specific, but a little easier to type).
|
inline |
Returns the index of this manifold within its particular section of the SnapPea census.
Note that indices for each section begin counting at zero.
|
inline |
Adds the given fibre to this Seifert fibred space.
This may be an exceptional fibre (alpha > 1) or it may be a regular fibre (alpha = 1). If it is a regular fibre, the obstruction constant b will be adjusted according to the value of beta.
Note that there is no restriction on the range of the second parameter beta. If it is out of the usual range 0 <= beta < alpha, it will be pulled back into this range and the excess will be pushed into the obstruction constant b.
fibre | the fibre to insert. The first parameter of this fibre (i.e., its index) must be strictly positive, and the two parameters of this fibre must be coprime. |
void regina::SFSpace::insertFibre | ( | long | alpha, |
long | beta | ||
) |
Adds the given fibre to this Seifert fibred space.
This may be an exceptional fibre (alpha > 1) or it may be a regular fibre (alpha = 1). If it is a regular fibre, the obstruction constant b will be adjusted according to the value of beta.
Note that there is no restriction on the range of the second parameter beta. If it is out of the usual range 0 <= beta < alpha, it will be pulled back into this range and the excess will be pushed into the obstruction constant b.
alpha | the first parameter (i.e., the index) of the fibre to insert; this must be strictly positive. |
beta | the second parameter of the fibre to insert; this must have no common factors with the first parameter alpha. |
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inlinevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
pure virtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implemented in regina::SFSpace, regina::GraphTriple, regina::GraphPair, regina::GraphLoop, regina::SnapPeaCensusManifold, regina::TorusBundle, regina::LensSpace, regina::SimpleSurfaceBundle, and regina::Handlebody.
LensSpace* regina::SFSpace::isLensSpace | ( | ) | const |
Determines if this Seifert fibred space is a Lens space.
If this is a Lens space, the LensSpace returned will be newly created and it will be up to the caller of this routine to destroy it.
null
if this is not a Lens space.
|
inline |
Returns whether this handlebody is orientable.
true
if this handlebody is orientable, or false
if this handlebody is non-orientable.
|
inline |
Creates a clone of the given lens space.
cloneMe | the lens space to clone. |
|
inline |
Creates a new lens space with the given parameters.
See the class notes for details.
newP | the first parameter p of the lens space L(p,q). |
newQ | the second parameter q of the lens space L(p,q). Note that there are no range restrictions whatsoever on this parameter. |
|
inline |
Returns a reference to the 2-by-2 matrix describing how the two boundary tori of the Seifert fibred space are joined together.
See the class notes for details on precisely how this matrix is represented.
|
inline |
Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces are joined together.
See the class notes for details on precisely how this matrix is represented.
|
inline |
Returns a reference to the 2-by-2 matrix describing how the two requested bounded Seifert fibred spaces are joined together.
See the class notes for details on precisely how these matrices are represented.
The argument which indicates which particular join should be examined. A value of 0 denotes the join between the central space and the first end space (corresponding to matrix M in the class notes), whereas a value of 1 denotes the join between the central space and the second end space (corresponding to matrix M' in the class notes).
which | indicates which particular join should be examined; this should be 0 or 1 as described above. |
|
inline |
Returns the monodromy describing how the upper and lower torus boundaries are identified.
See the class notes for details.
std::string regina::Manifold::name | ( | ) | const |
Returns the common name of this 3-manifold as a human-readable string.
|
inline |
Returns the obstruction constant b for this Seifert fibred space.
The obstruction constant corresponds to the insertion of an additional (1,b) fibre. It can be modified by calling insertFibre() with a value of alpha = 1. It will also be modified whenever insertFibre() is called with beta out of range (beta < 0 or beta >= alpha), since each exceptional fibre must be stored in standard form (0 <= beta < alpha).
|
inline |
Determines whether this and the given handlebody represent different 3-manifolds.
compare | the handlebody with which this will be compared. |
true
if and only if this and the given handlebody are not homeomorphic.
|
inline |
Determines whether this and the given lens space are non-homeomorphic 3-manifolds.
Note that the manifolds may be homeomorphic even if they were initialised with different parameters.
compare | the lens space with which this will be compared. |
true
if and only if this and the given lens space are non-homeomorphic.
|
inline |
Determines if this and the given exceptional fibre are different.
This requires the fibres to have different values for alpha and/or to have different values for beta.
compare | the fibre with which this will be compared. |
true
if and only if this and the given fibre are different.
|
inline |
Determines whether this and the given structure do not contain precisely the same representations of precisely the same Seifert fibred spaces.
Note that this routine examines the particular representation of the Seifert fibred space. Different Seifert parameters that give the same 3-manifold will be regarded as different by this routine.
compare | the representation with which this will be compared. |
true
if and only if this and the given Seifert fibred space representations are different.
|
inline |
Determines whether this and the given surface bundle represent different 3-manifolds.
compare | the surface bundle with which this will be compared. |
true
if and only if this and the given surface bundle are non-homeomorphic.
|
inline |
Determines whether this and the given structure represent different 3-manifolds from the SnapPea census.
As of Regina 5.0, this test respects the recent discovery that the manifolds x101
and x103
are homeomorphic. For details, see B.B., A duplicate pair in the SnapPea census, Experimental Mathematics, 23:170-173, 2014.
compare | the structure with which this will be compared. |
true
if and only if this and the given structure represent different SnapPea census manifolds. bool regina::GraphLoop::operator< | ( | const GraphLoop & | compare | ) | const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space.
The ordering imposed on graph manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.
All that this routine really offers is a well-defined way of ordering graph manifold representations.
compare | the representation with which this will be compared. |
true
if and only if this is "smaller" than the given graph manifold representation. bool regina::GraphPair::operator< | ( | const GraphPair & | compare | ) | const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space.
The ordering imposed on graph manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.
All that this routine really offers is a well-defined way of ordering graph manifold representations.
compare | the representation with which this will be compared. |
true
if and only if this is "smaller" than the given graph manifold representation. bool regina::GraphTriple::operator< | ( | const GraphTriple & | compare | ) | const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space.
The ordering imposed on graph manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.
All that this routine really offers is a well-defined way of ordering graph manifold representations.
compare | the representation with which this will be compared. |
true
if and only if this is "smaller" than the given graph manifold representation. bool regina::Manifold::operator< | ( | const Manifold & | compare | ) | const |
Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold.
The ordering imposed on 3-manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.
The ordering also depends on the particular representation of the 3-manifold that is used. As an example, different representations of the same Seifert fibred space might well be ordered differently.
All that this routine really offers is a well-defined way of ordering 3-manifold representations.
compare | the 3-manifold representation with which this will be compared. |
true
if and only if this is "smaller" than the given 3-manifold representation.
|
inline |
Determines if this exceptional fibre is smaller than the given fibre.
Fibres are sorted by alpha and then by beta.
compare | the fibre with which this will be compared. |
true
if and only if this is smaller than the given fibre. bool regina::SFSpace::operator< | ( | const SFSpace & | compare | ) | const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space.
The ordering imposed on Seifert fibred space representations is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.
All that this routine really offers is a well-defined way of ordering Seifert fibred space representations.
compare | the representation with which this will be compared. |
true
if and only if this is "smaller" than the given Seifert fibred space representation. std::ostream& regina::operator<< | ( | std::ostream & | out, |
const SFSFibre & | f | ||
) |
Writes the given fibre in human-readable format to the given output stream.
The fibre will be written in the format (alpha,beta)
with no newline appended.
out | the output stream to which to write. |
f | the fibre to write. |
|
inline |
Makes this exceptional fibre a clone of the given fibre.
cloneMe | the exceptional fibre to clone. |
void regina::SFSpace::operator= | ( | const SFSpace & | cloneMe | ) |
Modifies this Seifert fibred space to be a clone of the given space.
cloneMe | the Seifert fibred space to clone. |
|
inline |
Determines whether this and the given handlebody represent the same 3-manifold.
compare | the handlebody with which this will be compared. |
true
if and only if this and the given handlebody are homeomorphic.
|
inline |
Determines whether this and the given lens space are homeomorphic 3-manifolds.
Note that this may be true even if they were initialised with different parameters.
compare | the lens space with which this will be compared. |
true
if and only if this and the given lens space are homeomorphic.
|
inline |
Determines if this and the given exceptional fibre are identical.
This requires both fibres to have the same values for alpha and the same values for beta.
compare | the fibre with which this will be compared. |
true
if and only if this and the given fibre are identical. bool regina::SFSpace::operator== | ( | const SFSpace & | compare | ) | const |
Determines whether this and the given structure contain precisely the same representations of precisely the same Seifert fibred spaces.
Note that this routine examines the particular representation of the Seifert fibred space. Different Seifert parameters that give the same 3-manifold will be regarded as not equal by this routine.
compare | the representation with which this will be compared. |
true
if and only if this and the given Seifert fibred space representations are identical.
|
inline |
Determines whether this and the given surface bundle represent the same 3-manifold.
compare | the surface bundle with which this will be compared. |
true
if and only if this and the given surface bundle are homeomorphic.
|
inline |
Determines whether this and the given structure represent the same 3-manifold from the SnapPea census.
As of Regina 5.0, this test respects the recent discovery that the manifolds x101
and x103
are homeomorphic. For details, see B.B., A duplicate pair in the SnapPea census, Experimental Mathematics, 23:170-173, 2014.
compare | the structure with which this will be compared. |
true
if and only if this and the given structure represent the same SnapPea census manifold.
|
inline |
|
inline |
Returns the first parameter p of this lens space L(p,q).
See the class notes for details.
|
inline |
Returns the total number of punctures in the base orbifold.
In other words, this routine returns the total number of real torus or Klein bottle boundary components in the overall 3-manifold.
Note that reflector boundaries on the base orbifold are not counted here; only the ordinary boundary components that give rise to real 3-manifold boundaries are included.
Both untwisted and twisted punctures (giving rise to torus and Klein bottle boundaries respectively in the 3-manifold) are counted by this routine.
|
inline |
Returns the number of punctures of the given type in the base orbifold.
In other words, this routine returns the number of real boundary components of the given type in the overall 3-manifold.
This routine either counts only twisted punctures (which give rise to Klein bottle boundaries), or only untwisted punctures (which give rise to torus boundaries).
Either way, reflector boundaries on the base orbifold are not counted here; only ordinary boundary components that give rise to real 3-manifold boundaries are considered.
twisted | true if only twisted punctures should be counted (those that give fibre-reversing paths and Klein bottle boundaries), or false if only untwisted punctures should be counted (those that are fibre-preserving and give torus boundaries). |
|
inline |
Returns the second parameter q of this lens space L(p,q).
See the class notes for details.
The value of q returned will be the smallest q between 0 and p-1 inclusive that produces the same 3-manifold as this lens space. This means it might not be the value of q that was used to initialise this lens space.
void regina::SFSpace::reduce | ( | bool | mayReflect = true | ) |
Reduces the parameters of this Seifert fibred space to a simpler form if possible, without changing the underlying fibration.
In some cases the parameters of the Seifert fibred space may be simplified by taking a mirror image of the entire 3-manifold. The argument mayReflect signifies whether this is allowed.
This routine will not change the curves made by the fibres and the base orbifold on any boundary components (i.e., boundaries caused by punctures in the base orbifold).
true
then the entire 3-manifold might be replaced with its mirror image, in which case any subsequent modifications (such as inserting additional fibres or altering the base orbifold) may give unexpected results.mayReflect | true if we are allowed to take a mirror image of the entire 3-manifold, or false if we are not. |
|
inline |
Replaces this space with its mirror image.
Specifically, all exceptional fibres and the obstruction constant b will be negated. Note that the obstruction constant will generally undergo further change as the exceptional fibres are standardised into the usual 0 <= beta < alpha form.
This routine will not change the curves made by the fibres and the base orbifold on any boundary components (i.e., boundaries caused by punctures in the base orbifold), with the exception that each base curve will be reflected.
|
inline |
Returns whether or not a reflection was used when creating the requested alternative space.
This determines the conversion between boundary curves for all boundary tori after the first.
More specifically, if no reflection was used then the directed fibre and base curves are identical for the original and alternative spaces. If a reflection was used, then the directed fibres are identical but the directed base curves are reversed.
The conversion between curves on the first boundary torus is generally more complex, and is returned as a matrix by the conversion() routine.
which | indicates which of the alternatives is being queried; this must be between 0 and size()-1 inclusive. |
true
if a reflection was used in creating the requested alternative space, or false
if no reflection was used.
|
inline |
Returns the total number of reflector boundary components of the base orbifold.
This includes both twisted and untwisted reflector boundaries.
|
inline |
Returns the number of reflector boundary components of the given type in the base orbifold.
This either counts only twisted reflector boundaries, or only untwisted reflector boundaries.
twisted | true if only twisted reflector boundaries should be counted (those that give fibre-reversing paths), or false if only untwisted reflector boundaries should be counted. |
|
inline |
Returns the section of the SnapPea census to which this manifold belongs.
This will be one of the section constants defined in this class.
|
inline |
Returns a reference to the bounded Seifert fibred space that is joined to itself.
|
inline |
Returns a reference to one of the two bounded Seifert fibred spaces that are joined together.
which | 0 if the first Seifert fibred space is to be returned, or 1 if the second space is to be returned. |
regina::SFSAltSet::SFSAltSet | ( | const SFSpace * | sfs | ) |
Creates a new set of alternatives for the given Seifert fibred space.
Note that in general, none of the alternatives will have a representation identical to the given space (generally these alternative representations will be simpler if possible).
sfs | the original Seifert fibred space for which we are creating a set of alternative representations. |
|
inline |
Creates a new uninitialised exceptional fibre.
|
inline |
Creates a new exceptional fibre that is a clone of the given fibre.
cloneMe | the exceptional fibre to clone. |
|
inline |
Creates a new exceptional fibre with the given parameters.
newAlpha | the first parameter (the index) of this exceptional fibre; this must be strictly positive. |
newBeta | the second parameter of this exceptional fibre; this must have no common factors with the first parameter newAlpha. |
|
inline |
Creates a new Seifert fibred space with base orbifold the 2-sphere and no exceptional fibres.
|
inline |
Creates a new Seifert fibred space of the given class with the given base orbifold and no exceptional fibres.
o1
, o2
, n1
, n2
, n3
or n4
. Likewise, if there are punctures and/or reflector boundary components, then useClass is one of the five classes bo1
, bo2
, bn1
, bn2
or bn3
. bo2
or bn3
.useClass | indicates whether the base orbifold is closed and/or orientable, and gives information about fibre-reversing paths in the 3-manifold. See the SFSpace class notes and the classType enumeration notes for details. |
genus | the genus of the base orbifold (the number of tori or projective planes that it contains). Note that for non-orientable base surfaces, this is the non-orientable genus. |
punctures | the number of untwisted ordinary boundary components of the base orbifold. Here "ordinary" means that the puncture gives rise to a real 3-manifold boundary (i.e., this is not a reflector boundary of the base orbifold). |
puncturesTwisted | the number of twisted ordinary boundary components of the base orbifold. Here "ordinary" means that the puncture gives rise to a real 3-manifold boundary (i.e., this is not a reflector boundary of the base orbifold). |
reflectors | the number of untwisted reflector boundary components of the base orbifold. These are in addition to the ordinary boundary components described by punctures. |
reflectorsTwisted | the number of twisted reflector boundary components of the base orbifold. These are in addition to the ordinary boundary components described by puncturesTwisted. |
|
inline |
Creates a new Seifert fibred space that is a clone of the given space.
cloneMe | the Seifert fibred space to clone. |
|
inline |
Creates a clone of the given surface bundle.
cloneMe | the surface bundle to clone. |
|
inline |
Creates a new surface bundle of the given type.
newType | the specific type of surface bundle to represent. This must be one of the 3-manifold constants defined in this class. |
|
inline |
Returns the number of alternative spaces in this set.
|
inline |
Creates a new SnapPea census manifold with the given parameters.
newSection | the section of the SnapPea census to which this manifold belongs. This must be one of the section constants defined in this class. |
newIndex | specifies which particular manifold within the given section is represented. The indices for each section begin counting at zero, and so this index must be between 0 and k-1, where k is the total number of manifolds in the given section. |
|
inline |
Creates a clone of the given SnapPea census manifold.
cloneMe | the census manifold to clone. |
std::string regina::Manifold::structure | ( | ) | const |
Returns details of the structure of this 3-manifold that might not be evident from its common name.
For instance, for an orbit space S^3/G this routine might return the full Seifert structure.
This routine may return the empty string if no additional details are deemed necessary.
std::string regina::Manifold::TeXName | ( | ) | const |
Returns the common name of this 3-manifold in TeX format.
No leading or trailing dollar signs will be included.
|
inline |
Creates a new trivial torus bundle over the circle.
In other words, this routine creates a torus bundle with the identity monodromy.
|
inline |
Creates a new torus bundle over the circle using the given monodromy.
newMonodromy | describes precisely how the upper and lower torus boundaries are identified. See the class notes for details. |
|
inline |
Creates a clone of the given torus bundle.
cloneMe | the torus bundle to clone. |
|
inline |
Creates a new torus bundle over the circle using the given monodromy.
The four elements of the monodromy matrix are passed separately. They combine to give the full monodromy matrix M as follows:
[ mon00 mon01 ] M = [ ] [ mon10 mon11 ]
mon00 | the (0,0) element of the monodromy matrix. |
mon01 | the (0,1) element of the monodromy matrix. |
mon10 | the (1,0) element of the monodromy matrix. |
mon11 | the (1,1) element of the monodromy matrix. |
|
inline |
Returns the specific type of surface bundle being represented.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
inlinevirtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
pure virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implemented in regina::SFSpace, regina::GraphTriple, regina::GraphPair, regina::GraphLoop, regina::SnapPeaCensusManifold, regina::TorusBundle, regina::LensSpace, regina::SimpleSurfaceBundle, and regina::Handlebody.
|
virtual |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.
For instance, for an orbit space S^3/G this routine might write the full Seifert structure.
This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.
None
.out | the output stream to which to write. |
Reimplemented from regina::Manifold.
|
inlinevirtual |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.
For instance, for an orbit space S^3/G this routine might write the full Seifert structure.
This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.
None
.out | the output stream to which to write. |
Reimplemented in regina::SFSpace, and regina::SnapPeaCensusManifold.
|
inlinevirtual |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.
For instance, for an orbit space S^3/G this routine might write the full Seifert structure.
This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.
None
.out | the output stream to which to write. |
Reimplemented from regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
inlinevirtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
pure virtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out | the output stream to which to write. |
Implemented in regina::SFSpace, regina::GraphTriple, regina::GraphPair, regina::GraphLoop, regina::SnapPeaCensusManifold, regina::TorusBundle, regina::LensSpace, regina::SimpleSurfaceBundle, and regina::Handlebody.
|
inline |
Writes a detailed text representation of this object to the given output stream.
Subclasses must not override this routine. They should override writeName() and writeStructure() instead.
out | the output stream to which to write. |
|
inline |
Writes a short text representation of this object to the given output stream.
Subclasses must not override this routine. They should override writeName() instead.
out | the output stream to which to write. |
regina::GraphLoop::~GraphLoop | ( | ) |
Destroys this structure along with the bounded Seifert fibred space and the matching matrix.
regina::GraphPair::~GraphPair | ( | ) |
Destroys this structure along with the component Seifert fibred spaces and the matching matrix.
regina::GraphTriple::~GraphTriple | ( | ) |
Destroys this structure along with the component Seifert fibred spaces and matching matrices.
|
inlinevirtual |
Destroys this handlebody.
|
inlinevirtual |
Destroys this lens space.
|
inlinevirtual |
A destructor that does nothing.
|
inlinevirtual |
Destroys this Seifert fibred space.
|
inlinevirtual |
Destroys this structure.
long regina::SFSFibre::alpha |
The first parameter of this (alpha, beta) fibre.
Note that this is the index of the exceptional fibre. This parameter must always be strictly positive.
long regina::SFSFibre::beta |
The second parameter of this (alpha, beta) fibre.
This parameter must have no common factors with alpha.
|
static |
Represents the projective plane bundle over the circle.
|
static |
Represents the orientable 2-sphere bundle over the circle.
|
static |
Represents the non-orientable twisted 2-sphere bundle over the circle.
|
static |
Represents the collection of manifolds formed from five or fewer tetrahedra (both orientable and non-orientable).
There are 415 manifolds in this section.
|
static |
Represents the collection of non-orientable manifolds formed from six tetrahedra.
There are 259 manifolds in this section.
|
static |
Represents the collection of orientable manifolds formed from six tetrahedra.
There are 962 manifolds in this section.
|
static |
Represents the collection of non-orientable manifolds formed from seven tetrahedra.
There are 887 manifolds in this section.
|
static |
Represents the collection of orientable manifolds formed from seven tetrahedra.
There are 3552 manifolds in this section.