Regina Calculation Engine

A packet representing a collection of normal surfaces in a 3manifold. More...
#include <surfaces/nnormalsurfacelist.h>
Classes  
struct  SurfaceInserter 
An output iterator used to insert surfaces into an NNormalSurfaceList. More...  
class  VectorIterator 
A bidirectional iterator that runs through the raw vectors for surfaces in this list. More...  
Public Member Functions  
virtual  ~NNormalSurfaceList () 
Destroys this list and all the surfaces within. More...  
NormalCoords  getFlavour () const 
Deprecated routine to return the coordinate system being used by the surfaces stored in this set. More...  
NormalCoords  flavour () const 
Deprecated routine to return the coordinate system being used by the surfaces stored in this set. More...  
NormalCoords  coords () const 
Returns the coordinate system being used by the surfaces stored in this set. More...  
NormalList  which () const 
Returns details of which normal surfaces this list represents within the underlying triangulation. More...  
NormalAlg  algorithm () const 
Returns details of the algorithm that was used to enumerate this list. More...  
bool  allowsAlmostNormal () const 
Determines if the coordinate system being used allows for almost normal surfaces, that is, allows for octagonal discs. More...  
bool  allowsSpun () const 
Determines if the coordinate system being used allows for spun normal surfaces. More...  
bool  allowsOriented () const 
Determines if the coordinate system being used allows for transversely oriented normal surfaces. More...  
bool  isEmbeddedOnly () const 
Returns whether this list was constructed to contain only properly embedded surfaces. More...  
NTriangulation *  getTriangulation () const 
Returns the triangulation in which these normal surfaces live. More...  
unsigned long  getNumberOfSurfaces () const 
Returns the number of surfaces stored in this set. More...  
const NNormalSurface *  getSurface (unsigned long index) const 
Returns the surface at the requested index in this set. More...  
void  writeAllSurfaces (std::ostream &out) const 
Writes the number of surfaces in this set followed by the details of each surface to the given output stream. More...  
virtual void  writeTextShort (std::ostream &out) const 
Writes this object in short text format to the given output stream. More...  
virtual void  writeTextLong (std::ostream &out) const 
Writes this object in long text format to the given output stream. More...  
virtual bool  dependsOnParent () const 
Determines if this packet depends upon its parent. More...  
NNormalSurfaceList *  quadToStandard () const 
Converts the set of all embedded vertex normal surfaces in quadrilateral space to the set of all embedded vertex normal surfaces in standard (triquad) space. More...  
NNormalSurfaceList *  quadOctToStandardAN () const 
Converts the set of all embedded vertex almost normal surfaces in quadrilateraloctagon space to the set of all embedded vertex almost normal surfaces in the standard triquadoct space. More...  
NNormalSurfaceList *  standardToQuad () const 
Converts the set of all embedded vertex normal surfaces in standard (triquad) space to the set of all embedded vertex normal surfaces in quadrilateral space. More...  
NNormalSurfaceList *  standardANToQuadOct () const 
Converts the set of all embedded vertex almost normal surfaces in standard triquadoct space to the set of all embedded vertex almost normal surfaces in the smaller quadrilateraloctagon space. More...  
NNormalSurfaceList *  filterForLocallyCompatiblePairs () const 
Creates a new list filled with the surfaces from this list that have at least one locally compatible partner. More...  
NNormalSurfaceList *  filterForDisjointPairs () const 
Creates a new list filled with the surfaces from this list that have at least one disjoint partner. More...  
NNormalSurfaceList *  filterForPotentiallyIncompressible () const 
Creates a new list filled with only the surfaces from this list that "might" represent twosided incompressible surfaces. More...  
NMatrixInt *  recreateMatchingEquations () const 
Returns a newly created matrix containing the matching equations that were used to create this normal surface list. More...  
VectorIterator  beginVectors () const 
An iterator that gives access to the raw vectors for surfaces in this list, pointing to the beginning of this surface list. More...  
VectorIterator  endVectors () const 
An iterator that gives access to the raw vectors for surfaces in this list, pointing past the end of this surface list. More...  
Public Member Functions inherited from regina::NPacket  
NPacket (NPacket *parent=0)  
Constructor that inserts the new packet into the overall tree structure. More...  
virtual  ~NPacket () 
Destructor that also orphans this packet and destroys all of its descendants. More...  
virtual PacketType  getPacketType () const =0 
Returns the unique integer ID representing this type of packet. More...  
virtual std::string  getPacketTypeName () const =0 
Returns an English name for this type of packet. More...  
const std::string &  getPacketLabel () const 
Returns the label associated with this individual packet. More...  
std::string  getHumanLabel () const 
Returns the label associated with this individual packet, adjusted if necessary for humanreadable output. More...  
void  setPacketLabel (const std::string &newLabel) 
Sets the label associated with this individual packet. More...  
std::string  getFullName () const 
Returns a descriptive text string for the packet. More...  
std::string  makeUniqueLabel (const std::string &base) const 
Returns a new label that cannot be found anywhere in the entire tree structure. More...  
bool  makeUniqueLabels (NPacket *reference) 
Ensures that all packet labels in both this and the given packet tree combined are distinct. More...  
bool  hasTag (const std::string &tag) const 
Determines whether this packet has the given associated tag. More...  
bool  hasTags () const 
Determines whether this packet has any associated tags at all. More...  
bool  addTag (const std::string &tag) 
Associates the given tag with this packet. More...  
bool  removeTag (const std::string &tag) 
Removes the association of the given tag with this packet. More...  
void  removeAllTags () 
Removes all associated tags from this packet. More...  
const std::set< std::string > &  getTags () const 
Returns the set of all tags associated with this packet. More...  
bool  listen (NPacketListener *listener) 
Registers the given packet listener to listen for events on this packet. More...  
bool  isListening (NPacketListener *listener) 
Determines whether the given packet listener is currently listening for events on this packet. More...  
bool  unlisten (NPacketListener *listener) 
Unregisters the given packet listener so that it no longer listens for events on this packet. More...  
NPacket *  getTreeParent () const 
Determines the parent packet in the tree structure. More...  
NPacket *  getFirstTreeChild () const 
Determines the first child of this packet in the tree structure. More...  
NPacket *  getLastTreeChild () const 
Determines the last child of this packet in the tree structure. More...  
NPacket *  getNextTreeSibling () const 
Determines the next sibling of this packet in the tree structure. More...  
NPacket *  getPrevTreeSibling () const 
Determines the previous sibling of this packet in the tree structure. More...  
NPacket *  getTreeMatriarch () const 
Determines the matriarch (the root) of the tree to which this packet belongs. More...  
unsigned  levelsDownTo (const NPacket *descendant) const 
Counts the number of levels between this packet and its given descendant in the tree structure. More...  
unsigned  levelsUpTo (const NPacket *ancestor) const 
Counts the number of levels between this packet and its given ancestor in the tree structure. More...  
bool  isGrandparentOf (const NPacket *descendant) const 
Determines if this packet is equal to or an ancestor of the given packet in the tree structure. More...  
unsigned long  getNumberOfChildren () const 
Returns the number of immediate children of this packet. More...  
unsigned long  getNumberOfDescendants () const 
Returns the total number of descendants of this packet. More...  
unsigned long  getTotalTreeSize () const 
Determines the total number of packets in the tree or subtree for which this packet is matriarch. More...  
void  insertChildFirst (NPacket *child) 
Inserts the given packet as the first child of this packet. More...  
void  insertChildLast (NPacket *child) 
Inserts the given packet as the last child of this packet. More...  
void  insertChildAfter (NPacket *newChild, NPacket *prevChild) 
Inserts the given packet as a child of this packet at the given location in this packet's child list. More...  
void  makeOrphan () 
Cuts this packet away from its parent in the tree structure and instead makes it matriarch of its own tree. More...  
void  reparent (NPacket *newParent, bool first=false) 
Cuts this packet away from its parent in the tree structure, and inserts it as a child of the given packet instead. More...  
void  swapWithNextSibling () 
Swaps this packet with its next sibling in the sequence of children beneath their common parent packet. More...  
void  moveUp (unsigned steps=1) 
Moves this packet the given number of steps towards the beginning of its sibling list. More...  
void  moveDown (unsigned steps=1) 
Moves this packet the given number of steps towards the end of its sibling list. More...  
void  moveToFirst () 
Moves this packet to be the first in its sibling list. More...  
void  moveToLast () 
Moves this packet to be the last in its sibling list. More...  
void  sortChildren () 
Sorts the immediate children of this packet according to their packet labels. More...  
NPacket *  nextTreePacket () 
Finds the next packet after this in a complete depthfirst iteration of the entire tree structure to which this packet belongs. More...  
const NPacket *  nextTreePacket () const 
Finds the next packet after this in a complete depthfirst iteration of the entire tree structure to which this packet belongs. More...  
NPacket *  firstTreePacket (const std::string &type) 
Finds the first packet of the requested type in a complete depthfirst iteration of the tree structure. More...  
const NPacket *  firstTreePacket (const std::string &type) const 
Finds the first packet of the requested type in a complete depthfirst iteration of the tree structure. More...  
NPacket *  nextTreePacket (const std::string &type) 
Finds the next packet after this of the requested type in a complete depthfirst iteration of the entire tree structure. More...  
const NPacket *  nextTreePacket (const std::string &type) const 
Finds the next packet after this of the requested type in a complete depthfirst iteration of the entire tree structure. More...  
NPacket *  findPacketLabel (const std::string &label) 
Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...  
const NPacket *  findPacketLabel (const std::string &label) const 
Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...  
bool  isPacketEditable () const 
Determines whether this packet can be altered without invalidating or otherwise upsetting any of its immediate children. More...  
NPacket *  clone (bool cloneDescendants=false, bool end=true) const 
Clones this packet (and possibly its descendants), assigns to it a suitable unused label and inserts the clone into the tree as a sibling of this packet. More...  
void  writeXMLFile (std::ostream &out) const 
Writes a complete XML file containing the subtree with this packet as matriarch. More...  
std::string  internalID () const 
Returns a unique string ID that identifies this packet. More...  
Public Member Functions inherited from regina::ShareableObject  
ShareableObject ()  
Default constructor that does nothing. More...  
virtual  ~ShareableObject () 
Default destructor that does nothing. More...  
std::string  str () const 
Returns the output from writeTextShort() as a string. More...  
std::string  toString () const 
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More...  
std::string  detail () const 
Returns the output from writeTextLong() as a string. More...  
std::string  toStringLong () const 
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. More...  
Static Public Member Functions  
static NNormalSurfaceList *  enumerate (NTriangulation *owner, NormalCoords coords, NormalList which=NS_LIST_DEFAULT, NormalAlg algHints=NS_ALG_DEFAULT, NProgressTracker *tracker=0) 
A unified routine for enumerating various classes of normal surfaces within a given triangulation. More...  
static NNormalSurfaceList *  enumerate (NTriangulation *owner, NormalCoords coords, bool embeddedOnly, NProgressTracker *tracker=0) 
Deprecated method for enumerating all vertex normal surfaces using the given coordinate system. More...  
static NNormalSurfaceList *  enumerateStandardDirect (NTriangulation *owner) 
Deprecated method that uses a slowbutdirect procedure to enumerate all embedded vertex normal surfaces in standard coordinates, without using the faster procedure that works via quadrilateral coordinates. More...  
static NNormalSurfaceList *  enumerateStandardANDirect (NTriangulation *owner) 
Deprecated method that uses a slowbutdirect procedure to enumerate all embedded vertex almost normal surfaces in standard almost normal coordinates, without using the faster procedure that works via quadrilateraloctagon coordinates. More...  
static NNormalSurfaceList *  enumerateFundPrimal (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true, NNormalSurfaceList *vtxSurfaces=0, NProgressTracker *tracker=0) 
Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the primal Hilbert basis algorithm. More...  
static NNormalSurfaceList *  enumerateFundDual (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true, NProgressTracker *tracker=0) 
Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the dual Hilbert basis algorithm. More...  
static NNormalSurfaceList *  enumerateFundFullCone (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true) 
Deprecated method that uses an extremely slow procedure to enumerate all embedded fundamental surfaces in the given triangulation, by running Normaliz over the full (and typically very large) solution cone, and only enforcing embedded constraints (such as the quadrilateral constraints) afterwards. More...  
static NNormalSurfaceList *  enumerateFundCD (NTriangulation *owner, NormalCoords coords, bool embeddedOnly=true) 
Deprecated method that uses an extremely slow modified ContejeanDevie procedure to enumerate all embedded fundamental surfaces in the given triangulation. More...  
static NXMLPacketReader *  getXMLReader (NPacket *parent, NXMLTreeResolver &resolver) 
Static Public Member Functions inherited from regina::NPacket  
static NXMLPacketReader *  getXMLReader (NPacket *parent, NXMLTreeResolver &resolver) 
Returns a newly created XML element reader that will read the contents of a single XML packet element. More...  
Static Public Attributes  
static const NormalCoords  STANDARD 
Represents standard trianglequadrilateral coordinates for normal surfaces. More...  
static const NormalCoords  AN_STANDARD 
Represents standard trianglequadrilateraloctagon coordinates for octagonal almost normal surfaces. More...  
static const NormalCoords  QUAD 
Represents quadrilateral coordinates for normal surfaces. More...  
static const NormalCoords  AN_QUAD_OCT 
Represents quadrilateraloctagon coordinates for octagonal almost normal surfaces. More...  
static const NormalCoords  EDGE_WEIGHT 
Represents edge weight coordinates for normal surfaces. More...  
static const NormalCoords  FACE_ARCS 
Represents triangle arc coordinates for normal surfaces. More...  
static const NormalCoords  AN_LEGACY 
Indicates that a list of almost normal surfaces was created using Regina 4.5.1 or earlier, where surfaces with more than one octagon of the same type were stripped out of the final solution set. More...  
static const NormalCoords  ORIENTED 
Represents standard trianglequadrilateral coordinates for transversely oriented normal surfaces. More...  
static const NormalCoords  ORIENTED_QUAD 
Represents quadrilateral coordinates for transversely oriented normal surfaces. More...  
Protected Member Functions  
NNormalSurfaceList (NormalCoords coords, NormalList which, NormalAlg algorithm)  
Creates an empty list of normal surfaces with the given parameters. More...  
virtual NPacket *  internalClonePacket (NPacket *parent) const 
Makes a newly allocated copy of this packet. More...  
virtual void  writeXMLPacketData (std::ostream &out) const 
Writes a chunk of XML containing the data for this packet only. More...  
Protected Member Functions inherited from regina::NPacket  
void  writeXMLPacketTree (std::ostream &out) const 
Writes a chunk of XML containing the subtree with this packet as matriarch. More...  
Protected Attributes  
std::vector< NNormalSurface * >  surfaces 
Contains the normal surfaces stored in this packet. More...  
NormalCoords  coords_ 
Stores which coordinate system is being used by the normal surfaces in this packet. More...  
NormalList  which_ 
Indicates which normal surfaces these represent within the underlying triangulation. More...  
NormalAlg  algorithm_ 
Stores the details of the enumeration algorithm that was used to generate this list. More...  
Friends  
class  regina::NXMLNormalSurfaceListReader 
Additional Inherited Members  
Public Types inherited from regina::NPacket  
typedef ChangeEventSpan  ChangeEventBlock 
A deprecated typedef for ChangeEventSpan. More...  
A packet representing a collection of normal surfaces in a 3manifold.
Such a packet must always be a child packet of the triangulation from which the surfaces were obtained. If this triangulation changes, the information contained in this packet will become invalid.
See the NNormalSurfaceVector class notes for details of what to do when introducing a new coordinate system.
Normal surface lists should be created using the routine enumerate(), which is new as of Regina 3.95.
Feature: Allow custom matching equations.
Feature: Allow enumeration with some coordinates explicitly set to zero.
Feature: Allow generating only closed surfaces.
Feature: Generate facets of the solution space representing embedded surfaces.

inlinevirtual 
Destroys this list and all the surfaces within.

inlineprotected 
Creates an empty list of normal surfaces with the given parameters.
coords  the coordinate system to be used for filling this list. 
which  indicates which normal surfaces these will represent within the underlying triangulation. 
algorithm  details of the enumeration algorithm that will be used to fill this list. 

inline 
Returns details of the algorithm that was used to enumerate this list.
These may not be the same NormalAlg flags that were passed to enumerate(). In particular, default values will have be explicitly filled in, invalid and/or redundant values will have been removed, and unavailable and/or unsupported combinations of algorithm flags will be replaced with whatever algorithm was actually used.
bool regina::NNormalSurfaceList::allowsAlmostNormal  (  )  const 
Determines if the coordinate system being used allows for almost normal surfaces, that is, allows for octagonal discs.
true
if and only if almost normal surfaces are allowed. bool regina::NNormalSurfaceList::allowsOriented  (  )  const 
Determines if the coordinate system being used allows for transversely oriented normal surfaces.
true
if and only if transverse orientations are supported. bool regina::NNormalSurfaceList::allowsSpun  (  )  const 
Determines if the coordinate system being used allows for spun normal surfaces.
true
if and only if spun normal surface are supported.

inline 
An iterator that gives access to the raw vectors for surfaces in this list, pointing to the beginning of this surface list.

inline 
Returns the coordinate system being used by the surfaces stored in this set.

inlinevirtual 
Determines if this packet depends upon its parent.
This is true if the parent cannot be altered without invalidating or otherwise upsetting this packet.
true
if and only if this packet depends on its parent. Implements regina::NPacket.

inline 
An iterator that gives access to the raw vectors for surfaces in this list, pointing past the end of this surface list.
This iterator is not dereferenceable.

static 
A unified routine for enumerating various classes of normal surfaces within a given triangulation.
The NormalCoords argument allows you to specify an underlying coordinate system (e.g., standard coordinates, quadrilateral coordinates or almost normal coordinates).
The NormalList argument is a combination of flags that allows you to specify exactly which normal surfaces you require. This includes (i) whether you want all vertex surfaces or all fundamental surfaces, which defaults to NS_VERTEX if you specify neither or both; and (ii) whether you want only properly embedded surfaces or you also wish to include immersed and/or singular surfaces, which defaults to NS_EMBEDDED_ONLY if you specify neither or both.
The NormalAlg argument is a combination of flags that allows you to control the underlying enumeration algorithm. These flags are treated as hints only: if your selection of algorithm is invalid, unavailable or unsupported then Regina will choose something more appropriate. Unless you have some specialised need, the default NS_ALG_DEFAULT (which makes no hints at all) will allow Regina to choose what it thinks will be the most efficient method.
The enumerated surfaces will be stored in a new normal surface list, and their representations will be scaled down to use the smallest possible integer coordinates. This normal surface list will be inserted into the packet tree as the last child of the given triangulation. This triangulation must remain the parent of this normal surface list, and must not change while this normal surface list remains in existence.
If a progress tracker is passed, the normal surface enumeration will take place in a new thread and this routine will return immediately. If the user cancels the operation from another thread, then the normal surface list will not be inserted into the packet tree (but the caller of this routine will still need to delete it). Regarding progress tracking, this routine will declare and work through a series of stages whose combined weights sum to 1; typically this means that the given tracker must not have been used before.
If no progress tracker is passed, the enumeration will run in the current thread and this routine will return only when the enumeration is complete. Note that this enumeration can be extremely slow for larger triangulations.
owner  the triangulation upon which this list of normal surfaces will be based. 
coords  the coordinate system to be used. 
which  indicates which normal surfaces should be enumerated. 
algHints  passes requests to Regina for which specific enumeration algorithm should be used. 
tracker  a progress tracker through which progress will be reported, or 0 if no progress reporting is required. 

inlinestatic 
Deprecated method for enumerating all vertex normal surfaces using the given coordinate system.
Users should now call enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details, including all arguments, returns values, preconditions and postconditions.
enumerate(owner, coords, NS_EMBEDDED_ONLY, NS_ALG_DEFAULT, tracker)
if embeddedOnly is true
, or enumerate(owner, coords, NS_IMMERSED_SINGULAR, NS_ALG_DEFAULT, tracker)
if embeddedOnly is false
.

inlinestatic 
Deprecated method that uses an extremely slow modified ContejeanDevie procedure to enumerate all embedded fundamental surfaces in the given triangulation.
For details of the algorithm, see B. A. Burton, "Fundamental normal surfaces and the enumeration of Hilbert bases", arXiv:1111.7055v1, Nov 2011.
Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.
enumerate(owner, coords, NS_FUNDAMENTAL  NS_EMBEDDED_ONLY, NS_HILBERT_CD)
if embeddedOnly is true
, or enumerate(owner, coords, NS_FUNDAMENTAL  NS_IMMERSED_SINGULAR, NS_HILBERT_CD)
if embeddedOnly is false
.owner  the triangulation upon which this list of normal surfaces will be based. 
coords  the coordinate system to be used. 
embeddedOnly  true if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true . 

inlinestatic 
Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the dual Hilbert basis algorithm.
For details of the algorithm, see B. A. Burton, "Enumerating fundamental normal surfaces: Algorithms, experiments and invariants", to appear in ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments, arXiv:1111.7055.
Users can still access this procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.
enumerate(owner, coords, NS_FUNDAMENTAL  NS_EMBEDDED_ONLY, NS_HILBERT_DUAL, tracker)
if embeddedOnly is true
, or enumerate(owner, coords, NS_FUNDAMENTAL  NS_IMMERSED_SINGULAR, NS_HILBERT_DUAL, tracker)
if embeddedOnly is false
.owner  the triangulation upon which this list of normal surfaces will be based. 
coords  the coordinate system to be used. 
embeddedOnly  true if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true . 
tracker  a progress tracker through which progress will be reported, or 0 if no progress reporting is required. 

inlinestatic 
Deprecated method that uses an extremely slow procedure to enumerate all embedded fundamental surfaces in the given triangulation, by running Normaliz over the full (and typically very large) solution cone, and only enforcing embedded constraints (such as the quadrilateral constraints) afterwards.
Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.
enumerate(owner, coords, NS_FUNDAMENTAL  NS_EMBEDDED_ONLY, NS_HILBERT_FULLCONE)
if embeddedOnly is true
, or enumerate(owner, coords, NS_FUNDAMENTAL  NS_IMMERSED_SINGULAR, NS_HILBERT_FULLCONE)
if embeddedOnly is false
.owner  the triangulation upon which this list of normal surfaces will be based. 
coords  the coordinate system to be used. 
embeddedOnly  true if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true . 

inlinestatic 
Deprecated method that enumerates all fundamental normal surfaces in the given triangulation using the primal Hilbert basis algorithm.
For details of the algorithm, see B. A. Burton, "Enumerating fundamental normal surfaces: Algorithms, experiments and invariants", to appear in ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments, arXiv:1111.7055.
Users can still access this procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.
enumerate(owner, coords, NS_FUNDAMENTAL  NS_EMBEDDED_ONLY, NS_HILBERT_PRIMAL, tracker)
if embeddedOnly is true
, or enumerate(owner, coords, NS_FUNDAMENTAL  NS_IMMERSED_SINGULAR, NS_HILBERT_PRIMAL, tracker)
if embeddedOnly is false
.owner  the triangulation upon which this list of normal surfaces will be based. 
coords  the coordinate system to be used. 
embeddedOnly  true if only embedded normal surfaces are to be produced, or false if immersed and singular normal surfaces are also to be produced; this defaults to true . 
vtxSurfaces  the set of all vertex normal surfaces as enumerated under the same coordinate system and constraints as given here; this may be 0 if unknown. 
tracker  a progress tracker through which progress will be reported, or 0 if no progress reporting is required. 

inlinestatic 
Deprecated method that uses a slowbutdirect procedure to enumerate all embedded vertex almost normal surfaces in standard almost normal coordinates, without using the faster procedure that works via quadrilateraloctagon coordinates.
Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.
enumerate(owner, NS_AN_STANDARD, NS_LIST_DEFAULT, NS_VERTEX_STD_DIRECT)
.owner  the triangulation upon which this list of surfaces will be based. 

inlinestatic 
Deprecated method that uses a slowbutdirect procedure to enumerate all embedded vertex normal surfaces in standard coordinates, without using the faster procedure that works via quadrilateral coordinates.
Users can still access this slower procedure if they need to; however, they should do this via enumerate(NTriangulation*, NormalCoords, NormalList, NormalAlg, NProgressTracker*) instead. See the documentation for that routine for further details.
enumerate(owner, NS_STANDARD, NS_LIST_DEFAULT, NS_VERTEX_STD_DIRECT)
.owner  the triangulation upon which this list of surfaces will be based. 
NNormalSurfaceList* regina::NNormalSurfaceList::filterForDisjointPairs  (  )  const 
Creates a new list filled with the surfaces from this list that have at least one disjoint partner.
In other words, a surface S from this list will be placed in the new list if and only if there is some other surface T in this list for which S and T can be made to intersect nowhere at all, without changing either normal isotopy class. See NNormalSurface::disjoint() for further details on disjointness testing.
This routine cannot deal with empty, disconnected or noncompact surfaces. Such surfaces will be silently ignored, and will not be used in any disjointness tests (in particular, they will never be considered as a "disjoint partner" for any other surface).
The new list will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the new list will also be returned from this routine.
This original list is not altered in any way. Likewise, the surfaces in the new list are deep copies of the originals (so they can be altered without affecting the original surfaces).
true
. NNormalSurfaceList* regina::NNormalSurfaceList::filterForLocallyCompatiblePairs  (  )  const 
Creates a new list filled with the surfaces from this list that have at least one locally compatible partner.
In other words, a surface S from this list will be placed in the new list if and only if there is some other surface T in this list for which S and T are locally compatible. See NNormalSurface::locallyCompatible() for further details on compatibility testing.
The new list will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the new list will also be returned from this routine.
This original list is not altered in any way. Likewise, the surfaces in the new list are deep copies of the originals (so they can be altered without affecting the original surfaces).
true
.NNormalSurfaceList* regina::NNormalSurfaceList::filterForPotentiallyIncompressible  (  )  const 
Creates a new list filled with only the surfaces from this list that "might" represent twosided incompressible surfaces.
More precisely, we consider all twosided surfaces in this list, as well as the twosided double covers of all onesided surfaces in this list (see below for details on how onesided surfaces are handled). Each of these surfaces is examined using relatively fast heuristic tests for incompressibility. Any surface that is definitely not incompressible is thrown away, and all other surfaces are placed in the new list.
Therefore, it is guaranteed that every incompressible surface from the old list will be placed in the new list. However, it is not known whether any given surface in the new list is indeed incompressible.
See NNormalSurface::isIncompressible() for the definition of incompressibility that is used here. Note in particular that spheres are never considered incompressible.
As indicated above, this filter works exclusively with twosided surfaces. If a surface in this list is onesided, the heuristic incompressibility tests will be run on its twosided double cover. Nevertheless, if the tests pass, the original onesided surface (not the double cover) will be added to the new list.
The new list will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the new list will also be returned from this routine.
This original list is not altered in any way. Likewise, the surfaces in the new list are deep copies of the originals (so they can be altered without affecting the original surfaces).
Currently the heuristic tests include (i) throwing away all vertex links and thin edge links, and then (ii) cutting along the remaining surfaces and running NTriangulation::hasSimpleCompressingDisc() on the resulting bounded triangulations. For more details on these tests see "The WeberSeifert dodecahedral space is nonHaken", Benjamin A. Burton, J. Hyam Rubinstein and Stephan Tillmann, Trans. Amer. Math. Soc. 364:2 (2012), pp. 911932.
true
.

inline 
Deprecated routine to return the coordinate system being used by the surfaces stored in this set.

inline 
Deprecated routine to return the coordinate system being used by the surfaces stored in this set.

inline 
Returns the number of surfaces stored in this set.

inline 
Returns the surface at the requested index in this set.
index  the index of the requested surface in this set; this must be between 0 and getNumberOfSurfaces()1 inclusive. 
NTriangulation* regina::NNormalSurfaceList::getTriangulation  (  )  const 
Returns the triangulation in which these normal surfaces live.

protectedvirtual 
Makes a newly allocated copy of this packet.
This routine should not insert the new packet into the tree structure, clone the packet's associated tags or give the packet a label. It should also not clone any descendants of this packet.
You may assume that the new packet will eventually be inserted into the tree beneath either the same parent as this packet or a clone of that parent.
parent  the parent beneath which the new packet will eventually be inserted. 
Implements regina::NPacket.

inline 
Returns whether this list was constructed to contain only properly embedded surfaces.
If this returns false
, it does not guarantee that immersed and/or singular surfaces are present; it merely indicates that they were not deliberately excluded (for instance, the quadrilateral constraints were not enforced).
true
if this list was constructed to contain only properly embedded surfaces, or false
otherwise. NNormalSurfaceList* regina::NNormalSurfaceList::quadOctToStandardAN  (  )  const 
Converts the set of all embedded vertex almost normal surfaces in quadrilateraloctagon space to the set of all embedded vertex almost normal surfaces in the standard triquadoct space.
This routine is the almost normal analogue to the quadToStandard() conversion routine; see the quadToStandard() documentation for further information.
true
.NNormalSurfaceList* regina::NNormalSurfaceList::quadToStandard  (  )  const 
Converts the set of all embedded vertex normal surfaces in quadrilateral space to the set of all embedded vertex normal surfaces in standard (triquad) space.
The initial list in quadrilateral space is taken to be this normal surface list; the final list in standard space will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the final list will also be returned from this routine.
This routine can only be used with normal surfaces, not almost normal surfaces. For almost normal surfaces, see the similar routine quadOctToStandardAN().
This procedure is available for any triangulation whose vertex links are all spheres and/or discs, and is much faster than enumerating surfaces directly in standard triquad coordinates. The underlying algorithm is described in detail in "Converting between quadrilateral and standard solution sets in normal surface theory", Benjamin A. Burton, Algebr. Geom. Topol. 9 (2009), 21212174.
Typically users do not need to call this routine directly, since the standard enumerate() routine will use it implicitly where possible. That is, when asked for standard vertex surfaces, enumerate() will first find all quadrilateral vertex surfaces and then use this procedure to convert them to standard vertex surfaces; this is generally orders of magnitude faster than enumerating surfaces directly in standard coordinates.
Nevertheless, this standalone routine is provided as a convenience for users who already have a set of quadrilateral vertex surfaces, and who simply wish to convert them to a set of standard vertex surfaces without the cost of implicitly enumerating the quadrilateral vertex surfaces again.
It should be noted that this routine does not simply convert vectors from one form to another; instead it converts a full solution set of vertex surfaces in quadrilateral coordinates to a full solution set of vertex surfaces in standard coordinates. Typically there are many more vertex surfaces in standard coordinates (all of which this routine will find).
This routine will run some very basic sanity checks before starting. Specifically, it will check the validity and vertex links of the underlying triangulation, and will verify that the coordinate system and embeddedonly flag are set to NS_QUAD and true
respectively. If any of these checks fails, this routine will do nothing and return 0.
true
.

inline 
Returns a newly created matrix containing the matching equations that were used to create this normal surface list.
The destruction of this matrix is the responsibility of the caller of this routine. Multiple calls to this routine will result in the construction of multiple matrices. This routine in fact merely calls makeMatchingEquations() with the appropriate parameters.
The format of the matrix is identical to that returned by makeMatchingEquations().
NNormalSurfaceList* regina::NNormalSurfaceList::standardANToQuadOct  (  )  const 
Converts the set of all embedded vertex almost normal surfaces in standard triquadoct space to the set of all embedded vertex almost normal surfaces in the smaller quadrilateraloctagon space.
This routine is the almost normal analogue to the standardToQuad() conversion routine; see the standardToQuad() documentation for further information.
true
.NNormalSurfaceList* regina::NNormalSurfaceList::standardToQuad  (  )  const 
Converts the set of all embedded vertex normal surfaces in standard (triquad) space to the set of all embedded vertex normal surfaces in quadrilateral space.
The initial list in standard space is taken to be this normal surface list; the final list in quadrilateral space will be inserted as a new child packet of the underlying triangulation (specifically, as the final child). As a convenience, the final list will also be returned from this routine.
This routine can only be used with normal surfaces, not almost normal surfaces. For almost normal surfaces, see the similar routine standardANToQuadOct().
This procedure is available for any triangulation whose vertex links are all spheres and/or discs. The underlying algorithm is described in detail in "Converting between quadrilateral and standard solution sets in normal surface theory", Benjamin A. Burton, Algebr. Geom. Topol. 9 (2009), 21212174.
It should be noted that this routine does not simply convert vectors from one form to another; instead it converts a full solution set of vertex surfaces in standard coordinates to a full solution set of vertex surfaces in quadrilateral coordinates. Typically there are far fewer vertex surfaces in quadrilateral coordinates (all of which this routine will find).
This routine will run some very basic sanity checks before starting. Specifically, it will check the validity and vertex links of the underlying triangulation, and will verify that the coordinate system and embeddedonly flag are set to NS_STANDARD and true
respectively. If any of these checks fails, this routine will do nothing and return 0.
true
.

inline 
Returns details of which normal surfaces this list represents within the underlying triangulation.
This may not be the same NormalList that was passed to enumerate(). In particular, default values will have be explicitly filled in (such as NS_VERTEX and/or NS_EMBEDDED_ONLY), and invalid and/or redundant values will have been removed.
void regina::NNormalSurfaceList::writeAllSurfaces  (  std::ostream &  out  )  const 
Writes the number of surfaces in this set followed by the details of each surface to the given output stream.
Output will be over many lines.
out  the output stream to which to write. 

virtual 
Writes this object in long text format to the given output stream.
The output should provide the user with all the information they could want. The output should be humanreadable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out  the output stream to which to write. 
Reimplemented from regina::ShareableObject.

virtual 
Writes this object in short text format to the given output stream.
The output should be humanreadable, should fit on a single line, and should not end with a newline.
out  the output stream to which to write. 
Implements regina::ShareableObject.

protectedvirtual 
Writes a chunk of XML containing the data for this packet only.
You may assume that the packet opening tag (including the packet type and label) has already been written, and that all child packets followed by the corresponding packet closing tag will be written immediately after this routine is called. This routine need only write the internal data stored in this specific packet.
out  the output stream to which the XML should be written. 
Implements regina::NPacket.

protected 
Stores the details of the enumeration algorithm that was used to generate this list.
This might not be the same as the algorithmHints flag passed to the corresponding enumeration routine (e.g., if invalid or inappropriate flags were passed).

static 
Indicates that a list of almost normal surfaces was created using Regina 4.5.1 or earlier, where surfaces with more than one octagon of the same type were stripped out of the final solution set.
As of Regina 4.6 such surfaces are now included in the solution set, since we need them if we wish to enumerate all almost normal surfaces (not just the vertex almost normal surfaces).
This coordinate system is only used with legacy data files; new vectors and lists cannot be created in this coordinate system. The underlying coordinates are identical to those of AN_STANDARD.

static 
Represents quadrilateraloctagon coordinates for octagonal almost normal surfaces.
For details, see "Quadrilateraloctagon coordinates for almost normal surfaces", Benjamin A. Burton, Experiment. Math. 19 (2010), 285315.

static 
Represents standard trianglequadrilateraloctagon coordinates for octagonal almost normal surfaces.

protected 
Stores which coordinate system is being used by the normal surfaces in this packet.

static 
Represents edge weight coordinates for normal surfaces.
This coordinate system is for representation only; surface vectors and lists cannot be created in this coordinate system.

static 
Represents triangle arc coordinates for normal surfaces.
This coordinate system is for representation only; surface vectors and lists cannot be created in this coordinate system.

static 
Represents standard trianglequadrilateral coordinates for transversely oriented normal surfaces.

static 
Represents quadrilateral coordinates for transversely oriented normal surfaces.

static 
Represents quadrilateral coordinates for normal surfaces.
For details, see "Normal surface Qtheory", Jeffrey L. Tollefson, Pacific J. Math. 183 (1998), no. 2, 359–374.

static 
Represents standard trianglequadrilateral coordinates for normal surfaces.

protected 
Contains the normal surfaces stored in this packet.

protected 
Indicates which normal surfaces these represent within the underlying triangulation.