Finite Type (Vassiliev) Invariants: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
Line 6: | Line 6: | ||
<!--Robot Land, no human edits to "END"--> |
<!--Robot Land, no human edits to "END"--> |
||
{{HelpLine| |
{{HelpLine| |
||
n = |
n = 2 | |
||
in = Vassiliev | |
in = <nowiki>Vassiliev</nowiki> | |
||
out= Vassiliev[2][K] computes the (standardly normalized) type 2 Vassiliev invariant of the knot K, i.e., the coefficient of z^2 in Conway[K][z]. Vassiliev[3][K] computes the (standardly normalized) type 3 Vassiliev invariant of the knot K, i.e., 3J''(1)-(1/36)J'''(1) where J is the Jones polynomial of K.}} |
out= <nowiki>Vassiliev[2][K] computes the (standardly normalized) type 2 Vassiliev invariant of the knot K, i.e., the coefficient of z^2 in Conway[K][z]. Vassiliev[3][K] computes the (standardly normalized) type 3 Vassiliev invariant of the knot K, i.e., 3J''(1)-(1/36)J'''(1) where J is the Jones polynomial of K.</nowiki>}} |
||
<!--END--> |
<!--END--> |
||
Line 23: | Line 23: | ||
<!--Robot Land, no human edits to "END"--> |
<!--Robot Land, no human edits to "END"--> |
||
{{Graphics| |
{{Graphics| |
||
n =3 | |
n = 3 | |
||
in =ListPlot[ |
in = <nowiki>ListPlot[ |
||
Join @@ Table[ |
Join @@ Table[ |
||
K = Knot[10, k] ; v2 = Vassiliev[2][K]; v3 = Vassiliev[3][K]; |
K = Knot[10, k] ; v2 = Vassiliev[2][K]; v3 = Vassiliev[3][K]; |
||
Line 31: | Line 31: | ||
], |
], |
||
PlotStyle -> PointSize[0.02], PlotRange -> All, AspectRatio -> 1 |
PlotStyle -> PointSize[0.02], PlotRange -> All, AspectRatio -> 1 |
||
] | |
]</nowiki> | |
||
img= |
img= Finite_Type_Vassiliev_Invariants_Out_3.gif | |
||
out= -Graphics-}} |
out= <nowiki>-Graphics-</nowiki>}} |
||
<!--END--> |
<!--END--> |
Revision as of 08:19, 3 September 2005
(For In[1] see Setup)
|
Thus, for example, let us reproduce Willerton's "fish" (arXiv:math.GT/0104061), the result of plotting the values of against the values of , where is the (standardly normalized) type 2 invariant of , is the (standardly normalized) type 3 invariant of , and where runs over a set of knots with equal crossing numbers (10, in the example below):