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...  
bool  isHyperbolic () const 
Returns whether or not this is a finitevolume hyperbolic manifold. 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...  
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...  
Input and Output  
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...  
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.

inherited 
Returns the output from writeTextLong() as a string.

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.

inherited 
Returns the common name of this 3manifold as a humanreadable string.

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.

inherited 
Returns details of the structure of this 3manifold 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.

inherited 
Returns the common name of this 3manifold in TeX format.
No leading or trailing dollar signs will be included.

inlinevirtual 
Returns whether or not this is a finitevolume hyperbolic manifold.
true
if this is a finitevolume hyperbolic manifold, or false
if not. Implements regina::NManifold.

inherited 
Determines in a fairly adhoc fashion whether this representation of this 3manifold is "smaller" than the given representation of the given 3manifold.
The ordering imposed on 3manifolds 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 3manifold 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 welldefined way of ordering 3manifold representations.
compare  the 3manifold representation with which this will be compared. 
true
if and only if this is "smaller" than the given 3manifold representation.

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.

inherited 
Returns the output from writeTextShort() as a string.
__str__()
function.

inlineinherited 
A deprecated alias for str(), which returns the output from writeTextShort() as a string.

inlineinherited 
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.

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.

inlinevirtualinherited 
Writes details of the structure of this 3manifold 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.
out  the output stream to which to write. 
Reimplemented in regina::NSFSpace, and regina::NSnapPeaCensusManifold.

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.

inlinevirtualinherited 
Writes this object in long text format to the given output stream.
The output should provide the user with all the information they could want. The output should be humanreadable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out  the output stream to which to write. 
Reimplemented from regina::ShareableObject.

inlinevirtualinherited 
Writes this object in short text format to the given output stream.
The output should be humanreadable, should fit on a single line, and should not end with a newline.
out  the output stream to which to write. 
Implements regina::ShareableObject.