Regina Calculation Engine
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regina::NLensSpace Class Reference

Represents a general lens space. More...

#include <manifold/nlensspace.h>

Inheritance diagram for regina::NLensSpace:
regina::NManifold regina::Output< NManifold >

Public Member Functions

 NLensSpace (unsigned long newP, unsigned long newQ)
 Creates a new lens space with the given parameters. More...
 
 NLensSpace (const NLensSpace &cloneMe)
 Creates a clone of the given lens space. More...
 
virtual ~NLensSpace ()
 Destroys this lens space. More...
 
unsigned long p () const
 Returns the first parameter p of this lens space L(p,q). More...
 
REGINA_DEPRECATED unsigned long getP () const
 Deprecated routine that 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...
 
REGINA_DEPRECATED unsigned long getQ () const
 Deprecated routine that returns the second parameter q of this lens space L(p,q). More...
 
bool operator== (const NLensSpace &compare) const
 Determines whether this and the given lens space are homeomorphic 3-manifolds. More...
 
bool operator!= (const NLensSpace &compare) const
 Determines whether this and the given lens space are non-homeomorphic 3-manifolds. More...
 
NTriangulationconstruct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...
 
NAbelianGrouphomology () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool isHyperbolic () const
 Returns whether or not this is a finite-volume hyperbolic manifold. More...
 
std::ostream & 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 & writeTeXName (std::ostream &out) const
 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...
 
REGINA_DEPRECATED std::string getName () const
 Deprecated routine that 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...
 
REGINA_DEPRECATED std::string getTeXName () const
 Deprecated routine that 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...
 
REGINA_DEPRECATED std::string getStructure () const
 Deprecated routine that returns details of the structure of this 3-manifold that might not be evident from its common name. More...
 
NAbelianGrouphomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
REGINA_DEPRECATED NAbelianGroupgetHomologyH1 () const
 Deprecated routine that returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool operator< (const NManifold &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...
 
REGINA_DEPRECATED std::string toString () const
 A deprecated alias for str(). More...
 
REGINA_DEPRECATED std::string toStringLong () const
 A deprecated alias for detail(). 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 S^1 x S^2, and L(p,1) is the circle bundle over S^2 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> = [+/- r^2 q/p] in Q/Z where r is an integer.

All optional NManifold routines are implemented for this class.

Constructor & Destructor Documentation

regina::NLensSpace::NLensSpace ( unsigned long  newP,
unsigned long  newQ 
)
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
newPthe first parameter p of the lens space L(p,q).
newQthe second parameter q of the lens space L(p,q). Note that there are no range restrictions whatsoever on this parameter.
regina::NLensSpace::NLensSpace ( const NLensSpace cloneMe)
inline

Creates a clone of the given lens space.

Parameters
cloneMethe lens space to clone.
regina::NLensSpace::~NLensSpace ( )
inlinevirtual

Destroys this lens space.

Member Function Documentation

NTriangulation* regina::NLensSpace::construct ( ) const
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 NManifold. The default implemention of this routine returns 0.

Returns
a triangulation of this 3-manifold, or 0 if the appropriate construction routine has not yet been implemented.

Reimplemented from regina::NManifold.

std::string regina::Output< NManifold , 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.
NAbelianGroup * regina::NManifold::getHomologyH1 ( ) const
inlineinherited

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

Deprecated:
This routine has been renamed to homology(). See the homology() documentation for further details.
std::string regina::NManifold::getName ( ) const
inlineinherited

Deprecated routine that returns the common name of this 3-manifold as a human-readable string.

Deprecated:
This routine has been renamed to name(). See the name() documentation for further details.
unsigned long regina::NLensSpace::getP ( ) const
inline

Deprecated routine that returns the first parameter p of this lens space L(p,q).

Deprecated:
This routine has been renamed to p(). See the p() documentation for further details.
unsigned long regina::NLensSpace::getQ ( ) const
inline

Deprecated routine that returns the second parameter q of this lens space L(p,q).

Deprecated:
This routine has been renamed to q(). See the q() documentation for further details.
std::string regina::NManifold::getStructure ( ) const
inlineinherited

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

Deprecated:
This routine has been renamed to structure(). See the structure() documentation for further details.
std::string regina::NManifold::getTeXName ( ) const
inlineinherited

Deprecated routine that returns the common name of this 3-manifold in TeX format.

Deprecated:
This routine has been renamed to TeXName(). See the TeXName() documentation for further details.
NAbelianGroup* regina::NLensSpace::homology ( ) const
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 NManifold. 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).

Returns
the first homology group of this 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NManifold.

NAbelianGroup * regina::NManifold::homologyH1 ( ) const
inlineinherited

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 NManifold. 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).

Returns
the first homology group of this 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.
bool regina::NLensSpace::isHyperbolic ( ) const
inlinevirtual

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::NManifold.

std::string regina::NManifold::name ( ) const
inherited

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

Returns
the common name of this 3-manifold.
bool regina::NLensSpace::operator!= ( const NLensSpace compare) const
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.

Parameters
comparethe lens space with which this will be compared.
Returns
true if and only if this and the given lens space are non-homeomorphic.
bool regina::NManifold::operator< ( const NManifold 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
comparethe 3-manifold representation with which this will be compared.
Returns
true if and only if this is "smaller" than the given 3-manifold representation.
bool regina::NLensSpace::operator== ( const NLensSpace compare) const
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.

Parameters
comparethe lens space with which this will be compared.
Returns
true if and only if this and the given lens space are homeomorphic.
unsigned long regina::NLensSpace::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.
unsigned long regina::NLensSpace::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.

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

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python:
In addition to str(), this is also used as the Python "stringification" function __str__().
Returns
a short text representation of this object.
std::string regina::NManifold::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 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.

Returns
a string describing additional structural details.
std::string regina::NManifold::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.
REGINA_DEPRECATED std::string regina::Output< NManifold , false >::toString ( ) const
inherited

A deprecated alias for str().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type str() instead.
Returns
a short text representation of this object.
REGINA_DEPRECATED std::string regina::Output< NManifold , false >::toStringLong ( ) const
inherited

A deprecated alias for detail().

Deprecated:
This routine has (at long last) been deprecated; use the simpler-to-type detail() instead.
Returns
a long text representation of this object.
std::string regina::Output< NManifold , false >::utf8 ( ) const
inherited

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

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.
std::ostream& regina::NLensSpace::writeName ( std::ostream &  out) const
virtual

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

Python:
The parameter out does not exist; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NManifold.

std::ostream & regina::NManifold::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 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.

Python:
The parameter out does not exist; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Reimplemented in regina::NSFSpace, and regina::NSnapPeaCensusManifold.

std::ostream& regina::NLensSpace::writeTeXName ( std::ostream &  out) const
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.

Warning
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; instead standard output will always be used. Moreover, this routine returns None.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NManifold.

void regina::NManifold::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.
Parameters
outthe output stream to which to write.
void regina::NManifold::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.
Parameters
outthe output stream to which to write.

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

Copyright © 1999-2016, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).