Regina Calculation Engine
Public Member Functions | List of all members
regina::NLensSpace Class Reference

Represents a general lens space. More...

#include <manifold/nlensspace.h>

Inheritance diagram for regina::NLensSpace:
regina::NManifold regina::ShareableObject regina::boost::noncopyable

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 getP () const
 Returns the first parameter p of this lens space L(p,q). More...
 
unsigned long getQ () const
 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...
 
NTriangulationconstruct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...
 
NAbelianGroupgetHomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. 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...
 
- Public Member Functions inherited from regina::NManifold
virtual ~NManifold ()
 A destructor that does nothing. More...
 
std::string getName () const
 Returns the common name of this 3-manifold as a human-readable string. More...
 
std::string getTeXName () const
 Returns the common name of this 3-manifold in TeX format. More...
 
std::string getStructure () const
 Returns details of the structure of this 3-manifold that might not be evident from its common name. 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...
 
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream. More...
 
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing. More...
 
virtual ~ShareableObject ()
 Default destructor that does nothing. More...
 
std::string str () const
 Returns the output from writeTextShort() as a string. More...
 
std::string toString () const
 A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...
 
std::string detail () const
 Returns the output from writeTextLong() as a string. More...
 
std::string toStringLong () const
 A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...
 

Additional Inherited Members

- Protected Member Functions inherited from regina::boost::noncopyable
 noncopyable ()
 A constructor which does nothing. More...
 
 ~noncopyable ()
 A destructor which does nothing. 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.

Test:
Included in the test suite.

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.

NAbelianGroup* regina::NLensSpace::getHomologyH1 ( ) 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.

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.

unsigned long regina::NLensSpace::getP ( ) 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::getQ ( ) 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.

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.
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; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NManifold.

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; standard output will be used.
Parameters
outthe output stream to which to write.
Returns
a reference to the given output stream.

Implements regina::NManifold.


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

Copyright © 1999-2013, 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@debian.org).