Pensieve header: Making table.tex.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Talks\\UNC-1610"];
Once[<< KnotTheory`];
tab=Join[{Knot[0,1]->{0., 𝔼[1,0,0,0]}},Get["../../2016-09/tab.m"]];
tab /. (K_->{_,z_}) :> (z1[K]=z);
Ribbons={Knot[0,1],Knot[6,1],Knot[8,8],Knot[8,9],Knot[8,20],Knot[9,27],Knot[9,41],Knot[9,46],Knot[10,3],Knot[10,22],Knot[10,35],Knot[10,42],Knot[10,48],Knot[10,75],Knot[10,87],Knot[10,99],Knot[10,123],Knot[10,129],Knot[10,137],Knot[10,140],Knot[10,153],Knot[10,155]};

z1[Knot[3,1]]

al[K_] := z1[K][[1]];
ap[K_] :=  al[K]/. (t^(n_.))/; n<0 :> 0;

al /@ AllKnots[{0,5}]

ap /@ AllKnots[{0,5}]

e[K_] := Expand[Together[(((t z1[K][[4]] /. c|u|w->0)+((al[K])^3)(t^2) D[al[K],t])/((((t-1))^2)((al[K])^2)))]];
ep[K_] :=  e[K]/. (t^(n_.))/; n<0 :> 0;

Table[K->e[K], {K,AllKnots[{3,10}]}] >> etab.m

ep /@ AllKnots[{0,5}]

SymmetryType /@ AllKnots[{0,10}] // Union

KnotLine[K_] := StringReplace["\\rolcell{n_k}{n^t_{k}}{ap}{ep}{G}{U}{R}{C}", {
"n" -> ToString@K[[1]],
"k" -> ToString@K[[2]],
"t" -> If[AlternatingQ[K], "a", "n"],
"ap"-> ToString[ap[K], FormatType -> TeXForm],
"ep"-> ToString[ep[K], FormatType -> TeXForm],
"G" -> ToString@ThreeGenus@K,
"U" -> ToString@UnknottingNumber@K,
"R" -> If[MemberQ[Ribbons, K], "\\gY", "\\N"],
"C" -> If[MemberQ[{FullyAmphicheiral, NegativeAmphicheiral, ""}, SymmetryType@K], "\\oY", "\\N"]
}]

KnotLine /@ AllKnots[{0,6}]

Make[n_] := StringJoin@@Table[
StringJoin[StringJoin@@Riffle[L, " &\n"], " \\\\\n\\hline\n"],
{L, Partition[KnotLine /@ AllKnots[{0,n}], UpTo@2]}
];
Make[6]

DeleteFile["table.tex"];
WriteString["table.tex", Make[10]];
Close["table.tex"]