(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 5563, 155] NotebookOptionsPosition[ 5202, 138] NotebookOutlinePosition[ 5548, 153] CellTagsIndexPosition[ 5505, 150] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["p-distance-like function, p = 1 or 2", FontColor->RGBColor[1, 0, 0]], " " }], "Subsubsection", CellChangeTimes->{ 3.660181618220235*^9, 3.660184034295927*^9, {3.6601893465576572`*^9, 3.660189364123288*^9}, {3.810604606458789*^9, 3.810604621033659*^9}, { 3.810606338083911*^9, 3.810606344235671*^9}, {3.8208176469252195`*^9, 3.820817678930338*^9}, 3.820820661130023*^9}, ExpressionUUID -> "de88d8d0-428a-453c-95ca-4c7b3214de68"], Cell[BoxData[{ RowBox[{ RowBox[{ StyleBox["Input", FontColor->RGBColor[1, 0, 0]], StyleBox[":", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{"data", " ", "points", " ", "x"}], FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{"y", " ", "\[Element]", " ", SuperscriptBox["\[DoubleStruckCapitalR]", "n"]}], FontColor->RGBColor[0, 0, 1]], StyleBox[",", FontColor->RGBColor[0, 0, 1]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{ RowBox[{"parameter", " ", "p"}], "=", RowBox[{"1", " ", "or", " ", "2"}]}], FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["Output", FontColor->RGBColor[1, 0, 0]], StyleBox[":", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{"p", "-", RowBox[{ "distance", " ", "between", " ", "the", " ", "points", " ", "x"}]}], FontColor->RGBColor[0, 0, 1]]}], StyleBox[",", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{ RowBox[{"y", " ", "\[Element]", " ", SuperscriptBox["\[DoubleStruckCapitalR]", "n"]}], ";"}], FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["Submodules", FontColor->RGBColor[1, 0, 0]], StyleBox[":", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{"none", " ", "needed"}], FontColor->RGBColor[0, 0, 1]]}], StyleBox[" ", FontColor->RGBColor[0, 0, 1]]}], "\[IndentingNewLine]"}], "Text", CellChangeTimes->{{3.6601845794856844`*^9, 3.6601846899806786`*^9}, { 3.660186755205906*^9, 3.6601868132380075`*^9}, {3.660186887322538*^9, 3.660186904732168*^9}, 3.6601873822646074`*^9, {3.660187491261999*^9, 3.660187494023204*^9}, {3.6601891375640907`*^9, 3.660189139748094*^9}, { 3.660190256179655*^9, 3.660190256803656*^9}, 3.660466434060449*^9, { 3.807100827229907*^9, 3.807100836299094*^9}, {3.8099091408928237`*^9, 3.8099091534489975`*^9}, {3.8106045751586*^9, 3.810604577705879*^9}, { 3.8106054451792607`*^9, 3.8106054855099106`*^9}, {3.810605742334792*^9, 3.8106058418409033`*^9}, {3.8106059545408173`*^9, 3.8106061037401776`*^9}, 3.810606226194319*^9, {3.8106063520774174`*^9, 3.8106063728987107`*^9}, { 3.810606694418968*^9, 3.8106066991601353`*^9}, 3.81060674109476*^9, { 3.8106071920304637`*^9, 3.810607197381454*^9}, 3.8106074745440893`*^9, 3.8208177013385096`*^9, {3.82081907179665*^9, 3.820819073696807*^9}, { 3.82228711809196*^9, 3.8222871632562675`*^9}}, FontSize->12, ExpressionUUID -> "4fd676fc-c13f-4903-9a01-53de6594de3f"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"d", "[", RowBox[{"x_", ",", "y_", ",", "p_"}], "]"}], ":=", RowBox[{ RowBox[{"Norm", "[", RowBox[{ RowBox[{"x", "-", "y"}], ",", "p"}], "]"}], "^", "p", " "}]}]}]], "Input", CellChangeTimes->{{3.6601845794856844`*^9, 3.6601846899806786`*^9}, { 3.660186755205906*^9, 3.6601868132380075`*^9}, {3.660186887322538*^9, 3.660186904732168*^9}, 3.6601873822646074`*^9, {3.660187491261999*^9, 3.660187494023204*^9}, {3.6601891375640907`*^9, 3.660189139748094*^9}, { 3.660190256179655*^9, 3.660190256803656*^9}, 3.660466434060449*^9, { 3.807100827229907*^9, 3.807100836299094*^9}, {3.8099091408928237`*^9, 3.8099091534489975`*^9}, {3.8106045751586*^9, 3.810604577705879*^9}, { 3.8106054451792607`*^9, 3.8106054855099106`*^9}, {3.810605742334792*^9, 3.8106058418409033`*^9}, {3.8106059545408173`*^9, 3.8106061037401776`*^9}, 3.810606226194319*^9, {3.8106063520774174`*^9, 3.8106063728987107`*^9}, { 3.810606694418968*^9, 3.8106066991601353`*^9}, 3.81060674109476*^9, { 3.8106071920304637`*^9, 3.810607197381454*^9}, 3.8106074745440893`*^9, 3.8208177013385096`*^9, {3.82081907179665*^9, 3.820819073696807*^9}, 3.82228711809196*^9}, ExpressionUUID -> "4fd676fc-c13f-4903-9a01-53de6594de3f"] }, Open ]] }, WindowSize->{754, 262}, WindowMargins->{{0, Automatic}, {Automatic, 85}}, FrontEndVersion->"11.0 for Microsoft Windows (64-bit) (September 21, 2016)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 472, 10, 39, "Subsubsection"], Cell[1055, 34, 2801, 75, 83, "Text"], Cell[3859, 111, 1327, 24, 50, "Input"] }, Open ]] } ] *)