Arc Presentations: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
DrorsRobot (talk | contribs) No edit summary |
No edit summary |
||
| Line 8: | Line 8: | ||
in = <nowiki>ArcPresentation</nowiki> | |
in = <nowiki>ArcPresentation</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>}} |
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>}} |
||
<!--END--> |
|||
<!--$$ap = ArcPresentation["K11n11"]$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$Draw[ap]$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$ap0 = ArcPresentation["K11n11", Reduce -> 0]$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$?Draw$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$Draw[ap0]$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$Reflect[ap_ArcPresentation] := ArcPresentation @@ ( |
|||
(Last /@ Sort[Reverse /@ Position[ap, #]]) & /@ Range[Length[ap]] |
|||
)$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$Reflect[ap] // Draw$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$MinesweeperMatrix[ap_ArcPresentation] := Module[ |
|||
{l, CurrentRow, c1, c2, k, s}, |
|||
l = Length[ap]; |
|||
CurrentRow = Table[0, {l}]; |
|||
Table[ |
|||
{c1, c2} = Sort[ap[[k]]]; |
|||
s = Sign[{-1, 1}.ap[[k]]]; |
|||
Do[ |
|||
CurrentRow[[c]] += s, |
|||
{c, c1, c2 - 1} |
|||
]; |
|||
CurrentRow, |
|||
{k, l} |
|||
] |
|||
]; |
|||
$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$$Draw[ap, OverlayMatrix -> MinesweeperMatrix[ap]]$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
|||
<!--$${Det[t^MinesweeperMatrix[ap]], Alexander[ap][t]} // Factor$$--> |
|||
<!--Robot Land, no human edits to "END"--> |
|||
<!--END--> |
<!--END--> |
||
Revision as of 22:03, 1 December 2007
(For In[1] see Setup)
| ||||
