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  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 3manifolds. More...  
bool  operator!= (const NLensSpace &compare) const 
Determines whether this and the given lens space are nonhomeomorphic 3manifolds. More...  
NTriangulation *  construct () const 
Returns a triangulation of this 3manifold, if such a construction has been implemented. More...  
NAbelianGroup *  homology () 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  name () const 
Returns the common name of this 3manifold as a humanreadable string. More...  
REGINA_DEPRECATED std::string  getName () const 
Deprecated routine that returns the common name of this 3manifold as a humanreadable string. More...  
std::string  TeXName () const 
Returns the common name of this 3manifold in TeX format. More...  
REGINA_DEPRECATED std::string  getTeXName () const 
Deprecated routine that returns the common name of this 3manifold in TeX format. More...  
std::string  structure () const 
Returns details of the structure of this 3manifold 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 3manifold that might not be evident from its common name. More...  
NAbelianGroup *  homologyH1 () const 
Returns the first homology group of this 3manifold, if such a routine has been implemented. More...  
REGINA_DEPRECATED NAbelianGroup *  getHomologyH1 () const 
Deprecated routine that returns the first homology group of this 3manifold, if such a routine has been implemented. 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...  
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...  
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 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 humanreadable, 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.

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

inlineinherited 
Deprecated routine that returns the common name of this 3manifold as a humanreadable string.

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

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

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

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

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.
This routine can also be accessed via the alias homologyH1() (a name that is more specific, but a little longer to type).
Reimplemented from regina::NManifold.

inlineinherited 
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.
This routine can also be accessed via the alias homology() (a name that is less specific, but a little easier to type).

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

inline 
Determines whether this and the given lens space are nonhomeomorphic 3manifolds.
Note that the manifolds may be homeomorphic 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 nonhomeomorphic.

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.

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 a short text representation of this object.
This text should be humanreadable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
__str__()
.

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.

inherited 
A deprecated alias for str().

inherited 
A deprecated alias for detail().

inherited 
Returns a short text representation of this object using unicode characters.
Like str(), this text should be humanreadable, 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 UTF8.

virtual 
Writes the common name of this 3manifold as a humanreadable string to the given output stream.
None
.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.
None
.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.
None
.out  the output stream to which to write. 
Implements regina::NManifold.

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.
out  the output stream to which to write. 

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.
out  the output stream to which to write. 