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\\\"[\\\", 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->{20., {3., 17.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"], ImageSizeCache->{20., {3., 17.}}]}, Dynamic[ System`InformationDump`mouseOver$$]], Alignment->Left, Appearance->{"Default" -> None}, ButtonFunction:>FEPrivate`Set[ 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"InformationGridPlain", StripOnInput->False], InformationData[<| "ObjectType" -> "Symbol", "Usage" -> "\!\(\*RowBox[{StyleBox[\"expr\", \"TI\"], \"[\", RowBox[{\"[\", \ StyleBox[\"i\", \"TI\"], \"]\"}], \"]\"}]\) or \!\(\*RowBox[{\"Part\", \"[\", \ RowBox[{StyleBox[\"expr\", \"TI\"], \",\", StyleBox[\"i\", \"TI\"]}], \"]\"}]\ \) gives 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 \!\(\*StyleBox[\"s\", \"TI\"]\).\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 \ \!\(\*StyleBox[\"expr\", \"TI\"]\).", "Documentation" -> <| "Local" -> "paclet:ref/Part", "Web" -> "http://reference.wolfram.com/language/ref/Part.html"|>, "OwnValues" -> None, "UpValues" -> None, "DownValues" -> None, "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, "FormatValues" -> None, "Options" -> None, "Attributes" -> {NHoldRest, Protected, ReadProtected}, "FullName" -> "System`Part"|>, False]]], "Output", CellChangeTimes->{3.7892845036479063`*^9, 3.789302666899078*^9, 3.82034540010848*^9}, CellLabel->"Out[13]=",ExpressionUUID->"2dfe9b1a-5c4e-4f17-958d-6a65583b5356"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ls", "\[LeftDoubleBracket]", RowBox[{"2", ";;", "7"}], "\[RightDoubleBracket]"}]], "Input", CellChangeTimes->{{3.72552883559135*^9, 3.72552886588441*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"70778cc1-0ac1-4121-8499-6fc98444e8eb"], Cell[BoxData[ RowBox[{"{", RowBox[{"b", ",", "c", ",", "d", ",", "e", ",", "f", ",", "g"}], "}"}]], "Output", CellChangeTimes->{3.725528868981234*^9, 3.7256250566955957`*^9, 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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[<| "ObjectType" -> "Symbol", "Usage" -> "\!\(\*RowBox[{\"PolynomialRemainder\", \"[\", RowBox[{StyleBox[\"p\", \ \"TI\"], \",\", StyleBox[\"q\", \"TI\"], \",\", StyleBox[\"x\", \"TI\"]}], \ \"]\"}]\) gives the remainder from dividing \!\(\*StyleBox[\"p\", \"TI\"]\) \ by \!\(\*StyleBox[\"q\", \"TI\"]\), treated as polynomials in \!\(\*StyleBox[\ \"x\", \"TI\"]\). ", "Documentation" -> <| "Local" -> "paclet:ref/PolynomialRemainder", "Web" -> "http://reference.wolfram.com/language/ref/PolynomialRemainder.html"|>, "OwnValues" -> None, "UpValues" -> None, "DownValues" -> None, "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, "FormatValues" -> None, "Options" -> {Modulus -> 0}, "Attributes" -> {Protected}, "FullName" -> "System`PolynomialRemainder"|>, False]]], "Output", CellChangeTimes->{3.789290195400036*^9, 3.789306324615367*^9, 3.7893066274521837`*^9, 3.820485514674384*^9, 3.820519182360321*^9, 3.852205755512672*^9}, CellLabel-> "Out[121]=",ExpressionUUID->"fb6fb9cb-4fa1-4599-9c41-6296c5039249"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PolynomialRemainder", "[", RowBox[{ RowBox[{"\[CapitalPhi]", "[", SuperscriptBox["z", "2"], "]"}], ",", RowBox[{"\[CapitalPhi]", "[", "z", "]"}], ",", "z"}], "]"}]], "Input", CellChangeTimes->{{3.727519953285391*^9, 3.727520009583549*^9}, { 3.727520054534025*^9, 3.7275200694398317`*^9}}, CellLabel-> "In[122]:=",ExpressionUUID->"64945fe8-0c44-43b8-a93b-49f662303304"], Cell[BoxData["0"], "Output", CellChangeTimes->{3.727520070805272*^9, 3.727614361815495*^9, 3.789290195415091*^9, 3.7893064230423727`*^9, 3.82048552141848*^9, 3.820519231224272*^9, 3.852205921443461*^9}, CellLabel-> "Out[122]=",ExpressionUUID->"a963c945-c797-42d1-9222-8e26d9960661"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "PolynomialReduce"}]], "Input", CellChangeTimes->{{3.789306496283382*^9, 3.789306506178393*^9}}, CellLabel-> "In[126]:=",ExpressionUUID->"ed2018fb-5b43-45b1-b65b-9409942be2cc"], Cell[BoxData[ InterpretationBox[ StyleBox[ FrameBox[ DynamicModuleBox[{System`InformationDump`open$$ = False, System`InformationDump`mouseOver$$ = False}, PaneSelectorBox[{True-> TagBox[GridBox[{ { ItemBox[ PaneBox[ StyleBox["\<\" Symbol\"\>", "InformationTitleText", StripOnInput->False, BaseStyle -> None], FrameMargins->{{4, 0}, {-1, 1}}], BaseStyle->"InformationTitleBackground", StripOnInput->False], ItemBox[ PaneBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIcon"]], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIconHot"]]}, Dynamic[ CurrentValue["MouseOver"]]], Appearance->None, BaseStyle->"Link", ButtonData->"paclet:ref/PolynomialReduce", ButtonNote->"paclet:ref/PolynomialReduce"], "\"paclet:ref/PolynomialReduce\""], FrameMargins->{{0, 4}, {0, 2}}], BaseStyle->"InformationTitleBackground", StripOnInput->False]}, { ItemBox[ PaneBox[ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"PolynomialReduce\\\", \ \\\"[\\\", RowBox[{StyleBox[\\\"poly\\\", \\\"TI\\\"], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"poly\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"poly\\\ \", \\\"TI\\\"], StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\ \[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}]}], \\\"]\\\"}]\\) yields a list representing a \ reduction of \\!\\(\\*StyleBox[\\\"poly\\\", \\\"TI\\\"]\\) in terms of the \ \\!\\(\\*SubscriptBox[StyleBox[\\\"poly\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \ \\\"TI\\\"]]\\). The list has the form \\!\\(\\*RowBox[{\\\"{\\\", \ RowBox[{RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"a\\\", \ \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", \ SubscriptBox[StyleBox[\\\"a\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\ \"}], \\\",\\\", StyleBox[\\\"b\\\", \\\"TI\\\"]}], \\\"}\\\"}]\\), where \\!\ \\(\\*StyleBox[\\\"b\\\", \\\"TI\\\"]\\) is minimal and \ \\!\\(\\*RowBox[{RowBox[{SubscriptBox[StyleBox[\\\"a\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\" \\\", SubscriptBox[StyleBox[\\\"poly\\\ \", \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]]}], \\\"+\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"a\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\" \\\", SubscriptBox[StyleBox[\\\"poly\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]]}], \\\"+\\\", StyleBox[\\\"\[Ellipsis]\\\", \ \\\"TR\\\"], \\\"+\\\", StyleBox[\\\"b\\\", \\\"TI\\\"]}]\\) is exactly \ \\!\\(\\*StyleBox[\\\"poly\\\", \\\"TI\\\"]\\). \"\>", "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}}, StyleBox[GridBox[{ { TagBox[ TooltipBox[ StyleBox["\<\" Documentation\"\>", "InformationRowLabel", StripOnInput->False], "\"Documentation\"", TooltipStyle->"TextStyling"], Annotation[#, "Documentation", "Tooltip"]& ], TemplateBox[{ TemplateBox[{ "\"Local \[RightGuillemet]\"", "paclet:ref/PolynomialReduce", "paclet:ref/PolynomialReduce", "Link", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"], "\" \"", StyleBox[ "\"|\"", "InformationRowLabel", StripOnInput -> False], "\" \"", TemplateBox[{"\"Web \[RightGuillemet]\"", { URL[ "http://reference.wolfram.com/language/ref/\ PolynomialReduce.html"], None}, "http://reference.wolfram.com/language/ref/\ PolynomialReduce.html", "Hyperlink", { RGBColor[0.9686274509803922, 0.4666666666666667, 0.]}, BaseStyle -> { RGBColor[0.0784313725490196, 0.1568627450980392, 0.6]}}, "HyperlinkTemplate"]}, "RowDefault"]}, { PaneSelectorBox[{True-> ButtonBox[ PaneSelectorBox[{False-> TemplateBox[{"\[ThickSpace]", "\"\[ThickSpace]\"", StyleBox[ "\"Options\"", "InformationRowLabel", StripOnInput -> False], DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpener"]]}, "RowWithSeparators"], True-> TemplateBox[{"\[ThickSpace]", "\"\[ThickSpace]\"", StyleBox[ "\"Options\"", "InformationRowLabel", StripOnInput -> False], DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"]]}, "RowWithSeparators"]}, Dynamic[ CurrentValue["MouseOver"]], FrameMargins->0, ImageSize->Automatic], Appearance->None, BaseStyle->None, ButtonFunction:>(Part[System`InformationDump`open$$, 3] = False), Evaluator->Automatic, FrameMargins->0, ImageMargins->0, Method->"Preemptive"], False-> ButtonBox[ PaneSelectorBox[{False-> TemplateBox[{"\[ThickSpace]", "\"\[ThickSpace]\"", StyleBox[ "\"Options\"", "InformationRowLabel", StripOnInput -> False], DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "RightPointerOpener"]]}, "RowWithSeparators"], True-> TemplateBox[{"\[ThickSpace]", "\"\[ThickSpace]\"", StyleBox[ "\"Options\"", "InformationRowLabel", StripOnInput -> False], DynamicBox[ FEPrivate`FrontEndResource[ "FEBitmaps", "RightPointerOpenerHot"]]}, "RowWithSeparators"]}, Dynamic[ CurrentValue["MouseOver"]], FrameMargins->0, ImageSize->Automatic], Appearance->None, BaseStyle->None, ButtonFunction:>(Part[System`InformationDump`open$$, 3] = True), Evaluator->Automatic, FrameMargins->0, ImageMargins->0, Method->"Preemptive"]}, Dynamic[ FEPrivate`Part[System`InformationDump`open$$, 3]]], PaneSelectorBox[{True->GridBox[{ { RowBox[{ "CoefficientDomain", "\[Rule]", "RationalFunctions"}]}, { RowBox[{"Modulus", "\[Rule]", "0"}]}, { RowBox[{"MonomialOrder", "\[Rule]", "Lexicographic"}]}, { RowBox[{"ParameterVariables", "\[Rule]", RowBox[{"{", "}"}]}]}, { RowBox[{"Tolerance", "\[Rule]", "0"}]}, { StyleBox[ TemplateBox[{ "\"(\"", "\"\[InvisibleSpace]\"", "5", "\" total)\""}, "RowDefault"], "InformationRowOpener", StripOnInput->False]} }, BaselinePosition->{Baseline, {1, 1}}, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{1.}}}], False-> RowBox[{ RowBox[{ "CoefficientDomain", "\[Rule]", "RationalFunctions"}], "\[ThinSpace]", StyleBox["\<\"\[Ellipsis]\"\>", "InformationRowOpener", StripOnInput->False], "\[ThinSpace]", StyleBox[ TemplateBox[{ "\"(\"", "\"\[InvisibleSpace]\"", "5", "\" total)\""}, "RowDefault"], "InformationRowOpener", StripOnInput->False]}]}, Dynamic[ FEPrivate`Part[System`InformationDump`open$$, 3]], BaselinePosition->Baseline, ImageSize->Automatic]}, { TagBox[ TooltipBox[ StyleBox["\<\" Attributes\"\>", "InformationRowLabel", StripOnInput->False], "\"Attributes\"", TooltipStyle->"TextStyling"], Annotation[#, "Attributes", "Tooltip"]& ], RowBox[{"{", RowBox[{"Protected", ",", "ReadProtected"}], "}"}]}, { TagBox[ TooltipBox[ StyleBox["\<\" Full Name\"\>", "InformationRowLabel", StripOnInput->False], "\"FullName\"", TooltipStyle->"TextStyling"], Annotation[#, "FullName", "Tooltip"]& ], "\<\"System`PolynomialReduce\"\>"} }, AutoDelete->False, GridBoxAlignment->{"Columns" -> {Right, Left}}, GridBoxDividers->None, GridBoxItemSize->{"Columns" -> {Automatic, Automatic}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.8]}, Offset[0.2]}}], "DialogStyle", StripOnInput->False], DynamicModuleValues:>{}]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxDividers->{"Columns" -> {{False}}, "Rows" -> {{False}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[3.6]}, Offset[0.2]}}], FrameMargins->{{6, 6}, {6, 3}}], ""}, { ItemBox[ TagBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "UpPointerOpener"]], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "UpPointerOpenerHot"]]}, Dynamic[ System`InformationDump`mouseOver$$]], Alignment->Left, Appearance->{"Default" -> None}, ButtonFunction:>FEPrivate`Set[ System`InformationDump`open$$, False], Evaluator->Automatic, FrameMargins->{{9, 0}, {0, 0}}, ImageMargins->0, ImageSize->Full, Method->"Preemptive"], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[System`InformationDump`mouseOver$$, 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"], False-> TagBox[GridBox[{ { ItemBox[ PaneBox[ StyleBox["\<\" Symbol\"\>", "InformationTitleText", StripOnInput->False], FrameMargins->{{4, 0}, {-1, 1}}], BaseStyle->"InformationTitleBackground", StripOnInput->False], ItemBox[ PaneBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIcon"], ImageSizeCache->{26., {3., 23.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "InformationHelpIconHot"], ImageSizeCache->{26., {3., 23.}}]}, Dynamic[ CurrentValue["MouseOver"]]], Appearance->None, BaseStyle->"Link", ButtonData->"paclet:ref/PolynomialReduce", ButtonNote->"paclet:ref/PolynomialReduce"], "\"paclet:ref/PolynomialReduce\""], FrameMargins->{{0, 4}, {0, 2}}], BaseStyle->"InformationTitleBackground", StripOnInput->False]}, { ItemBox[ PaneBox[ StyleBox["\<\"\\!\\(\\*RowBox[{\\\"PolynomialReduce\\\", \ \\\"[\\\", RowBox[{StyleBox[\\\"poly\\\", \\\"TI\\\"], \\\",\\\", \ RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"poly\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"poly\\\ \", \\\"TI\\\"], StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\ \[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\"}], \\\",\\\", RowBox[{\\\"{\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], StyleBox[\\\"1\\\", \ \\\"TR\\\"]], \\\",\\\", SubscriptBox[StyleBox[\\\"x\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\ \"TR\\\"]}], \\\"}\\\"}]}], \\\"]\\\"}]\\) yields a list representing a \ reduction of \\!\\(\\*StyleBox[\\\"poly\\\", \\\"TI\\\"]\\) in terms of the \ \\!\\(\\*SubscriptBox[StyleBox[\\\"poly\\\", \\\"TI\\\"], StyleBox[\\\"i\\\", \ \\\"TI\\\"]]\\). The list has the form \\!\\(\\*RowBox[{\\\"{\\\", \ RowBox[{RowBox[{\\\"{\\\", RowBox[{SubscriptBox[StyleBox[\\\"a\\\", \ \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\",\\\", \ SubscriptBox[StyleBox[\\\"a\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\",\\\", StyleBox[\\\"\[Ellipsis]\\\", \\\"TR\\\"]}], \\\"}\\\ \"}], \\\",\\\", StyleBox[\\\"b\\\", \\\"TI\\\"]}], \\\"}\\\"}]\\), where \\!\ \\(\\*StyleBox[\\\"b\\\", \\\"TI\\\"]\\) is minimal and \ \\!\\(\\*RowBox[{RowBox[{SubscriptBox[StyleBox[\\\"a\\\", \\\"TI\\\"], \ StyleBox[\\\"1\\\", \\\"TR\\\"]], \\\" \\\", SubscriptBox[StyleBox[\\\"poly\\\ \", \\\"TI\\\"], StyleBox[\\\"1\\\", \\\"TR\\\"]]}], \\\"+\\\", \ RowBox[{SubscriptBox[StyleBox[\\\"a\\\", \\\"TI\\\"], StyleBox[\\\"2\\\", \ \\\"TR\\\"]], \\\" \\\", SubscriptBox[StyleBox[\\\"poly\\\", \\\"TI\\\"], \ StyleBox[\\\"2\\\", \\\"TR\\\"]]}], \\\"+\\\", StyleBox[\\\"\[Ellipsis]\\\", \ \\\"TR\\\"], \\\"+\\\", StyleBox[\\\"b\\\", \\\"TI\\\"]}]\\) is exactly \ \\!\\(\\*StyleBox[\\\"poly\\\", \\\"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->{20., {3., 17.}}], True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "DownPointerOpenerHot"], ImageSizeCache->{20., {3., 17.}}]}, 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[<| "ObjectType" -> "Symbol", "Usage" -> "\!\(\*RowBox[{\"PolynomialReduce\", \"[\", RowBox[{StyleBox[\"poly\", \ \"TI\"], \",\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"poly\", \ \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"poly\", \ \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \ \"TR\"]}], \"}\"}], \",\", RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}]}], \"]\"}]\) yields a list \ representing a reduction of \!\(\*StyleBox[\"poly\", \"TI\"]\) in terms of \ the \!\(\*SubscriptBox[StyleBox[\"poly\", \"TI\"], StyleBox[\"i\", \ \"TI\"]]\). The list has the form \!\(\*RowBox[{\"{\", RowBox[{RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"a\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"a\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", StyleBox[\"b\", \ \"TI\"]}], \"}\"}]\), where \!\(\*StyleBox[\"b\", \"TI\"]\) is minimal and \!\ \(\*RowBox[{RowBox[{SubscriptBox[StyleBox[\"a\", \"TI\"], StyleBox[\"1\", \ \"TR\"]], \" \", SubscriptBox[StyleBox[\"poly\", \"TI\"], StyleBox[\"1\", \ \"TR\"]]}], \"+\", RowBox[{SubscriptBox[StyleBox[\"a\", \"TI\"], StyleBox[\"2\ \", \"TR\"]], \" \", SubscriptBox[StyleBox[\"poly\", \"TI\"], StyleBox[\"2\", \ \"TR\"]]}], \"+\", StyleBox[\"\[Ellipsis]\", \"TR\"], \"+\", StyleBox[\"b\", \ \"TI\"]}]\) is exactly \!\(\*StyleBox[\"poly\", \"TI\"]\). 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