(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 24355, 804]*) (*NotebookOutlinePosition[ 24992, 826]*) (* CellTagsIndexPosition[ 24948, 822]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ RowBox[{"<<", StyleBox[ RowBox[{"LinearAlgebra", StyleBox["`", "MB"], "MatrixManipulation", StyleBox["`", "MB"]}]]}]], "Input"], Cell[BoxData[ StyleBox[\(<< NumberTheory`AlgebraicNumberFields`\), FontFamily->"Courier"]], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(FusionAtlasPaths = \ {"\", "\<~/Documents/math \ papers/fusionatlas/code/package/\>"};\)\), "\n", \(\($Path = $Path~Join~FusionAtlasPaths;\)\), "\[IndentingNewLine]", \(<< FusionAtlas`\)}], "Input"], Cell[BoxData[ InterpretationBox[\("Loading FusionAtlas` version 0\n\ "\[InvisibleSpace]"Read more at http://tqft.net/wiki/Atlas_of_subfactors"\), SequenceForm[ "Loading FusionAtlas` version 0\n", "Read more at http://tqft.net/wiki/Atlas_of_subfactors"], Editable->False]], "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(testGraph = GradedGraph[{{0}}, {{1}}, {{1}}]\)], "Input"], Cell[BoxData[ \(GradedGraph[{{0}}, {{1}}, {{1}}]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(RankAtDepth[GradedGraph[], 1]\)], "Input"], Cell[BoxData[ \(RankAtDepth[GradedGraph[], 1]\)], "Output"] }, Open ]], Cell[BoxData[ \(RankAtDepth[g_GradedGraph, \ n_Integer] /; 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x \[NotEqual] 0]; \[IndentingNewLine]\t If[p \[Equal] Length[e], \ Return[$Failed]]; \[IndentingNewLine]\t e\[LeftDoubleBracket]p\[RightDoubleBracket] = 0; \[IndentingNewLine]\t\(e\[LeftDoubleBracket] p + 1\[RightDoubleBracket]++\); \[IndentingNewLine]\t Partition[e, n]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(IncrementNonSymMatrix[IdentityMatrix[2]]\)], "Input"], Cell[BoxData[ \({{0, 1}, {0, 1}}\)], "Output"] }, Open ]], Cell[BoxData[ \(FunnyTranspose[p_Integer, n_Integer] := Ceiling[p/n] + n*\((Mod[p, n, 1] - 1)\)\)], "Input"], Cell[BoxData[ \(NextDiagonal[p_Integer, n_Integer] := p + Floor[p/n] + 1\)], "Input"], Cell[BoxData[ \(IncrementSymMatrix[m_] := \[IndentingNewLine]\t Module[{e = Flatten[m], n = Length[m\[LeftDoubleBracket]1\[RightDoubleBracket]], p, q}, \[IndentingNewLine]\t\tp = FindFirst[e, x_\ /; \ x \[NotEqual] 0]; \[IndentingNewLine]\t\tq = FunnyTranspose[p, n]; \[IndentingNewLine]\t\tIf[ p \[Equal] Length[e], \ Return[$Failed]]; \[IndentingNewLine]\t\te\[LeftDoubleBracket] p\[RightDoubleBracket] = 0; 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EvenQ[Length[x]]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(FindGraphExtensionsUpToRankAndDepth[DimensionOfGenerator[#] < 2 &]\)[ a2Graph, 6, 6]\)], "Input"], Cell[BoxData[ \({GradedGraph[{{0}}, {{1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}, {1, 0}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}, {0, 1}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, \ {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, \ {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}, \ {1}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{0}}, {{1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}}, {{0}}, {{1}}, {{0}}]}\)], "Output"] }, Open ]], Cell[BoxData[ \(PositivityTest[g_GradedGraph] := And @@ \((\(# \[GreaterEqual] 1 &\) /@ \ N[Flatten[DimensionsByDepth[g]]])\)\)], "Input"], Cell[BoxData[ \(\(FindPositivesRandD[c_]\)[g_GradedGraph, totalRank_, depth_] := DeleteCases[\(FindGraphExtensionsUpToRankAndDepth[c]\)[g, totalRank, depth], x_ /; \(! PositivityTest[x]\)]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(DeleteCases[\(FindPositivesRandD[DimensionOfGenerator[#] <= 2 &]\)[ a2Graph, 6, 6], x_ /; DimensionOfGenerator[x] < 2]\)], "Input"], Cell[BoxData[ \({GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{1, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}, {1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}], GradedGraph[{{0}}, {{1}}, {{1}}, {{1}}, {{0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}}, {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}, {0, 1}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}, {1, 0}}, {{0, 0}, {0, 0}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{0}}, {{1}}, {{1}}], GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}}, {{0}}, {{1}}, {{1}}]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(DimensionsByDepth[ GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{1, 0}}, {{0}}, {{1}}, {{1}}]]\)], "Input"], Cell[BoxData[ \({{1}, {2}, {2, 1}, {2}, {2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(RankAtDepth[ GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{1}}], 5]\)], "Input"], Cell[BoxData[ \(RankAtDepth[ GradedGraph[{{0}}, {{1}}, {{0}}, {{1}, {1}}, {{0, 0}, {0, 0}}, {{0, 1}}, {{1}}], 5]\)], "Output"] }, Open ]], Cell[BoxData[ \(zGraph[n_Integer]\ := \[IndentingNewLine]GradedGraph @@ Append[\[IndentingNewLine]\t Join\ @@ Table[\[IndentingNewLine]\t{{{0}}, {{1}}}\[IndentingNewLine]\t, \ \ {i, 1, n - 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