Regina Calculation Engine

Represents a general lens space. More...
#include <manifold/nlensspace.h>
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 3manifolds. More...  
NTriangulation *  construct () const 
Returns a triangulation of this 3manifold, if such a construction has been implemented. More...  
NAbelianGroup *  getHomologyH1 () const 
Returns the first homology group of this 3manifold, if such a routine has been implemented. More...  
std::ostream &  writeName (std::ostream &out) const 
Writes the common name of this 3manifold as a humanreadable string to the given output stream. More...  
std::ostream &  writeTeXName (std::ostream &out) const 
Writes the common name of this 3manifold 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 3manifold as a humanreadable string. More...  
std::string  getTeXName () const 
Returns the common name of this 3manifold in TeX format. More...  
std::string  getStructure () const 
Returns details of the structure of this 3manifold that might not be evident from its common name. More...  
bool  operator< (const NManifold &compare) const 
Determines in a fairly adhoc fashion whether this representation of this 3manifold is "smaller" than the given representation of the given 3manifold. More...  
virtual std::ostream &  writeStructure (std::ostream &out) const 
Writes details of the structure of this 3manifold 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...  
Represents a general lens space.
The lens space L(p,q) is the 3manifold you get by p/q Dehn surgery on the unknot. For instance, L(1,0) and L(1,1) are the 3sphere, 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.

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 
Creates a clone of the given lens space.
cloneMe  the lens space to clone. 

inlinevirtual 
Destroys this lens space.

virtual 
Returns a triangulation of this 3manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3manifold (for instance, if this 3manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3manifolds have construction routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.
Reimplemented from regina::NManifold.

virtual 
Returns the first homology group of this 3manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3manifold then this routine will return 0.
The details of which 3manifolds 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.
Reimplemented from regina::NManifold.

inline 
Returns the first parameter p of this lens space L(p,q).
See the class notes for details.

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 p1 inclusive that produces the same 3manifold as this lens space. This means it might not be the value of q that was used to initialise this lens space.

inline 
Determines whether this and the given lens space are homeomorphic 3manifolds.
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.

virtual 
Writes the common name of this 3manifold as a humanreadable string to the given output stream.
out  the output stream to which to write. 
Implements regina::NManifold.

virtual 
Writes the common name of this 3manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
out  the output stream to which to write. 
Implements regina::NManifold.