Regina Calculation Engine
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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)=default | |
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... | |
LensSpace & | operator= (const LensSpace &cloneMe)=default |
Sets this to be a clone of the given lens space. More... | |
Triangulation< 3 > * | construct () const override |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
AbelianGroup * | homology () const override |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | isHyperbolic () const override |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | writeName (std::ostream &out) const override |
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 override |
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.
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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.
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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__()
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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.