Represents a directed knot or link in the 3-sphere. More...
#include <link/link.h>
Inheritance diagram for regina::Link:
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 ©) | |
| Constructs a new copy of the given link. More... | |
| Link (const Link ©, 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... | |
| Crossing * | crossing (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... | |
| Link * | parallel (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 TreeDecomposition & | niceTreeDecomposition () 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... | |
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 Link * | fromData (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 Link * | fromKnotSig (const std::string &sig) |
| Recovers a knot diagram from its signature. More... | |
| static Link * | fromGauss (const std::string &str) |
| Creates a new knot from a classical Gauss code. More... | |
| template<typename Iterator > | |
| static Link * | fromGauss (Iterator begin, Iterator end) |
| Creates a new knot from a classical Gauss code. More... | |
| static Link * | fromOrientedGauss (const std::string &str) |
| Creates a new knot from an "oriented" variant of the Gauss code. More... | |
| template<typename Iterator > | |
| static Link * | fromOrientedGauss (Iterator begin, Iterator end) |
| Creates a new knot from an "oriented" variant of the Gauss code. More... | |
| static Link * | fromJenkins (const std::string &str) |
| Builds a link from the text representation described by Bob Jenkins. More... | |
| static Link * | fromJenkins (std::istream &in) |
| Builds a link from the text representation described by Bob Jenkins. More... | |
| static Link * | fromDT (const std::string &str) |
| Creates a new knot from either alphabetical or numerical Dowker-Thistlethwaite notation. More... | |
| template<typename Iterator > | |
| static Link * | fromDT (Iterator begin, Iterator end) |
| Creates a new knot from an integer sequence using the numerical variant of Dowker-Thistlethwaite notation. More... | |
| static XMLPacketReader * | xmlReader (Packet *parent, XMLTreeResolver &resolver) |
| virtual Packet * | internalClonePacket (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
|
inherited |
The type of object being pointed to.
Member Function Documentation
◆ detail()
|
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()
|
inlineinherited |
Is there one or more SafePtr currently pointing to this object?
◆ str()
|
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()
|
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:
- link/link.h