LinKnot functions


For each LinKnot function the left link shows recorded Mathematica session, and the right link provides interactive webMathematica computation. E.g., by clicking on the link ReductionKnotLink in (webMathematica ReductionKnotLink) you will go to the page for webMathematica computation. Each link "Ref" gives the reference in the text of the book where the function and its theorethical background is described.


Input knots and links

ReductionKnotLink (webMathematica ReductionKnotLink)  *Ref*

GetPdatabyTracking (webMathematica GetPdatabyTracking)  *Ref*   *Ref*


Draw knots and links

ShowKnotfromPdata (webMathematica ShowKnotfromPdata)  *Ref*

ShowKnotbyOpengl (webMathematica ShowKnotbyOpengl)  *Ref*

WritheKnotFromPdata (webMathematica WritheKnotFromPdata)  *Ref*   *Ref*

GetMirrorImageKnot (webMathematica GetMirrorImageKnot)  *Ref*   *Ref*


Braid representations

GetBraidRep (webMathematica GetBraidRep)  *Ref*

ShowBraid (webMathematica ShowBraid)  *Ref*

KnotFromBraid (webMathematica KnotFromBraid)  *Ref*


Mutation of a knot

MutationOfTangle (webMathematica MutationOfTangle)  *Ref*


Data conversion

KnotbyDT (webMathematica KnotbyDT)  *Ref*

fFindCon (webMathematica fFindCon *Ref*


Input knots and links in Conway notation

fCreatePData (webMathematica fCreatePData)  *Ref*   *Ref*

Dow (webMathematica Dow)  *Ref*

fGenSign (webMathematica fGenSign)  *Ref*

fDToDDirect (webMathematica fDToDDirect)  *Ref*

fGenSignDirProd (webMathematica fGenSignDirProd)  *Ref*


Polynomial and other invariants

fAlexPoly (webMathematica fAlexPoly)  *Ref*

SkeinPolynomial (webMathematica Skein Polynomial)  *Ref*

KauffmanPolynomial (webMathematica KauffmanPolynomial)  *Ref*

A2Invariant (webMathematica A2Invariant *Ref*

ColouredJones (webMathematica ColouredJones *Ref*

Kh (webMathematica Kh *Ref*

Vassiliev (webMathematica Vassiliev *Ref*

LinksGould (webMathematica LinksGould *Ref*

LinksGouldInv (webMathematica LinksGouldInv *Ref*


Data base of knots and links

NumberOfKL (webMathematica NumberOfKL)  *Ref*

GetKnotLink (webMathematica GetKnotLink)  *Ref*


Projections and minimal Dowker codes

fProjections (webMathematica fProjections) *Ref*

fDiffProjectionsAltKL (webMathematica fDiffProjectionsAltKL)  *Ref*

MinDowProjAltKL (webMathematica MinDowProjAltKL)  *Ref*

MinDowAltKL (webMathematica MinDowAltKL)  *Ref*   *Ref*   *Ref*

SameAltProjKL (webMathematica SameAltProjKL)  *Ref*

SameAltConKL (webMathematica SameAltConKL*Ref*  *Ref*   *Ref*   *Ref


Gauss codes

fGaussExtSigns (webMathematica fGaussExtSigns)  *Ref*

fOrientedLink (webMathematica fOrientedLink)  *Ref*


Component number and linking number

fComponentNo (webMathematica fComponentNo)  *Ref*

LinkingNo (webMathematica LinkingNo)  *Ref*


Unknotting or unlinking number of a KL

UnKnotLink (webMathematica UnKnotLink)  *Ref*

fGap (webMathematica fGap)  *Ref*

fAllStatesProj (webMathematica fAllStatesProj)  *Ref*


Cutting and splitting

fBreakComp (webMathematica fBreakComp)  *Ref*

BreakCoAll (webMathematica BreakCoAll)  *Ref*

CuttNo (webMathematica CuttNo)  *Ref*

NoSelfCrossNo (webMathematica NoSelfCrossNo)  *Ref*

SplittNo (webMathematica SplittNo *Ref*

fCuttRealKL (webMathematica fCuttRealKL)  *Ref*


Chirality and symmetries

AmphiProjAltKL (webMathematica AmphiProjAltKL)  *Ref*

AmphiAltKL (webMathematica AmphiAltKL)  *Ref*

AmphiQ (webMathematica AmphiQ)  *Ref*

fJablanPoly (webMathematica JablanPoly *Ref*   *Ref*

LiangPoly (webMathematica LiangPoly *Ref*   *Ref*

PeriodProjAltKL (webMathematica PeriodProjAltKL *Ref*

PeriodAltKL (webMathematica PeriodAltKL *Ref*

Symm (webMathematica Symm)  *Ref*

MaxSymmProjAltKL (webMathematica MaxSymmProjAltKL)  *Ref*


Generators and colorability

fGenerators (webMathematica fGenerators)  *Ref*

fColTest (webMathematica fColTest)  *Ref*


Seifert matrix and signature

fSeifert (webMathematica fSeifert)  *Ref*

fSignat (webMathematica fSignat)  *Ref*


Prime KLs

fPrimeKL (webMathematica fPrimeKL)  *Ref*


Torus KLs

fTorusKL (webMathematica fTorusKL)  *Ref*


KLs and graphs

fGraphInc (webMathematica fGraphInc)  *Ref*

fGraphKL (webMathematica fGraphKL)  *Ref*   *Ref*

fMidEdgeGraph (webMathematica fMidEdgeGraph)  *Ref*

fKLfromGraph (webMathematica fKLfromGraph)  *Ref*   *Ref*

fKLinGraph (webMathematica fKLinGraph)  *Ref*

fAddDig (webMathematica fAddDig)  *Ref*

fPrimeGraph (webMathematica fPrimeGraph)  *Ref*


Planar embedding

fPlanarEmbKL (webMathematica fPlanarEmbKL)  *Ref*

fPlanarEmbGraph (webMathematica fPlanarEmbGraph)  *Ref*

DrawPlanarEmbGraph (webMathematica DrawPlanarEmbGraph)  *Ref*

fEdmonds (webMathematica fEdmonds)  *Ref*


Conversion functions

fClassicToCon (webMathematica fClassicToCon)  *Ref*

fPDataFromDow (webMathematica fPDataFromDow)  *Ref*   *Ref*

fPDataFromDowker (webMathematica fPDataFromDowker)  *Ref*

fDowfromPD (webMathematica fDowfromPD)  *Ref*

fKnotscapeDow (webMathematica fKnotscapeDow)  *Ref*   *Ref

fSignsKL (webMathematica fSignsKL)  *Ref*  *Ref*


Rational KLs

RatReduce (webMathematica RatReduce)  *Ref*

RationalKL (webMathematica RationalKL)  *Ref*

RK (webMathematica RK *Ref*

R (webMathematica R *Ref*

RL (webMathematica RL *Ref*

RationalAmphiK (webMathematica RationalAmphiK)  *Ref*

RationalAmphiL (webMathematica RationalAmphiL)  *Ref*

RatGenSourKL (webMathematica RatGenSourKL)  *Ref*

RatSourceKLNo (webMathematica RatSourceKLNo)  *Ref*

RatLinkU1 (webMathematica RatLinkU1)  *Ref*

RatLinkU0 (webMathematica RatLinkU0) *Ref*

RatKnotGenU1 (webMathematica RatKnotGenU1)  *Ref*

RatKnotGenU0 (webMathematica RatKnotGenU0)  *Ref*

MSigRat (webMathematica MSigRat)  *Ref*

AllStatesRational (webMathematica AllStatesRational)  *Ref*

UnR (webMathematica UnR)  *Ref*   *Ref*

UnRFixProj (webMathematica UnRFixProj*Ref*

fGapRat (webMathematica fGapRat)  *Ref*

NMoveRat (webMathematica NMoveRat)  *Ref*


Basic polyhedra

fBasicPoly (webMathematica fBasicPoly *Ref*

fCompositePoly (webMathematica fCompositePoly)  *Ref*

fPolyFlype (webMathematica fPolyFlype)  *Ref*

fProdTangles (webMathematica fProdTangles) *Ref*

fSumTangles (webMathematica fSumTangles)  *Ref*


Derivation of KLs

fDowCodes (webMathematica fDowCodes)  *Ref*

fStellarBasic (webMathematica fStellarBasic)  *Ref*

fStellar (webMathematica fStellar)  *Ref*

fStellarPlus (webMathematica fStellarPlus)  *Ref*

fStellarNalt (webMathematica fStellarNalt)  *Ref*

fGenKL (webMathematica GenKL)  *Ref*

fNinvStellar (webMathematica fNinvStellar *Ref*


KLs and logic

fBoolean (webMathematica fBoolean *Ref*

fDiffSeq (webMathematica fDiffSeq *Ref*

fKauffAlg (webMathematica fKauffAlg *Ref*

fBalanced (webMathematica fBalanced *Ref*

fAutoSigInp (webMathematica fAutoSigInp *Ref*

fAutoKL (webMathematica fAutoKL *Ref*


Graphics for KnotPlot

fCreateGraphics (webMathematica fCreateGraphics)  *Ref*


Conversion functions to Knot Theory

fConwayToPD (webMathematica fConwayToPD *Ref*

fKnotscapeDowToPD (webMathematica fKnotscapeDowToPD *Ref*

fDowkerToPD (webMathematica fDowkerToPD *Ref*

fPdataToPD (webMathematica fPdataToPD *Ref*

BR (webMathematica BR *Ref*

fBraidW (webMathematica fBraidW *Ref*

fPDfromBW (webMathematica fPDfromBW *Ref*


Derivation of basic polyhedra

fAllClosures (webMathematica fAllClosures*Ref*

fBasicTan (webMathematica fBasicTan *Ref*

fMakeBP (webMathematica fMakeBP *Ref*

fMakeAllnsBP (webMathematica fMakeAllnsBP *Ref*


Chord diagrams

ListOfOneFactors (webMathematica ListOfOneFactors *Ref*

fMulTan (webMathematica fMulTan *Ref*

fGenSet (webMathematica fGenSet *Ref*

fMulTanTab (webMathematica fMulTanTab *Ref*


Tangle types

fTangleType (webMathematica fTangleType *Ref*

fMakeType (webMathematica fMakeType *Ref*



fViaToKL (webMathematica fViaToKL *Ref*

fDiffViae (webMathematica fDiffViae *Ref*