(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 255318, 5508] NotebookOptionsPosition[ 253336, 5439] NotebookOutlinePosition[ 253679, 5454] CellTagsIndexPosition[ 253636, 5451] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Remainder Graphs", "Title", CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { 3.7766045987280684`*^9, 3.7766046009303617`*^9}}], Cell["Adam Rumpf, 10/10/2017", "Text", CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { 3.776604609573964*^9, 3.776604613651633*^9}}], Cell[CellGroupData[{ Cell["Introduction", "Section", CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], Cell[TextData[{ "This Notebook defines a variety of functions for calculating and displaying \ remainder graphs. The remainder graph for any positive integer ", Cell[BoxData[ FormBox["n", TraditionalForm]], FormatType->"TraditionalForm"], " is defined with vertex set ", Cell[BoxData[ FormBox[ RowBox[{"0", ",", "1", ",", "...", ",", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}], TraditionalForm]], FormatType->"TraditionalForm"], " and with two types of directed edge. For each vertex ", Cell[BoxData[ FormBox["i", TraditionalForm]], FormatType->"TraditionalForm"], ", there is a ", StyleBox["black", FontSlant->"Italic"], " directed edge ", Cell[BoxData[ FormBox[ RowBox[{"i", "\[DirectedEdge]", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "1"}], ")"}], " ", "mod", " ", "n"}]}], TraditionalForm]], FormatType->"TraditionalForm"], " and a ", StyleBox["green", FontSlant->"Italic"], " directed edge ", Cell[BoxData[ FormBox[ RowBox[{"i", "\[DirectedEdge]", RowBox[{"10", "i", " ", "mod", " ", "n"}]}], TraditionalForm]], FormatType->"TraditionalForm"], ". 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