(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 11.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 596103, 13926] NotebookOptionsPosition[ 552127, 13157] NotebookOutlinePosition[ 552780, 13180] CellTagsIndexPosition[ 552692, 13175] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Scientific Programming 2", "Chapter", CellChangeTimes->{{3.724943992364118*^9, 3.724944007146431*^9}, 3.725524593957123*^9},ExpressionUUID->"d90cc9ee-2f1b-4f3e-b72d-\ 3d49e4e77ba1"], Cell[CellGroupData[{ Cell["First steps in working with expressions", "Subchapter", CellChangeTimes->{{3.7255283244776773`*^9, 3.725528347152596*^9}, { 3.7255283926508713`*^9, 3.725528412827997*^9}},ExpressionUUID->"f95585d2-5acf-4389-bb5d-\ 08c192ce9439"], Cell[CellGroupData[{ Cell["Parts of expressions", "Subsection", CellChangeTimes->{{3.725528439462122*^9, 3.725528451270318*^9}},ExpressionUUID->"ee98bd50-83eb-4ca8-aa26-\ 40b0f2c6a169"], Cell["\<\ Everything in Mathematica is an expression. 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RowBox[{StyleBox[\\\"i\\\", \\\"TI\\\"], \\\",\\\", \ StyleBox[\\\"j\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \ \\\"TR\\\"]}], \\\"]\\\"}], \\\"]\\\"}]\\) or \\!\\(\\*RowBox[{\\\"Part\\\", \ \\\"[\\\", RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\ \"i\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"j\\\", \\\"TI\\\"], \\\",\\\", \ StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"]\\\"}]\\) is equivalent to \ \\!\\(\\*RowBox[{RowBox[{RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \ \\\"[\\\", RowBox[{\\\"[\\\", StyleBox[\\\"i\\\", \\\"TI\\\"], \\\"]\\\"}], \ \\\"]\\\"}], \\\"[\\\", RowBox[{\\\"[\\\", StyleBox[\\\"j\\\", \\\"TI\\\"], \ \\\"]\\\"}], \\\"]\\\"}], StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}]\\). \\n\ \\!\\(\\*RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \\\"[\\\", RowBox[{\\\"[\ \\\", RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"i\\\", \ \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", \ SubscriptBox[StyleBox[\\\"i\\\", 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\\\"]\\\"}]\\) gives parts \\!\\(\\*StyleBox[\\\"m\\\", \ \\\"TI\\\"]\\) through \\!\\(\\*StyleBox[\\\"n\\\", \\\"TI\\\"]\\) in steps \ of \\!\\(\\*StyleBox[\\\"s\\\", \ \\\"TI\\\"]\\).\\n\\!\\(\\*RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \ \\\"[\\\", RowBox[{\\\"[\\\", StyleBox[\\\"\\\\\\\"\\\\!\\\\(\\\\*StyleBox[\\\ \\\\\"key\\\\\\\",\\\\\\\"TI\\\\\\\"]\\\\)\\\\\\\"\\\", \ ShowStringCharacters->True], \\\"]\\\"}], \\\"]\\\"}]\\) gives the value \ associated with the key \\\"\\!\\(\\*StyleBox[\\\"key\\\", \\\"TI\\\"]\\)\\\" \ in an association \\!\\(\\*StyleBox[\\\"expr\\\", \ \\\"TI\\\"]\\).\\n\\!\\(\\*RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \ \\\"[\\\", RowBox[{\\\"[\\\", RowBox[{\\\"Key\\\", \\\"[\\\", \ StyleBox[\\\"k\\\", \\\"TI\\\"], \\\"]\\\"}], \\\"]\\\"}], \\\"]\\\"}]\\) \ gives the value associated with an arbitrary key \\!\\(\\*StyleBox[\\\"k\\\", \ \\\"TI\\\"]\\) in the association \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\ \\).\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { ItemBox[ TagBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpener"], ImageSizeCache->{13., {2., 11.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"], ImageSizeCache->{13., {2., 11.}}]}, Dynamic[ System`InformationDump`mouseOver$$]], Alignment->Left, Appearance->{"Default" -> None}, ButtonFunction:>FEPrivate`Set[ System`InformationDump`open$$, True], Evaluator->Automatic, FrameMargins->{{9, 0}, {0, 0}}, ImageMargins->0, ImageSize->Full, Method->"Preemptive"], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[System`InformationDump`mouseOver$$, True], "MouseExited" :> FEPrivate`Set[System`InformationDump`mouseOver$$, False], Method -> 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the \!\(\*StyleBox[\"i\", \"TI\"]\)\!\(\*SuperscriptBox[\"\[Null]\", \ \"th\"]\) part of \!\(\*StyleBox[\"expr\", \"TI\"]\). \n\ \!\(\*RowBox[{StyleBox[\"expr\", \"TI\"], \"[\", RowBox[{\"[\", \ RowBox[{\"-\", StyleBox[\"i\", \"TI\"]}], \"]\"}], \"]\"}]\) counts from the \ end. \n\!\(\*RowBox[{StyleBox[\"expr\", \"TI\"], \"[\", RowBox[{\"[\", \ RowBox[{StyleBox[\"i\", \"TI\"], \",\", StyleBox[\"j\", \"TI\"], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"]\"}], \"]\"}]\) or \ \!\(\*RowBox[{\"Part\", \"[\", RowBox[{StyleBox[\"expr\", \"TI\"], \",\", \ StyleBox[\"i\", \"TI\"], \",\", StyleBox[\"j\", \"TI\"], \",\", StyleBox[\"\ \[Ellipsis]\", \"TR\"]}], \"]\"}]\) is equivalent to \ \!\(\*RowBox[{RowBox[{RowBox[{StyleBox[\"expr\", \"TI\"], \"[\", \ RowBox[{\"[\", StyleBox[\"i\", \"TI\"], \"]\"}], \"]\"}], \"[\", \ RowBox[{\"[\", StyleBox[\"j\", \"TI\"], \"]\"}], \"]\"}], StyleBox[\"\ \[Ellipsis]\", \"TR\"]}]\). \n\!\(\*RowBox[{StyleBox[\"expr\", \"TI\"], \ \"[\", RowBox[{\"[\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"i\", \ \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"i\", \ \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \ \"TR\"]}], \"}\"}], \"]\"}], \"]\"}]\) gives a list of the parts \ \!\(\*SubscriptBox[StyleBox[\"i\", \"TI\"], StyleBox[\"1\", \"TR\"]]\), \ \!\(\*SubscriptBox[StyleBox[\"i\", \"TI\"], StyleBox[\"2\", \"TR\"]]\), \ \[Ellipsis] of \!\(\*StyleBox[\"expr\", \"TI\"]\). \n\ \!\(\*RowBox[{StyleBox[\"expr\", \"TI\"], \"[\", RowBox[{\"[\", \ RowBox[{StyleBox[\"m\", \"TI\"], \";;\", StyleBox[\"n\", \"TI\"]}], \"]\"}], \ \"]\"}]\) gives parts \!\(\*StyleBox[\"m\", \"TI\"]\) through \!\(\*StyleBox[\ \"n\", \"TI\"]\).\n\!\(\*RowBox[{StyleBox[\"expr\", \"TI\"], \"[\", \ RowBox[{\"[\", RowBox[{StyleBox[\"m\", \"TI\"], \";;\", StyleBox[\"n\", \ \"TI\"], \";;\", StyleBox[\"s\", \"TI\"]}], \"]\"}], \"]\"}]\) gives parts \!\ \(\*StyleBox[\"m\", \"TI\"]\) through \!\(\*StyleBox[\"n\", \"TI\"]\) in \ steps of 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\\!\\(\\*StyleBox[\\\"f\\\", \\\"TI\\\"]\\) to the element at \ position \\!\\(\\*StyleBox[\\\"n\\\", \\\"TI\\\"]\\) in \ \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\\). If \ \\!\\(\\*StyleBox[\\\"n\\\", \\\"TI\\\"]\\) is negative, the position is \ counted from the end. \\n\\!\\(\\*RowBox[{\\\"MapAt\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"f\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"expr\\\", \\\ \"TI\\\"], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{StyleBox[\\\"i\\\", \\\"TI\\\ \"], \\\",\\\", StyleBox[\\\"j\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"\ \[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}]}], \\\"]\\\"}]\\) applies \ \\!\\(\\*StyleBox[\\\"f\\\", \\\"TI\\\"]\\) to the part of \\!\\(\\*StyleBox[\ \\\"expr\\\", \\\"TI\\\"]\\) at position \\!\\(\\*RowBox[{\\\"{\\\", \ RowBox[{StyleBox[\\\"i\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"j\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \ \\\"}\\\"}]\\). \\n\\!\\(\\*RowBox[{\\\"MapAt\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"f\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"expr\\\", \\\ \"TI\\\"], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ 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expression.\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { PaneBox[GridBox[{ { DynamicModuleBox[{System`InformationDump`open$$ = { False, False, False, False, False, False, False, False, False, False, False, False}}, StyleBox[GridBox[{ { TagBox[ TooltipBox[ StyleBox["\<\" Documentation\"\>", "InformationRowLabel", StripOnInput->False], "\"Documentation\"", TooltipStyle->"TextStyling"], Annotation[#, "Documentation", "Tooltip"]& ], TemplateBox[{ TemplateBox[{ "\"Local \[RightGuillemet]\"", "paclet:ref/MapAt", "paclet:ref/MapAt", "Link", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"],"\" \"",StyleBox[ "\"|\"", "InformationRowLabel", StripOnInput -> False], 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TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIcon"], ImageSizeCache->{16., {5., 11.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIconHot"], ImageSizeCache->{16., {5., 11.}}]}, Dynamic[ CurrentValue["MouseOver"]]], Appearance->None, BaseStyle->"Link", ButtonData->"paclet:ref/MapAt", ButtonNote->"paclet:ref/MapAt"], "\"paclet:ref/MapAt\""], FrameMargins->{{0, 4}, {0, 2}}], BaseStyle->"InformationTitleBackground", StripOnInput->False]}, { ItemBox[ PaneBox[ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"MapAt\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"f\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"expr\\\", \\\ \"TI\\\"], \\\",\\\", StyleBox[\\\"n\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) \ applies \\!\\(\\*StyleBox[\\\"f\\\", \\\"TI\\\"]\\) to the element at \ position \\!\\(\\*StyleBox[\\\"n\\\", \\\"TI\\\"]\\) in \ \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\\). If \ \\!\\(\\*StyleBox[\\\"n\\\", \\\"TI\\\"]\\) is negative, the position is \ counted from the end. \\n\\!\\(\\*RowBox[{\\\"MapAt\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"f\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"expr\\\", \\\ \"TI\\\"], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{StyleBox[\\\"i\\\", \\\"TI\\\ \"], \\\",\\\", StyleBox[\\\"j\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"\ \[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}]}], \\\"]\\\"}]\\) applies \ \\!\\(\\*StyleBox[\\\"f\\\", \\\"TI\\\"]\\) to the part of \\!\\(\\*StyleBox[\ \\\"expr\\\", \\\"TI\\\"]\\) at position \\!\\(\\*RowBox[{\\\"{\\\", \ RowBox[{StyleBox[\\\"i\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"j\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \ \\\"}\\\"}]\\). \\n\\!\\(\\*RowBox[{\\\"MapAt\\\", \\\"[\\\", \ RowBox[{StyleBox[\\\"f\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"expr\\\", \\\ \"TI\\\"], \\\",\\\", RowBox[{\\\"{\\\", RowBox[{RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"i\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"j\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"i\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"j\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \ \\\"TR\\\"]}], \\\"}\\\"}]}], \\\"]\\\"}]\\) applies \ \\!\\(\\*StyleBox[\\\"f\\\", \\\"TI\\\"]\\) to parts of \ \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\\) at several positions. \ \\n\\!\\(\\*RowBox[{\\\"MapAt\\\", \\\"[\\\", RowBox[{StyleBox[\\\"f\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"pos\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) \ represents an operator form of MapAt that can be applied to an \ expression.\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { ItemBox[ TagBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpener"], ImageSizeCache->{13., {2., 11.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"], ImageSizeCache->{13., {2., 11.}}]}, Dynamic[ System`InformationDump`mouseOver$$]], Alignment->Left, Appearance->{"Default" -> None}, ButtonFunction:>FEPrivate`Set[ System`InformationDump`open$$, True], Evaluator->Automatic, FrameMargins->{{9, 0}, {0, 0}}, ImageMargins->0, ImageSize->Full, Method->"Preemptive"], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[System`InformationDump`mouseOver$$, True], "MouseExited" :> FEPrivate`Set[System`InformationDump`mouseOver$$, False], Method -> "Preemptive", PassEventsDown -> Automatic, PassEventsUp -> True}]], BaseStyle->"InformationTitleBackground", StripOnInput->False], "\[SpanFromLeft]"} }, AutoDelete->False, FrameStyle->Directive[ GrayLevel[0.8], Thickness[Tiny]], GridBoxAlignment->{"Columns" -> {Left, Right}, "Rows" -> {{Center}}}, GridBoxDividers->{ "Columns" -> {{None}}, "Rows" -> {False, {True}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]}, Dynamic[System`InformationDump`open$$], BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], DynamicModuleValues:>{}], BaseStyle->"InformationGridFrame", StripOnInput->False], "InformationGridPlain", StripOnInput->False], InformationData[ Association[ "ObjectType" -> "Symbol", "Usage" -> "\!\(\*RowBox[{\"MapAt\", \"[\", RowBox[{StyleBox[\"f\", \"TI\"], \",\", \ StyleBox[\"expr\", \"TI\"], \",\", StyleBox[\"n\", \"TI\"]}], \"]\"}]\) \ applies \!\(\*StyleBox[\"f\", \"TI\"]\) to the element at position \ \!\(\*StyleBox[\"n\", \"TI\"]\) in \!\(\*StyleBox[\"expr\", \"TI\"]\). If \ \!\(\*StyleBox[\"n\", \"TI\"]\) is negative, the position is counted from the \ end. \n\!\(\*RowBox[{\"MapAt\", \"[\", RowBox[{StyleBox[\"f\", \"TI\"], \ \",\", StyleBox[\"expr\", \"TI\"], \",\", RowBox[{\"{\", RowBox[{StyleBox[\"i\ \", \"TI\"], \",\", StyleBox[\"j\", \"TI\"], \",\", StyleBox[\"\[Ellipsis]\", \ \"TR\"]}], \"}\"}]}], \"]\"}]\) applies \!\(\*StyleBox[\"f\", \"TI\"]\) to \ the part of \!\(\*StyleBox[\"expr\", \"TI\"]\) at position \ \!\(\*RowBox[{\"{\", RowBox[{StyleBox[\"i\", \"TI\"], \",\", StyleBox[\"j\", \ \"TI\"], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}]\). \n\ \!\(\*RowBox[{\"MapAt\", \"[\", RowBox[{StyleBox[\"f\", \"TI\"], \",\", \ StyleBox[\"expr\", \"TI\"], \",\", RowBox[{\"{\", RowBox[{RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"i\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"j\", \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"i\", \"TI\"], StyleBox[\"2\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"j\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}]}], \"]\"}]\) applies \ \!\(\*StyleBox[\"f\", \"TI\"]\) to parts of \!\(\*StyleBox[\"expr\", \ \"TI\"]\) at several positions. \n\!\(\*RowBox[{\"MapAt\", \"[\", \ RowBox[{StyleBox[\"f\", \"TI\"], \",\", StyleBox[\"pos\", \"TI\"]}], \ \"]\"}]\) represents an operator form of MapAt that can be applied to an \ expression.", "Documentation" -> Association[ "Local" -> "paclet:ref/MapAt", "Web" -> "http://reference.wolfram.com/language/ref/MapAt.html"], "OwnValues" -> None, "UpValues" -> None, "DownValues" -> None, "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, "FormatValues" -> None, "Options" -> None, "Attributes" -> {Protected}, "FullName" -> "System`MapAt"], False]]], "Output", CellChangeTimes->{3.789286517702738*^9}, CellLabel-> "Out[175]=",ExpressionUUID->"1698a412-d2d9-4708-8467-18cf5b356d0a"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Map", "[", RowBox[{"h", ",", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.725801243635947*^9, 3.725801245068203*^9}}, CellLabel-> "In[176]:=",ExpressionUUID->"f478ceb9-e208-4339-bd8d-458a219d4bb9"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"h", "[", "a", "]"}], ",", RowBox[{"h", "[", "b", "]"}], ",", RowBox[{"h", "[", "c", "]"}], ",", RowBox[{"h", "[", "d", "]"}], ",", RowBox[{"h", "[", "e", "]"}]}], "}"}]], "Output", CellChangeTimes->{3.725801245530424*^9, 3.7572502327082157`*^9, 3.789286527628552*^9}, CellLabel-> "Out[176]=",ExpressionUUID->"d2a89455-8e32-4a99-87c0-dd788f0df56e"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MapAt", "[", RowBox[{"h", ",", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e"}], "}"}], ",", "3"}], "]"}]], "Input", 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\"TI\"]\) elements for which \ \!\(\*RowBox[{StyleBox[\"crit\", \"TI\"], \"[\", SubscriptBox[StyleBox[\"e\", \ \"TI\"], StyleBox[\"i\", \"TI\"]], \"]\"}]\) is True. \n\ \!\(\*RowBox[{\"Select\", \"[\", StyleBox[\"crit\", \"TI\"], \"]\"}]\) \ represents an operator form of Select that can be applied to an expression. ", "Documentation" -> Association[ "Local" -> "paclet:ref/Select", "Web" -> "http://reference.wolfram.com/language/ref/Select.html"], "OwnValues" -> None, "UpValues" -> None, "DownValues" -> None, "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, "FormatValues" -> None, "Options" -> None, "Attributes" -> {Protected}, "FullName" -> "System`Select"], False]]], "Output", CellChangeTimes->{3.789289133577667*^9}, CellLabel-> "Out[210]=",ExpressionUUID->"70f12cd6-a526-4fa2-bfed-f6281e54f33a"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "Cases"}]], "Input", CellChangeTimes->{{3.725547026456772*^9, 3.725547031047155*^9}}, CellLabel-> "In[211]:=",ExpressionUUID->"026a0141-e9f5-4921-9a9b-d42513bc2ea8"], Cell[BoxData[ InterpretationBox[ StyleBox[ FrameBox[ DynamicModuleBox[{System`InformationDump`open$$ = False, System`InformationDump`mouseOver$$ = False}, PaneSelectorBox[{True-> TagBox[GridBox[{ { ItemBox[ PaneBox[ StyleBox["\<\" Symbol\"\>", 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StyleBox[\\\"levelspec\\\", \ \\\"TI\\\"]}], \\\"]\\\"}]\\) gives a list of all parts of \\!\\(\\*StyleBox[\ \\\"expr\\\", \\\"TI\\\"]\\) on levels specified by \ \\!\\(\\*StyleBox[\\\"levelspec\\\", \\\"TI\\\"]\\) that match the pattern. \ \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \\\"[\\\", RowBox[{StyleBox[\\\"expr\\\", \ \\\"TI\\\"], \\\",\\\", RowBox[{StyleBox[\\\"pattern\\\", \\\"TI\\\"], \\\"\ \[Rule]\\\", StyleBox[\\\"rhs\\\", \\\"TI\\\"]}], \\\",\\\", \ StyleBox[\\\"levelspec\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) gives the values of \ \\!\\(\\*StyleBox[\\\"rhs\\\", \\\"TI\\\"]\\) that match the pattern. \ \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \\\"[\\\", RowBox[{StyleBox[\\\"expr\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"pattern\\\", \\\"TI\\\"], \\\",\\\", \ StyleBox[\\\"levelspec\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"n\\\", \ \\\"TI\\\"]}], \\\"]\\\"}]\\) gives the first \\!\\(\\*StyleBox[\\\"n\\\", \\\ \"TI\\\"]\\) parts in \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\\) that \ match the pattern. \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \\\"[\\\", \ StyleBox[\\\"pattern\\\", \\\"TI\\\"], \\\"]\\\"}]\\) represents an operator \ form of Cases that can be applied to an expression.\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { PaneBox[GridBox[{ { DynamicModuleBox[{System`InformationDump`open$$ = { False, False, False, False, False, False, False, False, False, False, False, False}}, StyleBox[GridBox[{ { TagBox[ TooltipBox[ StyleBox["\<\" Documentation\"\>", "InformationRowLabel", StripOnInput->False], "\"Documentation\"", TooltipStyle->"TextStyling"], Annotation[#, "Documentation", "Tooltip"]& ], TemplateBox[{ TemplateBox[{ "\"Local \[RightGuillemet]\"", "paclet:ref/Cases", "paclet:ref/Cases", "Link", { RGBColor[0.9686274509803922, 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corresponding to the \ \\!\\(\\*SubscriptBox[StyleBox[\\\"e\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \\\ \"TI\\\"]]\\) that match the pattern. \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \ \\\"[\\\", RowBox[{StyleBox[\\\"expr\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\ \"pattern\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"levelspec\\\", \ \\\"TI\\\"]}], \\\"]\\\"}]\\) gives a list of all parts of \\!\\(\\*StyleBox[\ \\\"expr\\\", \\\"TI\\\"]\\) on levels specified by \ \\!\\(\\*StyleBox[\\\"levelspec\\\", \\\"TI\\\"]\\) that match the pattern. \ \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \\\"[\\\", RowBox[{StyleBox[\\\"expr\\\", \ \\\"TI\\\"], \\\",\\\", RowBox[{StyleBox[\\\"pattern\\\", \\\"TI\\\"], \\\"\ \[Rule]\\\", StyleBox[\\\"rhs\\\", \\\"TI\\\"]}], \\\",\\\", \ StyleBox[\\\"levelspec\\\", \\\"TI\\\"]}], \\\"]\\\"}]\\) gives the values of \ \\!\\(\\*StyleBox[\\\"rhs\\\", \\\"TI\\\"]\\) that match the pattern. \ \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \\\"[\\\", RowBox[{StyleBox[\\\"expr\\\", \ \\\"TI\\\"], \\\",\\\", StyleBox[\\\"pattern\\\", \\\"TI\\\"], \\\",\\\", \ StyleBox[\\\"levelspec\\\", \\\"TI\\\"], \\\",\\\", StyleBox[\\\"n\\\", \ \\\"TI\\\"]}], \\\"]\\\"}]\\) gives the first \\!\\(\\*StyleBox[\\\"n\\\", \\\ \"TI\\\"]\\) parts in \\!\\(\\*StyleBox[\\\"expr\\\", \\\"TI\\\"]\\) that \ match the pattern. \\n\\!\\(\\*RowBox[{\\\"Cases\\\", \\\"[\\\", \ StyleBox[\\\"pattern\\\", \\\"TI\\\"], \\\"]\\\"}]\\) represents an operator \ form of Cases that can be applied to an expression.\"\>", "InformationUsageText", StripOnInput->False, LineSpacing->{1.5, 1.5, 3.}], FrameMargins->{{10, 10}, {8, 10}}], BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False], ItemBox["\<\"\"\>", BaseStyle->"InformationUsageSubtitleBackground", StripOnInput->False]}, { ItemBox[ TagBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpener"], ImageSizeCache->{13., {2., 11.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", 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\"TI\"]}]}], \"]\"}]\) \ gives a list of the values of \!\(\*StyleBox[\"rhs\", \"TI\"]\) corresponding \ to the \!\(\*SubscriptBox[StyleBox[\"e\", \"TI\"], StyleBox[\"i\", \"TI\"]]\) \ that match the pattern. \n\!\(\*RowBox[{\"Cases\", \"[\", \ RowBox[{StyleBox[\"expr\", \"TI\"], \",\", StyleBox[\"pattern\", \"TI\"], \",\ \", StyleBox[\"levelspec\", \"TI\"]}], \"]\"}]\) gives a list of all parts of \ \!\(\*StyleBox[\"expr\", \"TI\"]\) on levels specified by \ \!\(\*StyleBox[\"levelspec\", \"TI\"]\) that match the pattern. \n\ \!\(\*RowBox[{\"Cases\", \"[\", RowBox[{StyleBox[\"expr\", \"TI\"], \",\", \ RowBox[{StyleBox[\"pattern\", \"TI\"], \"\[Rule]\", StyleBox[\"rhs\", \ \"TI\"]}], \",\", StyleBox[\"levelspec\", \"TI\"]}], \"]\"}]\) gives the \ values of \!\(\*StyleBox[\"rhs\", \"TI\"]\) that match the pattern. \n\ \!\(\*RowBox[{\"Cases\", \"[\", RowBox[{StyleBox[\"expr\", \"TI\"], \",\", \ StyleBox[\"pattern\", \"TI\"], \",\", StyleBox[\"levelspec\", \"TI\"], \",\", \ StyleBox[\"n\", 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