Regina Calculation Engine
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
regina::Dim4GluingPerms Class Reference

Represents a specific set of gluing permutations to complement a particular pairwise matching of pentachoron facets. More...

#include <census/dim4gluingperms.h>

Inheritance diagram for regina::Dim4GluingPerms:
regina::NGenericGluingPerms< 4 > regina::Dim4GluingPermSearcher

Public Member Functions

 Dim4GluingPerms (const Dim4GluingPerms &cloneMe)
 Creates a new set of gluing permutations that is a clone of the given permutation set. More...
 
 Dim4GluingPerms (std::istream &in)
 Reads a new set of gluing permutations from the given input 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...
 
REGINA_DEPRECATED const FacetPairing< dim > * getFacetPairing () const
 Deprecated routine that returns the specific pairing of simplex facets that this set of gluing permutations complements. More...
 
NPerm< dim+1 > gluingPerm (const FacetSpec< dim > &source) const
 Returns the gluing permutation associated with the given simplex facet. More...
 
NPerm< 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...
 
virtual void dumpData (std::ostream &out) const
 Dumps all internal data in a plain text format to the given output stream. More...
 

Protected Member Functions

 Dim4GluingPerms (const Dim4FacetPairing *pairing)
 Creates a new permutation set. More...
 
int & permIndex (const FacetSpec< dim > &source)
 Returns the index into array NPerm<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 NPerm<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 NPerm<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 NPerm<dim+1>::Sn_1 describing how the the given facet is joined to its partner. More...
 
int gluingToIndex (const FacetSpec< dim > &source, const NPerm< dim+1 > &gluing) const
 Returns the index into array NPerm<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 NPerm< dim+1 > &gluing) const
 Returns the index into array NPerm<dim+1>::Sn_1 corresponding to the given gluing permutation from the given facet to its partner. More...
 
NPerm< 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 NPerm<dim+1>::Sn_1. More...
 
NPerm< 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 NPerm<dim+1>::Sn_1. More...
 

Protected Attributes

const FacetPairing< dim > * pairing_
 The facet pairing that this permutation set complements. More...
 
int * permIndices_
 The index into array NPerm<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...
 

Detailed Description

Represents a specific set of gluing permutations to complement a particular pairwise matching of pentachoron facets.

Given a pairwise matching of facets (as described by class Dim4FacetPairing), each facet that is matched with some other facet will have an associated permutation of five elements (as described by class NPerm5).

If a facet is matched with some other facet, the two associated permutations in this set will be inverses. If a facet is left deliberately unmatched, it will have no associated permutation in this set.

Such a set of permutations models part of the structure of a 4-manifold triangulation, in which each pentachoron facet that is glued to another facet has a corresponding gluing permutation (and the matched facet has the inverse gluing permutation).

Python:
Not present.

Constructor & Destructor Documentation

§ Dim4GluingPerms() [1/3]

regina::Dim4GluingPerms::Dim4GluingPerms ( const Dim4GluingPerms cloneMe)
inline

Creates a new set of gluing permutations that is a clone of the given permutation set.

Parameters
cloneMethe gluing permutations to clone.

§ Dim4GluingPerms() [2/3]

regina::Dim4GluingPerms::Dim4GluingPerms ( std::istream &  in)
inline

Reads a new set of gluing permutations from the given input stream.

This routine reads data in the format written by dumpData().

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.

§ Dim4GluingPerms() [3/3]

regina::Dim4GluingPerms::Dim4GluingPerms ( const Dim4FacetPairing pairing)
inlineprotected

Creates a new permutation set.

All internal arrays will be allocated but not initialised.

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 Dim4FacetPairing::isCanonical(). Note that all facet pairings constructed by Dim4FacetPairing::findAllPairings() are of this form.
Parameters
pairingthe specific pairing of pentachoron facets that this permutation set will complement.

Member Function Documentation

§ dumpData()

virtual void regina::NGenericGluingPerms< dim >::dumpData ( std::ostream &  out) const
virtualinherited

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 in regina::Dim4GluingPermSearcher.

§ facetPairing()

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

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

Returns
the corresponding simplex facet pairing.

§ getFacetPairing()

const FacetPairing< dim > * regina::NGenericGluingPerms< dim >::getFacetPairing ( ) const
inlineinherited

Deprecated routine that returns the specific pairing of simplex facets that this set of gluing permutations complements.

Deprecated:
This routine has been renamed to facetPairing(). See the facetPairing() documentation for further details.

§ gluingPerm() [1/2]

NPerm< dim+1 > regina::NGenericGluingPerms< 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]

NPerm< dim+1 > regina::NGenericGluingPerms< 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::NGenericGluingPerms< dim >::gluingToIndex ( const FacetSpec< dim > &  source,
const NPerm< dim+1 > &  gluing 
) const
protectedinherited

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

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

Indices into array NPerm<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 NPerm<dim+1>::Sn_1 corresponding to the given gluing permutation; this will be between 0 and dim!-1 inclusive.

§ gluingToIndex() [2/2]

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

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

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

Indices into array NPerm<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 NPerm<dim+1>::Sn_1 corresponding to the given gluing permutation; this will be between 0 and dim!-1 inclusive.

§ indexToGluing() [1/2]

NPerm< dim+1 > regina::NGenericGluingPerms< 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 NPerm<dim+1>::Sn_1.

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

Indices into array NPerm<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 NPerm<dim+1>::Sn_1; this must be between 0 and dim!-1 inclusive.
Returns
the gluing permutation corresponding to the given index into NPerm<dim+1>::Sn_1.

§ indexToGluing() [2/2]

NPerm< dim+1 > regina::NGenericGluingPerms< 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 NPerm<dim+1>::Sn_1.

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

Indices into array NPerm<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 NPerm<dim+1>::Sn_1; this must be between 0 and dim!-1 inclusive.
Returns
the gluing permutation corresponding to the given index into NPerm<dim+1>::Sn_1.

§ inputError()

bool regina::NGenericGluingPerms< 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.

§ permIndex() [1/4]

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

Returns the index into array NPerm<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::NGenericGluingPerms< dim >::permIndex ( unsigned  simp,
unsigned  facet 
)
inlineprotectedinherited

Returns the index into array NPerm<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::NGenericGluingPerms< dim >::permIndex ( const FacetSpec< dim > &  source) const
inlineprotectedinherited

Returns the index into array NPerm<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::NGenericGluingPerms< dim >::permIndex ( unsigned  simp,
unsigned  facet 
) const
inlineprotectedinherited

Returns the index into array NPerm<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.

§ size()

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

Returns the total number of simplices under consideration.

Returns
the number of simplices under consideration.

§ triangulate()

Triangulation<dim>* regina::NGenericGluingPerms< 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

§ inputError_

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

Has an error occurred during construction from an input stream?

§ pairing_

const FacetPairing<dim>* regina::NGenericGluingPerms< 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::NGenericGluingPerms< dim >::permIndices_
protectedinherited

The index into array NPerm<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.


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).