GSberveglieri/Phi4tools | Paclet Repository

GSberveglieri`Phi4tools`

NComponents

NComponents []
	represents the number Ν of field components.

Details and Options



Examples

(1)

Basic Examples

(1)

In[1]:=

Needs["GSberveglieri`Phi4tools`"]

Let's look at the

diagram for

(2)

for the

theory with

=3 quartic vertices, let's visualize it and print its symmetry factor for the

O(Ν)

model:

In[2]:=



VisualizeDiagram

[2,0,3,1],

SymmetryFactorDiagram

[2,0,3,1]

Out[2]=



4Ν



Using the function

InformationDiagram

with the option "Tensor"->"O(N)" is possible to get both these information at the same time, for example

In[3]:=

InformationDiagram

[4,0,3,1,"Tensor""O(N)"]

Out[3]=

External Legs	4
Cubic Vertices	0
Quartic Vertices	3
List Number	1
Nickel Index	ee11\|22\|ee\|
Symmetry Factor	 4 9 + 2GSberveglieri`Phi4tools`NComponents[] 9 + 2 GSberveglieri`Phi4tools`NComponents[] 27 , 4 27 , 4 27 
Diagram
Value	1

The actual contribution for a given Feynman diagram is given by the product between the value of the diagram and symmetry factor that can be printed with

ValueDiagram

and

SymmetryFactorDiagram

, respectively. For example at the order

for

(2)

In[4]:=

Simplify

ValueDiagram

[2,0,4].

SymmetryFactorDiagram

[2,0,4]

Out[4]=

(10.6771231575200337492

8.×

-19

)+Ν((8.72385710756608389503

6.×

-19

)+Ν((1.90029513235515074179

9.×

-20

)+(0.1038236839760586157907245574

1.2×

-27

)Ν))

We could also look at the theory with O(N) model broken to cubic symmetry with the option "Tensor"->"Cubic", for example

In[5]:=

InformationDiagram

[2,0,4,3,"Tensor""Cubic"]

Out[5]=

Failure



Reason: Invalid signature in CloudSystem`Signing`SignedExpression[DynamicModule[{Set[TypeSystem`NestedGrid`PackagePrivate`renderedGrid,Deploy[Style[Grid[{{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["External Legs",Style["External Legs",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["External Legs"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["External Legs"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes["2"],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["External Legs"]},"Item",False],"Mouse"],Rule[ImageSize,{{34,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["Cubic Vertices",Style["Cubic Vertices",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["Cubic Vertices"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Cubic Vertices"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes["0"],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Cubic Vertices"]},"Item",False],"Mouse"],Rule[ImageSize,{{34,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["Quartic Vertices",Style["Quartic Vertices",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["Quartic Vertices"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Quartic Vertices"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes["4"],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Quartic Vertices"]},"Item",False],"Mouse"],Rule[ImageSize,{{34,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["List Number",Style["List Number",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["List Number"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["List Number"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes["3"],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["List Number"]},"Item",False],"Mouse"],Rule[ImageSize,{{34,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["Nickel Index",Style["Nickel Index",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["Nickel Index"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Nickel Index"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation["e112|e3|333||",TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Nickel Index"]},"Item",False],"Mouse"],Rule[ImageSize,{{145.60000000000002`,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["Symmetry Factor",Style["Symmetry Factor",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["Symmetry Factor"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Symmetry Factor"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes[StyleBox[RowBox[{FractionBox["4","9"],"+",FractionBox[RowBox[{"4"," ",RowBox[{"\[CapitalNu]"}]}],"9"],"+",FractionBox[SuperscriptBox[RowBox[{"\[CapitalNu]"}],"2"],"9"],"+",FractionBox[RowBox[{"8"," ",RowBox[{"\[CapitalChi]"}]}],"3"],"+",FractionBox[RowBox[{"4"," ",RowBox[{"\[CapitalNu]"}]," ",RowBox[{"\[CapitalChi]"}]}],"3"],"+",FractionBox[RowBox[{"16"," ",SuperscriptBox[RowBox[{"\[CapitalChi]"}],"2"]}],"3"],"+",FractionBox[RowBox[{"2"," ",RowBox[{"\[CapitalNu]"}]," ",SuperscriptBox[RowBox[{"\[CapitalChi]"}],"2"]}],"3"],"+",RowBox[{"4"," ",SuperscriptBox[RowBox[{"\[CapitalChi]"}],"3"]}],"+",SuperscriptBox[RowBox[{"\[CapitalChi]"}],"4"]}],Rule[FontFamily,Dynamic[CurrentValue[{"StyleHints","CodeFont"}]]],Rule[ShowStringCharacters,True]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Symmetry Factor"]},"Item",False],"Mouse"],Rule[ImageSize,{{60,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["Diagram",Style["Diagram",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["Diagram"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Diagram"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes[StyleBox[GraphicsBox[NamespaceBox["NetworkGraphics",DynamicModuleBox[{Set[Typeset`graph,HoldComplete[Graph[{"o1",0,"o2",1,2,3},{Null,{{1,2},{3,4},{2,4},{2,4},{2,5},{4,6},{5,6},{5,6},{5,6}}},{Rule[EdgeStyle,{Rule[UndirectedEdge["o1",0],Directive[Dashing[{0,Small}],Thickness[Large]]],Rule[UndirectedEdge["o2",1],Directive[Dashing[{0,Small}],Thickness[Large]]]}],Rule[GraphLayout,"SpringEmbedding"],Rule[VertexSize,{0.15`}]}]]]},TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData["\n1:eJw1z3tM01cUB/CiFqcDZTycUcl4TAXGeA2HEeEIhMcIsI1tqTykBWUymVQM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\nWfE=\n "],{{Directive[Opacity[0.7`],Hue[0.6`,0.7`,0.5`]],StyleBox[{Arrowheads[0.`],ArrowBox[{1,2},0.07072212092779355`]},{Directive[Dashing[{0,Small}],Thickness[Large]]},Rule[StripOnInput,False]],{Arrowheads[0.`],ArrowBox[BezierCurveBox[{2,{1.2595954942239276`,1.2002222366265696`},4}],0.07072212092779355`]},{Arrowheads[0.`],ArrowBox[BezierCurveBox[{2,{1.2595977214022969`,0.8726625649754218`},4}],0.07072212092779355`]},{Arrowheads[0.`],ArrowBox[{2,5},0.07072212092779355`]},StyleBox[{Arrowheads[0.`],ArrowBox[{3,4},0.07072212092779355`]},{Directive[Dashing[{0,Small}],Thickness[Large]]},Rule[StripOnInput,False]],{Arrowheads[0.`],ArrowBox[{4,6},0.07072212092779355`]},{Arrowheads[0.`],ArrowBox[BezierCurveBox[{5,{1.2596013603876068`,0.17091914766510233`},6}],0.07072212092779355`]},{Arrowheads[0.`],ArrowBox[{5,6},0.07072212092779355`]},{Arrowheads[0.`],ArrowBox[BezierCurveBox[{5,{1.2596030884742286`,-0.1709138932295583`},6}],0.07072212092779355`]}},{Directive[Hue[0.6`,0.2`,0.8`],EdgeForm[Directive[GrayLevel[0],Opacity[0.7`]]]],DiskBox[1,0.07072212092779355`],DiskBox[2,0.07072212092779355`],DiskBox[3,0.07072212092779355`],DiskBox[4,0.07072212092779355`],DiskBox[5,0.07072212092779355`],DiskBox[6,0.07072212092779355`]}}]],MouseAppearanceTag["NetworkGraphics"]],Rule[AllowKernelInitialization,False]]],{Rule[FormatType,TraditionalForm],Rule[FrameTicks,None],Rule[DefaultBaseStyle,{"NetworkGraphics",Rule[FrontEnd`GraphicsHighlightColor,Hue[0.8`,1.`,0.6`]]}]}],Rule[FontFamily,Dynamic[CurrentValue[{"StyleHints","CodeFont"}]]],Rule[ShowStringCharacters,True]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Diagram"]},"Item",False],"Mouse"],Rule[ImageSize,{{60,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]},{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["Value",Style["Value",Rule[FontColor,RGBColor[0.27450980392156865`,0.5372549019607843`,0.792156862745098`]]]],"LinkHand"],RuleDelayed[{"MouseClicked",1},If[TypeSystem`NestedGrid`PackagePrivate`checkInteractivity[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`updateState[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][{Key["Value"]},1]]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Value"]},"RowHeader",False],"Mouse"],Rule[ImageSize,{{1,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[Background,GrayLevel[0.95`]],Rule[Alignment,{Left,Baseline}]],Item[Pane[Annotation[RawBoxes[StyleBox[InterpretationBox[TemplateBox[{RowBox[{"-","0.3952702973135737464729713474`26.596894180400454"}],"1.`1.550228353055094*^-25"},"Around",Rule[SyntaxForm,PlusMinus]],Around[-0.3952702973135737464729713474`27.596894180400454,0]],Rule[FontFamily,Dynamic[CurrentValue[{"StyleHints","CodeFont"}]]],Rule[ShowStringCharacters,True]]],TypeSystem`NestedGrid`PackagePrivate`$SliceMarker[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][{Key["Value"]},"Item",False],"Mouse"],Rule[ImageSize,{{60,Full},Automatic}],Rule[ImageMargins,{{5,3},{4,5}}]],Rule[ItemSize,{Full,Automatic}]]}},Rule[BaseStyle,{Rule[ContextMenu,Dynamic[CompoundExpression[TypeSystem`NestedGrid`PackagePrivate`$contextMenuTrigger,Which[UnsameQ[TypeSystem`NestedGrid`PackagePrivate`$lastOutputID,TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]],{},SameQ[TypeSystem`NestedGrid`PackagePrivate`$contextMenuTrigger,TypeSystem`NestedGrid`PackagePrivate`$lastContextMenuTrigger],TypeSystem`NestedGrid`PackagePrivate`$lastContextMenu,True,CompoundExpression[Set[TypeSystem`NestedGrid`PackagePrivate`$lastContextMenuTrigger,TypeSystem`NestedGrid`PackagePrivate`$contextMenuTrigger],Set[TypeSystem`NestedGrid`PackagePrivate`$lastContextMenu,Block[{Set[TypeSystem`NestedGrid`PackagePrivate`$globalScrollPos,{FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667}]},With[{Set[TypeSystem`NestedGrid`PackagePrivate`lastPath$,TypeSystem`NestedGrid`PackagePrivate`$lastPath],Set[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,TypeSystem`NestedGrid`PackagePrivate`$lastPathType],Set[TypeSystem`NestedGrid`PackagePrivate`isLeafHeader$,TypeSystem`NestedGrid`PackagePrivate`$lastPathIsLeafHeader],Set[TypeSystem`NestedGrid`PackagePrivate`headerHidden$,And[MatchQ[TypeSystem`NestedGrid`PackagePrivate`$lastPathType,Alternatives["RowHeader","ColumnHeader"]],TypeSystem`NestedGrid`PackagePrivate`headerHiddenQ[TypeSystem`NestedGrid`PackagePrivate`$lastPath,FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667]]],Set[TypeSystem`NestedGrid`PackagePrivate`allHidden$,TypeSystem`NestedGrid`PackagePrivate`allHiddenQ[TypeSystem`NestedGrid`PackagePrivate`$lastPath,FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667]],Set[TypeSystem`NestedGrid`PackagePrivate`anyHidden$,TypeSystem`NestedGrid`PackagePrivate`anyHiddenQ[TypeSystem`NestedGrid`PackagePrivate`$lastPath,FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667]],Set[TypeSystem`NestedGrid`PackagePrivate`sortDirection$,TypeSystem`NestedGrid`PackagePrivate`columnSortDirection[TypeSystem`NestedGrid`PackagePrivate`$lastPath,FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667["SortPaths"],FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667["SortDirections"]]],Set[TypeSystem`NestedGrid`PackagePrivate`haveData$,Not[FailureQ[TypeSystem`NestedGrid`PackagePrivate`datasetInitialData[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667]]]],Set[TypeSystem`NestedGrid`PackagePrivate`isKeyDummy$,Not[FreeQ[TypeSystem`NestedGrid`PackagePrivate`$lastPath,Keys]]]},Join[{If[Or[Not[TypeSystem`NestedGrid`PackagePrivate`haveData$],Not[TypeSystem`NestedGrid`PackagePrivate`anyHidden$],TypeSystem`NestedGrid`PackagePrivate`isKeyDummy$],Nothing,MenuItem[StringJoin["Show ",Which[Equal[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,"Item"],"",Equal[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,"RowHeader"],"Row",Equal[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,"ColumnHeader"],"Column",True,""]],KernelExecute[TypeSystem`NestedGrid`PackagePrivate`updateHiddenItems[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][TypeSystem`NestedGrid`PackagePrivate`lastPath$,"remove"]],Rule[MenuEvaluator,Automatic]]],If[Or[Not[TypeSystem`NestedGrid`PackagePrivate`haveData$],TypeSystem`NestedGrid`PackagePrivate`pathEmptyQ[TypeSystem`NestedGrid`PackagePrivate`$lastPath,FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667],TypeSystem`NestedGrid`PackagePrivate`isKeyDummy$,And[TypeSystem`NestedGrid`PackagePrivate`allHidden$,TypeSystem`NestedGrid`PackagePrivate`headerHidden$]],Nothing,MenuItem[StringJoin["Hide ",Which[Equal[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,"Item"],"",Equal[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,"RowHeader"],"Row",Equal[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,"ColumnHeader"],"Column",True,""]],KernelExecute[TypeSystem`NestedGrid`PackagePrivate`updateHiddenItems[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]]][TypeSystem`NestedGrid`PackagePrivate`lastPath$,"add"]],Rule[MenuEvaluator,Automatic]]],Delimiter},If[And[TypeSystem`NestedGrid`PackagePrivate`haveData$,MatchQ[TypeSystem`NestedGrid`PackagePrivate`lastPathType$,Alternatives["ColumnHeader","KeyDummy"]],TypeSystem`NestedGrid`PackagePrivate`isLeafHeader$,Not[TypeSystem`NestedGrid`PackagePrivate`allHidden$]],{If[UnsameQ[TypeSystem`NestedGrid`PackagePrivate`sortDirection$,"Ascending"],MenuItem["Sort",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`updateSort[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][TypeSystem`NestedGrid`PackagePrivate`lastPath$,"Ascending"]],Rule[MenuEvaluator,Automatic]],Nothing],If[UnsameQ[TypeSystem`NestedGrid`PackagePrivate`sortDirection$,"Descending"],MenuItem["Reverse Sort",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`updateSort[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][TypeSystem`NestedGrid`PackagePrivate`lastPath$,"Descending"]],Rule[MenuEvaluator,Automatic]],Nothing],If[UnsameQ[TypeSystem`NestedGrid`PackagePrivate`sortDirection$,None],MenuItem["Unsort",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`updateSort[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][TypeSystem`NestedGrid`PackagePrivate`lastPath$,None]],Rule[MenuEvaluator,Automatic]],Nothing],Delimiter},{}],{MenuItem["Copy Position to Clipboard",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`toCurrentPosition[TypeSystem`NestedGrid`PackagePrivate`copyClip]],Rule[MenuEvaluator,Automatic]],If[TypeSystem`NestedGrid`PackagePrivate`haveData$,MenuItem["Copy Data to Clipboard",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`toCurrentData[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`copyClip]],Rule[MenuEvaluator,Automatic]],Nothing],Delimiter,MenuItem["Paste Position in New Cell",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`toCurrentPosition[TypeSystem`NestedGrid`PackagePrivate`cellPaste]],Rule[MenuEvaluator,Automatic]],If[TypeSystem`NestedGrid`PackagePrivate`haveData$,MenuItem["Paste Data in New Cell",KernelExecute[TypeSystem`NestedGrid`PackagePrivate`toCurrentData[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`cellPaste]],Rule[MenuEvaluator,Automatic]],Nothing]}]]]]]]]]],Rule[FontFamily,"Source Sans Pro"],Rule[FontSize,14],Rule[FontWeight,Plain]}],Rule[Dividers,All],Rule[FrameStyle,GrayLevel[0.7490196078431373`]],Rule[Spacings,{0,0}],Rule[Alignment,Left],Rule[BaseStyle,{Rule[FontFamily,"Source Sans Pro"],Rule[FontSize,14],Rule[FontWeight,Plain]}]],Rule[LineBreakWithin,False],Rule[ContextMenu,{}],Rule[NumberMarks,False],Rule[ShowAutoStyles,False]]]],Set[TypeSystem`NestedGrid`PackagePrivate`initialQ,True]},Dynamic[TypeSystem`NestedGrid`PackagePrivate`setupViewPath[FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,CompoundExpression[If[Not[TypeSystem`NestedGrid`PackagePrivate`initialQ],Module[{Set[TypeSystem`NestedGrid`PackagePrivate`tmpGrid$,$Failed],Set[TypeSystem`NestedGrid`PackagePrivate`tmpData$,TypeSystem`NestedGrid`PackagePrivate`datasetData[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667]]},CompoundExpression[Set[TypeSystem`NestedGrid`PackagePrivate`tmpGrid$,If[FailureQ[TypeSystem`NestedGrid`PackagePrivate`tmpData$],TypeSystem`NestedGrid`PackagePrivate`renderedGrid,TypeSystem`NestedGrid`PackagePrivate`renderGrid[FE`TypeSystem`NestedGrid`PackagePrivate`$state$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$path$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$grid$$1250388124995014420419992319868413550667,TypeSystem`NestedGrid`PackagePrivate`localHold[FE`TypeSystem`NestedGrid`PackagePrivate`$outputID$$1250388124995014420419992319868413550667]][TypeSystem`NestedGrid`PackagePrivate`tmpData$]]],If[Not[FailureQ[TypeSystem`NestedGrid`PackagePrivate`tmpGrid$]],Set[TypeSystem`NestedGrid`PackagePrivate`renderedGrid,TypeSystem`NestedGrid`PackagePrivate`tmpGrid$]],Null]]],Set[TypeSystem`NestedGrid`PackagePrivate`initialQ,False],FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667,If[FailureQ[TypeSystem`NestedGrid`PackagePrivate`renderedGrid],TypeSystem`SparseGrid[TypeSystem`H["(data no longer present)"]],TypeSystem`NestedGrid`PackagePrivate`renderedGrid]]],RuleDelayed[TrackedSymbols,{FE`TypeSystem`NestedGrid`PackagePrivate`$vPos$$1250388124995014420419992319868413550667,FE`TypeSystem`NestedGrid`PackagePrivate`$hPos$$1250388124995014420419992319868413550667}]],RuleDelayed[DynamicModuleValues,{}]],"1:11ada643123e2b61:fe0573837e293bc49e95765abee25b6c"]

Tag: SecurityViolation



SeeAlso

XCubicRatio

▪

SymmetryFactorDiagram

▪

ValueDiagram

▪

InformationDiagram

TechNotes

▪

Perturbative Series Generation

RelatedGuides

▪

Phi4tools