Finite Type (Vassiliev) Invariants: Difference between revisions
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Thus, for example, let us reproduce [http://www.ma.hw.ac.uk/~simon/fishing.html Willerton's "fish"] ({{arXiv|math.GT/0104061}}), the result of plotting the values of <math>V_2(K)</math> against the values of <math>\pm V_3(K)</math>, where <math>V_2(K)</math> is the (standardly normalized) type 2 invariant of <math>K</math>, <math>V_3(K)</math> is the (standardly normalized) type 3 invariant of <math>K</math>, and where <math>K</math> runs over a set of knots with equal crossing numbers (10, in the example below): |
Thus, for example, let us reproduce [http://www.ma.hw.ac.uk/~simon/fishing.html Willerton's "fish"] ({{arXiv|math.GT/0104061}}), the result of plotting the values of <math>V_2(K)</math> against the values of <math>\pm V_3(K)</math>, where <math>V_2(K)</math> is the (standardly normalized) type 2 invariant of <math>K</math>, <math>V_3(K)</math> is the (standardly normalized) type 3 invariant of <math>K</math>, and where <math>K</math> runs over a set of knots with equal crossing numbers (10, in the example below): |
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< |
<!--$$ListPlot[ |
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Join @@ Table[ |
Join @@ Table[ |
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K = Knot[10, k] ; v2 = Vassiliev[2][K]; v3 = Vassiliev[3][K]; |
K = Knot[10, k] ; v2 = Vassiliev[2][K]; v3 = Vassiliev[3][K]; |
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{{v2, v3}, {v2, -v3}}, |
{{v2, v3}, {v2, -v3}}, |
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{k, 165} |
{k, 165} |
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], |
], |
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PlotStyle -> PointSize[0.02], PlotRange -> All, AspectRatio -> 1 |
PlotStyle -> PointSize[0.02], PlotRange -> All, AspectRatio -> 1 |
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]$$--> |
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]" |
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<!--END--> |
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] *> |
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Revision as of 22:43, 28 August 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):
