Represents a combinatorial isomorphism from one 4-manifold triangulation into another.
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| Isomorphism (unsigned nPentachora) |
| Creates a new isomorphism with no initialisation. More...
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| Isomorphism (const Isomorphism ©) |
| Creates a new copy of the given isomorphism. More...
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int & | pentImage (unsigned sourcePent) |
| A dimension-specific alias for simpImage(). More...
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int | pentImage (unsigned sourcePent) const |
| A dimension-specific alias for simpImage(). More...
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unsigned | size () const |
| Returns the number of simplices in the source triangulation associated with this isomorphism. More...
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REGINA_DEPRECATED unsigned | getSourceSimplices () const |
| A deprecated alias for size(), which returns the number of simplices in the source triangulation associated with this isomorphism. More...
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int & | simpImage (unsigned sourceSimp) |
| Determines the image of the given source simplex under this isomorphism. More...
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int | simpImage (unsigned sourceSimp) const |
| Determines the image of the given source simplex under this isomorphism. More...
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NPerm< dim+1 > & | facetPerm (unsigned sourceSimp) |
| Returns a read-write reference to the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism. More...
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NPerm< dim+1 > | facetPerm (unsigned sourceSimp) const |
| Determines the permutation that is applied to the (dim + 1) facets of the given source simplex under this isomorphism. More...
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FacetSpec< dim > | operator[] (const FacetSpec< dim > &source) const |
| Determines the image of the given source simplex facet under this isomorphism. More...
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bool | isIdentity () const |
| Determines whether or not this is an identity isomorphism. More...
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Triangulation< dim > * | apply (const Triangulation< dim > *original) const |
| Applies this isomorphism to the given triangulation, and returns the result as a new triangulation. More...
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void | applyInPlace (Triangulation< dim > *tri) const |
| Applies this isomorphism to the given triangulation, modifying the given triangulation directly. More...
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void | writeTextShort (std::ostream &out) const |
| Writes a short text representation of this object to the given output stream. More...
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void | writeTextLong (std::ostream &out) const |
| Writes a detailed text representation of this object to the given output stream. More...
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std::string | str () const |
| Returns a short text representation of this object. More...
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std::string | utf8 () const |
| Returns a short text representation of this object using unicode characters. More...
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std::string | detail () const |
| Returns a detailed text representation of this object. More...
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REGINA_DEPRECATED std::string | toString () const |
| A deprecated alias for str(). More...
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REGINA_DEPRECATED std::string | toStringLong () const |
| A deprecated alias for detail(). More...
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template<>
class regina::Isomorphism< 4 >
Represents a combinatorial isomorphism from one 4-manifold triangulation into another.
This is a specialisation of the generic Isomorphism class template; see the Isomorphism documentation for an overview of how this class works.
This 4-dimensional specialisation contains additional dimension-specific aliases for some commonly-used routines.
Applies this isomorphism to the given triangulation, and returns the result as a new triangulation.
An isomorphism represents a combinatorial map from a triangulation T to a triangulation U. This routine treats the given triangulation as the domain T, and returns the corresponding range U. The given triangulation T is not modified in any way.
In more detail: A new triangulation U is returned, so that this isomorphism represents a one-to-one, onto and boundary complete isomorphism from T to U. That is, T and U will be combinatorially identical triangulations, and this isomorphism describes the mapping from the simplices of T and their facets to the simplices of U and their facets.
The resulting triangulation U is newly created, and must be destroyed by the caller of this routine.
There are several preconditions to this routine. This routine does a small amount of sanity checking (and returns 0 if an error is detected), but it certainly does not check the full set of preconditions. It is up to the caller of this routine to verify that all of the following preconditions are met.
- Precondition
- The number of simplices in the given triangulation is precisely the number returned by size() for this isomorphism.
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The simplex images are precisely 0,1,...,size()-1 in some order (i.e., this isomorphism does not represent a mapping from a smaller triangulation into a larger triangulation).
- Parameters
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original | the triangulation to which this isomorphism should be applied. |
- Returns
- the new isomorphic triangulation, or 0 if a problem was encountered (i.e., an unmet precondition was noticed).
Applies this isomorphism to the given triangulation, modifying the given triangulation directly.
This is similar to apply(), except that instead of creating a new triangulation, the simplices and vertices of the given triangulation are modified in-place.
See apply() for further details on how this operation is performed.
As with apply(), there are several preconditions to this routine. This routine does a small amount of sanity checking (and returns without changes if an error is detected), but it certainly does not check the full set of preconditions. It is up to the caller of this routine to verify that all of the following preconditions are met.
- Precondition
- The number of simplices in the given triangulation is precisely the number returned by size() for this isomorphism.
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The simplex images are precisely 0,1,...,size()-1 in some order (i.e., this isomorphism does not represent a mapping from a smaller triangulation into a larger triangulation).
- Parameters
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tri | the triangulation to which this isomorphism should be applied. |
Returns a random isomorphism for the given number of simplices.
This isomorphism will reorder simplices 0 to nSimplices-1
in a random fashion, and for each simplex a random permutation of its (dim + 1) vertices will be selected.
The isomorphism will be newly constructed, and must be destroyed by the caller of this routine.
Note that both the STL random number generator and the standard C function rand() are used in this routine. All possible isomorphisms for the given number of simplices are equally likely.
- Parameters
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nSimplices | the number of simplices that the new isomorphism should operate upon. |
- Returns
- the newly constructed random isomorphism.