Regina Calculation Engine

A gluing permutation search class that offers a specialised search algorithm for when only compact (finite) 3manifold triangulations are required. More...
#include <census/ngluingpermsearcher.h>
Classes  
struct  TetEdgeState 
A structure used to track equivalence classes of tetrahedron edges as the gluing permutation set is constructed. More...  
struct  TetVertexState 
A structure used to track equivalence classes of tetrahedron vertices as the gluing permutation set is constructed. More...  
Public Types  
enum  PurgeFlags { PURGE_NONE = 0, PURGE_NON_MINIMAL = 1, PURGE_NON_PRIME = 2, PURGE_NON_MINIMAL_PRIME = 3, PURGE_NON_MINIMAL_HYP = 9, PURGE_P2_REDUCIBLE = 4 } 
Flags to indicate that our enumeration may (at the discretion of the enumeration algorithm) ignore certain classes of triangulations. More...  
typedef DimTraits< dim > ::FacetPairing  FacetPairing 
typedef DimTraits< dim >::Perm  Perm 
typedef DimTraits< dim >::Simplex  Simplex 
typedef DimTraits< dim > ::Triangulation  Triangulation 
Public Member Functions  
NCompactSearcher (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, int whichPurge, UseGluingPerms use, void *useArgs=0)  
Creates a new search manager for use when only compact 3manifold triangulations are required. More...  
NCompactSearcher (std::istream &in, UseGluingPerms use, void *useArgs=0)  
Initialises a new search manager based on data read from the given input stream. More...  
virtual  ~NCompactSearcher () 
Destroys this search manager and all supporting data structures. More...  
virtual void  dumpData (std::ostream &out) const 
Dumps all internal data in a plain text format to the given output stream. More...  
virtual void  runSearch (long maxDepth=1) 
Generates all possible gluing permutation sets that satisfy the current search criteria. More...  
bool  completePermSet () const 
Determines whether this search manager holds a complete gluing permutation set or just a partially completed search state. More...  
void  dumpTaggedData (std::ostream &out) const 
Dumps all internal data in a plain text format, along with a marker to signify which precise class the data belongs to. More...  
unsigned  getNumberOfTetrahedra () const 
Returns the total number of tetrahedra under consideration. More...  
const NFacePairing *  getFacePairing () const 
Returns the specific pairing of tetrahedron faces that this set of gluing permutations complements. More...  
bool  inputError () const 
Was an error found during construction from an input stream? More...  
unsigned  size () const 
Returns the total number of simplices under consideration. More...  
const FacetPairing *  getFacetPairing () const 
Returns the specific pairing of simplex facets that this set of gluing permutations complements. More...  
Perm  gluingPerm (const NFacetSpec< dim > &source) const 
Returns the gluing permutation associated with the given simplex facet. More...  
Perm  gluingPerm (unsigned simp, unsigned facet) const 
Returns the gluing permutation associated with the given simplex facet. More...  
Triangulation *  triangulate () const 
Returns a newly created triangulation as modelled by this set of gluing permutations and the associated simplex facet pairing. More...  
Static Public Member Functions  
static void  findAllPerms (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, bool finiteOnly, int whichPurge, UseGluingPerms use, void *useArgs=0) 
The main entry routine for running a search for all gluing permutation sets that complement a given face pairing. More...  
static NGluingPermSearcher *  bestSearcher (const NFacePairing *pairing, const NFacePairing::IsoList *autos, bool orientableOnly, bool finiteOnly, int whichPurge, UseGluingPerms use, void *useArgs=0) 
Constructs a search manager of the best possible class for the given search parameters. More...  
static NGluingPermSearcher *  readTaggedData (std::istream &in, UseGluingPerms use, void *useArgs=0) 
Creates a new search manager based on tagged data read from the given input stream. More...  
Static Public Attributes  
static const char  dataTag_ 
A character used to identify this class when reading and writing tagged data in text format. More...  
Protected Member Functions  
virtual char  dataTag () const 
Returns the character used to identify this class when storing tagged data in text format. More...  
int  findEdgeClass (int edgeID) const 
Returns the representative of the equivalence class containing the given tetrahedron edge. More...  
int  findEdgeClass (int edgeID, char &twisted) const 
Returns the representative of the equivalence class containing the given tetrahedron edge. More...  
int  mergeVertexClasses () 
Merge the classes of tetrahedron vertices as required by the new gluing made at stage orderElt of the search. More...  
bool  mergeEdgeClasses () 
Merge the classes of tetrahedron edges as required by the new gluing made at stage orderElt of the search. More...  
void  splitVertexClasses () 
Split the classes of tetrahedron vertices to mirror the undoing of the gluing at stage orderElt of the search. More...  
void  splitEdgeClasses () 
Split the classes of tetrahedron edges to mirror the undoing of the gluing at stage orderElt of the search. More...  
void  vtxBdryJoin (int vertexID, char end, int adjVertexID, char twist) 
Signifies that the boundary edges supplied by the vertex linking triangles for the two given tetrahedron vertices should be marked as adjacent. More...  
void  vtxBdryFixAdj (int vertexID) 
Adjusts the bdryNext and bdryTwist arrays for nearby tetrahedron vertices, to ensure that these arrays are consistent with the bdryNext and bdryTwist arrays stored with the given vertex. More...  
void  vtxBdryBackup (int vertexID) 
Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given tetrahedron vertex. More...  
void  vtxBdryRestore (int vertexID) 
Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given tetrahedron vertex. More...  
void  vtxBdryNext (int vertexID, int tet, int vertex, int bdryFace, int next[2], char twist[2]) 
Assuming the given edge of the vertex linking triangle for the given tetrahedron vertex lies on the boundary of the vertex link, this routine identifies the adjacent boundary edges of the vertex link in each direction. More...  
bool  vtxBdryLength1 (int vertexID) 
Determines whether one of the edges of the vertex linking triangle for the given tetrahedron vertex in fact forms an entire oneedge boundary component of the overall vertex link. More...  
bool  vtxBdryLength2 (int vertexID1, int vertexID2) 
Determines whether edges of the vertex linking triangles for each of the given tetrahedron vertices combine to form an entire twoedge boundary component of the overall vertex link, with one edge from each triangle. More...  
void  vtxBdryConsistencyCheck () 
Runs a number of tests on all tetrahedron vertices to locate consistency errors in the bdryEdges, bdryNext and bdryTwist members of the TetVertexState class. More...  
void  vtxBdryDump (std::ostream &out) 
Dumps a summary of bdryNext, bdryTwist and bdryEdges for every vertex of every tetrahedron to the given output stream. More...  
bool  isCanonical () const 
Compares the current set of gluing permutations with its preimage under each automorphism of the underlying face pairing, in order to see whether the current set is in canonical form (i.e., is lexicographically smallest). More...  
bool  badEdgeLink (const NTetFace &face) const 
Determines whether the permutations already constructed model a triangulation with an edge identified with itself in reverse. More...  
bool  lowDegreeEdge (const NTetFace &face, bool testDegree12, bool testDegree3) const 
Determines whether the permutations already constructed model a triangulation with a low degree edge. More...  
int &  permIndex (const NFacetSpec< dim > &source) 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...  
int &  permIndex (unsigned simp, unsigned facet) 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...  
const int &  permIndex (const NFacetSpec< dim > &source) const 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...  
const int &  permIndex (unsigned simp, unsigned facet) const 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner. More...  
int  gluingToIndex (const NFacetSpec< dim > &source, const Perm &gluing) const 
Returns the index into array Perm::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...  
int  gluingToIndex (unsigned simp, unsigned facet, const Perm &gluing) const 
Returns the index into array Perm::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...  
Perm  indexToGluing (const NFacetSpec< dim > &source, int index) const 
Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm::Sn_1. More...  
Perm  indexToGluing (unsigned simp, unsigned facet, int index) const 
Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm::Sn_1. More...  
Protected Attributes  
unsigned  nVertexClasses 
The number of equivalence classes of identified tetrahedron vertices. More...  
TetVertexState *  vertexState 
Used for tracking equivalence classes of identified tetrahedron vertices. More...  
int *  vertexStateChanged 
Tracks the way in which the vertexState[] array has been updated over time. More...  
unsigned  nEdgeClasses 
The number of equivalence classes of identified tetrahedron edges. More...  
TetEdgeState *  edgeState 
Used for tracking equivalence classes of identified tetrahedron edges. More...  
int *  edgeStateChanged 
Tracks the way in which the edgeState[] array has been updated over time. More...  
const NFacePairing::IsoList *  autos_ 
The set of isomorphisms that define equivalence of gluing permutation sets. More...  
bool  autosNew 
Did we create the isomorphism list autos_ ourselves (in which case we must destroy it also)? More...  
bool  orientableOnly_ 
Are we only searching for gluing permutations that correspond to orientable triangulations? More...  
bool  finiteOnly_ 
Are we only searching for gluing permutations that correspond to finite triangulations? More...  
int  whichPurge_ 
Are there any types of triangulation that we may optionally avoid constructing? This should be a bitwise OR of constants from the PurgeFlags enumeration. More...  
UseGluingPerms  use_ 
A routine to call each time a gluing permutation set is found during the search. More...  
void *  useArgs_ 
Additional usersupplied data to be passed as the second argument to the use_ routine. More...  
bool  started 
Has the search started yet? This helps distinguish between a new search and the resumption of a partially completed search. More...  
int *  orientation 
Keeps track of the orientation of each tetrahedron in the underlying triangulation. More...  
NTetFace *  order 
Describes the order in which gluing permutations are assigned to faces. More...  
int  orderSize 
The total number of edges in the face pairing graph, i.e., the number of elements of interest in the order[] array. More...  
int  orderElt 
Marks which element of order[] we are currently examining at this stage of the search. More...  
const FacetPairing *  pairing_ 
The facet pairing that this permutation set complements. More...  
int *  permIndices_ 
The index into array Perm::Sn_1 describing how each simplex facet is glued to its partner. More...  
bool  inputError_ 
Has an error occurred during construction from an input stream? More...  
Static Protected Attributes  
static const char  VLINK_CLOSED 
Signifies that a vertex link has been closed off (i.e., the link has no remaining boundary edges). More...  
static const char  VLINK_NON_SPHERE 
Signifies that a vertex link has been made into something other than a 2sphere with zero or more punctures. More...  
static const int  vertexLinkNextFace [4][4] 
Maintains an ordering of the three tetrahedron faces surrounding a vertex in a tetrahedron. More...  
static const int  vertexLinkPrevFace [4][4] 
Provides backwards links for the ordering described by vertexLinkNextFace. More...  
A gluing permutation search class that offers a specialised search algorithm for when only compact (finite) 3manifold triangulations are required.
The only constraints placed upon a triangulation are that every edge must be valid (i.e., not identified with itself in reverse), and that the link of every vertex must be a disk or a sphere.
The search algorithm uses modified unionfind structures on both edge and vertex equivalence classes to prune searches that are guaranteed to lead to bad edge or vertex links. For details see "Enumeration of nonorientable 3manifolds using facepairing graphs and unionfind", Benjamin A. Burton, Discrete Comput. Geom. 38 (2007), no. 3, 527–571; and "Detecting genus in vertex links for the fast enumeration of 3manifold triangulations", Benjamin A. Burton, in "ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation", ACM, 2011, pp. 5966.
No additional unwanted triangulations will be produced by this search (in contrast to other search classes, such as NClosedPrimeMinSearcher). That is, only compact 3manifolds will be produced.

inherited 
Flags to indicate that our enumeration may (at the discretion of the enumeration algorithm) ignore certain classes of triangulations.
These flags can be combined using bitwise OR.
See the NGluingPermSearcher constructor documentation for further details on how these flags are used.
regina::NCompactSearcher::NCompactSearcher  (  const NFacePairing *  pairing, 
const NFacePairing::IsoList *  autos,  
bool  orientableOnly,  
int  whichPurge,  
UseGluingPerms  use,  
void *  useArgs = 0 

) 
Creates a new search manager for use when only compact 3manifold triangulations are required.
For details on how a search manager is used, see the NGluingPermSearcher documentation. Note in particular that this class will be automatically used by NGluingPermSearcher::findAllPerms() if possible, so there is often no need for an end user to instantiate this class directly.
All constructor arguments are the same as for the NGluingPermSearcher constructor, though some arguments (such as finiteOnly) are not needed here since they are already implied by the specialised search context.
regina::NCompactSearcher::NCompactSearcher  (  std::istream &  in, 
UseGluingPerms  use,  
void *  useArgs = 0 

) 
Initialises a new search manager based on data read from the given input stream.
This may be a new search or a partially completed search.
This routine reads data in the format written by dumpData(). If you wish to read data whose precise class is unknown, consider using dumpTaggedData() and readTaggedData() instead.
If the data found in the input stream is invalid or incorrectly formatted, the routine inputError() will return true
but the contents of this object will be otherwise undefined.
The arguments use and useArgs are the same as for the NGluingPermSearcher constructor.
in  the input stream from which to read. 

inlinevirtual 
Destroys this search manager and all supporting data structures.

protectedinherited 
Determines whether the permutations already constructed model a triangulation with an edge identified with itself in reverse.
Note that such edges can only occur in nonorientable triangulations.
Tests that do not refer to the gluing permutation for the given face will not be run.
This routine is not fussy about the order in which gluing permutations are selected, as long as permutations not yet selected have the corresponding element of permIndices[] set to 1.
If finiteOnly_ is true
in the search criteria, additional tests will be run that can eliminate triangulations with nonorientable vertex links. Although these tests are not searching for bad edge links per se, they can be performed within this routine with very little additional work needing to be done.
face  the specific tetrahedron face upon which tests will be based. 
true
if the permutations under construction will lead to an edge identified with itself in reverse, or false
if no such edge is found.

staticinherited 
Constructs a search manager of the best possible class for the given search parameters.
Different subclasses of NGluingPermSearcher provide optimised search algorithms for different types of search.
Calling this routine and then calling runSearch() on the result has the same effect as the allinone routine findAllPerms(). Unless you have specialised requirements (such as partial searching), you are probably better calling findAllPerms() instead.
The resulting object is newly created, and must be destroyed by the caller of this routine.
See the NGluingPermSearcher constructor for documentation on the arguments to this routine.

inlineinherited 
Determines whether this search manager holds a complete gluing permutation set or just a partially completed search state.
This may assist the use_ routine when running partial depthbased searches. See runSearch() for further details.
true
if a complete gluing permutation set is held, or false
otherwise.

inlineprotectedvirtual 
Returns the character used to identify this class when storing tagged data in text format.
Reimplemented from regina::NGluingPermSearcher.
Reimplemented in regina::NClosedPrimeMinSearcher.

virtual 
Dumps all internal data in a plain text format to the given output stream.
This object can be recreated from this text data by calling the input stream constructor for this class.
This routine may be useful for transferring objects from one processor to another.
Note that subclass data is written after superclass data, so it is safe to dump data from a subclass and then recreate a new superclass object from that data (though subclassspecific information will of course be lost).
out  the output stream to which the data should be written. 
Reimplemented from regina::NGluingPermSearcher.
Reimplemented in regina::NClosedPrimeMinSearcher.

inherited 
Dumps all internal data in a plain text format, along with a marker to signify which precise class the data belongs to.
This routine can be used with readTaggedData() to transport objects from place to place whose precise class is unknown.
out  the output stream to which the data should be written. 

staticinherited 
The main entry routine for running a search for all gluing permutation sets that complement a given face pairing.
This routine examines the search parameters, chooses the best possible search algorithm, constructs an object of the corresponding subclass of NGluingPermSearcher and then calls runSearch().
See the NGluingPermSearcher constructor for documentation on the arguments to this routine. See the runSearch() method for documentation on how the search runs and returns its results.

inlineprotected 
Returns the representative of the equivalence class containing the given tetrahedron edge.
The class representative is defined to be the root of the corresponding unionfind tree.
See the TetEdgeState class for further details. See also the other variant of findEdgeClass(), which is slightly slower but which also tracks edge orientation.
edgeID  the index of a single tetrahedron edge; this must be between 0 and 6t1 inclusive, where t is the number of tetrahedra. See the TetEdgeState class notes for details on edge indexing. 

inlineprotected 
Returns the representative of the equivalence class containing the given tetrahedron edge.
The class representative is defined to be the root of the corresponding unionfind tree.
The argument twisted is also modified to indicate whether or not the identification of the given edge with the class representative preserves orientation. Note that this arugment is not initialised. Instead, if the identification is orientationpreserving then twisted will be left unmodified, and if it is orientationreversing then twisted will be changed from 0 to 1 or viceversa.
See the TetEdgeState class for further details. See also the other variant of findEdgeClass(), which is slightly faster but which does not track edge orientation.
edgeID  the index of a single tetrahedron edge; this must be between 0 and 6t1 inclusive, where t is the number of tetrahedra. See the TetEdgeState class notes for details on edge indexing. 
twisted  used to track edge orientation, as described above. This must be either 0 or 1 as it is passed into the function, and it will also be either 0 or 1 upon returning from the function. 

inlineinherited 
Returns the specific pairing of tetrahedron faces that this set of gluing permutations complements.

inherited 
Returns the specific pairing of simplex facets that this set of gluing permutations complements.

inlineinherited 
Returns the total number of tetrahedra under consideration.

inherited 
Returns the gluing permutation associated with the given simplex facet.
source  the simplex facet under investigation. 

inherited 
Returns the gluing permutation associated with the given simplex facet.
simp  the simplex under investigation (this must be strictly less than the total number of simplices under consideration). 
facet  the facet of the given simplex under investigation (between 0 and dim inclusive). 

protectedinherited 
Returns the index into array Perm::Sn_1 corresponding to the given gluing permutation from the given facet to its partner.
This need not be the index into Perm::Sn_1 that is currently stored for the given facet.
Indices into array Perm::Sn_1 are stored internally in the array permIndices_. Full gluing permutations on the other hand are used in constructing triangulations.
source  the simplex facet under investigation. 
gluing  a possible gluing permutation from the given simplex facet to its partner according to the underlying facet pairing. 

protectedinherited 
Returns the index into array Perm::Sn_1 corresponding to the given gluing permutation from the given facet to its partner.
This need not be the index into Perm::Sn_1 that is currently stored for the given facet.
Indices into array Perm::Sn_1 are stored internally in the array permIndices_. Full gluing permutations on the other hand are used in constructing triangulations.
simp  the simplex under investigation; this must be strictly less than the total number of simplices under consideration. 
facet  the facet of the given simplex under investigation; this must be between 0 and dim inclusive. 
gluing  a possible gluing permutation from the given simplex facet to its partner according to the underlying facet pairing. 

protectedinherited 
Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm::Sn_1.
This index into Perm::Sn_1 need not be the index that is currently stored for the given facet.
Indices into array Perm::Sn_1 are stored internally in the array permIndices_. Full gluing permutations on the other hand are used in constructing triangulations.
If the given simplex facet and its partner according to the underlying facet pairing are facets x and y of their respective simplices, then the resulting gluing permutation will map x to y.
source  the simplex facet under investigation. 
index  an index into Perm::Sn_1; this must be between 0 and dim!1 inclusive. 

protectedinherited 
Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm::Sn_1.
This index into Perm::Sn_1 need not be the index that is currently stored for the given facet.
Indices into array Perm::Sn_1 are stored internally in the array permIndices_. Full gluing permutations on the other hand are used in constructing triangulations.
If the given simplex facet and its partner according to the underlying facet pairing are facets x and y of their respective simplices, then the resulting gluing permutation will map x to y.
simp  the simplex under investigation; this must be strictly less than the total number of simplices under consideration. 
facet  the facet of the given simplex under investigation; this must be between 0 and dim inclusive. 
index  an index into Perm::Sn_1; this must be between 0 and dim!1 inclusive. 

inherited 
Was an error found during construction from an input stream?
This routine returns true
if an input stream constructor was used to create this object but the data in the input stream was invalid or incorrectly formatted.
If a different constructor was called (i.e., no input stream was used), then this routine will always return false
.
true
if an error occurred during construction from an input stream, or false
otherwise.

protectedinherited 
Compares the current set of gluing permutations with its preimage under each automorphism of the underlying face pairing, in order to see whether the current set is in canonical form (i.e., is lexicographically smallest).
true
if the current set is in canonical form, or false
otherwise.

protectedinherited 
Determines whether the permutations already constructed model a triangulation with a low degree edge.
Precisely which types of low degree edges are identified must be specified through parameters testDegree12 and testDegree3.
Tests that do not refer to the gluing permutation for the given face will not be run.
This routine is not fussy about the order in which gluing permutations are selected, as long as permutations not yet selected have the corresponding element of permIndices[] set to 1.
face  the specific tetrahedron face upon which tests will be based. 
testDegree12  true if we should test for nonboundary edges of degree 1 or 2. 
testDegree3  true if we should test for nonboundary edges of degree 3 involving three distinct tetrahedra. 
true
if the permutations under construction will lead to a lowdegree edge as specified by parameters testDegree12 and testDegree3, or false
if no such edge is found.

protected 
Merge the classes of tetrahedron edges as required by the new gluing made at stage orderElt of the search.
See the TetEdgeState class for details.
This routine returns a boolean that indicates whether this merge creates an invalid edge (i.e., an edge identified with itself in reverse).
true
if this merge creates an invalid edge, or false
if not.

protected 
Merge the classes of tetrahedron vertices as required by the new gluing made at stage orderElt of the search.
See the TetVertexState class for details.
This routine returns a bitwise (OR) combination of the VLINK_... flags defined earlier in this class. These flags describe what happened to the vertex links during this particular merge. In particular, they note when a vertex link is closed off, or is made into something other than a punctured 2sphere.

protectedinherited 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner.
Note that this permutation is not a gluing permutation as such, but rather a permutation of 0,...,dim1 only. For a real facet gluing permutation, see routine gluingPerm().
source  the simplex facet under investigation. 

protectedinherited 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner.
Note that this permutation is not a gluing permutation as such, but rather a permutation of 0,...,dim1 only. For a real facet gluing permutation, see routine gluingPerm().
simp  the simplex under investigation (this must be strictly less than the total number of simplices under consideration). 
facet  the facet of the given simplex under investigation (between 0 and dim inclusive). 

protectedinherited 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner.
Note that this permutation is not a gluing permutation as such, but rather a permutation of 0,...,dim1 only. For a real facet gluing permutation, see routine gluingPerm().
source  the simplex facet under investigation. 

protectedinherited 
Returns the index into array Perm::Sn_1 describing how the the given facet is joined to its partner.
Note that this permutation is not a gluing permutation as such, but rather a permutation of 0,...,dim1 only. For a real facet gluing permutation, see routine gluingPerm().
simp  the simplex under investigation (this must be strictly less than the total number of simplices under consideration). 
facet  the facet of the given simplex under investigation (between 0 and dim inclusive). 

staticinherited 
Creates a new search manager based on tagged data read from the given input stream.
This may be a new search or a partially completed search.
The tagged data should be in the format written by dumpTaggedData(). The precise class of the search manager will be determined from the tagged data, and does not need to be known in advance. This is in contrast to dumpData() and the input stream constructors, where the class of the data being read must be known at compile time.
If the data found in the input stream is invalid or incorrectly formatted, a null pointer will be returned. Otherwise a newly constructed search manager will be returned, and it is the responsibility of the caller of this routine to destroy it after use.
The arguments use and useArgs are the same as for the NGluingPermSearcher constructor.
in  the input stream from which to read. 

virtual 
Generates all possible gluing permutation sets that satisfy the current search criteria.
The search criteria are specified in the class constructor, or through the static method findAllPerms().
Each set of gluing permutations will be produced precisely once up to equivalence, where equivalence is defined by the given set of automorphisms of the given face pairing.
For each permutation set that is generated, routine use_ (as passed to the class constructor) will be called with that permutation set as an argument.
Once the generation of permutation sets has finished, routine use_ will be called once more, this time with null
as its first (permutation set) argument.
Subclasses corresponding to more specialised search criteria should override this routine to use a better optimised algorithm where possible.
It is possible to run only a partial search, branching to a given depth but no further. In this case, rather than producing complete gluing permutation sets, the search will produce a series of partiallycomplete NGluingPermSearcher objects. These partial searches may then be restarted by calling runSearch() once more (usually after being frozen or passed on to a different processor). If necessary, the use_ routine may call completePermSet() to distinguish between a complete set of gluing permutations and a partial search state.
Note that a restarted search will never drop below its initial depth. That is, calling runSearch() with a fixed depth can be used to subdivide the overall search space into many branches, and then calling runSearch() on each resulting partial search will complete each of these branches without overlap.
maxDepth  the depth of the partial search to run, or a negative number if a full search should be run (the default). 
Reimplemented from regina::NGluingPermSearcher.
Reimplemented in regina::NClosedPrimeMinSearcher.

inherited 
Returns the total number of simplices under consideration.

protected 
Split the classes of tetrahedron edges to mirror the undoing of the gluing at stage orderElt of the search.
See the TetEdgeState class for details.

protected 
Split the classes of tetrahedron vertices to mirror the undoing of the gluing at stage orderElt of the search.
See the TetVertexState class for details.

inherited 
Returns a newly created triangulation as modelled by this set of gluing permutations and the associated simplex facet pairing.
Each matched pair of facets and their associated permutations will be realised as two simplex facets in the triangulation glued together with the corresponding gluing permutation. Each unmatched facet will be realised as a boundary facet in the triangulation.
It is the responsibility of the caller of this routine to delete this triangulation once it is no longer required.

inlineprotected 
Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given tetrahedron vertex.
See the TetVertexState class for further information.
vertexID  the tetrahedron vertex on which to operate; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 

protected 
Runs a number of tests on all tetrahedron vertices to locate consistency errors in the bdryEdges, bdryNext and bdryTwist members of the TetVertexState class.
Any errors that are identified will be written to standard error. Note that some errors might be harmless (for instance, when a call to mergeVertexClasses() leaves processing incomplete because it has located a bad vertex link and expects the merge to be immediately undone).

protected 
Dumps a summary of bdryNext, bdryTwist and bdryEdges for every vertex of every tetrahedron to the given output stream.
The output format is relatively compact, and is subject to change in future versions of Regina. The output uses one line only, and a final newline is written.
See the TetVertexState class for further information.
out  the output stream to which to write. 

inlineprotected 
Adjusts the bdryNext and bdryTwist arrays for nearby tetrahedron vertices, to ensure that these arrays are consistent with the bdryNext and bdryTwist arrays stored with the given vertex.
It is assumed that the vertex linking triangle for the given tetrahedron vertex contributes at least one boundary edge to the vertex link. Recall from the TetVertexState class notes that the bdryNext and bdryTwist arrays for the given vertex describe the boundary edges that follow on in either direction from the boundary edges supplied by this triangle.
This routine locates the tetrahedron vertices that provide the neighbouring boundary edges, and adjusts the bdryNext and bdryTwist arrays for these neighbouring vertices to point back to the given vertex.
This routine is intended to assist with backtracking. This routine is safe to use if the given tetrahedron vertex points to itself (i.e., it provides a complete boundary cycle of three edges in the vertex link).
See the TetVertexState class for further information.
vertexID  the tetrahedron vertex to examine; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 

inlineprotected 
Signifies that the boundary edges supplied by the vertex linking triangles for the two given tetrahedron vertices should be marked as adjacent.
The bdryNext and bdryTwist arrays for each vertex will be adjusted to point to the other.
See the TetVertexState class for details.
vertexID  the first tetrahedron vertex on which to operate; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 
end  specifies in which direction the adjacent boundary edges lie. This must be either 0 or 1, and its value should correspond to the relevant index in the bdryNext and bdryTwist arrays for vertex vertexID. 
adjVertexID  the tetrahedron vertex whose boundary edges are adjacent to the boundary edges supplied by vertexID; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 
twist  0 if the orientations of the two boundary segments of vertex link are oriented in the same direction, or 1 if they are oriented in opposite directions; see the bdryTwist documentation for details. 

inlineprotected 
Determines whether one of the edges of the vertex linking triangle for the given tetrahedron vertex in fact forms an entire oneedge boundary component of the overall vertex link.
See the TetVertexState class for further information.
vertexID  the tetrahedron vertex to examine; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 
true
if a oneedge boundary component is formed as described above, or false
otherwise.

inlineprotected 
Determines whether edges of the vertex linking triangles for each of the given tetrahedron vertices combine to form an entire twoedge boundary component of the overall vertex link, with one edge from each triangle.
See the TetVertexState class for further information.
vertexID1  the first tetrahedron vertex to examine; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 
vertexID2  the second tetrahedron vertex to examine; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 
true
if a twoedge boundary component is formed as described above, or false
otherwise.

inlineprotected 
Assuming the given edge of the vertex linking triangle for the given tetrahedron vertex lies on the boundary of the vertex link, this routine identifies the adjacent boundary edges of the vertex link in each direction.
The given edge of the vertex linking triangle must belong to one of the two tetrahedron faces currently being joined.
The tetrahedron vertex to examine is passed in vertexID, tet and vertex, and the particular edge of the vertex linking triangle to examine is specified by bdryFace. Details of the adjacent boundary edges are returned in the arrays next and twist.
Note that the values returned might or might not correspond to the bdryNext and bdryTwist arrays of the TetVertexState class, since the TetVertexState arrays skip over adjacent edges belonging to the same vertex linking triangle.
If the given edge of the vertex linking triangle is not a boundary edge of the vertex link, the behaviour of this routine is undefined.
See the TetVertexState class for further information.
vertexID  the tetrahedron vertex to examine; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 
tet  the tetrahedron described by vertexID; this must be (vertexID / 4). It is passed separately to avoid a slow division operation. 
vertex  the tetrahedron vertex number described by vertexID; this must be (vertexID % 4). It is passed separately to avoid a slow modulus operation. 
bdryFace  the face number of the given tetrahedron containing the edge of the vertex linking triangle that is under consideration. This must be between 0 and 3 inclusive, and it may not be equal to vertex. 
next  returns the tetrahedron vertex supplying each adjacent boundary edge; see the TetVertexState::bdryNext notes for details on which directions correspond to array indices 0 and 1. 
twist  returns whether the orientations of the adjacent boundary edges are consistent with the orientation of this boundary edge; see the TetVertexState::bdryTwist notes for further information on orientations in the vertex link. 

inlineprotected 
Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given tetrahedron vertex.
See the TetVertexState class for further information.
vertexID  the tetrahedron vertex on which to operate; this must be between 0 and 4n1 inclusive, where n is the number of tetrahedra. 

protectedinherited 
The set of isomorphisms that define equivalence of gluing permutation sets.
Generally this is the set of all automorphisms of the underlying face pairing.

protectedinherited 
Did we create the isomorphism list autos_ ourselves (in which case we must destroy it also)?

static 
A character used to identify this class when reading and writing tagged data in text format.

protected 
Used for tracking equivalence classes of identified tetrahedron edges.
See the TetEdgeState description for details. This array has size 6n, where edge e of tetrahedron t has index 6t+e.

protected 
Tracks the way in which the edgeState[] array has been updated over time.
This array has size 8n. Suppose the gluing for order[i] affects face f of tetrahedron t. Then element 4i+v of this array describes how the gluing for order[i] affects the edge of tetrahedron t opposite vertices f and v (note that a quarter of this array will remain unused, since f and v are never equal).
If this identification of edges results in the tree with root edgeState[p] being grafted beneath the tree with root edgeState[q], this array will store the value p. Otherwise it will store the value 1.

protectedinherited 
Are we only searching for gluing permutations that correspond to finite triangulations?

protectedinherited 
Has an error occurred during construction from an input stream?

protected 
The number of equivalence classes of identified tetrahedron edges.

protected 
The number of equivalence classes of identified tetrahedron vertices.

protectedinherited 
Describes the order in which gluing permutations are assigned to faces.
Specifically, this order is order[0], order[1], ..., order[orderSize1].
Note that each element of this array corresponds to a single edge of the underlying face pairing graph, which in turn represents a tetrahedron face and its image under the given face pairing.
The specific tetrahedron face stored in this array for each edge of the underlying face pairing graph will be the smaller of the two identified tetrahedron faces (unless otherwise specified for a particular edge type; see NClosedPrimeMinSearcher for examples).

protectedinherited 
Marks which element of order[] we are currently examining at this stage of the search.

protectedinherited 
The total number of edges in the face pairing graph, i.e., the number of elements of interest in the order[] array.

protectedinherited 
Are we only searching for gluing permutations that correspond to orientable triangulations?

protectedinherited 
Keeps track of the orientation of each tetrahedron in the underlying triangulation.
Orientation is positive/negative, or 0 if unknown. Note that in some algorithms the orientation is simply +/1, and in some algorithms the orientation counts forwards or backwards from 0 according to how many times the orientation has been set or verified.

protectedinherited 
The facet pairing that this permutation set complements.
This is guaranteed to be the minimal representative of its facet pairing isomorphism class.

protectedinherited 
The index into array Perm::Sn_1 describing how each simplex facet is glued to its partner.
Note that this is not a gluing permutation as such but rather a permutation of 0,...,dim1 only (see the routines gluingToIndex() and indexToGluing() for conversions). If a permutation has not yet been selected (e.g., if this permutation set is still under construction) then this index is 1.

protectedinherited 
Has the search started yet? This helps distinguish between a new search and the resumption of a partially completed search.

protectedinherited 
A routine to call each time a gluing permutation set is found during the search.

protectedinherited 
Additional usersupplied data to be passed as the second argument to the use_ routine.

staticprotected 
Maintains an ordering of the three tetrahedron faces surrounding a vertex in a tetrahedron.
This ordering is consistent with the orientations of triangles in the vertex link used by TetVertexState::twistUp.
For vertex v (0..3), the tetrahedron face that follows f (0..3) in this ordering is vertexLinkNextFace[v][f]. The remaining array elements vertexLinkNextFace[v][v] are all 1.

staticprotected 
Provides backwards links for the ordering described by vertexLinkNextFace.
For vertex v (0..3), the tetrahedron face that precedes f (0..3) in this ordering is vertexLinkPrevFace[v][f]. The remaining array elements vertexLinkPrevFace[v][v] are all 1.

protected 
Used for tracking equivalence classes of identified tetrahedron vertices.
See the TetVertexState description for details. This array has size 4n, where vertex v of tetrahedron t has index 4t+v.

protected 
Tracks the way in which the vertexState[] array has been updated over time.
This array has size 8n, where element 4i+v describes how the gluing for order[i] affects vertex v of the corresponding tetrahedron (thus a quarter of this array will remain unused, since only three vertices are affected for each gluing).
If this identification of vertices results in the tree with root vertexState[p] being grafted beneath the tree with root vertexState[q], this array will store the value p. Otherwise it will store the value 1.

staticprotected 
Signifies that a vertex link has been closed off (i.e., the link has no remaining boundary edges).

staticprotected 
Signifies that a vertex link has been made into something other than a 2sphere with zero or more punctures.

protectedinherited 
Are there any types of triangulation that we may optionally avoid constructing? This should be a bitwise OR of constants from the PurgeFlags enumeration.
See the constructor documentation for further details on this search parameter.