(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 172285, 3704] NotebookOptionsPosition[ 169905, 3618] NotebookOutlinePosition[ 170293, 3635] CellTagsIndexPosition[ 170250, 3632] WindowFrame->Normal ContainsDynamic->True *) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["The Penultimate Alexander Polynomial", "Title", CellChangeTimes->{{3.429350922097*^9, 3.429350930175*^9}, { 3.4312872067958*^9, 3.4312872167174*^9}}], Cell["September 2008, Joint with Jana Archibald", "Text", CellChangeTimes->{{3.429350954998*^9, 3.429350974131*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"prog", "=", RowBox[{"Import", "[", "\[IndentingNewLine]", RowBox[{ "\"\\"", ",", "\[IndentingNewLine]", "\"\\""}], 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W[j,k] + (t[i]-1)W[j,l] + W[k,l] ]\\n\\n (* Variable Equivalences \ *)\\nReductionRules[Times[]] = {};\\nReductionRules[Equal[a_, b__]] := (# -> \ a) & /@ {b}; \\nReductionRules[eqs_Times] := Join @@ (ReductionRules /@ \ List@@eqs)\\n\\n (* AHD: Alexander Half Densities *)\\nAHD[eqs_, is_, \ -os_, p_] := AHD[eqs, is, os, Expand[-p]];\\nAHD /: Reduce[AHD[eqs_, is_, \ os_, p_]] := \\n AHD[eqs, Sort[is], WSort[os], WSort[p /. \ ReductionRules[eqs]]];\\nAHD /: AHD[eqs1_,is1_,os1_,p1_] \ AHD[eqs2_,is2_,os2_,p2_] := Module[\\n {glued = Intersection[Union[is1, \ is2], List@@Union[os1, os2]]}, \\n Reduce[AHD[\\n eqs1*eqs2 //. \ eq1_Equal*eq2_Equal /; \\n Intersection[List@@eq1, List@@eq2] =!= {} :> \ Union[eq1, eq2],\\n Complement[Union[is1, is2], glued],\\n IM[glued, \ WP[os1, os2]],\\n IM[glued, WP[p1, p2]]\\n]] ]\\n\\n (* pA on \ Circuit Diagrams *)\\npA[cd_CircuitDiagram, eqs___] := pA[cd, {}, \ AHD[Times[eqs], {}, W[], W[]]];\\npA[cd_CircuitDiagram, done_, ahd_AHD] := \ Module[\\n {pos = 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