Regina Calculation Engine
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Represents a closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus. More...
#include <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. | |
NGraphPair (NSFSpace *sfs0, NSFSpace *sfs1, const NMatrix2 &matchingReln) | |
Creates a new graph manifold as a pair of joined Seifert fibred spaces. | |
~NGraphPair () | |
Destroys this structure along with the component Seifert fibred spaces and the matching matrix. | |
const NSFSpace & | sfs (unsigned which) const |
Returns a reference to one of the two bounded Seifert fibred spaces that are joined together. | |
const NMatrix2 & | matchingReln () const |
Returns a reference to the 2-by-2 matrix describing how the two Seifert fibred spaces are joined together. | |
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. | |
NAbelianGroup * | getHomologyH1 () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. | |
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. | |
std::ostream & | writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. |
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.
regina::NGraphPair::NGraphPair | ( | NSFSpace * | sfs0, |
NSFSpace * | sfs1, | ||
long | mat00, | ||
long | mat01, | ||
long | mat10, | ||
long | mat11 | ||
) | [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. |
regina::NGraphPair::NGraphPair | ( | NSFSpace * | sfs0, |
NSFSpace * | sfs1, | ||
const NMatrix2 & | matchingReln | ||
) | [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.
NAbelianGroup* regina::NGraphPair::getHomologyH1 | ( | ) | const [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.
const NMatrix2 & regina::NGraphPair::matchingReln | ( | ) | const [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.
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. const NSFSpace & regina::NGraphPair::sfs | ( | unsigned | which | ) | const [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. |
std::ostream& regina::NGraphPair::writeName | ( | std::ostream & | out | ) | const [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.
std::ostream& regina::NGraphPair::writeTeXName | ( | std::ostream & | out | ) | const [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.