Represents a general lens space. More...

#include <manifold/lensspace.h>

Inheritance diagram for regina::LensSpace:

Public Member Functions
	LensSpace (unsigned long p, unsigned long q)
	Creates a new lens space with the given parameters. More...

	LensSpace (const LensSpace &)=default
	Creates a new copy of the given lens space. More...

unsigned long	p () const
	Returns the first parameter p of this lens space L(p,q). More...

unsigned long	q () const
	Returns the second parameter q of this lens space L(p,q). More...

bool	operator== (const LensSpace &compare) const
	Determines whether this and the given lens space have the same presentation. More...

bool	operator!= (const LensSpace &compare) const
	Determines whether this and the given lens space have different presentations. More...

LensSpace &	operator= (const LensSpace &)=default
	Sets this to be a copy of the given lens space. More...

void	swap (LensSpace &other) noexcept
	Swaps the contents of this and the given lens space. 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::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...

virtual std::ostream &	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	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...

Detailed Description

Represents a general lens space.

The lens space L(p,q) is the 3-manifold you get by p/q Dehn surgery on the unknot. For instance, L(1,0) and L(1,1) are the 3-sphere, L(0,1) is the product S¹ x S², and L(p,1) is the circle bundle over S² with Euler class p. In L(p,q) if you take a generator g of H_1 and evaluate the torsion linking form on it, then <g,g> = [± r² q/p] in Q/Z where r is an integer.

All 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

◆ LensSpace() [1/2]

regina::LensSpace::LensSpace	(	unsigned long	p,
		unsigned long	q
	)

inline

Creates a new lens space with the given parameters.

See the class notes for details.

Precondition: The two given parameters are coprime (have a gcd of 1).

Parameters

p	the first parameter p of the lens space L(p,q).
q	the second parameter q of the lens space L(p,q). Note that there are no range restrictions whatsoever on this parameter.

◆ LensSpace() [2/2]

regina::LensSpace::LensSpace ( const LensSpace & )

default

Creates a new copy of the given lens space.

Member Function Documentation

◆ construct()

Triangulation< 3 > regina::LensSpace::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::LensSpace::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.

◆ isHyperbolic()

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

inline

Determines whether this and the given lens space have different presentations.

Since the presentation is made canonical by the class constructor, this routine also identifies whether this and the given lens space are homeomorphic as 3-manifolds. This is in contrast to the comparison operators for other manifold classes (such as Seifert fibred spaces and graph manifolds), where the same manifold could have different presentations that compare as not equal.

Parameters

compare the lens space with which this should be compared.

Returns: true if and only if this and the given lens space have different presentations (i.e., are non-homeomorphic).

◆ 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=()

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

default

Sets this to be a copy of the given lens space.

Returns: a reference to this lens space.

◆ operator==()

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

inline

Determines whether this and the given lens space have the same presentation.

Since the presentation is made canonical by the class constructor, this routine also identifies whether this and the given lens space are homeomorphic as 3-manifolds. This is in contrast to the comparison operators for other manifold classes (such as Seifert fibred spaces and graph manifolds), where the same manifold could have different presentations that compare as not equal.

Parameters

compare the lens space with which this should be compared.

Returns: true if and only if this and the given lens space have the same presentation (i.e., are homeomorphic).

◆ p()

unsigned long regina::LensSpace::p ( ) const

inline

Returns the first parameter p of this lens space L(p,q).

See the class notes for details.

Returns: the first parameter.

◆ q()

unsigned long regina::LensSpace::q ( ) const

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.

◆ 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::LensSpace::swap ( LensSpace & other )

inlinenoexcept

Swaps the contents of this and the given lens space.

Parameters

other the lens space 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::LensSpace::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::Manifold::writeStructure ( std::ostream & out ) const

inlinevirtualinherited

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 in regina::SFSpace, and regina::SnapPeaCensusManifold.

◆ writeTeXName()

std::ostream & regina::LensSpace::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.

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

manifold/lensspace.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LensSpace() [1/2]

◆ LensSpace() [2/2]

Member Function Documentation

◆ construct()

◆ detail()

◆ homology()

◆ isHyperbolic()

◆ name()

◆ operator!=()

◆ operator<()

◆ operator=()

◆ operator==()

◆ p()

◆ q()

◆ str()

◆ structure()

◆ swap()

◆ texName()

◆ utf8()

◆ writeName()

◆ writeStructure()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()