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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[ 111512, 1983]*) (*NotebookOutlinePosition[ 112147, 2005]*) (* CellTagsIndexPosition[ 112103, 2001]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(<< AbstractAlgebra`Master`\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Elements[DihedralGroup[4]]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{1, Rot, Rot\^2, Rot\^3, Ref, Rot ** Ref, Rot\^2 ** Ref, Rot\^3 ** Ref}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(OrderOfAllElements[DihedralGroup[4]]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1"}, {"Rot", "4"}, {\(Rot\^2\), "2"}, {\(Rot\^3\), "4"}, {"Ref", "2"}, {\(Rot ** Ref\), "2"}, {\(Rot\^2 ** Ref\), "2"}, {\(Rot\^3 ** Ref\), "2"} }], "\[NoBreak]", ")"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(CayleyTable[DihedralGroup[4], Mode \[Rule] Visual];\)\)], "Input"], Cell[BoxData[ \(TraditionalForm\`"KEY for D[4]: label used \[Rule] element: {g1 \[Rule] \ 1, g2 \[Rule] Rot, g3 \[Rule] Rot^2, g4 \[Rule] Rot^3, g5 \[Rule] Ref, g6 \ \[Rule] Rot**Ref, g7 \[Rule] Rot^2**Ref, g8 \[Rule] Rot^3**Ref}"\)], "Print"], Cell[BoxData[ \(TraditionalForm\`"For each element, a different color is used. 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