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| Built-in Mathematica Symbol | See Also »|More About » |
KnotData |  |
| {"PretzelKnot",{n1,n2,...}} | (n1, n2, ...)-pretzel knot | |
| {"TorusKnot",{m,n}} | (m, n)-torus knot (m, n coprime) |
| "Image" | 3D image of the knot | |
| "ImageData" | graphics data for the 3D knot image | |
| "KnotDiagram" | 2D diagram of the knot | |
| "KnotDiagramData" | graphics data for the 2D knot diagram |
| "ArfInvariant" | Arf invariant | |
| "BraidIndex" | braid index | |
| "BridgeIndex" | bridge index | |
| "ColoringNumberSet" | list of colorable numbers | |
| "ConcordanceOrder" | concordance order | |
| "CrossingNumber" | crossing number | |
| "DegreeThreeVassiliev" | degree-3 Vassiliev invariant | |
| "DegreeTwoVassiliev" | degree-2 Vassiliev invariant | |
| "Determinant" | determinant | |
| "Genus" | genus of knot complement | |
| "HyperbolicVolume" | hyperbolic volume | |
| "NakanishiIndex" | Nakanishi index | |
| "OzsvathSzaboTau" | Ozsvath-Szabo tau invariant | |
| "Signature" | signature | |
| "SmoothFourGenus" | smooth 4-genus | |
| "StickNumber" | stick number | |
| "SuperbridgeIndex" | superbridge index | |
| "ThurstonBennequin" | Thurston-Bennequin number | |
| "TopologicalFourGenus" | topological 4-genus | |
| "UnknottingNumber" | unknotting number |
| "AlexanderPolynomial" | Alexander polynomial | |
| "BLMHoPolynomial" | BLMHo polynomial | |
| "BracketPolynomial" | normalized bracket polynomial | |
| "ConwayPolynomial" | Conway polynomial | |
| "HOMFLYPolynomial" | HOMFLY polynomial | |
| "JonesPolynomial" | Jones polynomial | |
| "KauffmanPolynomial" | Kauffman polynomial |
| "BraidDiagram" | 2D diagram of the knot as a braid | |
| "BraidDiagramData" | graphics data for the 2D braid diagram | |
| "BraidImage" | 3D image of the knot as a braid | |
| "BraidImageData" | graphics data for the 3D braid image |
| "AlexanderBriggsList" | Alexander-Briggs {n, k} list | |
| "AlexanderBriggsNotation" | Alexander-Briggs notation for display | |
| "BraidWord" | braid word as a list | |
| "BraidWordNotation" | braid word in algebraic notation | |
| "ConwayNotation" | Conway notation for display | |
| "ConwayString" | Conway notation as a string | |
| "DowkerList" | Dowker {i1, i2, i3, ...} list | |
| "DowkerNotation" | Dowker notation for display |
| "AlternateNames" | alternate English names | |
| "Name" | English or mathematical name | |
| "StandardName" | standard Mathematica name |
| "AlmostAlternating" | almost alternating | |
| "Alternating" | alternating | |
| "Amphichiral" | amphichiral | |
| "Chiral" | chiral | |
| "Hyperbolic" | hyperbolic | |
| "Invertible" | invertible | |
| "Nonalternating" | non-alternating | |
| "Prime" | prime | |
| "Ribbon" | ribbon | |
| "Satellite" | satellite | |
| "Slice" | slice | |
| "Torus" | torus | |
| "Twist" | twist |
| "Composite" | not prime | |
| "NonalmostAlternating" | not almost alternating | |
| "Nonhyperbolic" | not hyperbolic | |
| "Noninvertible" | not invertible | |
| "Nonribbon" | not ribbon | |
| "Nonsatellite" | not satellite | |
| "Nonslice" | not slice | |
| "Nontorus" | not torus | |
| "Nontwist" | not twist |
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