Regina Calculation Engine
|
Represents a general lens space. More...
#include <manifold/lensspace.h>
Public Member Functions | |
LensSpace (unsigned long newP, unsigned long newQ) | |
Creates a new lens space with the given parameters. More... | |
LensSpace (const LensSpace &cloneMe) | |
Creates a clone of the given lens space. More... | |
virtual | ~LensSpace () |
Destroys this lens space. More... | |
unsigned long | p () const |
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... | |
bool | operator== (const LensSpace &compare) const |
Determines whether this and the given lens space are homeomorphic 3-manifolds. More... | |
bool | operator!= (const LensSpace &compare) const |
Determines whether this and the given lens space are non-homeomorphic 3-manifolds. More... | |
Triangulation< 3 > * | construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
AbelianGroup * | homology () 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... | |
std::string | TeXName () const |
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... | |
AbelianGroup * | homologyH1 () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | operator< (const Manifold &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... | |
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 Manifold 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 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 Manifold. The default implemention of this routine returns 0.
Reimplemented from regina::Manifold.
|
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.
|
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 Manifold. 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::Manifold.
|
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 Manifold. 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 finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
|
inherited |
Returns the common name of this 3-manifold as a human-readable string.
|
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.
compare | the lens space with which this will be compared. |
true
if and only if this and the given lens space are non-homeomorphic.
|
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.
compare | the 3-manifold representation with which this will be compared. |
true
if and only if this is "smaller" than the given 3-manifold representation.
|
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.
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 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.
|
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.
__str__()
.
|
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.
|
inherited |
Returns the common name of this 3-manifold in TeX format.
No leading or trailing dollar signs will be included.
|
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.
|
virtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
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.
None
.out | the output stream to which to write. |
Reimplemented in regina::SFSpace, and regina::SnapPeaCensusManifold.
|
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.
None
.out | the output stream to which to write. |
Implements regina::Manifold.
|
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. |