Regina Calculation Engine
|
Represents a closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus. More...
#include <manifold/ngraphpair.h>
Public Member Functions | |
NGraphPair (NSFSpace *sfs0, NSFSpace *sfs1, long mat00, long mat01, long mat10, long mat11) | |
Creates a new graph manifold as a pair of joined Seifert fibred spaces. More... | |
NGraphPair (NSFSpace *sfs0, NSFSpace *sfs1, const NMatrix2 &matchingReln) | |
Creates a new graph manifold as a pair of joined Seifert fibred spaces. More... | |
~NGraphPair () | |
Destroys this structure along with the component Seifert fibred spaces and the matching matrix. More... | |
const NSFSpace & | sfs (unsigned which) const |
Returns a reference to one of the two bounded Seifert fibred spaces that are joined together. More... | |
const NMatrix2 & | matchingReln () const |
Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces are joined together. More... | |
bool | operator< (const NGraphPair &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More... | |
NAbelianGroup * | getHomologyH1 () 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 | getName () const |
Returns the common name of this 3-manifold as a human-readable string. More... | |
std::string | getTeXName () const |
Returns the common name of this 3-manifold in TeX format. More... | |
std::string | getStructure () const |
Returns details of the structure of this 3-manifold that might not be evident from its common name. More... | |
virtual NTriangulation * | construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
bool | operator< (const NManifold &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... | |
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 closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus.
Each Seifert fibred space must have just one boundary component, corresponding to a puncture in the base orbifold (with no fibre-reversing twist as one travels around this boundary).
The way in which the two spaces are joined is specified by a 2-by-2 matrix M. This matrix expresses the locations of the fibres and base orbifold of the second Seifert fibred space in terms of the first.
More specifically, suppose that f0 and o0 are generators of the common torus, where f0 represents a directed fibre in the first Seifert fibred space and o0 represents the oriented boundary of the corresponding base orbifold. Likewise, let f1 and o1 be generators of the common torus representing a directed fibre and the base orbifold of the second Seifert fibred space. Then the curves f0, o0, f1 and o1 are related as follows:
[f1] [f0] [ ] = M * [ ] [o1] [o0]
See the page on Notation for Seifert fibred spaces for details on some of the terminology used above.
The optional NManifold routine getHomologyH1() is implemented, but the optional routine construct() is not.
|
inline |
Creates a new graph manifold as a pair of joined Seifert fibred spaces.
The two bounded Seifert fibred spaces and the four elements of the 2-by-2 matching matrix are all passed separately. The elements of the matching matrix combine to give the full matrix M as follows:
[ mat00 mat01 ] M = [ ] [ mat10 mat11 ]
Note that the new object will take ownership of the two given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.
sfs0 | the first Seifert fibred space. |
sfs1 | the second Seifert fibred space. |
mat00 | the (0,0) element of the matching matrix. |
mat01 | the (0,1) element of the matching matrix. |
mat10 | the (1,0) element of the matching matrix. |
mat11 | the (1,1) element of the matching matrix. |
|
inline |
Creates a new graph manifold as a pair of joined Seifert fibred spaces.
The two bounded Seifert fibred spaces and the entire 2-by-2 matching matrix are each passed separately.
Note that the new object will take ownership of the two given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.
sfs0 | the first Seifert fibred space. |
sfs1 | the second Seifert fibred space. |
matchingReln | the 2-by-2 matching matrix. |
regina::NGraphPair::~NGraphPair | ( | ) |
Destroys this structure along with the component Seifert fibred spaces and the matching matrix.
|
inlinevirtualinherited |
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 NManifold. The default implemention of this routine returns 0.
Reimplemented in regina::NSFSpace, regina::NSnapPeaCensusManifold, regina::NLensSpace, and regina::NSimpleSurfaceBundle.
|
inherited |
Returns the output from writeTextLong() as a string.
|
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 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 3-manifold as a human-readable string.
|
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.
|
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::NManifold.
|
inline |
Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces are joined together.
See the class notes for details on precisely how this matrix is represented.
|
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. bool regina::NGraphPair::operator< | ( | const NGraphPair & | compare | ) | const |
Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space.
The ordering imposed on graph manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.
All that this routine really offers is a well-defined way of ordering graph manifold representations.
compare | the representation with which this will be compared. |
true
if and only if this is "smaller" than the given graph manifold representation.
|
inline |
Returns a reference to one of the two bounded Seifert fibred spaces that are joined together.
which | 0 if the first Seifert fibred space is to be returned, or 1 if the second space is to be returned. |
|
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 3-manifold as a human-readable 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 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.
out | the output stream to which to write. |
Reimplemented in regina::NSFSpace, and regina::NSnapPeaCensusManifold.
|
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.
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 human-readable, 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 human-readable, should fit on a single line, and should not end with a newline.
out | the output stream to which to write. |
Implements regina::ShareableObject.