Pensieve header: The GST-48 knot.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2016-09"];
<< OneSmidgen.m

Import["GST48-Marked.png"]

PD[GST48] = PD[
X[01,15,02,14], X[29,02,30,03], X[40,04,41,03], X[04,44,05,43], X[05,26,06,27],
X[95,07,96,06], X[07,01,08,96], X[08,14,09,13], X[28,09,29,10], X[41,11,42,10],
X[11,43,12,42], X[12,27,13,28], X[15,31,16,30], X[61,16,62,17], X[72,17,73,18],
X[83,18,84,19], X[34,20,35,19], X[20,89,21,90], X[92,21,93,22], X[22,79,23,80],
X[23,68,24,69], X[24,57,25,58], X[56,25,57,26], X[31,63,32,62], X[32,74,33,73],
X[33,85,34,84], X[35,50,36,51], X[81,37,82,36], X[70,38,71,37], X[59,39,60,38],
X[54,39,55,40], X[55,45,56,44], X[45,59,46,58], X[46,70,47,69], X[47,81,48,80],
X[91,49,92,48], X[49,91,50,90], X[82,52,83,51], X[71,53,72,52], X[60,54,61,53],
X[74,63,75,64], X[85,64,86,65], X[65,76,66,77], X[66,87,67,88], X[94,67,95,68],
X[86,75,87,76], X[77,88,78,89], X[93,78,94,79] ];

Alexander[GST48][t] // Factor

KnotSignature[GST48]

With[{f=-1+2 t-(t^2)-(t^3)+2 (t^4)-(t^5)+(t^8)}, Simplify[Alexander[GST48][t]==f(f/.t->1/t)]]

Dynamic[{Length[Z$todo], Z$x, Z$todo}]

(Subscript[t, _])=t; Z[GST48]

TimeUsed[]

z[K_] := Z[K];
za[K_] := z[K][[1]];
zp1[K_] := Factor[((z[K][[4]] /. c|u|w->0)/((t-1)((za[K])^2)))];
zp2[K_] := Factor[((Coefficient[z[K][[4]],c])/(((t^2)-1)(-4-t+(t^2))((za[K])^3)))];

With[{K=GST48},{Factor@za[K], zp1[K], zp2[K]}]

With[{K=GST48},{Vassiliev[2][K], Vassiliev[3][K]}]