Regina Calculation Engine
Classes | Public Types | Public Member Functions | Static Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes | Static Protected Attributes | List of all members
regina::GluingPermSearcher< 4 > Class Template Reference

A utility class for searching through all possible gluing permutation sets that correspond to a given pentachoron facet pairing. More...

#include <census/gluingpermsearcher4.h>

Inheritance diagram for regina::GluingPermSearcher< 4 >:
regina::GluingPerms< 4 >

Classes

struct  PentEdgeState
 A structure used to track equivalence classes of pentachoron edges as the gluing permutation set is constructed. More...
 
struct  PentTriangleState
 A structure used to track equivalence classes of pentachoron triangles as the gluing permutation set is constructed. More...
 

Public Types

typedef void(* Use) (const GluingPermSearcher< 4 > *, void *)
 A routine that can do arbitrary processing upon a set of gluing permutations. More...
 

Public Member Functions

 GluingPermSearcher (const FacetPairing< 4 > *pairing, const FacetPairing< 4 >::IsoList *autos, bool orientableOnly, bool finiteOnly, GluingPermSearcher< 4 >::Use use, void *useArgs=0)
 Initialises a new search for gluing permutation sets. More...
 
 GluingPermSearcher (std::istream &in, GluingPermSearcher< 4 >::Use use, void *useArgs=0)
 Initialises a new search manager based on data read from the given input stream. More...
 
virtual ~GluingPermSearcher ()
 Destroys this search manager and all supporting data structures. 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...
 
virtual void dumpData (std::ostream &out) const
 Dumps all internal data in a plain text format to the given output stream. 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< dim > * facetPairing () const
 Returns the specific pairing of simplex facets that this set of gluing permutations complements. More...
 
Perm< dim+1 > gluingPerm (const FacetSpec< dim > &source) const
 Returns the gluing permutation associated with the given simplex facet. More...
 
Perm< dim+1 > gluingPerm (unsigned simp, unsigned facet) const
 Returns the gluing permutation associated with the given simplex facet. More...
 
Triangulation< dim > * 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 FacetPairing< 4 > *pairing, const FacetPairing< 4 >::IsoList *autos, bool orientableOnly, bool finiteOnly, GluingPermSearcher< 4 >::Use use, void *useArgs=0)
 The main entry routine for running a search for all gluing permutation sets that complement a given pentachoron facet pairing. More...
 
static GluingPermSearcher< 4 > * bestSearcher (const FacetPairing< 4 > *pairing, const FacetPairing< 4 >::IsoList *autos, bool orientableOnly, bool finiteOnly, GluingPermSearcher< 4 >::Use use, void *useArgs=0)
 Constructs a search manager of the best possible class for the given search parameters. More...
 
static GluingPermSearcher< 4 > * readTaggedData (std::istream &in, GluingPermSearcher< 4 >::Use 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

bool isCanonical () const
 Compares the current set of gluing permutations with its preimage under each automorphism of the underlying facet pairing, in order to see whether the current set is in canonical form (i.e., is lexicographically smallest). More...
 
bool badTriangleLink (const FacetSpec< 4 > &facet) const
 Determines whether the permutations already constructed model a 4-manifold triangulation with a (2-dimensional) triangle identified with itself using a non-trivial rotation or reflection. More...
 
virtual char dataTag () const
 Returns the character used to identify this class when storing tagged data in text format. More...
 
int findTriangleClass (int triID) const
 Returns the representative of the equivalence class containing the given pentachoron triangle. More...
 
int findTriangleClass (int triID, Perm< 3 > &twist) const
 Returns the representative of the equivalence class containing the given pentachoron triangle. More...
 
bool mergeEdgeClasses ()
 Merges the classes of pentachoron edges as required by the new gluing made at stage orderElt of the search. More...
 
bool mergeTriangleClasses ()
 Merges the classes of pentachoron triangles as required by the new gluing made at stage orderElt of the search. More...
 
void splitEdgeClasses ()
 Splits the classes of pentachoron edges to mirror the undoing of the gluing at stage orderElt of the search. More...
 
void splitTriangleClasses ()
 Splits the classes of pentachoron triangles to mirror the undoing of the gluing at stage orderElt of the search. More...
 
void edgeBdryJoin (int edgeID, char end, int adjEdgeID, char twist)
 Signifies that the boundary edges supplied by the linking triangles for the two given pentachoron edges should be marked as adjacent. More...
 
void edgeBdryFixAdj (int edgeID)
 Adjusts the bdryNext and bdryTwist arrays for nearby pentachoron edges, to ensure that these arrays are consistent with the bdryNext and bdryTwist arrays stored with the given pentachoron edge. More...
 
void edgeBdryBackup (int edgeID)
 Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given pentachoron edge. More...
 
void edgeBdryRestore (int edgeID)
 Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given pentachoron edge. More...
 
void edgeBdryNext (int edgeID, int pent, int edge, int bdryFacet, int next[2], char twist[2])
 Assuming the given edge of the linking triangle for the given pentachoron edge lies on the boundary of the link, this routine identifies the adjacent boundary edges of the link in each direction. More...
 
bool edgeBdryLength1 (int edgeID)
 Determines whether one of the edges of the linking triangle for the given pentachoron edge in fact forms an entire one-edge boundary component of the overall 4-manifold edge link. More...
 
bool edgeBdryLength2 (int edgeID1, int edgeID2)
 Determines whether edges of the linking triangles for each of the given pentachoron edges combine to form an entire two-edge boundary component of the overall 4-manifold edge link, with one edge from each triangle. More...
 
void edgeBdryConsistencyCheck ()
 Runs a number of tests on all pentachoron edges to locate consistency errors in the bdryEdges, bdryNext and bdryTwist members of the PentEdgeState class. More...
 
void edgeBdryDump (std::ostream &out)
 Dumps a summary of bdryNext, bdryTwist and bdryEdges for every edge of every pentachoron to the given output stream. More...
 
int & permIndex (const FacetSpec< dim > &source)
 Returns the index into array Perm<dim+1>::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<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
 
const int & permIndex (const FacetSpec< dim > &source) const
 Returns the index into array Perm<dim+1>::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<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
 
int gluingToIndex (const FacetSpec< dim > &source, const Perm< dim+1 > &gluing) const
 Returns the index into array Perm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
 
int gluingToIndex (unsigned simp, unsigned facet, const Perm< dim+1 > &gluing) const
 Returns the index into array Perm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
 
Perm< dim+1 > indexToGluing (const FacetSpec< 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<dim+1>::Sn_1. More...
 
Perm< dim+1 > 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<dim+1>::Sn_1. More...
 

Protected Attributes

const FacetPairing< 4 >::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 (non-ideal) triangulations? More...
 
GluingPermSearcher< 4 >::Use use_
 A routine to call each time a gluing permutation set is found during the search. More...
 
void * useArgs_
 Additional user-supplied 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 pentachoron in the underlying triangulation. More...
 
FacetSpec< 4 > * order_
 Describes the order in which gluing permutations are assigned to pentachoron facets. More...
 
int orderSize_
 The total number of edges in the facet 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...
 
unsigned nEdgeClasses_
 The number of equivalence classes of identified pentachoron edges. More...
 
PentEdgeState * edgeState_
 Used for tracking equivalence classes of identified pentachoron edges. More...
 
int * edgeStateChanged_
 Tracks the way in which the edgeState_[] array has been updated over time. More...
 
unsigned nTriangleClasses_
 The number of equivalence classes of identified pentachoron triangles. More...
 
PentTriangleState * triState_
 Used for tracking equivalence classes of identified pentachoron triangles. More...
 
int * triStateChanged_
 Tracks the way in which the triState_[] array has been updated over time. More...
 
const FacetPairing< dim > * pairing_
 The facet pairing that this permutation set complements. More...
 
int * permIndices_
 The index into array Perm<dim+1>::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 int edgeLinkNextFacet [10][5]
 Maintains an ordering of the three pentachoron facets surrounding an edge in a pentachoron. More...
 
static const int edgeLinkPrevFacet [10][5]
 Provides backwards links for the ordering described by edgeLinkNextFacet. More...
 

Detailed Description

template<>
class regina::GluingPermSearcher< 4 >

A utility class for searching through all possible gluing permutation sets that correspond to a given pentachoron facet pairing.

Subclasses of GluingPermSearcher<4> correspond to specialised (and heavily optimised) search algorithms that may be used in sufficiently constrained scenarios. The main class GluingPermSearcher<4> offers a default (but slower) search algorithm that may be used in more general contexts.

The simplest way of performing a search through all possible gluing permutations is by calling the static method findAllPerms(). This will examine the search parameters and ensure that the best possible algorithm is used. For finer control over the program flow, the static method bestSearcher() can be used to create a search manager of the most suitable class and then runSearch() can be called on this object directly. For absolute control, a specific algorithm can be forced by explicitly constructing an object of the corresponding class (and again calling runSearch() on that object directly).

The search algorithm used by this base class employs modified union-find structures for both triangle and edge equivalence classes to prune searches that are guaranteed to lead to invalid triangles or edges. This is a 4-dimensional analogue to the algorithms described in "Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find", Benjamin A. Burton, Discrete Comput. Geom. 38 (2007), no. 3, 527–571.

Note that this class derives from GluingPerms<4>. The search will involve building and repeatedly modifying the inherited GluingPerms<4> data in-place.

Python:
Not present.

Member Typedef Documentation

◆ Use

typedef void(* regina::GluingPermSearcher< 4 >::Use) (const GluingPermSearcher< 4 > *, void *)

A routine that can do arbitrary processing upon a set of gluing permutations.

Such routines are used to process permutation sets that are found when running census-building routines such as findAllPerms().

The first parameter passed will be a set of gluing permutations (as this class derives from GluingPerms<4>). This set of gluing permutations must not be deallocated by this routine, since it may be used again later by the caller. The second parameter may contain arbitrary data; typically this will be the data passed to the relevant search routine, such as findAllPerms() or the GluingPermSearcher class constructor.

Note that the first parameter passed might be null to signal that gluing permutation generation has finished.

Constructor & Destructor Documentation

◆ GluingPermSearcher() [1/2]

regina::GluingPermSearcher< 4 >::GluingPermSearcher ( const FacetPairing< 4 > *  pairing,
const FacetPairing< 4 >::IsoList *  autos,
bool  orientableOnly,
bool  finiteOnly,
GluingPermSearcher< 4 >::Use  use,
void *  useArgs = 0 
)

Initialises a new search for gluing permutation sets.

The search is started by calling runSearch(). Note that the static method findAllPerms() handles both construction and searching, and is the preferred entry point for end users.

The arguments to this constructor describe the search parameters in detail, as well as what should be done with each gluing permutation set that is found.

The appropriate use of parameters orientableOnly and finiteOnly can significantly speed up the permutation set generation. For some combinations of these parameters entirely different algorithms are used.

Note that even if finiteOnly is set to true, some ideal triangulations might still slip through the net (since the full vertex links are not always constructed). However, setting finiteOnly to true will allow the census algorithm to take shortcuts and therefore run faster. The resulting triangulations may be tested for finiteness (and other properties) by calling triangulate().

Precondition
The given facet pairing is connected, i.e., it is possible to reach any pentachoron from any other pentachoron via a series of matched facet pairs.
The given facet pairing is in canonical form as described by FacetPairing<4>::isCanonical(). Note that all facet pairings constructed by FacetPairing<4>::findAllPairings() are of this form.
Parameters
pairingthe specific pairing of pentachoron facets that the generated permutation sets will complement.
autosthe collection of isomorphisms that define equivalence of permutation sets. These are used by runSearch(), which produces each permutation set precisely once up to equivalence. These isomorphisms must all be automorphisms of the given facet pairing, and will generally be the set of all such automorphisms. This parameter may be 0, in which case the set of all automorphisms of the given facet pairing will be generated and used.
orientableOnlytrue if only gluing permutations corresponding to orientable triangulations should be generated, or false if no such restriction should be imposed.
finiteOnlytrue if only gluing permutations corresponding to finite (non-ideal) triangulations are required, or false if there is no such requirement. Note that regardless of this value, some ideal triangulations might still be produced; see the notes above for details.
usethe function to call upon each permutation set that is found. The first parameter passed to this function will be a gluing permutation set. The second parameter will be parameter useArgs as was passed to this routine.
useArgsthe pointer to pass as the final parameter for the function use which will be called upon each permutation set found.

◆ GluingPermSearcher() [2/2]

regina::GluingPermSearcher< 4 >::GluingPermSearcher ( std::istream &  in,
GluingPermSearcher< 4 >::Use  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.

Warning
The data format is liable to change between Regina releases. Data in this format should be used on a short-term temporary basis only.
Parameters
inthe input stream from which to read.
useas for the main GluingPermSearcher<4> constructor.
useArgsas for the main GluingPermSearcher<4> constructor.

◆ ~GluingPermSearcher()

virtual regina::GluingPermSearcher< 4 >::~GluingPermSearcher ( )
virtual

Destroys this search manager and all supporting data structures.

Member Function Documentation

◆ badTriangleLink()

bool regina::GluingPermSearcher< 4 >::badTriangleLink ( const FacetSpec< 4 > &  facet) const
protected

Determines whether the permutations already constructed model a 4-manifold triangulation with a (2-dimensional) triangle identified with itself using a non-trivial rotation or reflection.

Tests that do not refer to the gluing permutation for the given pentachoron facet 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.

Parameters
facetthe specific pentachoron facet upon which tests will be based.
Returns
true if the permutations under construction will lead to a triangle identified with itself using a non-trivial rotation or reflection, or false if no such triangle is found.

◆ bestSearcher()

static GluingPermSearcher<4>* regina::GluingPermSearcher< 4 >::bestSearcher ( const FacetPairing< 4 > *  pairing,
const FacetPairing< 4 >::IsoList *  autos,
bool  orientableOnly,
bool  finiteOnly,
GluingPermSearcher< 4 >::Use  use,
void *  useArgs = 0 
)
static

Constructs a search manager of the best possible class for the given search parameters.

Different subclasses of GluingPermSearcher<4> 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 all-in-one 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 GluingPermSearcher<4> constructor for documentation on the arguments to this routine.

Precondition
The given facet pairing is connected, i.e., it is possible to reach any pentachoron from any other pentachoron via a series of matched facet pairs.
The given facet pairing is in canonical form as described by FacetPairing<4>::isCanonical(). Note that all facet pairings constructed by FacetPairing<4>::findAllPairings() are of this form.
Returns
the newly created search manager.

◆ completePermSet()

bool regina::GluingPermSearcher< 4 >::completePermSet ( ) const
inline

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 depth-based searches. See runSearch() for further details.

Returns
true if a complete gluing permutation set is held, or false otherwise.

◆ dataTag()

char regina::GluingPermSearcher< 4 >::dataTag ( ) const
inlineprotectedvirtual

Returns the character used to identify this class when storing tagged data in text format.

Returns
the class tag.

◆ dumpData()

virtual void regina::GluingPermSearcher< 4 >::dumpData ( std::ostream &  out) const
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 subclass-specific information will of course be lost).

Warning
The data format is liable to change between Regina releases. Data in this format should be used on a short-term temporary basis only.
Parameters
outthe output stream to which the data should be written.

Reimplemented from regina::GluingPerms< 4 >.

◆ dumpTaggedData()

void regina::GluingPermSearcher< 4 >::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.

This routine can be used with readTaggedData() to transport objects from place to place whose precise class is unknown.

Warning
The data format is liable to change between Regina releases. Data in this format should be used on a short-term temporary basis only.
Parameters
outthe output stream to which the data should be written.

◆ edgeBdryBackup()

void regina::GluingPermSearcher< 4 >::edgeBdryBackup ( int  edgeID)
inlineprotected

Copies the bdryNext and bdryTwist arrays to the bdryNextOld and bdryTwistOld arrays for the given pentachoron edge.

See the PentEdgeState class for further information.

Parameters
edgeIDthe pentachoron edge on which to operate; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.

◆ edgeBdryConsistencyCheck()

void regina::GluingPermSearcher< 4 >::edgeBdryConsistencyCheck ( )
protected

Runs a number of tests on all pentachoron edges to locate consistency errors in the bdryEdges, bdryNext and bdryTwist members of the PentEdgeState 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 mergeEdgeClasses() leaves processing incomplete because it has located a bad edge link and expects the merge to be immediately undone).

◆ edgeBdryDump()

void regina::GluingPermSearcher< 4 >::edgeBdryDump ( std::ostream &  out)
protected

Dumps a summary of bdryNext, bdryTwist and bdryEdges for every edge of every pentachoron 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 PentEdgeState class for further information.

Parameters
outthe output stream to which to write.

◆ edgeBdryFixAdj()

void regina::GluingPermSearcher< 4 >::edgeBdryFixAdj ( int  edgeID)
inlineprotected

Adjusts the bdryNext and bdryTwist arrays for nearby pentachoron edges, to ensure that these arrays are consistent with the bdryNext and bdryTwist arrays stored with the given pentachoron edge.

It is assumed that the linking triangle for the given pentachoron edge contributes at least one boundary edge to the 4-manifold edge link. Recall from the PentEdgeState class notes that the bdryNext and bdryTwist arrays for the given pentachoron edge describe the boundary edges that follow on in either direction from the boundary edges supplied by this triangle.

This routine locates the pentachoron edges that provide the neighbouring boundary edges of the link, and adjusts the bdryNext and bdryTwist arrays for these neighbouring pentachoron edges to point back to the given pentachoron edge.

This routine is intended to assist with backtracking. This routine is safe to use if the given pentachoron edge points to itself (i.e., it provides a complete boundary cycle of three edges in the 4-manifold edge link).

See the PentEdgeState class for further information.

Precondition
The linking triangle for the given pentachoron edge contributes at least one boundary edge to the 4-manifold edge link.
Parameters
edgeIDthe pentachoron edge to examine; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.

◆ edgeBdryJoin()

void regina::GluingPermSearcher< 4 >::edgeBdryJoin ( int  edgeID,
char  end,
int  adjEdgeID,
char  twist 
)
inlineprotected

Signifies that the boundary edges supplied by the linking triangles for the two given pentachoron edges should be marked as adjacent.

The bdryNext and bdryTwist arrays for each pentachoron edge will be adjusted to point to the other.

See the PentEdgeState class for details.

Parameters
edgeIDthe first pentachoron edge on which to operate; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.
endspecifies 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 edge edgeID.
adjEdgeIDthe pentachoron edge whose boundary edges are adjacent to the boundary edges supplied by edgeID; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.
twist0 if the orientations of the two boundary segments of edge link are oriented in the same direction, or 1 if they are oriented in opposite directions; see the bdryTwist documentation for details.

◆ edgeBdryLength1()

bool regina::GluingPermSearcher< 4 >::edgeBdryLength1 ( int  edgeID)
inlineprotected

Determines whether one of the edges of the linking triangle for the given pentachoron edge in fact forms an entire one-edge boundary component of the overall 4-manifold edge link.

See the PentEdgeState class for further information.

Parameters
edgeIDthe pentachoron edge to examine; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.
Returns
true if a one-edge boundary component is formed as described above, or false otherwise.

◆ edgeBdryLength2()

bool regina::GluingPermSearcher< 4 >::edgeBdryLength2 ( int  edgeID1,
int  edgeID2 
)
inlineprotected

Determines whether edges of the linking triangles for each of the given pentachoron edges combine to form an entire two-edge boundary component of the overall 4-manifold edge link, with one edge from each triangle.

See the PentEdgeState class for further information.

Parameters
edgeID1the first pentachoron edge to examine; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.
edgeID2the second pentachoron edge to examine; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.
Returns
true if a two-edge boundary component is formed as described above, or false otherwise.

◆ edgeBdryNext()

void regina::GluingPermSearcher< 4 >::edgeBdryNext ( int  edgeID,
int  pent,
int  edge,
int  bdryFacet,
int  next[2],
char  twist[2] 
)
protected

Assuming the given edge of the linking triangle for the given pentachoron edge lies on the boundary of the link, this routine identifies the adjacent boundary edges of the link in each direction.

The given edge of the linking triangle must belong to one of the two pentachoron facets currently being joined.

The pentachoron edge to examine is passed in edgeID, pent and edge, and the particular edge of the linking triangle to examine is specified by bdryFacet. 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 PentEdgeState class, since the PentEdgeState arrays skip over adjacent edges belonging to the same linking triangle.

If the given edge of the linking triangle is not a boundary edge of the 4-manifold edge link, the behaviour of this routine is undefined.

See the PentEdgeState class for further information.

Precondition
The pentachoron facet (pent, bdryFacet) is one of the two facets that are currently being joined together. That is, this facet is either order_[orderElt_] or its partner in the underlying pentachoron facet pairing.
Parameters
edgeIDthe pentachoron edge to examine; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.
pentthe pentachoron described by edgeID; this must be (edgeID / 10). It is passed separately to avoid a slow division operation.
edgethe pentachoron edge number described by edgeID; this must be (edgeID % 10). It is passed separately to avoid a slow modulus operation.
bdryFacetthe facet number of the given pentachoron containing the edge of the linking triangle that is under consideration. This must be between 0 and 4 inclusive.
nextreturns the pentachoron edge supplying each adjacent boundary edge of the link; see the PentEdgeState::bdryNext notes for details on which directions correspond to array indices 0 and 1.
twistreturns whether the orientations of the adjacent boundary edges are consistent with the orientation of this boundary edge; see the PentEdgeState::bdryTwist notes for further information on orientations in the link.

◆ edgeBdryRestore()

void regina::GluingPermSearcher< 4 >::edgeBdryRestore ( int  edgeID)
inlineprotected

Copies the bdryNextOld and bdryTwistOld arrays to the bdryNext and bdryTwist arrays for the given pentachoron edge.

See the PentEdgeState class for further information.

Parameters
edgeIDthe pentachoron edge on which to operate; this must be between 0 and 10n-1 inclusive, where n is the number of pentachora.

◆ facetPairing()

const FacetPairing< dim > * regina::GluingPerms< dim >::facetPairing ( ) const
inlineinherited

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

Returns
the corresponding simplex facet pairing.

◆ findAllPerms()

static void regina::GluingPermSearcher< 4 >::findAllPerms ( const FacetPairing< 4 > *  pairing,
const FacetPairing< 4 >::IsoList *  autos,
bool  orientableOnly,
bool  finiteOnly,
GluingPermSearcher< 4 >::Use  use,
void *  useArgs = 0 
)
static

The main entry routine for running a search for all gluing permutation sets that complement a given pentachoron facet pairing.

This routine examines the search parameters, chooses the best possible search algorithm, constructs an object of the corresponding subclass of GluingPermSearcher<4> and then calls runSearch().

See the GluingPermSearcher<4> constructor for documentation on the arguments to this routine. See the runSearch() method for documentation on how the search runs and returns its results.

Precondition
The given facet pairing is connected, i.e., it is possible to reach any pentachoron from any other pentachoron via a series of matched facet pairs.
The given facet pairing is in canonical form as described by FacetPairing<4>::isCanonical(). Note that all facet pairings constructed by FacetPairing<4>::findAllPairings() are of this form.

◆ findTriangleClass() [1/2]

int regina::GluingPermSearcher< 4 >::findTriangleClass ( int  triID) const
inlineprotected

Returns the representative of the equivalence class containing the given pentachoron triangle.

The class representative is defined to be the root of the corresponding union-find tree.

See the PentTriangleState class for further details. See also the other variant of findTriangleClass(), which is slower but which also tracks triangle rotations and reflections.

Parameters
triIDthe index of a single pentachoron triangle; this must be between 0 and 10p-1 inclusive, where p is the number of pentachora. See the PentTriangleState class notes for details on triangle indexing.
Returns
the index of the pentachoron triangle at the root of the union-find tree, i.e., the representative of the equivalence class.

◆ findTriangleClass() [2/2]

int regina::GluingPermSearcher< 4 >::findTriangleClass ( int  triID,
Perm< 3 > &  twist 
) const
inlineprotected

Returns the representative of the equivalence class containing the given pentachoron triangle.

The class representative is defined to be the root of the corresponding union-find tree.

The argument twist is also modified to indicate what rotation or reflection is used to identify vertices (0,1,2) of the given triangle with vertices (0,1,2) of the class representative. Note that this argument is not initialised. Instead, the original twist will be multiplied on the left by the mapping described above.

See the PentTriangleState class for further details. See also the other variant of findTriangleClass(), which is faster but which does not track triangle rotations and reflections.

Parameters
triIDthe index of a single pentachoron triangle; this must be between 0 and 10p-1 inclusive, where p is the number of pentachora. See the PentTriangleState class notes for details on triangle indexing.
twistused to track triangle rotations and reflections, as described above. This must be a mapping from (0,1,2) to (0,1,2) as it is passed into the function, and it will also be a mapping from (0,1,2) to (0,1,2) upon returning from the function.
Returns
the index of the pentachoron triangle at the root of the union-find tree, i.e., the representative of the equivalence class.

◆ gluingPerm() [1/2]

Perm< dim+1 > regina::GluingPerms< dim >::gluingPerm ( const FacetSpec< dim > &  source) const
inlineinherited

Returns the gluing permutation associated with the given simplex facet.

Precondition
The given facet is actually paired with some other facet in the underlying pairwise matching (see routine facetPairing()).
The given facet is a real simplex facet (not boundary, before-the-start or past-the-end).
Parameters
sourcethe simplex facet under investigation.
Returns
the associated gluing permutation.

◆ gluingPerm() [2/2]

Perm< dim+1 > regina::GluingPerms< dim >::gluingPerm ( unsigned  simp,
unsigned  facet 
) const
inlineinherited

Returns the gluing permutation associated with the given simplex facet.

Precondition
The given facet is actually paired with some other facet in the underlying pairwise matching (see routine facetPairing()).
Parameters
simpthe simplex under investigation (this must be strictly less than the total number of simplices under consideration).
facetthe facet of the given simplex under investigation (between 0 and dim inclusive).
Returns
the associated gluing permutation.

◆ gluingToIndex() [1/2]

int regina::GluingPerms< dim >::gluingToIndex ( const FacetSpec< dim > &  source,
const Perm< dim+1 > &  gluing 
) const
protectedinherited

Returns the index into array Perm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner.

This need not be the index into Perm<dim+1>::Sn_1 that is currently stored for the given facet.

Indices into array Perm<dim+1>::Sn_1 are stored internally in the array permIndices_. Full gluing permutations on the other hand are used in constructing triangulations.

Precondition
The given simplex facet has a partner according to the underlying facet pairing, i.e., is not a boundary facet.
If the given simplex facet and its partner are facets x and y of their respective simplices, then the given gluing permutation maps x to y.
Parameters
sourcethe simplex facet under investigation.
gluinga possible gluing permutation from the given simplex facet to its partner according to the underlying facet pairing.
Returns
the index into Perm<dim+1>::Sn_1 corresponding to the given gluing permutation; this will be between 0 and dim!-1 inclusive.

◆ gluingToIndex() [2/2]

int regina::GluingPerms< dim >::gluingToIndex ( unsigned  simp,
unsigned  facet,
const Perm< dim+1 > &  gluing 
) const
protectedinherited

Returns the index into array Perm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner.

This need not be the index into Perm<dim+1>::Sn_1 that is currently stored for the given facet.

Indices into array Perm<dim+1>::Sn_1 are stored internally in the array permIndices_. Full gluing permutations on the other hand are used in constructing triangulations.

Precondition
The given simplex facet has a partner according to the underlying facet pairing, i.e., is not a boundary facet.
If the given simplex facet and its partner are facets x and y of their respective simplices, then the given gluing permutation maps x to y.
Parameters
simpthe simplex under investigation; this must be strictly less than the total number of simplices under consideration.
facetthe facet of the given simplex under investigation; this must be between 0 and dim inclusive.
gluinga possible gluing permutation from the given simplex facet to its partner according to the underlying facet pairing.
Returns
the index into Perm<dim+1>::Sn_1 corresponding to the given gluing permutation; this will be between 0 and dim!-1 inclusive.

◆ indexToGluing() [1/2]

Perm< dim+1 > regina::GluingPerms< dim >::indexToGluing ( const FacetSpec< dim > &  source,
int  index 
) const
inlineprotectedinherited

Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm<dim+1>::Sn_1.

This index into Perm<dim+1>::Sn_1 need not be the index that is currently stored for the given facet.

Indices into array Perm<dim+1>::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.

Precondition
The given simplex facet has a partner according to the underlying facet pairing, i.e., is not a boundary facet.
Parameters
sourcethe simplex facet under investigation.
indexan index into Perm<dim+1>::Sn_1; this must be between 0 and dim!-1 inclusive.
Returns
the gluing permutation corresponding to the given index into Perm<dim+1>::Sn_1.

◆ indexToGluing() [2/2]

Perm< dim+1 > regina::GluingPerms< dim >::indexToGluing ( unsigned  simp,
unsigned  facet,
int  index 
) const
inlineprotectedinherited

Returns the gluing permutation from the given facet to its partner that corresponds to the given index into array Perm<dim+1>::Sn_1.

This index into Perm<dim+1>::Sn_1 need not be the index that is currently stored for the given facet.

Indices into array Perm<dim+1>::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.

Precondition
The given simplex facet has a partner according to the underlying facet pairing, i.e., is not a boundary facet.
Parameters
simpthe simplex under investigation; this must be strictly less than the total number of simplices under consideration.
facetthe facet of the given simplex under investigation; this must be between 0 and dim inclusive.
indexan index into Perm<dim+1>::Sn_1; this must be between 0 and dim!-1 inclusive.
Returns
the gluing permutation corresponding to the given index into Perm<dim+1>::Sn_1.

◆ inputError()

bool regina::GluingPerms< dim >::inputError ( ) const
inlineinherited

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.

Returns
true if an error occurred during construction from an input stream, or false otherwise.

◆ isCanonical()

bool regina::GluingPermSearcher< 4 >::isCanonical ( ) const
protected

Compares the current set of gluing permutations with its preimage under each automorphism of the underlying facet pairing, in order to see whether the current set is in canonical form (i.e., is lexicographically smallest).

Returns
true if the current set is in canonical form, or false otherwise.

◆ mergeEdgeClasses()

bool regina::GluingPermSearcher< 4 >::mergeEdgeClasses ( )
protected

Merges the classes of pentachoron edges as required by the new gluing made at stage orderElt of the search.

See the PentEdgeState class for details.

This routine returns a boolean that indicates whether this merge creates an invalid edge (i.e., an edge with identified with itself in reverse, or whose link is something other than a (possibly) punctured 2-sphere).

Returns
true if this merge creates an invalid edge, or false if not.

◆ mergeTriangleClasses()

bool regina::GluingPermSearcher< 4 >::mergeTriangleClasses ( )
protected

Merges the classes of pentachoron triangles as required by the new gluing made at stage orderElt of the search.

See the PentTriangleState class for details.

This routine returns a boolean that indicates whether this merge creates an invalid triangle (i.e., a triangle identified with itself using a non-trivial rotation or reflection).

Returns
true if this merge creates an invalid triangle, or false if not.

◆ permIndex() [1/4]

int & regina::GluingPerms< dim >::permIndex ( const FacetSpec< dim > &  source)
inlineprotectedinherited

Returns the index into array Perm<dim+1>::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,...,dim-1 only. For a real facet gluing permutation, see routine gluingPerm().

Precondition
The given facet is a real simplex facet (not boundary, before-the-start or past-the-end).
Parameters
sourcethe simplex facet under investigation.
Returns
a reference to the corresponding array index.

◆ permIndex() [2/4]

int & regina::GluingPerms< dim >::permIndex ( unsigned  simp,
unsigned  facet 
)
inlineprotectedinherited

Returns the index into array Perm<dim+1>::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,...,dim-1 only. For a real facet gluing permutation, see routine gluingPerm().

Parameters
simpthe simplex under investigation (this must be strictly less than the total number of simplices under consideration).
facetthe facet of the given simplex under investigation (between 0 and dim inclusive).
Returns
a reference to the corresponding array index.

◆ permIndex() [3/4]

const int & regina::GluingPerms< dim >::permIndex ( const FacetSpec< dim > &  source) const
inlineprotectedinherited

Returns the index into array Perm<dim+1>::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,...,dim-1 only. For a real facet gluing permutation, see routine gluingPerm().

Precondition
The given facet is a real simplex facet (not boundary, before-the-start or past-the-end).
Parameters
sourcethe simplex facet under investigation.
Returns
a reference to the corresponding array index.

◆ permIndex() [4/4]

const int & regina::GluingPerms< dim >::permIndex ( unsigned  simp,
unsigned  facet 
) const
inlineprotectedinherited

Returns the index into array Perm<dim+1>::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,...,dim-1 only. For a real facet gluing permutation, see routine gluingPerm().

Parameters
simpthe simplex under investigation (this must be strictly less than the total number of simplices under consideration).
facetthe facet of the given simplex under investigation (between 0 and dim inclusive).
Returns
a reference to the corresponding array index.

◆ readTaggedData()

static GluingPermSearcher<4>* regina::GluingPermSearcher< 4 >::readTaggedData ( std::istream &  in,
GluingPermSearcher< 4 >::Use  use,
void *  useArgs = 0 
)
static

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 smae as for the GluingPermSearcher<4> constructor.

Warning
The data format is liable to change between Regina releases. Data in this format should be used on a short-term temporary basis only.
Parameters
inthe input stream from which to read.

◆ runSearch()

virtual void regina::GluingPermSearcher< 4 >::runSearch ( long  maxDepth = -1)
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 facet 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 partially-complete GluingPermSearcher<4> 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.

Todo:
Feature: Allow cancellation of permutation set generation.
Parameters
maxDepththe depth of the partial search to run, or a negative number if a full search should be run (the default).

◆ size()

unsigned regina::GluingPerms< dim >::size ( ) const
inlineinherited

Returns the total number of simplices under consideration.

Returns
the number of simplices under consideration.

◆ splitEdgeClasses()

void regina::GluingPermSearcher< 4 >::splitEdgeClasses ( )
protected

Splits the classes of pentachoron edges to mirror the undoing of the gluing at stage orderElt of the search.

See the PentEdgeState class for details.

◆ splitTriangleClasses()

void regina::GluingPermSearcher< 4 >::splitTriangleClasses ( )
protected

Splits the classes of pentachoron triangles to mirror the undoing of the gluing at stage orderElt of the search.

See the PentTriangleState class for details.

◆ triangulate()

Triangulation<dim>* regina::GluingPerms< dim >::triangulate ( ) const
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.

Returns
a newly created triangulation modelled by this structure.

Member Data Documentation

◆ autos_

const FacetPairing<4>::IsoList* regina::GluingPermSearcher< 4 >::autos_
protected

The set of isomorphisms that define equivalence of gluing permutation sets.

Generally this is the set of all automorphisms of the underlying facet pairing.

◆ autosNew_

bool regina::GluingPermSearcher< 4 >::autosNew_
protected

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

◆ dataTag_

const char regina::GluingPermSearcher< 4 >::dataTag_
static

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

◆ edgeLinkNextFacet

const int regina::GluingPermSearcher< 4 >::edgeLinkNextFacet[10][5]
staticprotected

Maintains an ordering of the three pentachoron facets surrounding an edge in a pentachoron.

This ordering is consistent with the orientations of triangles in the edge link used by PentEdgeState::twistUp.

For edge e (0..9), the pentachoron facet that follows f (0..5) in this ordering is edgeLinkNextFacet[e][f]. Note that 2/5 of the values in this array remain unaccounted for; these remaining values are set to -1.

◆ edgeLinkPrevFacet

const int regina::GluingPermSearcher< 4 >::edgeLinkPrevFacet[10][5]
staticprotected

Provides backwards links for the ordering described by edgeLinkNextFacet.

For edge e (0..9), the pentachoron facet that follows f (0..5) in this ordering is edgeLinkPrevFacet[e][f]. Again 2/5 of the values in this array remain unaccounted for, and these remaining values are set to -1.

◆ edgeState_

PentEdgeState* regina::GluingPermSearcher< 4 >::edgeState_
protected

Used for tracking equivalence classes of identified pentachoron edges.

See the PentEdgeState description for details. This array has size 10n, where edge e of pentachoron p has index 10p+e.

◆ edgeStateChanged_

int* regina::GluingPermSearcher< 4 >::edgeStateChanged_
protected

Tracks the way in which the edgeState_[] array has been updated over time.

This array has size 25n. Suppose the gluing for order[i] affects facet k of pentachoron p. Then element 10i+e of this array describes how the gluing for order[i] affects edge e of pentachoron p. Note that almost half of this array will remain unused, since only six edges of a pentachoron are affected by any one gluing.

If this identification of edges results in the tree with root edgeState_[x] being grafted beneath the tree with root edgeState_[y], this array will store the value x. Otherwise it will store the value -1.

◆ finiteOnly_

bool regina::GluingPermSearcher< 4 >::finiteOnly_
protected

Are we only searching for gluing permutations that correspond to finite (non-ideal) triangulations?

◆ inputError_

bool regina::GluingPerms< dim >::inputError_
protectedinherited

Has an error occurred during construction from an input stream?

◆ nEdgeClasses_

unsigned regina::GluingPermSearcher< 4 >::nEdgeClasses_
protected

The number of equivalence classes of identified pentachoron edges.

◆ nTriangleClasses_

unsigned regina::GluingPermSearcher< 4 >::nTriangleClasses_
protected

The number of equivalence classes of identified pentachoron triangles.

◆ order_

FacetSpec<4>* regina::GluingPermSearcher< 4 >::order_
protected

Describes the order in which gluing permutations are assigned to pentachoron facets.

Specifically, this order is order_[0], order_[1], ..., order_[orderSize_-1].

Note that each element of this array corresponds to a single edge of the underlying facet pairing graph, which in turn represents a pentachoron facet and its image under the given facet pairing.

The specific pentachoron facet stored in this array for each edge of the underlying facet pairing graph will be the smaller of the two identified pentachoron facets.

◆ orderElt_

int regina::GluingPermSearcher< 4 >::orderElt_
protected

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

◆ orderSize_

int regina::GluingPermSearcher< 4 >::orderSize_
protected

The total number of edges in the facet pairing graph, i.e., the number of elements of interest in the order_[] array.

◆ orientableOnly_

bool regina::GluingPermSearcher< 4 >::orientableOnly_
protected

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

◆ orientation_

int* regina::GluingPermSearcher< 4 >::orientation_
protected

Keeps track of the orientation of each pentachoron 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.

◆ pairing_

const FacetPairing<dim>* regina::GluingPerms< dim >::pairing_
protectedinherited

The facet pairing that this permutation set complements.

This is guaranteed to be the minimal representative of its facet pairing isomorphism class.

◆ permIndices_

int* regina::GluingPerms< dim >::permIndices_
protectedinherited

The index into array Perm<dim+1>::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,...,dim-1 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.

◆ started_

bool regina::GluingPermSearcher< 4 >::started_
protected

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

◆ triState_

PentTriangleState* regina::GluingPermSearcher< 4 >::triState_
protected

Used for tracking equivalence classes of identified pentachoron triangles.

See the PentTriangleState description for details. This array has size 10n, where triangle f of pentachoron p has index 10p+f.

◆ triStateChanged_

int* regina::GluingPermSearcher< 4 >::triStateChanged_
protected

Tracks the way in which the triState_[] array has been updated over time.

This array has size [25n/2]. Suppose the gluing for order[i] affects facet k of pentachoron p. Then element 5i+v of this array describes how the gluing for order[i] affects the triangle of pentachoron p opposite vertices k and v (note that a fifth of this array will remain unused, since k and v are never equal).

If this identification of triangles results in the tree with root triState_[x] being grafted beneath the tree with root triState_[y], this array will store the value x. Otherwise it will store the value -1.

◆ use_

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

◆ useArgs_

void* regina::GluingPermSearcher< 4 >::useArgs_
protected

Additional user-supplied data to be passed as the second argument to the use_ routine.


The documentation for this class was generated from the following file:

Copyright © 1999-2016, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).