Regina Calculation Engine
Public Types | Public Member Functions | Static Public Attributes | List of all members
regina::Link Class Referenceabstract

Represents a directed knot or link in the 3-sphere. More...

#include <link/link.h>

Inheritance diagram for regina::Link:
regina::Packet regina::Output< Packet > regina::SafePointeeBase< Packet >

Public Types

typedef Packet SafePointeeType
 The type of object being pointed to. More...
 

Public Member Functions

std::string str () const
 Returns a short text representation of this object. More...
 
std::string utf8 () const
 Returns a short text representation of this object using unicode characters. More...
 
std::string detail () const
 Returns a detailed text representation of this object. More...
 
bool hasSafePtr () const
 Is there one or more SafePtr currently pointing to this object? More...
 
Constructors and Destructors
 Link ()
 Constructs an empty link. More...
 
 Link (size_t unknots)
 Constructs the unlink with the given number of components. More...
 
 Link (const Link &copy)
 Constructs a new copy of the given link. More...
 
 Link (const Link &copy, bool cloneProps)
 Constructs a new copy of the given link, with the option of whether or not to clone its computed properties also. More...
 
 Link (const std::string &description)
 "Magic" constructor that tries to find some way to interpret the given string as a link. More...
 
 ~Link ()
 Destroys this link. More...
 
Crossings and Components
bool isEmpty () const
 Determines whether this link is empty. More...
 
size_t size () const
 Returns the number of crossings in this link. More...
 
size_t countComponents () const
 Returns the number of components in this link. More...
 
Crossingcrossing (size_t index) const
 Returns a pointer to the crossing at the given index within this link. More...
 
StrandRef component (size_t index) const
 Returns a strand in the given component of this link. More...
 
StrandRef strand (int id) const
 Returns the strand in the link with the given integer ID. More...
 
StrandRef translate (const StrandRef &other) const
 Translates a strand reference for some other link into the corresponding strand reference for this link. More...
 
bool connected (const Crossing *a, const Crossing *b) const
 Determines whether the two given crossings are connected in the underlying 4-valent graph of the link diagram. More...
 
Editing
void swapContents (Link &other)
 Swaps the contents of this and the given link. More...
 
void change (Crossing *c)
 Switches the upper and lower strands of the given crossing. More...
 
void changeAll ()
 Switches the upper and lower strands of every crossing in the diagram. More...
 
void resolve (Crossing *c)
 Resolves the given crossing. More...
 
void reflect ()
 Converts this link into its reflection. More...
 
void rotate ()
 Rotates this link diagram, converting it into a different diagram of the same link. More...
 
void reverse ()
 Reverses the orientation of every component of this link. More...
 
bool r1 (Crossing *crossing, bool check=true, bool perform=true)
 Tests for and/or performs a type I Reidemeister move to remove a crossing. More...
 
bool r1 (StrandRef arc, int side, int sign, bool check=true, bool perform=true)
 Tests for and/or performs a type I Reidemeister move to add a new crossing. More...
 
bool r2 (StrandRef arc, bool check=true, bool perform=true)
 Tests for and/or performs a type II Reidemeister move to remove two crossings. More...
 
bool r2 (Crossing *crossing, bool check=true, bool perform=true)
 Tests for and/or performs a type II Reidemeister move to remove two crossings. More...
 
bool r2 (StrandRef upperArc, int upperSide, StrandRef lowerArc, int lowerSide, bool check=true, bool perform=true)
 Tests for and/or performs a type II Reidemeister move to add two new crossings. More...
 
bool r3 (StrandRef arc, int side, bool check=true, bool perform=true)
 Tests for and/or performs a type III Reidemeister move. More...
 
bool r3 (Crossing *crossing, int side, bool check=true, bool perform=true)
 Tests for and/or performs a type III Reidemeister move. More...
 
bool hasReducingPass () const
 Tests whether this knot has a pass move that will reduce the number of crossings. More...
 
bool intelligentSimplify ()
 Attempts to simplify the link diagram using fast and greedy heuristics. More...
 
bool simplifyToLocalMinimum (bool perform=true)
 Uses type I and II Reidemeister moves to reduce the link monotonically to some local minimum number of crossings. More...
 
bool simplifyExhaustive (int height=1, unsigned nThreads=1, ProgressTrackerOpen *tracker=nullptr)
 Attempts to simplify this knot diagram using a slow but exhaustive search through the Reidemeister graph. More...
 
template<typename Action , typename... Args>
bool rewrite (int height, unsigned nThreads, ProgressTrackerOpen *tracker, Action &&action, Args &&... args) const
 Explores all knot diagrams that can be reached from this via Reidemeister moves, without exceeding a given number of additional crossings. More...
 
void composeWith (const Link &other)
 Forms the composition of this with the given link. More...
 
Invariants and Related Properties
bool isAlternating () const
 Returns whether this knot diagram is alternating. More...
 
long linking () const
 Returns the linking number of this link. More...
 
long writhe () const
 Returns the writhe of this link diagram. More...
 
Triangulation< 3 > * complement (bool simplify=true) const
 Returns an ideal triangulation of the complement of this link in the 3-sphere. More...
 
Linkparallel (int k, Framing framing=FRAMING_SEIFERT) const
 Returns k cables of this link, all parallel to each other using the given framing. More...
 
const Laurent< Integer > & bracket (Algorithm alg=ALG_DEFAULT, ProgressTracker *tracker=nullptr) const
 Returns the Kauffman bracket polynomial of this link diagram. More...
 
bool knowsBracket () const
 Is the Kauffman bracket polynomial of this link diagram already known? See bracket() for further details. More...
 
const Laurent< Integer > & jones (Algorithm alg=ALG_DEFAULT, ProgressTracker *tracker=nullptr) const
 Returns the Jones polynomial of this link, but with all exponents doubled. More...
 
bool knowsJones () const
 Is the Jones polynomial of this link diagram already known? See jones() for further details. More...
 
const Laurent2< Integer > & homflyAZ (Algorithm alg=ALG_DEFAULT, ProgressTracker *tracker=nullptr) const
 Returns the HOMFLY polynomial of this link, as a polynomial in alpha and z. More...
 
const Laurent2< Integer > & homflyLM (Algorithm alg=ALG_DEFAULT, ProgressTracker *tracker=nullptr) const
 Returns the HOMFLY polynomial of this link, as a polynomial in l and m. More...
 
const Laurent2< Integer > & homfly (Algorithm alg=ALG_DEFAULT, ProgressTracker *tracker=nullptr) const
 Returns the HOMFLY polynomial of this link, as a polynomial in alpha and z. More...
 
bool knowsHomfly () const
 Is the HOMFLY polynomial of this link diagram already known? See homflyAZ() and homflyLM() for further details. More...
 
const TreeDecompositionniceTreeDecomposition () const
 Returns a nice tree decomposition of the planar 4-valent multigraph formed by this link diagram. More...
 
void useTreeDecomposition (const TreeDecomposition &td)
 Instructs Regina to use the given tree decomposition as the starting point whenever it needs a tree decomposition for this link. More...
 
Packet Administration
virtual void writeTextShort (std::ostream &out) const override
 Writes a short text representation of this object to the given output stream. More...
 
virtual void writeTextLong (std::ostream &out) const override
 Writes a detailed text representation of this object to the given output stream. More...
 
virtual bool dependsOnParent () const override
 Determines if this packet depends upon its parent. More...
 
Exporting Links
std::string brief () const
 Outputs this link in Regina's own brief format. More...
 
std::string gauss () const
 Outputs a classical Gauss code for this knot. More...
 
void gauss (std::ostream &out) const
 Writes a classical Gauss code for this knot to the given output stream. More...
 
std::string orientedGauss () const
 Outputs an oriented Gauss code for this knot. More...
 
void orientedGauss (std::ostream &out) const
 Writes an oriented Gauss code for this knot to the given output stream. More...
 
std::string jenkins () const
 Exports this link as a string using the text representation described by Bob Jenkins. More...
 
void jenkins (std::ostream &out) const
 Exports this link to the given output stream using the text representation described by Bob Jenkins. More...
 
std::string dt (bool alpha=false) const
 Outputs this knot using Dowker-Thistlethwaite notation. More...
 
void dt (std::ostream &out, bool alpha=false) const
 Writes this knot to the given output stream using Dowker-Thistlethwaite notation. More...
 
void writePACE (std::ostream &out) const
 Outputs the underlying planar 4-valent multigraph using the PACE text format. More...
 
std::string pace () const
 Returns a text representation of the underlying planar 4-valent multigraph, using the PACE text format. More...
 
std::string dumpConstruction () const
 Returns C++ code that can be used to reconstruct this link. More...
 
std::string knotSig (bool useReflection=true, bool useReversal=true) const
 Constructs the signature for this knot diagram. More...
 
Packet Identification
virtual PacketType type () const =0
 Returns the unique integer ID representing this type of packet. More...
 
virtual std::string typeName () const =0
 Returns an English name for this type of packet. More...
 
const std::string & label () const
 Returns the label associated with this individual packet. More...
 
std::string humanLabel () const
 Returns the label associated with this individual packet, adjusted if necessary for human-readable output. More...
 
std::string adornedLabel (const std::string &adornment) const
 Returns the label of this packet adorned with the given string. More...
 
void setLabel (const std::string &label)
 Sets the label associated with this individual packet. More...
 
std::string fullName () const
 Returns a descriptive text string for the packet. More...
 
Tags
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 > & tags () const
 Returns the set of all tags associated with this packet. More...
 
Event Handling
bool listen (PacketListener *listener)
 Registers the given packet listener to listen for events on this packet. More...
 
bool isListening (PacketListener *listener)
 Determines whether the given packet listener is currently listening for events on this packet. More...
 
bool unlisten (PacketListener *listener)
 Unregisters the given packet listener so that it no longer listens for events on this packet. More...
 
Tree Queries
Packetparent () const
 Determines the parent packet in the tree structure. More...
 
PacketfirstChild () const
 Determines the first child of this packet in the tree structure. More...
 
PacketlastChild () const
 Determines the last child of this packet in the tree structure. More...
 
PacketnextSibling () const
 Determines the next sibling of this packet in the tree structure. More...
 
PacketprevSibling () const
 Determines the previous sibling of this packet in the tree structure. More...
 
Packetroot () const
 Determines the root of the tree to which this packet belongs. More...
 
unsigned levelsDownTo (const Packet *descendant) const
 Counts the number of levels between this packet and its given descendant in the tree structure. More...
 
unsigned levelsUpTo (const Packet *ancestor) const
 Counts the number of levels between this packet and its given ancestor in the tree structure. More...
 
bool isGrandparentOf (const Packet *descendant) const
 Determines if this packet is equal to or an ancestor of the given packet in the tree structure. More...
 
size_t countChildren () const
 Returns the number of immediate children of this packet. More...
 
size_t countDescendants () const
 Returns the total number of strict descendants of this packet. More...
 
size_t totalTreeSize () const
 Determines the total number of packets in the tree or subtree for which this packet is matriarch. More...
 
Tree Manipulation
void insertChildFirst (Packet *child)
 Inserts the given packet as the first child of this packet. More...
 
void insertChildLast (Packet *child)
 Inserts the given packet as the last child of this packet. More...
 
void insertChildAfter (Packet *newChild, Packet *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 (Packet *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 transferChildren (Packet *newParent)
 Cuts all of this packet's children out of the packet tree, and reinserts them as children 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...
 
Searching and Iterating
SubtreeIterator begin ()
 Returns an iterator at the beginning of the range of packets in the subtree rooted at this packet. More...
 
SubtreeIterator end ()
 Returns an iterator beyond the end of the range of packets in the subtree rooted at this packet. More...
 
PacketDescendants descendants () const
 Returns a lightweight object for iterating through all strict descendants of this packet in the packet tree. More...
 
PacketChildren children () const
 Returns a lightweight object for iterating through the immediate children of this packet. More...
 
PacketnextTreePacket ()
 Finds the next packet after this in a complete depth-first iteration of the entire tree structure to which this packet belongs. More...
 
const PacketnextTreePacket () const
 Finds the next packet after this in a complete depth-first iteration of the entire tree structure to which this packet belongs. More...
 
PacketnextTreePacket (const std::string &type)
 Finds the next packet after this of the requested type in a complete depth-first iteration of the entire tree structure. More...
 
const PacketnextTreePacket (const std::string &type) const
 Finds the next packet after this of the requested type in a complete depth-first iteration of the entire tree structure. More...
 
PacketfirstTreePacket (const std::string &type)
 Finds the first packet of the requested type in a complete depth-first iteration of the tree structure. More...
 
const PacketfirstTreePacket (const std::string &type) const
 Finds the first packet of the requested type in a complete depth-first iteration of the tree structure. More...
 
PacketfindPacketLabel (const std::string &label)
 Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...
 
const PacketfindPacketLabel (const std::string &label) const
 Finds the packet with the requested label in the tree or subtree for which this packet is matriarch. More...
 
Packet Dependencies
bool isPacketEditable () const
 Determines whether this packet can be altered without invalidating or otherwise upsetting any of its immediate children. More...
 
Cloning
Packetclone (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...
 

Static Public Member Functions

Constructors and Destructors
static void safeDelete (Packet *p)
 Either destroys or orphans the given packet, according to whether it has safe pointers that currently reference it. More...
 

Static Public Attributes

static const char * jonesVar
 The name of the variable used in the Jones polynomial, as returned by jones(). More...
 
static const char * homflyAZVarX
 The name of the first variable used in the variant of the HOMFLY polynomial as returned by homflyAZ(). More...
 
static const char * homflyAZVarY
 The name of the second variable used in the variant of the HOMFLY polynomial as returned by homflyAZ(). More...
 
static const char * homflyLMVarX
 The name of the first variable used in the variant of the HOMFLY polynomial as returned by homflyLM(). More...
 
static const char * homflyLMVarY
 The name of the second variable used in the variant of the HOMFLY polynomial as returned by homflyLM(). More...
 
static const char * homflyVarX
 The name of the first variable used in the variant of the HOMFLY polynomial as returned by homfly(). More...
 
static const char * homflyVarY
 The name of the second variable used in the variant of the HOMFLY polynomial as returned by homfly(). More...
 

Building Links

class ModelLinkGraph
 
class Tangle
 
class XMLLinkCrossingsReader
 
class XMLLinkComponentsReader
 
template<typename... Args>
static LinkfromData (std::initializer_list< int > crossingSigns, std::initializer_list< Args >... components)
 Creates a new link from hard-coded information about its crossings and components. More...
 
static LinkfromKnotSig (const std::string &sig)
 Recovers a knot diagram from its signature. More...
 
static LinkfromGauss (const std::string &str)
 Creates a new knot from a classical Gauss code. More...
 
template<typename Iterator >
static LinkfromGauss (Iterator begin, Iterator end)
 Creates a new knot from a classical Gauss code. More...
 
static LinkfromOrientedGauss (const std::string &str)
 Creates a new knot from an "oriented" variant of the Gauss code. More...
 
template<typename Iterator >
static LinkfromOrientedGauss (Iterator begin, Iterator end)
 Creates a new knot from an "oriented" variant of the Gauss code. More...
 
static LinkfromJenkins (const std::string &str)
 Builds a link from the text representation described by Bob Jenkins. More...
 
static LinkfromJenkins (std::istream &in)
 Builds a link from the text representation described by Bob Jenkins. More...
 
static LinkfromDT (const std::string &str)
 Creates a new knot from either alphabetical or numerical Dowker-Thistlethwaite notation. More...
 
template<typename Iterator >
static LinkfromDT (Iterator begin, Iterator end)
 Creates a new knot from an integer sequence using the numerical variant of Dowker-Thistlethwaite notation. More...
 
static XMLPacketReaderxmlReader (Packet *parent, XMLTreeResolver &resolver)
 
virtual PacketinternalClonePacket (Packet *parent) const override
 Makes a newly allocated copy of this packet. More...
 
virtual void writeXMLPacketData (std::ostream &out) const override
 Writes a chunk of XML containing the data for this packet only. More...
 

File I/O

bool save (const char *filename, bool compressed=true) const
 Saves the subtree rooted at this packet to the given Regina data file, using Regina's native XML file format. More...
 
bool save (std::ostream &s, bool compressed=true) const
 Writes the subtree rooted at this packet to the given output stream, in the format of a Regina XML data file. More...
 
void writeXMLFile (std::ostream &out) const
 Writes the subtree rooted at this packet to the given output stream in Regina's native XML file format. More...
 
std::string internalID () const
 Returns a unique string ID that identifies this packet. More...
 
bool hasOwner () const
 Indicates whether some other object in the calculation engine is responsible for ultimately destroying this object. More...
 
void writeXMLPacketTree (std::ostream &out) const
 Writes a chunk of XML containing the subtree with this packet as matriarch. More...
 

Detailed Description

Represents a directed knot or link in the 3-sphere.

This class supports links with any number of components (including zero), and it also supports components with no crossings (which form additional unknot components of the overall link).

Member Typedef Documentation

◆ SafePointeeType

The type of object being pointed to.

Member Function Documentation

◆ detail()

std::string regina::Output< Packet , false >::detail ( ) const
inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns
a detailed text representation of this object.

◆ hasSafePtr()

bool regina::SafePointeeBase< Packet >::hasSafePtr
inlineinherited

Is there one or more SafePtr currently pointing to this object?

◆ str()

std::string regina::Output< Packet , false >::str ( ) const
inherited

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python:\n In addition to str(), this is also used as the
Python "stringification" function str().
Returns
a short text representation of this object.

◆ utf8()

std::string regina::Output< Packet , false >::utf8 ( ) const
inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.

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

Copyright © 1999-2018, 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).