From 8301ee2da24e239b0ed785adcee681ae6ff52ca1 Mon Sep 17 00:00:00 2001
From: Xisco Jimenez Forteza <you@example.com>
Date: Wed, 7 Oct 2020 16:46:36 +0200
Subject: [PATCH] adding rhoeff

---
 code/fRTOV.nb | 1633 +++++++++++++++++++++++++++++++++++++------------
 1 file changed, 1250 insertions(+), 383 deletions(-)

diff --git a/code/fRTOV.nb b/code/fRTOV.nb
index 53182f6..b4c062a 100644
--- a/code/fRTOV.nb
+++ b/code/fRTOV.nb
@@ -10,10 +10,10 @@
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 NotebookFileLineBreakTest
 NotebookDataPosition[       158,          7]
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-NotebookOptionsPosition[   1473493,      32413]
-NotebookOutlinePosition[   1473830,      32428]
-CellTagsIndexPosition[   1473787,      32425]
+NotebookDataLength[   1553087,      33934]
+NotebookOptionsPosition[   1511045,      33262]
+NotebookOutlinePosition[   1511384,      33277]
+CellTagsIndexPosition[   1511341,      33274]
 WindowFrame->Normal*)
 
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 definitions in context \\!\\(\\*RowBox[{\\\"\\\\\\\"NRLists`\\\\\\\"\\\"}]\\) \
-may shadow or be shadowed by other definitions.\"",2,3,1,19718159296837622620,
+may shadow or be shadowed by other definitions.\"",2,3,1,19721115528907403351,
    "Local","NRLists`TakeColumn"},
   "MessageTemplate2"]], "Message", "MSG",
  CellChangeTimes->{
@@ -154,10 +154,10 @@ may shadow or be shadowed by other definitions.\"",2,3,1,19718159296837622620,
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@@ -165,7 +165,7 @@ Cell[BoxData[
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 obsolete. The legacy version being loaded may conflict with current \
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+   19721115528907403351,"Local"},
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+                    
+                    TemplateBox[{
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+                    ImageSize->Automatic],
+                    Appearance->None,
+                    BaseStyle->None,
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+                    ButtonFunction:>(Part[System`InformationDump`open$$, 9] = 
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+                    ImageMargins->0,
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+                    DefaultBaseStyle->"Column",
+                    GridBoxAlignment->{"Columns" -> {{Left}}},
+                    GridBoxItemSize->{
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+                    Offset[0.2]}}], "DialogStyle",
+                StripOnInput->False],
+               DynamicModuleValues:>{}]}
+            },
+            DefaultBaseStyle->"Column",
+            GridBoxAlignment->{"Columns" -> {{Left}}},
+            GridBoxDividers->{"Columns" -> {{False}}, "Rows" -> {{False}}},
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+              
+              DynamicBox[FEPrivate`FrontEndResource[
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+             Appearance->{"Default" -> None},
+             
+             ButtonFunction:>FEPrivate`Set[
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+             Evaluator->Automatic,
+             FrameMargins->{{9, 0}, {0, 0}},
+             ImageMargins->0,
+             ImageSize->Full,
+             Method->"Preemptive"],
+            
+            EventHandlerTag[{
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+              "MouseExited" :> 
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+              Method -> "Preemptive", PassEventsDown -> Automatic, 
+              PassEventsUp -> True}]],
+           BaseStyle->"InformationTitleBackground",
+           StripOnInput->False], "\[SpanFromLeft]"}
+        },
+        AutoDelete->False,
+        FrameStyle->Directive[
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+          Thickness[Tiny]],
+        GridBoxAlignment->{"Columns" -> {Left, Right}, "Rows" -> {{Center}}},
+        GridBoxDividers->{
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+               ImageSizeCache->{10., {2., 8.}}]}, Dynamic[
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+             Appearance->{"Default" -> None},
+             
+             ButtonFunction:>FEPrivate`Set[
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+             Evaluator->Automatic,
+             FrameMargins->{{9, 0}, {0, 0}},
+             ImageMargins->0,
+             ImageSize->Full,
+             Method->"Preemptive"],
+            
+            EventHandlerTag[{
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+              "MouseExited" :> 
+              FEPrivate`Set[System`InformationDump`mouseOver$$, False], 
+              Method -> "Preemptive", PassEventsDown -> Automatic, 
+              PassEventsUp -> True}]],
+           BaseStyle->"InformationTitleBackground",
+           StripOnInput->False], "\[SpanFromLeft]"}
+        },
+        AutoDelete->False,
+        FrameStyle->Directive[
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+          Thickness[Tiny]],
+        GridBoxAlignment->{"Columns" -> {Left, Right}, "Rows" -> {{Center}}},
+        GridBoxDividers->{
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+        GridBoxItemSize->{
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+      BaselinePosition->Baseline,
+      FrameMargins->0,
+      ImageSize->Automatic],
+     DynamicModuleValues:>{}],
+    BaseStyle->"InformationGridFrame",
+    StripOnInput->False], "InformationGridPlain",
+   StripOnInput->False],
+  InformationData[
+   Association[
+   "ObjectType" -> "Symbol", "Usage" -> 
+    "TeffST[coords_,g_,{V\[CurlyPhi],\[CurlyPhi]}]. Compute ST-EF/JF Teff \
+tensor such Gab=8\[Pi] (Tab + Teff) following the convention of Misner et \
+al., that is, [S2] = 1, [S3] = 1. Allowed options for the Frame are Einstein, \
+Jordan", "Documentation" -> None, "OwnValues" -> None, "UpValues" -> None, 
+    "DownValues" -> 
+    Information`InformationValueForm[
+     DownValues, GRTensor`TeffST, {GRTensor`TeffST[
+         Pattern[GRTensor`Private`xx, 
+          Blank[]], 
+         Pattern[GRTensor`Private`g, 
+          Blank[]], {
+          Pattern[GRTensor`Private`V\[CurlyPhi], 
+           Blank[]], 
+          Pattern[GRTensor`Private`var\[CurlyPhi], 
+           Blank[]]}, 
+         Optional[
+          Pattern[GRTensor`Private`pert, 
+           Blank[]], 0], 
+         OptionsPattern[]] :> 
+       Block[{GRTensor`Private`covterm1, GRTensor`Private`covterm2, 
+          GRTensor`Private`dalem, GRTensor`Private`der, GRTensor`Private`gup, 
+          GRTensor`Private`frame, GRTensor`Private`perti, 
+          GRTensor`Private`res, GRTensor`Private`riscal, 
+          GRTensor`Private`riscalvars, GRTensor`Private`simpl, 
+          GRTensor`Private`sumder, GRTensor`Private`V\[CurlyPhi]c, 
+          GRTensor`Private`\[CurlyPhi]c, GRTensor`Private`\[Phi]term2}, 
+         GRTensor`Private`perti = OptionValue["PerturbationIndex"]; 
+         GRTensor`Private`frame = OptionValue["Frame"]; 
+         GRTensor`Private`simpl = OptionValue["SimplifyFunction"]; 
+         GRTensor`Private`riscal = GRTensor`Private`simpl[
+            GRTensor`RicciScalar[
+            GRTensor`Private`xx, GRTensor`Private`g, GRTensor`Private`pert, 
+             "PerturbationIndex" -> GRTensor`Private`perti]]; 
+         GRTensor`Private`riscalvars = Complement[GRTensor`Private`xx, 
+            Complement[GRTensor`Private`xx, 
+             GRTensor`AtomsList[GRTensor`Private`riscal]]]; 
+         GRTensor`Private`gup = Inverse[GRTensor`Private`g]; 
+         GRTensor`Private`\[CurlyPhi]c = 
+          Apply[GRTensor`Private`var\[CurlyPhi], GRTensor`Private`riscalvars]; 
+         GRTensor`Private`V\[CurlyPhi]c = 
+          ReplaceAll[
+           GRTensor`Private`V\[CurlyPhi], GRTensor`Private`var\[CurlyPhi] -> 
+            GRTensor`Private`\[CurlyPhi]c]; 
+         Which[GRTensor`Private`frame == "Einstein", 
+           GRTensor`Private`der = Table[D[GRTensor`Private`\[CurlyPhi]c, 
+                Part[GRTensor`Private`xx, GRTensor`Private`a]] 
+              D[GRTensor`Private`\[CurlyPhi]c, 
+                Part[GRTensor`Private`xx, GRTensor`Private`b]], {
+              GRTensor`Private`a, 
+               Length[GRTensor`Private`xx]}, {GRTensor`Private`b, 
+               Length[GRTensor`Private`xx]}]; 
+           GRTensor`Private`sumder = 
+            Sum[Part[
+               GRTensor`Private`gup, GRTensor`Private`a, GRTensor`Private`b] 
+              Part[GRTensor`Private`der, GRTensor`Private`a, 
+                GRTensor`Private`b], {GRTensor`Private`a, 
+               Length[GRTensor`Private`xx]}, {GRTensor`Private`b, 
+               Length[GRTensor`Private`xx]}]; 
+           GRTensor`Private`res = (1/(8 Pi)) (2 GRTensor`Private`der - 
+              GRTensor`Private`g 
+              GRTensor`Private`sumder - ((1/2) GRTensor`Private`g) 
+              GRTensor`Private`V\[CurlyPhi]c); Null, GRTensor`Private`frame == 
+           "Jordan", 
+           GRTensor`Private`dalem = 
+            GRTensor`DAlembert[
+             GRTensor`Private`xx, GRTensor`Private`g, 
+              GRTensor`Private`\[CurlyPhi]c]; 
+           GRTensor`Private`covterm1 = Table[
+              GRTensor`CovDer[
+              GRTensor`Private`xx, GRTensor`Private`g, 
+               GRTensor`Private`\[CurlyPhi]c, {GRTensor`Private`i}, "Valence" -> 
+               "Covariant", "Verbose" -> False], {GRTensor`Private`i, 
+               Length[GRTensor`Private`xx]}]; 
+           GRTensor`Private`covterm2 = Table[
+              GRTensor`CovDer[
+              GRTensor`Private`xx, GRTensor`Private`g, 
+               GRTensor`Private`covterm1, {
+               GRTensor`Private`i, GRTensor`Private`j}, "Valence" -> 
+               "Covariant", "Verbose" -> False], {GRTensor`Private`i, 
+               Length[GRTensor`Private`xx]}, {GRTensor`Private`j, 
+               Length[GRTensor`Private`xx]}]; 
+           GRTensor`Private`\[Phi]term2 = 
+            GRTensor`Private`covterm2 - GRTensor`Private`g 
+             GRTensor`Private`dalem; GRTensor`Private`res = If[
+              Not[
+               NumericQ[GRTensor`Private`pert]], 
+              Normal[
+               
+               Series[(1/(8 Pi)) (
+                 GRTensor`Private`\[Phi]term2 - (
+                  GRTensor`Private`V\[CurlyPhi]c/2) GRTensor`Private`g), {
+                GRTensor`Private`pert, 0, GRTensor`Private`perti}]], (1/(8 
+               Pi)) (GRTensor`Private`\[Phi]term2 - (
+                GRTensor`Private`V\[CurlyPhi]c/2) GRTensor`Private`g)]; Null, 
+           True, Print["Wrong option for Frame"]; Return[]; Null]; If[
+           NumberQ[GRTensor`Private`pert], 
+           Simplify[GRTensor`Private`res], 
+           Simplify[
+            Normal[
+             Series[
+             GRTensor`Private`res, {
+              GRTensor`Private`pert, 0, GRTensor`Private`perti}]]]]]}], 
+    "SubValues" -> None, "DefaultValues" -> None, "NValues" -> None, 
+    "FormatValues" -> None, 
+    "Options" -> {
+     "Frame" -> "Einstein", "Verbose" -> False, "PerturbationIndex" -> 1, 
+      "SimplifyFunction" -> Identity}, "Attributes" -> {}, "FullName" -> 
+    "GRTensor`TeffST"], False]]], "Output",
+ CellChangeTimes->{3.8110673054418383`*^9},
+ CellLabel->"Out[24]=",ExpressionUUID->"ab64cd6b-8d69-4fb9-91a1-2dfa63f2c831"]
+}, Open  ]],
+
+Cell[BoxData[
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+  RowBox[{
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+    RowBox[{"(", 
+     RowBox[{
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+      RowBox[{
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+       RowBox[{
+        SuperscriptBox["f", "\[Prime]",
+         MultilineFunction->None], "[", 
+        RowBox[{"R", "[", "t", "]"}], "]"}]}]}], ")"}]}], "+", 
+   RowBox[{"2", " ", 
+    RowBox[{"H", "[", "t", "]"}], " ", 
+    RowBox[{
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+      MultilineFunction->None], "[", "t", "]"}], " ", 
+    RowBox[{
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+      MultilineFunction->None], "[", 
+     RowBox[{"R", "[", "t", "]"}], "]"}]}], "+", 
+   RowBox[{
+    RowBox[{
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+      MultilineFunction->None], "[", 
+     RowBox[{"R", "[", "t", "]"}], "]"}], " ", 
+    RowBox[{
+     SuperscriptBox["R", "\[Prime]\[Prime]",
+      MultilineFunction->None], "[", "t", "]"}]}], "+", 
+   RowBox[{
+    SuperscriptBox[
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+      SuperscriptBox["R", "\[Prime]",
+       MultilineFunction->None], "[", "t", "]"}], "2"], " ", 
+    RowBox[{
+     SuperscriptBox["f", 
+      TagBox[
+       RowBox[{"(", "3", ")"}],
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+Cell[1454655, 32124, 2801, 59, 115, "Input",ExpressionUUID->"c07326d6-32ab-417f-bad0-e3d2a8450919"],
+Cell[1457459, 32185, 53546, 1072, 371, "Output",ExpressionUUID->"6bb2668f-d482-4eea-8433-a94f84b4c432"]
 }, Open  ]]
 }, Closed]]
 }, Closed]]
-- 
GitLab