Integração com o Wolfram|Alpha

Matemática avançada 

Números complexos

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NotebookWrite[ ButtonNotebook[], Cell[Typeset`newq$$, "WolframAlphaShort", FormatType -> "TextForm"], All], WolframAlphaClient`Private`open$\ 11741 = True; WolframAlphaClient`Private`extrudeFromFastParse[ "absolute value (4 + 2 i)", Defer[ Abs[4 + 2 I]], "Fast parse"]; WolframAlphaClient`Private`open$\ 11741 = False], Evaluator->Automatic, Method->"Queued"], Alignment->Right, StripOnInput->False]}, { PaneBox[ TagBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> StyleBox[ RowBox[{"Abs", "[", RowBox[{"4", " ", "+", " ", RowBox[{"2", "*", "I"}]}], "]"}], StripOnInput->False, NumberMarks->False], True-> StyleBox[ RowBox[{"Abs", "[", RowBox[{"4", " ", "+", " ", RowBox[{"2", "*", "I"}]}], "]"}], StripOnInput->False, ShowSyntaxStyles->False, NumberMarks->False, FontColor->RGBColor[1, 0.5, 0]]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{ShowStringCharacters -> True}, FrameMargins->0, ImageSize->Automatic], Alignment->Left, Appearance->None, BaseStyle->{}, ButtonFunction:>(SelectionMove[ ButtonNotebook[], All, ButtonCell]; 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NotebookWrite[ ButtonNotebook[], Cell[Typeset`newq$$, "WolframAlphaShort", FormatType -> "TextForm"], All], WolframAlphaClient`Private`open$\ 11741 = True; WolframAlphaClient`Private`extrudeFromFastParse[ "absolute value (4 + 2 i)", Defer[ Abs[4 + 2 I]], "Fast parse"]; WolframAlphaClient`Private`open$\ 11741 = False], Evaluator->Automatic, Method->"Queued"], Alignment->Right, StripOnInput->False]}, { PaneBox[ TagBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> StyleBox[ RowBox[{"Abs", "[", RowBox[{"4", " ", "+", " ", RowBox[{"2", "*", "I"}]}], "]"}], StripOnInput->False, NumberMarks->False], True-> StyleBox[ RowBox[{"Abs", "[", RowBox[{"4", " ", "+", " ", RowBox[{"2", "*", "I"}]}], "]"}], StripOnInput->False, ShowSyntaxStyles->False, NumberMarks->False, FontColor->RGBColor[1, 0.5, 0]]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{ShowStringCharacters -> True}, FrameMargins->0, ImageSize->Automatic], Alignment->Left, Appearance->None, BaseStyle->{}, ButtonFunction:>(SelectionMove[ ButtonNotebook[], All, ButtonCell]; 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X \!\(\* NamespaceBox["WolframAlphaQueryParseResults", DynamicModuleBox[{Typeset`q$$ = "residue of 1/(z^2+4)^2 at z=2i", Typeset`newq$$ = "residue of 1/(z^2+4)^2 at z=2i", Typeset`chosen$$ = "Residue[(4 + z^2)^(-2), {z, 2*I}]"}, PaneSelectorBox[{False-> DynamicModuleBox[{WolframAlphaClient`Private`show$$ = False}, TagBox[ FrameBox[ TagBox[GridBox[{ { InputFieldBox[Dynamic[Typeset`newq$$], String, Appearance->None, BaseStyle->{"CalculateInput"}, ContinuousAction->True, Enabled->True, FieldSize->{{1, 40}, {1, DirectedInfinity[1]}}], ItemBox[ ButtonBox[ PaneSelectorBox[{True-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "OrangeSquarePlus"], ImageSizeCache->{10., {3., 8.}}], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ], False-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "GraySquarePlus"], ImageSizeCache->{10., {3., 8.}}], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ]}, Dynamic[ WolframAlphaClient`Private`show$$], ImageSize->All], Appearance->None, ButtonFunction:>If[ Or[ CurrentValue["OptionKey"], CurrentValue["AltKey"]], SelectionMove[ ButtonNotebook[], All, ButtonCell, AutoScroll -> False]; NotebookWrite[ ButtonNotebook[], Cell[Typeset`newq$$, "WolframAlphaShort", FormatType -> "TextForm"], All], WolframAlphaClient`Private`open$\ 14116 = True; WolframAlphaClient`Private`extrudeFromFastParse[ "residue of 1/(z^2+4)^2 at z=2i", Defer[ Residue[(4 + z^2)^(-2), {z, 2 I}]], "Fast parse"]; WolframAlphaClient`Private`open$\ 14116 = False], Evaluator->Automatic, Method->"Queued"], Alignment->Right, StripOnInput->False]}, { PaneBox[ TagBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> StyleBox[ RowBox[{"Residue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "+", " ", RowBox[{"z", "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"z", ",", " ", RowBox[{"2", "*", "I"}]}], "}"}]}], "]"}], StripOnInput->False, NumberMarks->False], True-> StyleBox[ RowBox[{"Residue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "+", " ", RowBox[{"z", "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"z", ",", " ", RowBox[{"2", "*", "I"}]}], "}"}]}], "]"}], StripOnInput->False, ShowSyntaxStyles->False, NumberMarks->False, FontColor->RGBColor[1, 0.5, 0]]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{ShowStringCharacters -> True}, FrameMargins->0, ImageSize->Automatic], Alignment->Left, Appearance->None, BaseStyle->{}, ButtonFunction:>(SelectionMove[ ButtonNotebook[], All, ButtonCell]; NotebookWrite[ ButtonNotebook[], Cell[ BoxData[ RowBox[{"Residue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "+", " ", RowBox[{"z", "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"z", ",", " ", RowBox[{"2", "*", "I"}]}], "}"}]}], "]"}]], "Input"], All]; SelectionMove[ ButtonNotebook[], After, CellContents]), Evaluator->Automatic, ImageSize->Automatic, Method->"Preemptive"], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "RemoveResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "RemoveResults"]], "Tooltip"]& ], AppearanceElements->{}, BaseStyle->{ ShowStringCharacters -> True, "StandardForm", 12, ScriptLevel -> 0}, ImageSize->{Automatic, {1, 100}}, Scrollbars->{False, Automatic}], "\[SpanFromLeft]"} }, AutoDelete->False, BaselinePosition->{1, 1}, FrameStyle->GrayLevel[0.85], GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxDividers->{ "Columns" -> {{False}}, "Rows" -> {False, {True}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], Alignment->Top, Background->Dynamic[ FEPrivate`If[ FEPrivate`And[ FEPrivate`SameQ[ FEPrivate`Head[Typeset`newq$$], String], FEPrivate`UnsameQ[Typeset`q$$, Typeset`newq$$]], RGBColor[1., 0.975, 0.95], GrayLevel[1]]], BaselinePosition->Baseline, FrameStyle->GrayLevel[0.85], ImageSize->Automatic, RoundingRadius->5, StripOnInput->False], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[ WolframAlphaClient`Private`show$$, True], "MouseExited" :> FEPrivate`Set[ WolframAlphaClient`Private`show$$, False], PassEventsDown -> Automatic, PassEventsUp -> True}]], DynamicModuleValues:>{}], True-> TagBox[GridBox[{ { DynamicModuleBox[{WolframAlphaClient`Private`show$$ = False}, TagBox[ FrameBox[ TagBox[GridBox[{ { InputFieldBox[Dynamic[Typeset`newq$$], String, Appearance->None, BaseStyle->{"CalculateInput"}, ContinuousAction->True, Enabled->True, FieldSize->{{1, 40}, {1, DirectedInfinity[1]}}], ItemBox[ ButtonBox[ PaneSelectorBox[{True-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource[ "WABitmaps", "OrangeSquarePlus"]], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ], False-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "GraySquarePlus"]], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ]}, Dynamic[ WolframAlphaClient`Private`show$$], ImageSize->All], Appearance->None, ButtonFunction:>If[ Or[ CurrentValue["OptionKey"], CurrentValue["AltKey"]], SelectionMove[ ButtonNotebook[], All, ButtonCell, AutoScroll -> False]; NotebookWrite[ ButtonNotebook[], Cell[Typeset`newq$$, "WolframAlphaShort", FormatType -> "TextForm"], All], WolframAlphaClient`Private`open$\ 14116 = True; WolframAlphaClient`Private`extrudeFromFastParse[ "residue of 1/(z^2+4)^2 at z=2i", Defer[ Residue[(4 + z^2)^(-2), {z, 2 I}]], "Fast parse"]; WolframAlphaClient`Private`open$\ 14116 = False], Evaluator->Automatic, Method->"Queued"], Alignment->Right, StripOnInput->False]}, { PaneBox[ TagBox[ TooltipBox[ ButtonBox[ PaneSelectorBox[{False-> StyleBox[ RowBox[{"Residue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "+", " ", RowBox[{"z", "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"z", ",", " ", RowBox[{"2", "*", "I"}]}], "}"}]}], "]"}], StripOnInput->False, NumberMarks->False], True-> StyleBox[ RowBox[{"Residue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "+", " ", RowBox[{"z", "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"z", ",", " ", RowBox[{"2", "*", "I"}]}], "}"}]}], "]"}], StripOnInput->False, ShowSyntaxStyles->False, NumberMarks->False, FontColor->RGBColor[1, 0.5, 0]]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{ShowStringCharacters -> True}, FrameMargins->0, ImageSize->Automatic], Alignment->Left, Appearance->None, BaseStyle->{}, ButtonFunction:>(SelectionMove[ ButtonNotebook[], All, ButtonCell]; NotebookWrite[ ButtonNotebook[], Cell[ BoxData[ RowBox[{"Residue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"4", " ", "+", " ", RowBox[{"z", "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"z", ",", " ", RowBox[{"2", "*", "I"}]}], "}"}]}], "]"}]], "Input"], All]; SelectionMove[ ButtonNotebook[], After, CellContents]), Evaluator->Automatic, ImageSize->Automatic, Method->"Preemptive"], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "RemoveResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "RemoveResults"]], "Tooltip"]& ], AppearanceElements->{}, BaseStyle->{ ShowStringCharacters -> True, "StandardForm", 12, ScriptLevel -> 0}, ImageSize->{Automatic, {1, 100}}, Scrollbars->{False, Automatic}], "\[SpanFromLeft]"} }, AutoDelete->False, BaselinePosition->{1, 1}, FrameStyle->GrayLevel[0.85], GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxDividers->{ "Columns" -> {{False}}, "Rows" -> {False, {True}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], Alignment->Top, Background->Dynamic[ FEPrivate`If[ FEPrivate`And[ FEPrivate`SameQ[ FEPrivate`Head[Typeset`newq$$], String], FEPrivate`UnsameQ[Typeset`q$$, Typeset`newq$$]], RGBColor[1., 0.975, 0.95], GrayLevel[1]]], BaselinePosition->Baseline, FrameStyle->GrayLevel[0.85], ImageSize->Automatic, RoundingRadius->5, StripOnInput->False], EventHandlerTag[{ "MouseEntered" :> FEPrivate`Set[ WolframAlphaClient`Private`show$$, True], "MouseExited" :> FEPrivate`Set[ WolframAlphaClient`Private`show$$, False], PassEventsDown -> Automatic, PassEventsUp -> True}]], DynamicModuleValues:>{}]}, { InterpretationBox[ StyleBox[ DynamicBox[FEPrivate`FrontEndResource[ "FEExpressions", "NecklaceAnimator"][20]], AnimatorBoxOptions->{ImageSize->20}], Animator[Appearance -> "Necklace", ImageSize -> 20], BaseStyle->{Deployed -> True}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"]}, Dynamic[WolframAlphaClient`Private`open$14116], BaseStyle->{Deployed -> True}, ImageSize->Automatic], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)

Grafos e conjuntos

X \!\(\* NamespaceBox["WolframAlphaQueryResults", DynamicModuleBox[{Typeset`q$$ = "(complement S) intersect (A union B)", Typeset`opts$$ = { AppearanceElements -> { "Extrusion", "Warnings", "Assumptions", "Pods"}, Asynchronous -> All, Method -> {"ExtrusionChosen" -> { "VennDiagram", "Venn diagram", 1, 1, "Content"}, "Formats" -> { "cell", "minput", "moutput", "msound", "dataformats"}}}, Typeset`elements$$ = { "Extrusion", "Warnings", "Assumptions", "Pods"}, pod1$$ = XMLElement[ "pod", {"title" -> "Input interpretation", "scanner" -> "Identity", "id" -> "Input", "position" -> "100", "error" -> "false", "numsubpods" -> "1"}, { XMLElement["subpod", {"title" -> ""}, { XMLElement["minput", {}, {}], XMLElement["cell", {"compressed" -> False, "string" -> True}, { Cell[ BoxData[ FormBox[ TagBox[ FormBox[ TagBox[ RowBox[{ FormBox[ TemplateBox[{"S", "\"'\""}, "Row", DisplayFunction -> (RowBox[{#, " ", #2}]& ), InterpretationFunction -> (RowBox[{ StyleBox["Row", FontFamily -> "Bitstream Vera 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Teoria de números

X \!\(\* NamespaceBox["WolframAlphaQueryParseResults", DynamicModuleBox[{Typeset`q$$ = "greatest common divisor 1648, 884", Typeset`newq$$ = "greatest common divisor 1648, 884", Typeset`chosen$$ = "GCD[1648, 884]"}, PaneSelectorBox[{False-> DynamicModuleBox[{WolframAlphaClient`Private`show$$ = False}, TagBox[ FrameBox[ TagBox[GridBox[{ { InputFieldBox[Dynamic[Typeset`newq$$], String, Appearance->None, BaseStyle->{"CalculateInput"}, ContinuousAction->True, Enabled->True, FieldSize->{{1, 40}, {1, DirectedInfinity[1]}}], ItemBox[ ButtonBox[ PaneSelectorBox[{True-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "OrangeSquarePlus"], ImageSizeCache->{10., {3., 8.}}], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ], False-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "GraySquarePlus"], ImageSizeCache->{10., {3., 8.}}], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ]}, Dynamic[ WolframAlphaClient`Private`show$$], ImageSize->All], Appearance->None, ButtonFunction:>If[ Or[ CurrentValue["OptionKey"], CurrentValue["AltKey"]], SelectionMove[ ButtonNotebook[], All, ButtonCell, AutoScroll -> False]; 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In[1]:=

X \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "find sequence 0, 1, 10, 33, 76", WolframAlphaClient`Private`boxes$$ = RowBox[{"FindSequenceFunction", "[", RowBox[{"{", RowBox[{"0", ",", " ", "1", ",", " ", "10", ",", " ", "33", ",", " ", "76"}], "}"}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{211., {10., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)[x]

Out[1]=

In[2]:=

X Map[\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "find sequence 0, 1, 10, 33, 76", WolframAlphaClient`Private`boxes$$ = RowBox[{"FindSequenceFunction", "[", RowBox[{"{", RowBox[{"0", ",", " ", "1", ",", " ", "10", ",", " ", "33", ",", " ", "76"}], "}"}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{210., {11., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), Range[20]]

Out[2]=

In[3]:=

X ListLinePlot[\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "first 20 fibonacci numbers", WolframAlphaClient`Private`boxes$$ = RowBox[{"Fibonacci", "[", RowBox[{"Range", "[", RowBox[{"1", ",", " ", "20"}], "]"}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{196., {11., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), Mesh -> All, PlotRange -> All]

Out[3]=

Constantes matemáticas

In[4]:=

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Out[4]=

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In[5]:=

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Out[5]=