Represents a 3-manifold from the SnapPea cusped census. More...

#include <manifold/snappeacensusmfd.h>

Inheritance diagram for regina::SnapPeaCensusManifold:

Public Member Functions
	SnapPeaCensusManifold (char section, unsigned long index)
	Creates a new SnapPea census manifold with the given parameters. More...

	SnapPeaCensusManifold (const SnapPeaCensusManifold &)=default
	Creates a new copy of the given SnapPea census manifold. More...

char	section () const
	Returns the section of the SnapPea census to which this manifold belongs. More...

unsigned long	index () const
	Returns the index of this manifold within its particular section of the SnapPea census. More...

bool	operator== (const SnapPeaCensusManifold &compare) const
	Determines whether this and the given structure represent the same 3-manifold from the SnapPea census. More...

bool	operator!= (const SnapPeaCensusManifold &compare) const
	Determines whether this and the given structure represent different 3-manifolds from the SnapPea census. More...

SnapPeaCensusManifold &	operator= (const SnapPeaCensusManifold &)=default
	Sets this to be a copy of the given SnapPea census manifold. More...

void	swap (SnapPeaCensusManifold &other) noexcept
	Swaps the contents of this and the given SnapPea census manifold. More...

Triangulation< 3 >	construct () const override
	Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...

AbelianGroup	homology () const override
	Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...

bool	isHyperbolic () const override
	Returns whether or not this is a finite-volume hyperbolic manifold. More...

std::ostream &	writeName (std::ostream &out) const override
	Writes the common name of this 3-manifold as a human-readable string to the given output stream. More...

std::ostream &	writeTeXName (std::ostream &out) const override
	Writes the common name of this 3-manifold in TeX format to the given output stream. More...

std::ostream &	writeStructure (std::ostream &out) const override
	Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More...

std::string	name () const
	Returns the common name of this 3-manifold as a human-readable string. More...

std::string	texName () const
	Returns the common name of this 3-manifold in TeX format. More...

std::string	structure () const
	Returns details of the structure of this 3-manifold that might not be evident from its common name. More...

bool	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...

void	writeTextShort (std::ostream &out) const
	Writes a short text representation of this object to the given output stream. More...

void	writeTextLong (std::ostream &out) const
	Writes a detailed text representation of this object to the given output stream. More...

std::string	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 Attributes
static constexpr char	SEC_5 = 'm'
	Represents the collection of manifolds formed from five or fewer tetrahedra (both orientable and non-orientable). More...

static constexpr char	SEC_6_OR = 's'
	Represents the collection of orientable manifolds formed from six tetrahedra. More...

static constexpr char	SEC_6_NOR = 'x'
	Represents the collection of non-orientable manifolds formed from six tetrahedra. More...

static constexpr char	SEC_7_OR = 'v'
	Represents the collection of orientable manifolds formed from seven tetrahedra. More...

static constexpr char	SEC_7_NOR = 'y'
	Represents the collection of non-orientable manifolds formed from seven tetrahedra. More...

Detailed Description

Represents a 3-manifold from the SnapPea cusped census.

The SnapPea cusped census is the census of cusped hyperbolic 3-manifolds formed from up to seven tetrahedra. This census was tabulated by Callahan, Hildebrand and Weeks, and is shipped with SnapPea 3.0d3 (and also with Regina).

Note: The modern cusped hyperbolic census now extends to nine tetrahedra, and indeed the 9-tetrahedron database is accessible through the Census lookup routines. However, for the time being, the scope of these SnapPeaCensusManifold and SnapPeaCensusTri classes is restricted to the original Callahan-Hildebrand-Weeks 7-tetrahedron census only.

The census is split into five different sections according to number of tetrahedra and orientability. Each of these sections corresponds to one of the section constants defined in this class.

For further details regarding the SnapPea census, see "A census of cusped hyperbolic 3-manifolds", Patrick J. Callahan, Martin V. Hildebrand and Jeffrey R. Weeks, Math. Comp. 68 (1999), no. 225, pp. 321–332.

Note that this class is closely tied to SnapPeaCensusTri. In particular, the section constants defined in SnapPeaCensusTri and SnapPeaCensusManifold are identical, and so may be freely mixed. Furthermore, the section and index parameters of a SnapPeaCensusTri are identical to those of its corresponding SnapPeaCensusManifold.

All of the optional Manifold routines are implemented for this class.

This class supports copying but does not implement separate move operations, since its internal data is so small that copying is just as efficient. It implements the C++ Swappable requirement via its own member and global swap() functions, for consistency with the other manifold classes.

Constructor & Destructor Documentation

◆ SnapPeaCensusManifold() [1/2]

regina::SnapPeaCensusManifold::SnapPeaCensusManifold	(	char	section,
		unsigned long	index
	)

inline

Creates a new SnapPea census manifold with the given parameters.

Parameters

section	the section of the SnapPea census to which this manifold belongs. This must be one of the section constants defined in this class.
index	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.

◆ SnapPeaCensusManifold() [2/2]

regina::SnapPeaCensusManifold::SnapPeaCensusManifold ( const SnapPeaCensusManifold & )

default

Creates a new copy of the given SnapPea census manifold.

Member Function Documentation

◆ construct()

Triangulation< 3 > regina::SnapPeaCensusManifold::construct ( ) const

overridevirtual

Returns a triangulation of this 3-manifold, if such a construction has been implemented.

For details of which types of 3-manifolds have implemented this routine, see the class notes for each corresponding subclasses of Manifold.

The default implemention of this routine just throws a NotImplemented exception.

Exceptions

NotImplemented	Explicit construction has not yet been implemented for this particular 3-manifold.
FileError	The construction needs to be read from file (as opposed to computed on the fly), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its triangulations from the SnapPea census databases that are installed with Regina.

Returns: a triangulation of this 3-manifold, if this construction has been implemented.

Reimplemented from regina::Manifold.

◆ detail()

std::string regina::Output< Manifold , false >::detail ( ) const

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.

Returns: a detailed text representation of this object.

◆ homology()

AbelianGroup regina::SnapPeaCensusManifold::homology ( ) const

overridevirtual

Returns the first homology group of this 3-manifold, if such a routine has been implemented.

For details of which types of 3-manifolds have implemented this routine, see the class notes for each corresponding subclasses of Manifold.

The default implemention of this routine just throws a NotImplemented exception.

Exceptions

NotImplemented	Homology calculation has not yet been implemented for this particular 3-manifold.
FileError	The homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its results from the SnapPea census databases that are installed with Regina.

Returns: the first homology group of this 3-manifold, if this functionality has been implemented.

Reimplemented from regina::Manifold.

◆ index()

unsigned long regina::SnapPeaCensusManifold::index ( ) const

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.

Returns: the index of this manifold within its section.

◆ isHyperbolic()

bool regina::SnapPeaCensusManifold::isHyperbolic ( ) const

inlineoverridevirtual

Returns whether or not this is a finite-volume hyperbolic manifold.

Returns: true if this is a finite-volume hyperbolic manifold, or false if not.

Implements regina::Manifold.

◆ name()

std::string regina::Manifold::name ( ) const

inherited

Returns the common name of this 3-manifold as a human-readable string.

Returns: the common name of this 3-manifold.

◆ operator!=()

bool regina::SnapPeaCensusManifold::operator!= ( const SnapPeaCensusManifold & compare ) const

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.

Parameters

compare the structure with which this will be compared.

Returns: true if and only if this and the given structure represent different SnapPea census manifolds.

◆ operator<()

bool regina::Manifold::operator< ( const Manifold & compare ) const

inherited

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.

Warning: Currently this routine is only implemented in full for closed 3-manifolds. For most classes of bounded 3-manifolds, this routine simply compares the strings returned by name().

Parameters

compare the 3-manifold representation with which this will be compared.

Returns: true if and only if this is "smaller" than the given 3-manifold representation.

◆ operator=()

SnapPeaCensusManifold & regina::SnapPeaCensusManifold::operator= ( const SnapPeaCensusManifold & )

default

Sets this to be a copy of the given SnapPea census manifold.

Returns: a reference to this SnapPea census manifold.

◆ operator==()

bool regina::SnapPeaCensusManifold::operator== ( const SnapPeaCensusManifold & compare ) const

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.

Parameters

compare the structure with which this will be compared.

Returns: true if and only if this and the given structure represent the same SnapPea census manifold.

◆ section()

char regina::SnapPeaCensusManifold::section ( ) const

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.

Returns: the section of the SnapPea census.

◆ str()

std::string regina::Output< Manifold , false >::str ( ) const

inherited

Returns a short text representation of this object.

This text should be human-readable, should use plain ASCII characters where possible, and should not contain any newlines.

Within these limits, this short text ouptut should be as information-rich as possible, since in most cases this forms the basis for the Python __str__() and __repr__() functions.

Python: The Python "stringification" function __str__() will use precisely this function, and for most classes the Python __repr__() function will incorporate this into its output.

Returns: a short text representation of this object.

◆ structure()

std::string regina::Manifold::structure ( ) const

inherited

Returns details of the structure of this 3-manifold that might not be evident from its common name.

For instance, for an orbit space S³/G this routine might return the full Seifert structure.

This routine may return the empty string if no additional details are deemed necessary.

Returns: a string describing additional structural details.

◆ swap()

void regina::SnapPeaCensusManifold::swap ( SnapPeaCensusManifold & other )

inlinenoexcept

Swaps the contents of this and the given SnapPea census manifold.

Parameters

other the census manifold whose contents should be swapped with this.

◆ texName()

std::string regina::Manifold::texName ( ) const

inherited

Returns the common name of this 3-manifold in TeX format.

No leading or trailing dollar signs will be included.

Warning: The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.

Returns: the common name of this 3-manifold in TeX format.

◆ utf8()

std::string regina::Output< Manifold , false >::utf8 ( ) const

inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should not contain any newlines, and (within these constraints) should be as information-rich as is reasonable.

Unlike str(), this function may use unicode characters to make the output more pleasant to read. The string that is returned will be encoded in UTF-8.

Returns: a short text representation of this object.

◆ writeName()

std::ostream & regina::SnapPeaCensusManifold::writeName ( std::ostream & out ) const

overridevirtual

Writes the common name of this 3-manifold as a human-readable string to the given output stream.

Python: Not present. Instead use the variant name() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::Manifold.

◆ writeStructure()

std::ostream & regina::SnapPeaCensusManifold::writeStructure ( std::ostream & out ) const

overridevirtual

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 S³/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.

Python: Not present. Instead use the variant structure() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Reimplemented from regina::Manifold.

◆ writeTeXName()

std::ostream & regina::SnapPeaCensusManifold::writeTeXName ( std::ostream & out ) const

overridevirtual

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.

Warning: The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.

Python: Not present. Instead use the variant texName() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::Manifold.

◆ writeTextLong()

void regina::Manifold::writeTextLong ( std::ostream & out ) const

inlineinherited

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.

Python: Not present. Use detail() instead.

Parameters

out	the output stream to which to write.

◆ writeTextShort()

void regina::Manifold::writeTextShort ( std::ostream & out ) const

inlineinherited

Writes a short text representation of this object to the given output stream.

Subclasses must not override this routine. They should override writeName() instead.

Python: Not present. Use str() instead.

Parameters

out	the output stream to which to write.

Member Data Documentation

◆ SEC_5

constexpr char regina::SnapPeaCensusManifold::SEC_5 = 'm'

staticconstexpr

Represents the collection of manifolds formed from five or fewer tetrahedra (both orientable and non-orientable).

There are 415 manifolds in this section.

◆ SEC_6_NOR

constexpr char regina::SnapPeaCensusManifold::SEC_6_NOR = 'x'

staticconstexpr

Represents the collection of non-orientable manifolds formed from six tetrahedra.

There are 259 manifolds in this section.

◆ SEC_6_OR

constexpr char regina::SnapPeaCensusManifold::SEC_6_OR = 's'

staticconstexpr

Represents the collection of orientable manifolds formed from six tetrahedra.

There are 962 manifolds in this section.

◆ SEC_7_NOR

constexpr char regina::SnapPeaCensusManifold::SEC_7_NOR = 'y'

staticconstexpr

Represents the collection of non-orientable manifolds formed from seven tetrahedra.

There are 887 manifolds in this section.

◆ SEC_7_OR

constexpr char regina::SnapPeaCensusManifold::SEC_7_OR = 'v'

staticconstexpr

Represents the collection of orientable manifolds formed from seven tetrahedra.

There are 3552 manifolds in this section.

The documentation for this class was generated from the following file:

manifold/snappeacensusmfd.h

Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SnapPeaCensusManifold() [1/2]

◆ SnapPeaCensusManifold() [2/2]

Member Function Documentation

◆ construct()

◆ detail()

◆ homology()

◆ index()

◆ isHyperbolic()

◆ name()

◆ operator!=()

◆ operator<()

◆ operator=()

◆ operator==()

◆ section()

◆ str()

◆ structure()

◆ swap()

◆ texName()

◆ utf8()

◆ writeName()

◆ writeStructure()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()

Member Data Documentation

◆ SEC_5

◆ SEC_6_NOR

◆ SEC_6_OR

◆ SEC_7_NOR

◆ SEC_7_OR