Arc Presentations: Difference between revisions
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in = <nowiki>ArcPresentation</nowiki> | |
in = <nowiki>ArcPresentation</nowiki> | |
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out= <nowiki>ArcPresentation[{a1,b1}, {a2, b2}, ..., {an,bn}] is an arc presentation of a knot (as often used in the realm of Heegaard-Floer homologies), where ai is horizontal arc at row i connects column ai to column bi. ArcPresentation[K] returns an arc presentation of the knot K. ArcPresentation[K, Reduce -> r] attemps at most r reduction steps (using a naive reduction algorithm) following a naive creation of some arc presentation for K.</nowiki>}} |
out= <nowiki>ArcPresentation[{a1,b1}, {a2, b2}, ..., {an,bn}] is an arc presentation of a knot (as often used in the realm of Heegaard-Floer homologies), where ai is horizontal arc at row i connects column ai to column bi. ArcPresentation[K] returns an arc presentation of the knot K. ArcPresentation[K, Reduce -> r] attemps at most r reduction steps (using a naive reduction algorithm) following a naive creation of some arc presentation for K.</nowiki>}} |
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<!--END--> |
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<!--$$ap = ArcPresentation["K11n11"]$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$$Draw[ap]$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$$ap0 = ArcPresentation["K11n11", Reduce -> 0]$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$$?Draw$$--> |
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<!--END--> |
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<!--$$Draw[ap0]$$--> |
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<!--END--> |
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<!--$$Reflect[ap_ArcPresentation] := ArcPresentation @@ ( |
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(Last /@ Sort[Reverse /@ Position[ap, #]]) & /@ Range[Length[ap]] |
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)$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$$Reflect[ap] // Draw$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$$MinesweeperMatrix[ap_ArcPresentation] := Module[ |
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{l, CurrentRow, c1, c2, k, s}, |
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l = Length[ap]; |
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CurrentRow = Table[0, {l}]; |
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Table[ |
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{c1, c2} = Sort[ap[[k]]]; |
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s = Sign[{-1, 1}.ap[[k]]]; |
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Do[ |
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CurrentRow[[c]] += s, |
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{c, c1, c2 - 1} |
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]; |
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CurrentRow, |
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{k, l} |
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] |
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]; |
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$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$$Draw[ap, OverlayMatrix -> MinesweeperMatrix[ap]]$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
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<!--$${Det[t^MinesweeperMatrix[ap]], Alexander[ap][t]} // Factor$$--> |
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<!--Robot Land, no human edits to "END"--> |
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<!--END--> |
<!--END--> |
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Revision as of 21:03, 1 December 2007
(For In[1] see Setup)
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