Lots of work.

1 files changed, 692 insertions, 423 deletions

diff --git a/caselle_compare.nb b/caselle_compare.nb
index 19968c7..d2c852f 100644
--- a/caselle_compare.nb
+++ b/caselle_compare.nb
@@ -10,10 +10,10 @@
 NotebookFileLineBreakTest
 NotebookFileLineBreakTest
 NotebookDataPosition[       158,          7]
-NotebookDataLength[     94696,       2157]
-NotebookOptionsPosition[     89726,       2070]
-NotebookOutlinePosition[     90127,       2086]
-CellTagsIndexPosition[     90084,       2083]
+NotebookDataLength[    105372,       2426]
+NotebookOptionsPosition[    100295,       2338]
+NotebookOutlinePosition[    100694,       2354]
+CellTagsIndexPosition[    100651,       2351]
 WindowFrame->Normal*)
 
 (* Beginning of Notebook Content *)
@@ -170,7 +170,7 @@ Cell[BoxData[{
       RowBox[{"A", "[", "2", "]"}], "\[Rule]", "0.22823495175053052`"}]}], 
     "}"}]}], ";"}]}], "Input",
  CellChangeTimes->{{3.832146779562958*^9, 3.8321467886772203`*^9}},
- CellLabel->"In[15]:=",ExpressionUUID->"02a1f6e5-4144-4552-9463-2a226c1ee186"],
+ CellLabel->"In[2]:=",ExpressionUUID->"02a1f6e5-4144-4552-9463-2a226c1ee186"],
 
 Cell[BoxData[
  RowBox[{
@@ -310,25 +310,53 @@ Cell[BoxData[
   3.832239458672798*^9}, {3.832239576243064*^9, 3.832239576394759*^9}},
  CellLabel->"In[9]:=",ExpressionUUID->"7bddfed2-a761-4c62-bcdc-0460988fbd67"],
 
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"datNum", "=", 
+   RowBox[{"Thread", "[", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"Range", "[", 
+       RowBox[{"0", ",", "11"}], "]"}], ",", "Gls"}], "}"}], "]"}]}], 
+  ";"}]], "Input",
+ CellChangeTimes->{{3.832146079469277*^9, 3.832146080085175*^9}, {
+   3.832146220615906*^9, 3.832146230663995*^9}, 3.836571905035768*^9, {
+   3.836572227321196*^9, 3.836572228850659*^9}},
+ CellLabel->"In[11]:=",ExpressionUUID->"ec8b9383-61d6-44c2-b776-3d651fc19660"],
+
 Cell[CellGroupData[{
 
 Cell[BoxData[
- RowBox[{"datNum", "[", 
-  RowBox[{"[", "2", "]"}], "]"}]], "Input",
- CellChangeTimes->{{3.83214601815701*^9, 3.832146022692172*^9}},
- CellLabel->"In[45]:=",ExpressionUUID->"50295a31-c985-47a1-ab52-8a5871504ed9"],
+ RowBox[{"Export", "[", 
+  RowBox[{
+  "\"\<~/doc/research/first_order_singularities/paper/data/glow_series_\
+numeric.dat\>\"", ",", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"{", 
+      RowBox[{"#1", ",", 
+       RowBox[{"If", "[", 
+        RowBox[{
+         RowBox[{
+          RowBox[{"Head", "[", "#2", "]"}], "===", "Around"}], ",", 
+         RowBox[{"#2", "[", "\"\<Value\>\"", "]"}], ",", "#2"}], "]"}], ",", 
+       RowBox[{"If", "[", 
+        RowBox[{
+         RowBox[{
+          RowBox[{"Head", "[", "#2", "]"}], "===", "Around"}], ",", 
+         RowBox[{"#2", "[", "\"\<Uncertainty\>\"", "]"}], ",", "0"}], "]"}]}],
+       "}"}], "&"}], "@@@", "datNum"}]}], "]"}]], "Input",
+ CellChangeTimes->{{3.836571907042726*^9, 3.8365719075682077`*^9}, {
+  3.8365719679456177`*^9, 3.836572034954253*^9}, {3.836572067138021*^9, 
+  3.8365720932499523`*^9}},
+ CellLabel->"In[33]:=",ExpressionUUID->"cbeb62aa-7e89-4ec5-a1cb-d5012bac06fd"],
 
-Cell[BoxData[
- RowBox[{"{", 
-  RowBox[{"1", ",", 
-   InterpretationBox[
-    TemplateBox[{"1.3578383417065", "95", "10"},
-     "AroundSeq"],
-    Around[1.357838341706595496`18.132848067820845, 1.*^-14]]}], 
-  "}"}]], "Output",
- CellChangeTimes->{{3.832146019765203*^9, 3.832146023509615*^9}, 
-   3.832146068422765*^9, 3.832146460247183*^9},
- CellLabel->"Out[45]=",ExpressionUUID->"bc09ed81-20b7-4e22-a63a-1d663336b1b5"]
+Cell[BoxData["\<\"~/doc/research/first_order_singularities/paper/data/glow_\
+series_numeric.dat\"\>"], "Output",
+ CellChangeTimes->{
+  3.8365719078847313`*^9, {3.836572025847522*^9, 3.836572035446138*^9}, 
+   3.8365720941903563`*^9, 3.836572233522911*^9},
+ CellLabel->"Out[33]=",ExpressionUUID->"9ddcc7c6-de02-4d31-9401-bbbc5eefe582"]
 }, Open  ]],
 
 Cell[CellGroupData[{
@@ -340,10 +368,15 @@ Cell[BoxData[
     RowBox[{
      RowBox[{
       RowBox[{"coeffCas", "[", "1", "]"}], "==", 
-      RowBox[{"datNum", "[", 
-       RowBox[{"[", 
+      RowBox[{
+       RowBox[{"{", 
         RowBox[{
-         RowBox[{"2", ";;", "3"}], ",", "2"}], "]"}], "]"}]}], ",", 
+         RowBox[{"1", "!"}], ",", 
+         RowBox[{"2", "!"}]}], "}"}], 
+       RowBox[{"datNum", "[", 
+        RowBox[{"[", 
+         RowBox[{
+          RowBox[{"2", ";;", "3"}], ",", "2"}], "]"}], "]"}]}]}], ",", 
      RowBox[{"{", 
       RowBox[{"m0", ",", "h0"}], "}"}]}], "]"}], "[", 
    RowBox[{"[", "1", "]"}], "]"}]}]], "Input",
@@ -351,7 +384,8 @@ Cell[BoxData[
   3.8321464716527967`*^9, 3.8321464718044024`*^9}, {3.8321466387696667`*^9, 
   3.832146653175795*^9}, {3.832151934783225*^9, 3.8321519353348494`*^9}, {
   3.832152037225222*^9, 3.8321520374089203`*^9}, {3.832239305719432*^9, 
-  3.832239316046335*^9}},
+  3.832239316046335*^9}, {3.836984166958787*^9, 3.83698416798269*^9}, {
+  3.836984311313539*^9, 3.836984316617137*^9}},
  CellLabel->"In[12]:=",ExpressionUUID->"7efd85be-fd7d-435a-a870-214d8ec4025d"],
 
 Cell[BoxData[
@@ -359,71 +393,70 @@ Cell[BoxData[
   "Solve", "ratnz", 
    "\"Solve was unable to solve the system with inexact coefficients. The \
 answer was obtained by solving a corresponding exact system and numericizing \
-the result.\"", 2, 12, 3, 25143344835924279801, "Local"},
+the result.\"", 2, 12, 3, 31608996298011231244, "Local"},
   "MessageTemplate"]], "Message", "MSG",
  CellChangeTimes->{
   3.832146653505703*^9, 3.8321519356060266`*^9, 3.8321520375652533`*^9, {
    3.8321544205609913`*^9, 3.832154425785782*^9}, {3.832239276291945*^9, 
-   3.832239326773054*^9}, {3.836570087200712*^9, 3.836570104160351*^9}},
+   3.832239326773054*^9}, {3.836570087200712*^9, 3.836570104160351*^9}, {
+   3.8369749921742907`*^9, 3.836975002927493*^9}, 3.836984168350904*^9, 
+   3.8369843170148077`*^9, 3.8370700000102262`*^9, {3.837072474483852*^9, 
+   3.837072478715604*^9}},
  CellLabel->
   "During evaluation of \
-In[12]:=",ExpressionUUID->"495ad979-d632-478f-8e0f-56a8e4f9987f"],
+In[12]:=",ExpressionUUID->"2e43731b-67a2-4964-9c03-694bb26aa975"],
 
 Cell[BoxData[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"m0", "\[Rule]", 
     InterpretationBox[
-     TemplateBox[{"1.00576267284062", "0", "7"},
+     TemplateBox[{"-1.00576267284062", "0", "7"},
       "AroundSeq"],
-     Around[1.0057626728406195`, 7.407086999594733*^-15]]}], ",", 
+     Around[-1.0057626728406195`, 7.407086999594733*^-15]]}], ",", 
    RowBox[{"h0", "\[Rule]", 
     InterpretationBox[
      TemplateBox[{"0.2591817983", "42", "11"},
       "AroundSeq"],
-     Around[0.2591817983420855, 1.0588943216503217`*^-11]]}]}], 
+     Around[0.2591817983420855, 1.0588943216503216`*^-11]]}]}], 
   "}"}]], "Output",
  CellChangeTimes->{{3.832145993018977*^9, 3.832146075354514*^9}, {
    3.832146456457759*^9, 3.83214647211082*^9}, 3.832146653511766*^9, 
    3.832151935612179*^9, 3.8321520375710917`*^9, {3.8321544206488857`*^9, 
    3.8321544257922564`*^9}, {3.8322392763285713`*^9, 
-   3.8322393267777767`*^9}, {3.836570087516891*^9, 3.8365701041934032`*^9}},
- CellLabel->"Out[12]=",ExpressionUUID->"2e2d8ac6-c3fd-4636-a145-e07805271602"]
+   3.8322393267777767`*^9}, {3.836570087516891*^9, 3.8365701041934032`*^9}, {
+   3.836974992241055*^9, 3.836975002932447*^9}, 3.836984168357218*^9, 
+   3.836984317019814*^9, 3.837070000054738*^9, {3.837072474543331*^9, 
+   3.837072478720648*^9}},
+ CellLabel->"Out[12]=",ExpressionUUID->"325e2b46-9d64-4724-8091-36718f8f11a2"]
 }, Open  ]],
 
 Cell[CellGroupData[{
 
-Cell[BoxData[
+Cell[BoxData[{
  RowBox[{
-  RowBox[{"m0", "/", 
-   SuperscriptBox[
-    RowBox[{"hCas", "[", "1", "]"}], "15"]}], "/.", "m0rule"}]], "Input",
- CellChangeTimes->{{3.832239524531241*^9, 3.8322395731787653`*^9}},
- CellLabel->"In[13]:=",ExpressionUUID->"111093b6-716a-4bf7-a45a-dac15b888b04"],
-
-Cell[BoxData[
- InterpretationBox[
-  TemplateBox[{"3.91346457", "68", "24", 
-    SuperscriptBox["10", "23"]},
-   "AroundSeqExp"],
-  Around[3.913464576785271*^23, 2.3982849751474694`*^14]]], "Output",
- CellChangeTimes->{{3.8322395263809423`*^9, 3.832239573513529*^9}, 
-   3.836570106674327*^9},
- CellLabel->"Out[13]=",ExpressionUUID->"f4db1aaf-ffb6-4069-b376-c6b46e4be074"]
-}, Open  ]],
+  RowBox[{"ClearAll", "[", "h0", "]"}], ";", 
+  RowBox[{"ClearAll", "[", "m0", "]"}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{"h0", "=", 
+  RowBox[{
+   RowBox[{"h0", "[", "\"\<Value\>\"", "]"}], "/.", 
+   "m0rule"}]}], "\[IndentingNewLine]", 
+ RowBox[{"m0", "=", 
+  RowBox[{
+   RowBox[{"m0", "[", "\"\<Value\>\"", "]"}], "/.", "m0rule"}]}]}], "Input",
+ CellChangeTimes->{{3.8369847488424397`*^9, 3.836984792561878*^9}},
+ CellLabel->"In[13]:=",ExpressionUUID->"28731a52-d222-49b4-aebb-262f9a5d4dd5"],
 
-Cell[CellGroupData[{
+Cell[BoxData["0.2591817983420855`"], "Output",
+ CellChangeTimes->{{3.83698477315833*^9, 3.8369847927282743`*^9}, 
+   3.837070002329464*^9, 3.837072479312191*^9},
+ CellLabel->"Out[14]=",ExpressionUUID->"65626e49-d3af-4115-b5d3-96f63b95604e"],
 
 Cell[BoxData[
- RowBox[{"Head", "[", 
-  RowBox[{"Gls", "[", 
-   RowBox[{"[", "1", "]"}], "]"}], "]"}]], "Input",
- CellChangeTimes->{{3.836572055804084*^9, 3.836572059789261*^9}},
- CellLabel->"In[30]:=",ExpressionUUID->"35006d51-03e9-4e09-8401-8176648f7474"],
-
-Cell[BoxData["Around"], "Output",
- CellChangeTimes->{3.836572060163045*^9},
- CellLabel->"Out[30]=",ExpressionUUID->"021cf2ad-b5c4-4865-a718-f51958ee0792"]
+ RowBox[{"-", "1.0057626728406195`"}]], "Output",
+ CellChangeTimes->{{3.83698477315833*^9, 3.8369847927282743`*^9}, 
+   3.837070002329464*^9, 3.837072479313409*^9},
+ CellLabel->"Out[15]=",ExpressionUUID->"fe83a208-ae15-4c69-a7c9-b98329954997"]
 }, Open  ]],
 
 Cell[CellGroupData[{
@@ -439,189 +472,336 @@ Cell[BoxData[
   3.832239333006241*^9, 3.83223933347838*^9}, {3.832239464537035*^9, 
   3.832239465688715*^9}, {3.832239596747369*^9, 3.832239610347269*^9}, {
   3.832239661037331*^9, 3.83223966189207*^9}},
- CellLabel->"In[93]:=",ExpressionUUID->"f42f7737-f59e-4289-8153-b78626e30f0e"],
+ CellLabel->"In[16]:=",ExpressionUUID->"f42f7737-f59e-4289-8153-b78626e30f0e"],
 
 Cell[BoxData[
  RowBox[{"{", 
   RowBox[{
-   InterpretationBox[
-    TemplateBox[{"1.28038403638", "02", "35"},
-     "AroundSeq"],
-    Around[1.280384036380197, 3.4873754010149197`*^-12]], ",", 
-   InterpretationBox[
-    TemplateBox[{"0.16625752423", "7", "4"},
-     "AroundSeq"],
-    Around[0.16625752423710902`, 3.65085742707853*^-12]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-0.03998986398", "4", "4"},
-     "AroundSeq"],
-    Around[-0.03998986398383036, 4.214923021493555*^-12]], ",", 
-   InterpretationBox[
-    TemplateBox[{"0.00793393859", "4", "6"},
-     "AroundSeq"],
-    Around[0.0079339385941567, 5.5085778849645144`*^-12]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-0.00027904634", "6", "9"},
-     "AroundSeq"],
-    Around[-0.0002790463457692103, 8.678222971301997*^-12]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-0.0006680802", "61", "14"},
-     "AroundSeq"],
-    Around[-0.0006680802614227734, 1.449046104189115*^-11]]}], 
-  "}"}]], "Output",
+   RowBox[{"-", "1.280384036380197`"}], ",", 
+   RowBox[{"-", "0.166257524237109`"}], ",", "0.03998986398383036`", ",", 
+   RowBox[{"-", "0.00793393859415671`"}], ",", "0.00027904634576921466`", ",",
+    "0.0006680802614227808`"}], "}"}]], "Output",
  CellChangeTimes->{
   3.832239333786672*^9, {3.8322394618672743`*^9, 3.832239465919291*^9}, {
-   3.83223957814188*^9, 3.832239613896473*^9}, 3.83223966232157*^9},
- CellLabel->"Out[93]=",ExpressionUUID->"554f67c9-f7db-464a-bb28-41d81dcbec1c"]
+   3.83223957814188*^9, 3.832239613896473*^9}, 3.83223966232157*^9, 
+   3.8369843208154488`*^9, 3.8370724800639668`*^9},
+ CellLabel->"Out[16]=",ExpressionUUID->"c7c2e58e-e6d9-436b-9cc9-4238f4205a5a"]
 }, Open  ]],
 
 Cell[BoxData[
  RowBox[{
-  RowBox[{"datNum", "=", 
-   RowBox[{"Thread", "[", 
-    RowBox[{"{", 
-     RowBox[{
-      RowBox[{"Range", "[", 
-       RowBox[{"0", ",", "11"}], "]"}], ",", "Gls"}], "}"}], "]"}]}], 
-  ";"}]], "Input",
- CellChangeTimes->{{3.832146079469277*^9, 3.832146080085175*^9}, {
-   3.832146220615906*^9, 3.832146230663995*^9}, 3.836571905035768*^9, {
-   3.836572227321196*^9, 3.836572228850659*^9}},
- CellLabel->"In[32]:=",ExpressionUUID->"ec8b9383-61d6-44c2-b776-3d651fc19660"],
-
-Cell[CellGroupData[{
-
-Cell[BoxData[
- RowBox[{"Export", "[", 
   RowBox[{
-  "\"\<~/doc/research/first_order_singularities/paper/data/glow_series_\
-numeric.dat\>\"", ",", 
    RowBox[{
+    RowBox[{"invDerivativeList", "[", "n_", "]"}], "[", "f_", "]"}], "[", 
+   "x_", "]"}], ":=", 
+  RowBox[{"Module", "[", "\[IndentingNewLine]", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"xp", ",", "dfs", ",", "fp", ",", "Pns"}], "}"}], ",", 
+    "\[IndentingNewLine]", 
     RowBox[{
-     RowBox[{"{", 
-      RowBox[{"#1", ",", 
-       RowBox[{"If", "[", 
+     RowBox[{"dfs", "=", 
+      RowBox[{
+       RowBox[{"Rest", "[", 
+        RowBox[{"NestList", "[", 
+         RowBox[{
+          RowBox[{
+           RowBox[{"D", "[", 
+            RowBox[{"#", ",", "xp"}], "]"}], "&"}], ",", 
+          RowBox[{"f", "[", "xp", "]"}], ",", "n"}], "]"}], "]"}], "/.", 
+       RowBox[{"xp", "->", "x"}]}]}], ";", "\[IndentingNewLine]", 
+     RowBox[{"Pns", "=", 
+      RowBox[{
+       RowBox[{"FoldList", "[", 
         RowBox[{
          RowBox[{
-          RowBox[{"Head", "[", "#2", "]"}], "===", "Around"}], ",", 
-         RowBox[{"#2", "[", "\"\<Value\>\"", "]"}], ",", "#2"}], "]"}], ",", 
-       RowBox[{"If", "[", 
+          RowBox[{"{", 
+           RowBox[{"Pm", ",", "m"}], "}"}], "\[Function]", " ", 
+          RowBox[{
+           RowBox[{
+            RowBox[{
+             RowBox[{"fp", "'"}], "[", "xp", "]"}], " ", 
+            RowBox[{"D", "[", 
+             RowBox[{"Pm", ",", "xp"}], "]"}]}], "-", 
+           RowBox[{
+            RowBox[{"(", 
+             RowBox[{
+              RowBox[{"2", " ", "m"}], "-", "1"}], ")"}], 
+            RowBox[{
+             RowBox[{"fp", "''"}], "[", "xp", "]"}], " ", "Pm"}]}]}], ",", 
+         "1", ",", 
+         RowBox[{"Range", "[", 
+          RowBox[{"n", "-", "1"}], "]"}]}], "]"}], "/.", 
+       RowBox[{
         RowBox[{
          RowBox[{
-          RowBox[{"Head", "[", "#2", "]"}], "===", "Around"}], ",", 
-         RowBox[{"#2", "[", "\"\<Uncertainty\>\"", "]"}], ",", "0"}], "]"}]}],
-       "}"}], "&"}], "@@@", "datNum"}]}], "]"}]], "Input",
- CellChangeTimes->{{3.836571907042726*^9, 3.8365719075682077`*^9}, {
-  3.8365719679456177`*^9, 3.836572034954253*^9}, {3.836572067138021*^9, 
-  3.8365720932499523`*^9}},
- CellLabel->"In[33]:=",ExpressionUUID->"cbeb62aa-7e89-4ec5-a1cb-d5012bac06fd"],
-
-Cell[BoxData["\<\"~/doc/research/first_order_singularities/paper/data/glow_\
-series_numeric.dat\"\>"], "Output",
- CellChangeTimes->{
-  3.8365719078847313`*^9, {3.836572025847522*^9, 3.836572035446138*^9}, 
-   3.8365720941903563`*^9, 3.836572233522911*^9},
- CellLabel->"Out[33]=",ExpressionUUID->"9ddcc7c6-de02-4d31-9401-bbbc5eefe582"]
-}, Open  ]],
+          RowBox[{"Derivative", "[", "m_", "]"}], "[", "fp", "]"}], "[", "xp",
+          "]"}], ":>", 
+        RowBox[{"dfs", "[", 
+         RowBox[{"[", "m", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", 
+     RowBox[{"MapIndexed", "[", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"{", 
+         RowBox[{"Pn", ",", "i"}], "}"}], "\[Function]", 
+        RowBox[{"Pn", "/", 
+         SuperscriptBox[
+          RowBox[{"dfs", "[", 
+           RowBox[{"[", "1", "]"}], "]"}], 
+          RowBox[{
+           RowBox[{"2", 
+            RowBox[{"i", "[", 
+             RowBox[{"[", "1", "]"}], "]"}]}], "-", "1"}]]}]}], ",", "Pns"}], 
+      "]"}]}]}], "\[IndentingNewLine]", "]"}]}]], "Input",
+ CellChangeTimes->{{3.83698298732085*^9, 3.836983017577533*^9}, {
+  3.8369830656105223`*^9, 3.836983192220652*^9}, {3.8369852957954073`*^9, 
+  3.836985418901877*^9}, {3.836985491119132*^9, 3.836985540335959*^9}, {
+  3.836985603761368*^9, 3.8369856038652277`*^9}, {3.836986669957045*^9, 
+  3.836986682421062*^9}},
+ CellLabel->"In[17]:=",ExpressionUUID->"275ca4b6-77bf-4727-923f-67c9c37ad46e"],
 
 Cell[CellGroupData[{
 
-Cell[BoxData[
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{"totCas", "=", "17"}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"ds", "=", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"invDerivativeList", "[", "totCas", "]"}], "[", 
+     RowBox[{"\[Theta]", "\[Function]", 
+      FractionBox[
+       RowBox[{"hCas", "[", "\[Theta]", "]"}], 
+       SuperscriptBox[
+        RowBox[{"(", 
+         RowBox[{"t", "[", "\[Theta]", "]"}], ")"}], 
+        RowBox[{"\[CapitalDelta]", "[", "2", "]"}]]]}], "]"}], "[", 
+    "\[Theta]0Cas", "]"}]}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"dMs", "=", 
+   RowBox[{
+    RowBox[{"m0", " ", 
+     RowBox[{"Rest", "[", 
+      RowBox[{"NestList", "[", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"D", "[", 
+          RowBox[{"#", ",", "\[Theta]"}], "]"}], "&"}], ",", 
+        FractionBox["\[Theta]", 
+         SuperscriptBox[
+          RowBox[{"(", 
+           RowBox[{
+            SuperscriptBox["\[Theta]", "2"], "-", "1"}], ")"}], 
+          RowBox[{"1", "/", "8"}]]], ",", "totCas"}], "]"}], "]"}]}], "/.", 
+    RowBox[{"\[Theta]", "->", "\[Theta]0Cas"}]}]}], 
+  ";"}], "\[IndentingNewLine]", 
  RowBox[{"datCas", "=", 
-  RowBox[{
+  RowBox[{"Table", "[", 
    RowBox[{
-    RowBox[{"NestList", "[", 
+    RowBox[{
+     RowBox[{"Sum", "[", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"dMs", "[", 
+         RowBox[{"[", "k", "]"}], "]"}], 
+        RowBox[{"BellY", "[", 
+         RowBox[{"n", ",", "k", ",", 
+          RowBox[{"ds", "[", 
+           RowBox[{"[", 
+            RowBox[{";;", 
+             RowBox[{"n", "-", "k", "+", "1"}]}], "]"}], "]"}]}], "]"}]}], 
+       ",", 
+       RowBox[{"{", 
+        RowBox[{"k", ",", "1", ",", "n"}], "}"}]}], "]"}], "/", 
      RowBox[{
-      RowBox[{"dd\[Xi]", "[", "hCas", "]"}], ",", 
-      RowBox[{"m0", " ", 
-       FractionBox["\[Theta]", 
-        SuperscriptBox[
-         RowBox[{"(", 
-          RowBox[{
-           SuperscriptBox["\[Theta]", "2"], "-", "1"}], ")"}], 
-         RowBox[{"1", "/", "8"}]]]}], ",", "10"}], "]"}], "/.", 
-    RowBox[{"\[Theta]", "->", "\[Theta]0Cas"}]}], "/.", "m0rule"}]}]], "Input",\
-
- CellChangeTimes->{{3.832146080982091*^9, 3.832146136030287*^9}, {
-   3.832146166615106*^9, 3.832146187807186*^9}, {3.832146248416617*^9, 
-   3.8321462996333437`*^9}, 3.8321545081565647`*^9, {3.832154839236245*^9, 
-   3.832154839322452*^9}},
- CellLabel->"In[14]:=",ExpressionUUID->"a79b1406-8855-4788-85f8-e01146acbc0b"],
+      RowBox[{"(", 
+       RowBox[{"n", "+", "1"}], ")"}], "!"}]}], ",", 
+    RowBox[{"{", 
+     RowBox[{"n", ",", "1", ",", "totCas"}], "}"}]}], "]"}]}]}], "Input",
+ CellChangeTimes->CompressedData["
+1:eJxTTMoPSmViYGCQAGIQHXVsxuTiaW8cpepuTAPRt/4wzgbRDhmJB0C0AfeT
+IyDaefWB42B5s2LWciBd8vg9F4iWm+0rAKIn5SyRBNFNksv1QPSRyuv6IDry
+Dp8DiOYzEQbTj2QUA0D0ylfKYPqeomIImJ6UGQqiy/K0UkC0yGE9MN2VltcE
+ons2t7aAaOWou2dAtHDoXzBdsUlNsQJI+3A4KINolltbdEC0jKGiLYhOmRju
+D6J7Ns4NBNE2EZ7nQHS3uDeYFhCceBtEm5TnPATR3usq0yqBdF1aP5iuqduT
+B6L7Zx0E0yq1U65UAek9VV3XQPSOV4nhC4G0jsR8MJ1QPqcKRGc0zQfTXDKC
+p0D0uX4ZMF0eMa1nEZB+eng+mAYA2XPFWw==
+  "],
+ CellLabel->"In[18]:=",ExpressionUUID->"9e250256-8cd3-402a-bc21-3ee002bb1f82"],
 
 Cell[BoxData[
  RowBox[{"{", 
   RowBox[{
-   InterpretationBox[
-    TemplateBox[{"1.3578383417065", "96", "10"},
-     "AroundSeq"],
-    Around[1.3578383417065958`, 1.0000000000000002`*^-14]], ",", 
-   InterpretationBox[
-    TemplateBox[{"0.09790657944", "0", "4"},
-     "AroundSeq"],
-    Around[0.09790657944000002, 4.000000129977332*^-12]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-0.2150219943", "3", "5"},
-     "AroundSeq"],
-    Around[-0.21502199433323033`, 4.846069847889282*^-11]], ",", 
-   InterpretationBox[
-    TemplateBox[{"1.275438112", "0", "9"},
-     "AroundSeq"],
-    Around[1.275438111980478, 8.99846810474221*^-10]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-13.1943759", "67", "24"},
-     "AroundSeq"],
-    Around[-13.194375967404621`, 2.4265468926938114`*^-8]], ",", 
-   InterpretationBox[
-    TemplateBox[{"199.409126", "0", "9"},
-     "AroundSeq"],
-    Around[199.40912595141498`, 8.737534828617298*^-7]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-4004.42550", "0.00004"},
-     "Around"],
-    Around[-4004.4254982941143`, 0.00003908326367837291]], ",", 
-   InterpretationBox[
-    TemplateBox[{"100787.9920", "0.0021"},
-     "Around"],
-    Around[100787.99199788233`, 0.0020814305200299176`]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-3.057071", "42", "13", 
-      SuperscriptBox["10", "6"]},
-     "AroundSeqExp"],
-    Around[-3.0570714230898526`*^6, 0.1286182540195812]], ",", 
-   InterpretationBox[
-    TemplateBox[{"1.0865807", "0", "9", 
-      SuperscriptBox["10", "8"]},
-     "AroundSeqExp"],
-    Around[1.0865806967349882`*^8, 9.049523786749958]], ",", 
-   InterpretationBox[
-    TemplateBox[{"-4.431930", "7", "7", 
-      SuperscriptBox["10", "9"]},
-     "AroundSeqExp"],
-    Around[-4.431930709816816*^9, 714.3183514973954]]}], "}"}]], "Output",
- CellChangeTimes->{{3.8321460949067373`*^9, 3.832146137791162*^9}, 
-   3.832146172640996*^9, 3.832146235521159*^9, {3.8321462717412853`*^9, 
-   3.832146275952108*^9}, 3.8321463349718313`*^9, 3.8321464558511057`*^9, 
-   3.832146509817857*^9, 3.83214669949054*^9, 3.832151975553176*^9, 
-   3.832152083287957*^9, 3.832154510903532*^9, 3.832154883538463*^9, 
-   3.836570442389636*^9},
- CellLabel->"Out[14]=",ExpressionUUID->"5d5e77cf-f1ea-4666-9e43-e8dbd0de9153"]
+   RowBox[{"-", "0.04895328972000001`"}], ",", "0.0358369990555384`", ",", 
+   RowBox[{"-", "0.05314325466585322`"}], ",", "0.10995313306170523`", ",", 
+   RowBox[{"-", "0.27695711937696654`"}], ",", "0.7945288687091524`", ",", 
+   RowBox[{"-", "2.499702182487203`"}], ",", "8.424469309661326`", ",", 
+   RowBox[{"-", "29.943251122547245`"}], ",", "111.02920849909947`", ",", 
+   RowBox[{"-", "426.1281183859369`"}], ",", "1682.8930954771286`", ",", 
+   RowBox[{"-", "6808.202478556653`"}], ",", "28115.088082925722`", ",", 
+   RowBox[{"-", "118184.25755733704`"}], ",", "504553.6128947737`", ",", 
+   RowBox[{"-", "2.183603153706728`*^6"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.83698713111462*^9, 3.836987321633688*^9, 
+  3.8369882151463833`*^9, 3.83698833312978*^9, 3.837070043781701*^9, 
+  3.837070402550199*^9, 3.837072865049255*^9},
+ CellLabel->"Out[21]=",ExpressionUUID->"1690ea78-e2c3-4e83-a9e5-8be735e0bca3"]
 }, Open  ]],
 
-Cell[BoxData[
+Cell[CellGroupData[{
+
+Cell[BoxData[{
  RowBox[{
-  RowBox[{"datOurs", "=", 
+  RowBox[{"totOurs", "=", "17"}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"ds", "=", 
    RowBox[{
     RowBox[{
-     RowBox[{"dFd\[Xi]LowList", "[", 
-      RowBox[{"n1", ",", "h1"}], "]"}], "[", "9", "]"}], "/.", "sol1"}]}], 
-  ";"}]], "Input",
- CellChangeTimes->{{3.832145390968719*^9, 3.8321454292735577`*^9}, {
-   3.832145976500745*^9, 3.832145979699314*^9}, {3.832146795410326*^9, 
-   3.832146803058391*^9}, {3.832146853819456*^9, 3.832146854323563*^9}, {
-   3.83214967637575*^9, 3.832149676470541*^9}, {3.832154514224004*^9, 
-   3.832154515788747*^9}, 3.832154755609396*^9, {3.836572237598887*^9, 
-   3.836572247372046*^9}},
- CellLabel->"In[34]:=",ExpressionUUID->"4221e07f-e3c2-4004-a825-7339ebc77c40"],
+     RowBox[{"invDerivativeList", "[", "totOurs", "]"}], "[", 
+     RowBox[{"\[Theta]", "\[Function]", 
+      FractionBox[
+       RowBox[{
+        RowBox[{"h1", "[", "\[Theta]", "]"}], "/.", "sol1"}], 
+       SuperscriptBox[
+        RowBox[{"(", 
+         RowBox[{"t", "[", "\[Theta]", "]"}], ")"}], 
+        RowBox[{"\[CapitalDelta]", "[", "2", "]"}]]]}], "]"}], "[", 
+    RowBox[{"\[Theta]c", "/.", "sol1"}], "]"}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"dFRegs", "=", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"NestList", "[", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"D", "[", 
+         RowBox[{"#", ",", "\[Theta]"}], "]"}], "&"}], ",", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"RFReg", "[", "n1", "]"}], "[", "\[Theta]", "]"}], "/.", 
+        "sol1"}], ",", "totOurs"}], "]"}], "/.", 
+     RowBox[{"\[Theta]", "->", "\[Theta]c"}]}], "/.", "sol1"}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"dF", "=", 
+   RowBox[{"dFRegs", "+", 
+    RowBox[{"Table", "[", 
+     RowBox[{
+      RowBox[{"Piecewise", "[", 
+       RowBox[{"{", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{
+           RowBox[{"AL", " ", 
+            RowBox[{"m", "!"}], " ", 
+            RowBox[{"Gamma", "[", 
+             RowBox[{"m", "-", "1"}], "]"}], " ", 
+            RowBox[{
+             RowBox[{"B", "^", 
+              RowBox[{"(", 
+               RowBox[{"m", "-", "1"}], ")"}]}], "/", "\[Pi]"}]}], ",", 
+           RowBox[{"m", ">", "1"}]}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"0", ",", "True"}], "}"}]}], "}"}], "]"}], ",", 
+      RowBox[{"{", 
+       RowBox[{"m", ",", "0", ",", "totOurs"}], "}"}]}], "]"}]}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"dMs", "=", 
+   RowBox[{
+    RowBox[{
+     RowBox[{
+      RowBox[{"Rest", "[", 
+       RowBox[{"NestList", "[", 
+        RowBox[{
+         RowBox[{
+          RowBox[{"D", "[", 
+           RowBox[{"#", ",", "\[Theta]"}], "]"}], "&"}], ",", 
+         RowBox[{
+          FractionBox[
+           RowBox[{"fp", "[", "\[Theta]", "]"}], 
+           SuperscriptBox[
+            RowBox[{"t", "[", "\[Theta]", "]"}], "2"]], "-", 
+          RowBox[{
+           FractionBox["1", 
+            RowBox[{"8", "\[Pi]"}]], 
+           RowBox[{"Log", "[", 
+            SuperscriptBox[
+             RowBox[{"t", "[", "\[Theta]", "]"}], "2"], "]"}]}]}], ",", 
+         "totOurs"}], "]"}], "]"}], "/.", 
+      RowBox[{"\[Theta]", "->", "\[Theta]c"}]}], "/.", 
+     RowBox[{"Map", "[", 
+      RowBox[{
+       RowBox[{
+        RowBox[{
+         RowBox[{
+          RowBox[{
+           RowBox[{"Derivative", "[", "#", "]"}], "[", "fp", "]"}], "[", 
+          "\[Theta]c", "]"}], "->", 
+         RowBox[{"dF", "[", 
+          RowBox[{"[", 
+           RowBox[{"#", "+", "1"}], "]"}], "]"}]}], "&"}], ",", 
+       RowBox[{"Range", "[", 
+        RowBox[{"0", ",", "totOurs"}], "]"}]}], "]"}]}], "/.", "sol1"}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{"datOurs", "=", 
+  RowBox[{"Table", "[", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"Sum", "[", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"dMs", "[", 
+         RowBox[{"[", "k", "]"}], "]"}], 
+        RowBox[{"BellY", "[", 
+         RowBox[{"n", ",", "k", ",", 
+          RowBox[{"ds", "[", 
+           RowBox[{"[", 
+            RowBox[{";;", 
+             RowBox[{"n", "-", "k", "+", "1"}]}], "]"}], "]"}]}], "]"}]}], 
+       ",", 
+       RowBox[{"{", 
+        RowBox[{"k", ",", "1", ",", "n"}], "}"}]}], "]"}], "/", 
+     RowBox[{
+      RowBox[{"(", "n", ")"}], "!"}]}], ",", 
+    RowBox[{"{", 
+     RowBox[{"n", ",", "1", ",", "totOurs"}], "}"}]}], "]"}]}]}], "Input",
+ CellChangeTimes->CompressedData["
+1:eJwd0Esow3EAB/DRlEetMeWR5N+QlsY0jxU1j/LaU5aZy7YQteYw2aZQwoEl
+G9kyilFiUh45KWThsKi1mrzKI4elzcnBY/l/f4dvn8P3e/pS+oG2nngGg5FH
+B2ouXPOmxY/a7NHbRXj3G+eG4j7dKSxNefPBeu/pJekrTAlm2sHXaDLMdUvZ
+0GHYyILjWZt86LOGSmDnA0sMWUIO8SWHUsCtMJf4RFHtREe/Cg4Zed0w/ZxP
+nO41jkPbweQE5Goe/ZCj+iNa9gspC60kUcyFzLvDYpgjoGpgt71DDm17K0pY
+rW6+hjMZrUR2qv0eCs2GZ6hQiiKw8WrrF2rHZuOttEddz8TAmZwN3+XLaXCC
+ivJgcNdeDK+lWgEs+ywogw0/GSLoYewooUER0sKSJJsOpnsqjFCSX0WUBb+n
+YMujfA5G2vROKPVvL8Hzptiqlfxf6YGuwLEX3qpPiHXOIvUa7ZWbR3yTfQ3D
+8pEYURJeyFzHjnlD/Ac6Hgav
+  
+  "],ExpressionUUID->"f81ed9c7-d940-4314-963c-c36ea0215ef3"],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   RowBox[{"-", "1.3578383417066047`"}], ",", 
+   RowBox[{"-", "0.04895328971999913`"}], ",", "0.038589364046676934`", ",", 
+   RowBox[{"-", "0.06639683866958071`"}], ",", "0.17282494938877094`", ",", 
+   RowBox[{"-", "0.5982136876234695`"}], ",", "2.5836539597308135`", ",", 
+   RowBox[{"-", "13.385542500325027`"}], ",", "80.92156022471416`", ",", 
+   RowBox[{"-", "559.2327437492248`"}], ",", "4348.6528801653585`", ",", 
+   RowBox[{"-", "37577.54203132622`"}], ",", "357215.5775388312`", ",", 
+   RowBox[{"-", "3.7046351622097627`*^6"}], ",", "4.162364375588009`*^7", ",", 
+   RowBox[{"-", "5.036541248157173`*^8"}], ",", "6.529768978407632`*^9"}], 
+  "}"}]], "Output",
+ CellChangeTimes->{
+  3.83698713111462*^9, 3.83698732721172*^9, {3.836987527713932*^9, 
+   3.836987541172042*^9}, {3.8369877357608957`*^9, 3.836987748867478*^9}, {
+   3.8369877874156313`*^9, 3.836987793551597*^9}, 3.836988034596339*^9, 
+   3.836988124923636*^9, {3.836988167393293*^9, 3.83698817337673*^9}, 
+   3.836988304258202*^9, 3.8369887429546413`*^9, 3.8370701493666887`*^9, 
+   3.83707078354727*^9},
+ CellLabel->"Out[37]=",ExpressionUUID->"2234af5e-068b-46a3-beaf-99a907ef5184"]
+}, Open  ]],
 
 Cell[CellGroupData[{
 
@@ -630,32 +810,31 @@ Cell[BoxData[
   RowBox[{
   "\"\<~/doc/research/first_order_singularities/paper/data/glow_series_ours_0.\
 dat\>\"", ",", 
-   RowBox[{"Table", "[", 
+   RowBox[{"Prepend", "[", 
     RowBox[{
-     RowBox[{"{", 
-      RowBox[{"i", ",", 
-       RowBox[{
-        RowBox[{"Chop", "@", 
+     RowBox[{"Table", "[", 
+      RowBox[{
+       RowBox[{"{", 
+        RowBox[{"i", ",", 
          RowBox[{"datOurs", "[", 
-          RowBox[{"[", 
-           RowBox[{"i", "+", "1"}], "]"}], "]"}]}], "/", 
-        RowBox[{"i", "!"}]}]}], "}"}], ",", 
+          RowBox[{"[", "i", "]"}], "]"}]}], "}"}], ",", 
+       RowBox[{"{", 
+        RowBox[{"i", ",", "1", ",", 
+         RowBox[{"Length", "[", "datOurs", "]"}]}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
-      RowBox[{"i", ",", "0", ",", 
-       RowBox[{
-        RowBox[{"Length", "[", "datOurs", "]"}], "-", "1"}]}], "}"}]}], 
-    "]"}]}], "]"}]], "Input",
+      RowBox[{"0", ",", "0"}], "}"}]}], "]"}]}], "]"}]], "Input",
  CellChangeTimes->{{3.8365725090188103`*^9, 3.836572511033183*^9}, {
   3.836572551269373*^9, 3.836572621026455*^9}, {3.8365727308332853`*^9, 
-  3.836572735579463*^9}},
+  3.836572735579463*^9}, {3.8369881356397867`*^9, 3.8369881529196568`*^9}},
  CellLabel->"In[38]:=",ExpressionUUID->"dd088f15-420b-4212-8186-b62091ac9d6c"],
 
 Cell[BoxData["\<\"~/doc/research/first_order_singularities/paper/data/glow_\
 series_ours_0.dat\"\>"], "Output",
  CellChangeTimes->{
   3.8365725114300337`*^9, {3.8365725984285917`*^9, 3.8365726212484303`*^9}, 
-   3.8365727364325037`*^9},
- CellLabel->"Out[38]=",ExpressionUUID->"9a70ffe7-9718-4df2-80c1-4de5b7c7d436"]
+   3.8365727364325037`*^9, {3.836988153130045*^9, 3.836988182958664*^9}, 
+   3.836988333167184*^9, 3.8370701494196787`*^9, 3.8370707835909777`*^9},
+ CellLabel->"Out[38]=",ExpressionUUID->"21b5cf8e-7f0a-45f7-ab93-9e8ebe789a07"]
 }, Open  ]],
 
 Cell[CellGroupData[{
@@ -665,27 +844,58 @@ Cell[BoxData[
   RowBox[{
   "\"\<~/doc/research/first_order_singularities/paper/data/glow_series_\
 caselle.dat\>\"", ",", 
-   RowBox[{"Table", "[", 
+   RowBox[{"Prepend", "[", 
     RowBox[{
+     RowBox[{"Table", "[", 
+      RowBox[{
+       RowBox[{"{", 
+        RowBox[{"i", ",", 
+         RowBox[{
+          RowBox[{"Prepend", "[", 
+           RowBox[{"datCas", ",", 
+            RowBox[{
+             RowBox[{"Gls", "[", 
+              RowBox[{"[", "2", "]"}], "]"}], "[", "\"\<Value\>\"", "]"}]}], 
+           "]"}], "[", 
+          RowBox[{"[", "i", "]"}], "]"}]}], "}"}], ",", 
+       RowBox[{"{", 
+        RowBox[{"i", ",", "1", ",", 
+         RowBox[{"1", "+", 
+          RowBox[{"Length", "[", "datCas", "]"}]}]}], "}"}]}], "]"}], ",", 
      RowBox[{"{", 
-      RowBox[{"i", ",", 
-       RowBox[{
-        RowBox[{
-         RowBox[{"datCas", "[", 
-          RowBox[{"[", "i", "]"}], "]"}], "[", "\"\<Value\>\"", "]"}], "/", 
-        RowBox[{"i", "!"}]}]}], "}"}], ",", 
-     RowBox[{"{", 
-      RowBox[{"i", ",", "1", ",", 
-       RowBox[{"Length", "[", "datCas", "]"}]}], "}"}]}], "]"}]}], 
-  "]"}]], "Input",
+      RowBox[{"0", ",", "0"}], "}"}]}], "]"}]}], "]"}]], "Input",
  CellChangeTimes->{{3.836572923916615*^9, 3.8365729684861917`*^9}, {
-  3.8365730212450933`*^9, 3.836573024451941*^9}},
- CellLabel->"In[40]:=",ExpressionUUID->"e7fdb778-fd9a-4c13-95dc-aefbf5b8a29f"],
+   3.8365730212450933`*^9, 3.836573024451941*^9}, {3.8369870331179867`*^9, 
+   3.836987040227461*^9}, {3.836988096983111*^9, 3.836988122791327*^9}, 
+   3.836988222777315*^9, {3.83698825888205*^9, 3.836988260282138*^9}},
+ CellLabel->"In[22]:=",ExpressionUUID->"e7fdb778-fd9a-4c13-95dc-aefbf5b8a29f"],
 
 Cell[BoxData["\<\"~/doc/research/first_order_singularities/paper/data/glow_\
 series_caselle.dat\"\>"], "Output",
- CellChangeTimes->{3.83657297081538*^9, 3.836573024753381*^9},
- CellLabel->"Out[40]=",ExpressionUUID->"01370c9d-9462-41f0-8dcc-9775da2fb959"]
+ CellChangeTimes->{3.836988223024967*^9, 3.836988260494157*^9, 
+  3.836988333199574*^9, 3.837070149473012*^9, 3.837070783629765*^9, 
+  3.837072865499703*^9},
+ CellLabel->"Out[22]=",ExpressionUUID->"a5e80f1a-5f57-4a7a-ad79-17c92282d141"]
+}, Open  ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Gls", "[", 
+  RowBox[{"[", "1", "]"}], "]"}]], "Input",
+ CellChangeTimes->{{3.836985954144209*^9, 3.836985955175076*^9}},
+ CellLabel->
+  "In[176]:=",ExpressionUUID->"feb08355-9ad1-4257-9f97-e394177d7e32"],
+
+Cell[BoxData[
+ InterpretationBox[
+  TemplateBox[{"0.0", "1.0", 
+    SuperscriptBox["10", "-14"]},
+   "AroundExp"],
+  Around[0., 1.*^-14]]], "Output",
+ CellChangeTimes->{3.836985955307584*^9},
+ CellLabel->
+  "Out[176]=",ExpressionUUID->"87e29f54-9d68-4261-96d4-95d24dcdc36a"]
 }, Open  ]],
 
 Cell[CellGroupData[{
@@ -693,17 +903,14 @@ Cell[CellGroupData[{
 Cell[BoxData[
  RowBox[{"ListLogPlot", "[", 
   RowBox[{"{", "\[IndentingNewLine]", 
-   RowBox[{"datNum", ",", 
-    RowBox[{"Abs", "@", "datCas"}], ",", 
-    RowBox[{"Thread", "[", 
-     RowBox[{"{", 
-      RowBox[{
-       RowBox[{"Range", "[", 
-        RowBox[{"0", ",", 
-         RowBox[{
-          RowBox[{"Length", "[", "datOurs", "]"}], "-", "1"}]}], "]"}], ",", 
-       "datOurs"}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], 
-  "]"}]], "Input",
+   RowBox[{
+    RowBox[{"Abs", "@", "datNum"}], ",", 
+    RowBox[{"Abs", "@", 
+     RowBox[{"Prepend", "[", 
+      RowBox[{"datCas", ",", 
+       RowBox[{"Gls", "[", 
+        RowBox[{"[", "2", "]"}], "]"}]}], "]"}]}]}], "\[IndentingNewLine]", 
+   "}"}], "]"}]], "Input",
  CellChangeTimes->{{3.8291280118781147`*^9, 3.829128118103051*^9}, {
    3.829128192513464*^9, 3.82912819312051*^9}, {3.829128371940607*^9, 
    3.829128493270048*^9}, {3.8291285364471493`*^9, 3.8291285366627502`*^9}, {
@@ -716,11 +923,14 @@ Cell[BoxData[
    3.8321461019658613`*^9, 3.832146103005608*^9}, {3.83214636465071*^9, 
    3.832146365018457*^9}, {3.8321468071147757`*^9, 3.83214683603503*^9}, {
    3.832151906798731*^9, 3.832151920438457*^9}, {3.83215203026543*^9, 
-   3.8321520312326193`*^9}},
- CellLabel->"In[20]:=",ExpressionUUID->"e61ed118-a102-4290-8440-cba17b87145b"],
+   3.8321520312326193`*^9}, {3.836984203191142*^9, 3.8369842034070263`*^9}, {
+   3.836984260736669*^9, 3.836984270504239*^9}, {3.836985883270376*^9, 
+   3.8369858862218723`*^9}, {3.836985919726593*^9, 3.836985961239354*^9}},
+ CellLabel->
+  "In[189]:=",ExpressionUUID->"e61ed118-a102-4290-8440-cba17b87145b"],
 
 Cell[BoxData[
- GraphicsBox[{{{{{}, 
+ GraphicsBox[{{{{
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
           LineBox[{{1., 0.3058939805973312}, {1., 0.3058939805973386}}], 
@@ -728,122 +938,201 @@ Cell[BoxData[
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{2., -2.3237415260246084`}, {2., -2.323741525983753}}], 
-          LineBox[{{2., -2.323741525983753}, {2., -2.3237415259428977`}}]}},
+          LineBox[{{2., -3.0168887065845538`}, {2., -3.0168887065436985`}}], 
+          LineBox[{{2., -3.0168887065436985`}, {2., -3.016888706502843}}]}},
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{3., -1.4559292669525052`}, {3., -1.4559292643794253`}}], 
-          LineBox[{{3., -1.4559292643794253`}, {3., -1.4559292618063453`}}]}},
+          LineBox[{{3., -3.24768873618056}, {3., -3.2476887336074802`}}], 
+          LineBox[{{3., -3.2476887336074802`}, {3., -3.2476887310344003`}}]}},
         
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{4., 0.49511742142021525`}, {4., 0.4951174360481992}}], 
-          LineBox[{{4., 0.4951174360481992}, {4., 0.4951174506761829}}]}},
+          LineBox[{{4., -2.6829364089277306`}, {4., -2.6829363942997464`}}], 
+          LineBox[{{4., -2.6829363942997464`}, {4., -2.6829363796717627`}}]}},
+        
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{5., 3.0940399563540724`}, {5., 3.09404001073627}}], 
-          LineBox[{{5., 3.09404001073627}, {5., 3.094040065118465}}]}},
+          LineBox[{{5., -1.6934517864279734`}, {5., -1.6934517320457758`}}], 
+          LineBox[{{5., -1.6934517320457758`}, {5., -1.693451677663581}}]}},
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{6., 6.1624758838184075`}, {6., 6.16247740087889}}], 
-          LineBox[{{6., 6.16247740087889}, {6., 6.162478917937071}}]}},
+          LineBox[{{6., -0.4167753281916941}, {6., -0.41677381113121115`}}], 
+          LineBox[{{6., -0.41677381113121115`}, {6., -0.4167722940730296}}]}},
+        
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{7., 9.602775387951214}, {7., 9.60277640917097}}], 
-          LineBox[{{7., 9.60277640917097}, {7., 9.602777430389681}}]}},
+          LineBox[{{7., 1.077614026885801}, {7., 1.077615048105556}}], 
+          LineBox[{{7., 1.077615048105556}, {7., 1.0776160693242682`}}]}},
         Antialiasing->False]}, 
       {RGBColor[0.368417, 0.506779, 0.709798], 
        StyleBox[{{}, {
-          LineBox[{{8., 13.351873817000742`}, {8., 13.352514637272591`}}], 
-          LineBox[{{8., 13.352514637272591`}, {8., 13.35315504715679}}]}},
-        Antialiasing->False]}}, {
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{1., 0.30589398059733136`}, {1., 0.30589398059733874`}}], 
-          LineBox[{{1., 0.30589398059733874`}, {1., 0.30589398059734607`}}]}},
-        
-        Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{2., -2.3237415260246084`}, {2., -2.323741525983753}}], 
-          LineBox[{{2., -2.323741525983753}, {2., -2.3237415259428977`}}]}},
-        Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{3., -1.5370149570877314`}, {3., -1.537014956862356}}], 
-          LineBox[{{3., -1.537014956862356}, {3., -1.5370149566369802`}}]}},
-        Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{4., 0.2432897361215771}, {4., 0.2432897368270969}}], 
-          LineBox[{{4., 0.2432897368270969}, {4., 0.24328973753261673`}}]}},
+          LineBox[{{8., 2.747270914255491}, {8., 2.7479117345273405`}}], 
+          LineBox[{{8., 2.7479117345273405`}, {8., 2.7485521444115397`}}]}},
+        Antialiasing->False]}}, 
+     {RGBColor[0.880722, 0.611041, 0.142051], 
+      StyleBox[{{}, {
+         LineBox[{{1., 0.3058939805973312}, {1., 0.3058939805973386}}], 
+         LineBox[{{1., 0.3058939805973386}, {1., 0.3058939805973459}}]}},
+       Antialiasing->False]}}, {{
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{1., 0.3058939805973459}, 
+             Offset[{3, 0}, {1., 0.3058939805973459}]}, {{1., 
+             0.3058939805973459}, 
+             Offset[{-3, 0}, {1., 0.3058939805973459}]}, {{1., 
+             0.3058939805973312}, 
+             Offset[{3, 0}, {1., 0.3058939805973312}]}, {{1., 
+             0.3058939805973312}, 
+             Offset[{-3, 0}, {1., 0.3058939805973312}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{5., 2.5797906738871794`}, {5., 2.5797906757262563`}}], 
-          LineBox[{{5., 2.5797906757262563`}, {5., 2.579790677565333}}]}},
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{2., -3.016888706502843}, 
+             Offset[{3, 0}, {2., -3.016888706502843}]}, {{
+             2., -3.016888706502843}, 
+             Offset[{-3, 0}, {2., -3.016888706502843}]}, {{
+             2., -3.0168887065845538`}, 
+             Offset[{3, 0}, {2., -3.0168887065845538`}]}, {{
+             2., -3.0168887065845538`}, 
+             Offset[{-3, 0}, {2., -3.0168887065845538`}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{6., 5.295358619156995}, {6., 5.295358623538708}}], 
-          LineBox[{{6., 5.295358623538708}, {6., 5.295358627920421}}]}},
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{3., -3.2476887310344003`}, 
+             Offset[{3, 0}, {3., -3.2476887310344003`}]}, {{
+             3., -3.2476887310344003`}, 
+             Offset[{-3, 0}, {3., -3.2476887310344003`}]}, {{
+             3., -3.24768873618056}, 
+             Offset[{3, 0}, {3., -3.24768873618056}]}, {{
+             3., -3.24768873618056}, 
+             Offset[{-3, 0}, {3., -3.24768873618056}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{7., 8.29515539333424}, {7., 8.295155403094258}}], 
-          LineBox[{{7., 8.295155403094258}, {7., 8.295155412854276}}]}},
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{4., -2.6829363796717627`}, 
+             Offset[{3, 0}, {4., -2.6829363796717627`}]}, {{
+             4., -2.6829363796717627`}, 
+             Offset[{-3, 0}, {4., -2.6829363796717627`}]}, {{
+             4., -2.6829364089277306`}, 
+             Offset[{3, 0}, {4., -2.6829364089277306`}]}, {{
+             4., -2.6829364089277306`}, 
+             Offset[{-3, 0}, {4., -2.6829364089277306`}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{8., 11.520774479866512`}, {8., 11.520774500518085`}}], 
-          LineBox[{{8., 11.520774500518085`}, {8., 11.520774521169658`}}]}},
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{5., -1.693451677663581}, 
+             Offset[{3, 0}, {5., -1.693451677663581}]}, {{
+             5., -1.693451677663581}, 
+             Offset[{-3, 0}, {5., -1.693451677663581}]}, {{
+             5., -1.6934517864279734`}, 
+             Offset[{3, 0}, {5., -1.6934517864279734`}]}, {{
+             5., -1.6934517864279734`}, 
+             Offset[{-3, 0}, {5., -1.6934517864279734`}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{9., 14.932967922312375`}, {9., 14.932967964384751`}}], 
-          LineBox[{{9., 14.932967964384751`}, {9., 14.932968006457125`}}]}},
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{6., -0.4167722940730296}, 
+             Offset[{3, 0}, {6., -0.4167722940730296}]}, {{
+             6., -0.4167722940730296}, 
+             Offset[{-3, 0}, {6., -0.4167722940730296}]}, {{
+             6., -0.4167753281916941}, 
+             Offset[{3, 0}, {6., -0.4167753281916941}]}, {{
+             6., -0.4167753281916941}, 
+             Offset[{-3, 0}, {6., -0.4167753281916941}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{10., 18.50371645081476}, {10., 18.50371653409918}}], 
-          LineBox[{{10., 18.50371653409918}, {10., 18.503716617383592`}}]}},
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{7., 1.0776160693242682`}, 
+             Offset[{3, 0}, {7., 1.0776160693242682`}]}, {{7., 
+             1.0776160693242682`}, 
+             Offset[{-3, 0}, {7., 1.0776160693242682`}]}, {{7., 
+             1.077614026885801}, Offset[{3, 0}, {7., 1.077614026885801}]}, {{
+             7., 1.077614026885801}, 
+             Offset[{-3, 0}, {7., 1.077614026885801}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
         Antialiasing->False]}, 
-      {RGBColor[0.880722, 0.611041, 0.142051], 
-       StyleBox[{{}, {
-          LineBox[{{11., 22.212100991027132`}, {11., 22.212101152202578`}}], 
-          LineBox[{{11., 22.212101152202578`}, {11., 22.212101313378}}]}},
-        Antialiasing->False]}}}, {}}, {
+      {RGBColor[0.368417, 0.506779, 0.709798], 
+       StyleBox[{
+         GeometricTransformationBox[
+          LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+         GeometricTransformationBox[
+          LineBox[{{{8., 2.7485521444115397`}, 
+             Offset[{3, 0}, {8., 2.7485521444115397`}]}, {{8., 
+             2.7485521444115397`}, 
+             Offset[{-3, 0}, {8., 2.7485521444115397`}]}, {{8., 
+             2.747270914255491}, Offset[{3, 0}, {8., 2.747270914255491}]}, {{
+             8., 2.747270914255491}, 
+             Offset[{-3, 0}, {8., 2.747270914255491}]}}], {{{1., 0.}, {0., 
+           1.}}, {0., 0.}}]},
+        Antialiasing->False]}}, 
+     {RGBColor[0.880722, 0.611041, 0.142051], 
+      StyleBox[{
+        GeometricTransformationBox[
+         LineBox[{}], {{{1., 0.}, {0., 1.}}, {0., 0.}}], 
+        GeometricTransformationBox[
+         LineBox[{{{1., 0.3058939805973459}, 
+            Offset[{3, 0}, {1., 0.3058939805973459}]}, {{1., 
+            0.3058939805973459}, 
+            Offset[{-3, 0}, {1., 0.3058939805973459}]}, {{1., 
+            0.3058939805973312}, Offset[{3, 0}, {1., 0.3058939805973312}]}, {{
+            1., 0.3058939805973312}, 
+            Offset[{-3, 0}, {1., 0.3058939805973312}]}}], {{{1., 0.}, {0., 
+          1.}}, {0., 0.}}]},
+       Antialiasing->False]}}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
       AbsoluteThickness[1.6], 
-     PointBox[{{1., 0.3058939805973386}, {2., -2.323741525983753}, {
-      3., -1.4559292643794253`}, {4., 0.4951174360481992}, {5., 
-      3.09404001073627}, {6., 6.16247740087889}, {7., 9.60277640917097}, {8., 
-      13.352514637272591`}, {9., 17.374061165823296`}, {10., 
-      21.625033700634212`}, {11., 26.085288777828126`}}]}, 
+     PointBox[{{1., 0.3058939805973386}, {2., -3.0168887065436985`}, {
+      3., -3.2476887336074802`}, {4., -2.6829363942997464`}, {
+      5., -1.6934517320457758`}, {6., -0.41677381113121115`}, {7., 
+      1.077615048105556}, {8., 2.7479117345273405`}, {9., 
+      4.572233685741827}, {10., 6.520621127558696}, {11., 
+      8.582980931954241}}]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.012833333333333334`],
       AbsoluteThickness[1.6], 
-     PointBox[{{1., 0.30589398059733874`}, {2., -2.323741525983753}, {
-      3., -1.537014956862356}, {4., 0.2432897368270969}, {5., 
-      2.5797906757262563`}, {6., 5.295358623538708}, {7., 
-      8.295155403094258}, {8., 11.520774500518085`}, {9., 
-      14.932967964384751`}, {10., 18.50371653409918}, {11., 
-      22.212101152202578`}}]}, 
-    {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.012833333333333334`],
-      AbsoluteThickness[1.6], 
-     PointBox[{{1., 0.30589398059734246`}, {2., -2.323741525983774}, {
-      3., -1.463019114084386}, {4., 0.465947996316923}, {5., 
-      3.0320156927845257`}, {6., 6.065443960311892}, {7., 
-      9.474366021505318}, {8., 13.198778109365042`}, {9., 
-      17.195307773271686`}}]}}, {{}, {}}},
+     PointBox[{{1., 0.3058939805973386}, {2., -3.016888706543698}, {
+      3., -3.3287744260904106`}, {4., -2.934764093520849}, {
+      5., -2.207701067055789}, {6., -1.2838925884713879`}, {
+      7., -0.2300059579711514}, {8., 0.9161715977728528}, {9., 
+      2.1311404843033004`}, {10., 3.399303961023672}, {11., 
+      4.709793306328703}, {12., 6.054740048438777}, {13., 
+      7.428269671957708}, {14., 8.825883411079555}, {15., 10.2440616536727}, {
+      16., 11.680000190290155`}}]}}, {{}, {}}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->{True, True},
   AxesLabel->{None, None},
-  AxesOrigin->{0., -4.546909369396598},
+  AxesOrigin->{0., -4.50329621506643},
   DisplayFunction->Identity,
   Frame->{{False, False}, {False, False}},
   FrameLabel->{{None, None}, {None, None}},
@@ -853,7 +1142,6 @@ Cell[BoxData[
   GridLines->{None, None},
   GridLinesStyle->Directive[
     GrayLevel[0.5, 0.4]],
-  ImageSize->{414.0000000000002, Automatic},
   Method->{
    "OptimizePlotMarkers" -> True, "OptimizePlotMarkers" -> True, 
     "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
@@ -865,7 +1153,7 @@ Cell[BoxData[
          Part[#, 1]], 
         Exp[
          Part[#, 2]]}& )}},
-  PlotRange->{{0., 11.}, {-4.546909369396598, 26.085288777828126`}},
+  PlotRange->{{0., 16.}, {-4.50329621506643, 11.680000190290155`}},
   PlotRangeClipping->True,
   PlotRangePadding->{{
      Scaled[0.02], 
@@ -873,65 +1161,45 @@ Cell[BoxData[
      Scaled[0.02], 
      Scaled[0.05]}},
   Ticks->FrontEndValueCache[{Automatic, 
-     Charting`ScaledTicks[{Log, Exp}]}, {Automatic, {{2.302585092994046, 
-       FormBox["10", TraditionalForm], {0.01, 0.}}, {11.512925464970229`, 
+     Charting`ScaledTicks[{Log, Exp}]}, {Automatic, {{-4.605170185988091, 
        FormBox[
-        TemplateBox[{"10", "5"}, "Superscript", SyntaxForm -> SuperscriptBox],
-         TraditionalForm], {0.01, 0.}}, {20.72326583694641, 
+        TagBox[
+         InterpretationBox[
+          StyleBox["\"0.01\"", ShowStringCharacters -> False], 0.01, 
+          AutoDelete -> True], NumberForm[#, {
+           DirectedInfinity[1], 2}]& ], TraditionalForm], {0.01, 0.}}, {0., 
+       FormBox["1", TraditionalForm], {0.01, 0.}}, {4.605170185988092, 
+       FormBox["100", TraditionalForm], {0.01, 0.}}, {9.210340371976184, 
        FormBox[
-        TemplateBox[{"10", "9"}, "Superscript", SyntaxForm -> SuperscriptBox],
-         TraditionalForm], {0.01, 0.}}, {-6.907755278982137, 
-       FormBox[
-        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 
-       0.}}, {-4.605170185988091, 
-       FormBox[
-        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 
-       0.}}, {-2.3025850929940455`, 
-       FormBox[
-        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {0., 
+        TemplateBox[{"10", "4"}, "Superscript", SyntaxForm -> SuperscriptBox],
+         TraditionalForm], {0.01, 0.}}, {-2.3025850929940455`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      4.605170185988092, 
+      2.302585092994046, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       6.907755278982137, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      9.210340371976184, 
+      11.512925464970229`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       13.815510557964274`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      16.11809565095832, 
-       FormBox[
-        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      18.420680743952367`, 
-       FormBox[
-        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      23.025850929940457`, 
+      14.22097566607244, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      25.328436022934504`, 
+      14.508657738524219`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      27.631021115928547`, 
-       FormBox[
-        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
-      29.933606208922594`, 
+      14.73180128983843, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 
        0.}}}}]]], "Output",
- CellChangeTimes->{
-  3.8292190385400677`*^9, 3.829219088509445*^9, 3.8292203752304993`*^9, 
-   3.829362528741741*^9, 3.832145985334715*^9, {3.83214610321945*^9, 
-   3.832146139205316*^9}, 3.832146173390081*^9, 3.832146239819025*^9, {
-   3.832146343090296*^9, 3.832146365218691*^9}, 3.832146512787468*^9, 
-   3.8321467072616997`*^9, {3.832146811961604*^9, 3.832146837071911*^9}, 
-   3.8321477095082703`*^9, 3.832151921021535*^9, 3.832151975632756*^9, {
-   3.832152031506322*^9, 3.832152044695828*^9}, 3.832152083368902*^9, 
-   3.832154526555648*^9, 3.8365707096084023`*^9},
- CellLabel->"Out[20]=",ExpressionUUID->"6cada30c-d260-4892-8f67-49af9e1c1a05"]
+ CellChangeTimes->{3.8369859615296097`*^9, 3.836987016307529*^9},
+ CellLabel->
+  "Out[189]=",ExpressionUUID->"2e45389f-59c7-4eaf-9b3a-270214fa013e"]
 }, Open  ]],
 
 Cell[BoxData[""], "Input",
@@ -2068,9 +2336,9 @@ Cell[BoxData[
  CellLabel->"Out[91]=",ExpressionUUID->"b48c9c3b-23cc-4864-8ea2-6e98855eb77d"]
 }, Open  ]]
 },
-WindowSize->{1435.5, 790.5},
+WindowSize->{891.75, 1060.5},
 WindowMargins->{{2.25, Automatic}, {2.25, Automatic}},
-FrontEndVersion->"12.1 for Linux ARM (32-bit) (August 18, 2020)",
+FrontEndVersion->"12.3 for Linux x86 (64-bit) (May 11, 2021)",
 StyleDefinitions->"Default.nb",
 ExpressionUUID->"d257fbda-2be1-4221-9ac8-5153716cfc00"
 ]
@@ -2085,79 +2353,80 @@ CellTagsIndex->{}
 *)
 (*NotebookFileOutline
 Notebook[{
-Cell[558, 20, 596, 10, 29, "Input",ExpressionUUID->"94557b52-cc86-4010-b22d-6b74ac4aad03"],
-Cell[1157, 32, 7539, 107, 71, "Input",ExpressionUUID->"872503c3-0779-4b87-805f-13a088f459e3"],
-Cell[8699, 141, 1257, 31, 113, "Input",ExpressionUUID->"02a1f6e5-4144-4552-9463-2a226c1ee186"],
-Cell[9959, 174, 2710, 69, 113, "Input",ExpressionUUID->"d8831e63-87f3-498c-8951-21f347e539ff"],
-Cell[12672, 245, 941, 24, 73, "Input",ExpressionUUID->"04b6d9c8-662b-43f2-955f-87d9d6c7b622"],
-Cell[13616, 271, 915, 20, 50, "Input",ExpressionUUID->"bd6b698e-6871-43fa-9d98-7385cc594c9c"],
-Cell[14534, 293, 752, 17, 47, "Input",ExpressionUUID->"7bddfed2-a761-4c62-bcdc-0460988fbd67"],
+Cell[558, 20, 596, 10, 24, "Input",ExpressionUUID->"94557b52-cc86-4010-b22d-6b74ac4aad03"],
+Cell[1157, 32, 7539, 107, 55, "Input",ExpressionUUID->"872503c3-0779-4b87-805f-13a088f459e3"],
+Cell[8699, 141, 1256, 31, 105, "Input",ExpressionUUID->"02a1f6e5-4144-4552-9463-2a226c1ee186"],
+Cell[9958, 174, 2710, 69, 121, "Input",ExpressionUUID->"d8831e63-87f3-498c-8951-21f347e539ff"],
+Cell[12671, 245, 941, 24, 59, "Input",ExpressionUUID->"04b6d9c8-662b-43f2-955f-87d9d6c7b622"],
+Cell[13615, 271, 915, 20, 40, "Input",ExpressionUUID->"bd6b698e-6871-43fa-9d98-7385cc594c9c"],
+Cell[14533, 293, 752, 17, 38, "Input",ExpressionUUID->"7bddfed2-a761-4c62-bcdc-0460988fbd67"],
+Cell[15288, 312, 494, 12, 22, "Input",ExpressionUUID->"ec8b9383-61d6-44c2-b776-3d651fc19660"],
 Cell[CellGroupData[{
-Cell[15311, 314, 226, 4, 29, "Input",ExpressionUUID->"50295a31-c985-47a1-ab52-8a5871504ed9"],
-Cell[15540, 320, 418, 10, 36, "Output",ExpressionUUID->"bc09ed81-20b7-4e22-a63a-1d663336b1b5"]
+Cell[15807, 328, 943, 23, 41, "Input",ExpressionUUID->"cbeb62aa-7e89-4ec5-a1cb-d5012bac06fd"],
+Cell[16753, 353, 334, 5, 25, "Output",ExpressionUUID->"9ddcc7c6-de02-4d31-9401-bbbc5eefe582"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[15995, 335, 811, 19, 29, "Input",ExpressionUUID->"7efd85be-fd7d-435a-a870-214d8ec4025d"],
-Cell[16809, 356, 649, 13, 22, "Message",ExpressionUUID->"495ad979-d632-478f-8e0f-56a8e4f9987f"],
-Cell[17461, 371, 853, 19, 36, "Output",ExpressionUUID->"2e2d8ac6-c3fd-4636-a145-e07805271602"]
+Cell[17124, 363, 1038, 25, 22, "Input",ExpressionUUID->"7efd85be-fd7d-435a-a870-214d8ec4025d"],
+Cell[18165, 390, 825, 16, 22, "Message",ExpressionUUID->"2e43731b-67a2-4964-9c03-694bb26aa975"],
+Cell[18993, 408, 1025, 22, 26, "Output",ExpressionUUID->"325e2b46-9d64-4724-8091-36718f8f11a2"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[18351, 395, 285, 6, 31, "Input",ExpressionUUID->"111093b6-716a-4bf7-a45a-dac15b888b04"],
-Cell[18639, 403, 371, 8, 35, "Output",ExpressionUUID->"f4db1aaf-ffb6-4069-b376-c6b46e4be074"]
+Cell[20055, 435, 523, 12, 55, "Input",ExpressionUUID->"28731a52-d222-49b4-aebb-262f9a5d4dd5"],
+Cell[20581, 449, 240, 3, 25, "Output",ExpressionUUID->"65626e49-d3af-4115-b5d3-96f63b95604e"],
+Cell[20824, 454, 257, 4, 25, "Output",ExpressionUUID->"fe83a208-ae15-4c69-a7c9-b98329954997"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[19047, 416, 256, 5, 29, "Input",ExpressionUUID->"35006d51-03e9-4e09-8401-8176648f7474"],
-Cell[19306, 423, 154, 2, 33, "Output",ExpressionUUID->"021cf2ad-b5c4-4865-a718-f51958ee0792"]
+Cell[21118, 463, 531, 11, 24, "Input",ExpressionUUID->"f42f7737-f59e-4289-8153-b78626e30f0e"],
+Cell[21652, 476, 583, 11, 25, "Output",ExpressionUUID->"c7c2e58e-e6d9-436b-9cc9-4238f4205a5a"]
 }, Open  ]],
+Cell[22250, 490, 2575, 70, 108, "Input",ExpressionUUID->"275ca4b6-77bf-4727-923f-67c9c37ad46e"],
 Cell[CellGroupData[{
-Cell[19497, 430, 531, 11, 31, "Input",ExpressionUUID->"f42f7737-f59e-4289-8153-b78626e30f0e"],
-Cell[20031, 443, 1212, 31, 36, "Output",ExpressionUUID->"554f67c9-f7db-464a-bb28-41d81dcbec1c"]
+Cell[24850, 564, 2358, 66, 109, "Input",ExpressionUUID->"9e250256-8cd3-402a-bc21-3ee002bb1f82"],
+Cell[27211, 632, 960, 15, 44, "Output",ExpressionUUID->"1690ea78-e2c3-4e83-a9e5-8be735e0bca3"]
 }, Open  ]],
-Cell[21258, 477, 494, 12, 29, "Input",ExpressionUUID->"ec8b9383-61d6-44c2-b776-3d651fc19660"],
 Cell[CellGroupData[{
-Cell[21777, 493, 943, 23, 51, "Input",ExpressionUUID->"cbeb62aa-7e89-4ec5-a1cb-d5012bac06fd"],
-Cell[22723, 518, 334, 5, 33, "Output",ExpressionUUID->"9ddcc7c6-de02-4d31-9401-bbbc5eefe582"]
+Cell[28208, 652, 4388, 128, 156, "Input",ExpressionUUID->"f81ed9c7-d940-4314-963c-c36ea0215ef3"],
+Cell[32599, 782, 1199, 20, 44, "Output",ExpressionUUID->"2234af5e-068b-46a3-beaf-99a907ef5184"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[23094, 528, 812, 20, 50, "Input",ExpressionUUID->"a79b1406-8855-4788-85f8-e01146acbc0b"],
-Cell[23909, 550, 2252, 56, 58, "Output",ExpressionUUID->"5d5e77cf-f1ea-4666-9e43-e8dbd0de9153"]
+Cell[33835, 807, 882, 21, 41, "Input",ExpressionUUID->"dd088f15-420b-4212-8186-b62091ac9d6c"],
+Cell[34720, 830, 435, 6, 25, "Output",ExpressionUUID->"21b5cf8e-7f0a-45f7-ab93-9e8ebe789a07"]
 }, Open  ]],
-Cell[26176, 609, 672, 14, 29, "Input",ExpressionUUID->"4221e07f-e3c2-4004-a825-7339ebc77c40"],
 Cell[CellGroupData[{
-Cell[26873, 627, 855, 23, 32, "Input",ExpressionUUID->"dd088f15-420b-4212-8186-b62091ac9d6c"],
-Cell[27731, 652, 315, 5, 33, "Output",ExpressionUUID->"9a70ffe7-9718-4df2-80c1-4de5b7c7d436"]
+Cell[35192, 841, 1195, 29, 41, "Input",ExpressionUUID->"e7fdb778-fd9a-4c13-95dc-aefbf5b8a29f"],
+Cell[36390, 872, 349, 5, 25, "Output",ExpressionUUID->"a5e80f1a-5f57-4a7a-ad79-17c92282d141"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[28083, 662, 756, 20, 32, "Input",ExpressionUUID->"e7fdb778-fd9a-4c13-95dc-aefbf5b8a29f"],
-Cell[28842, 684, 254, 3, 33, "Output",ExpressionUUID->"01370c9d-9462-41f0-8dcc-9775da2fb959"]
+Cell[36776, 882, 228, 5, 22, "Input",ExpressionUUID->"feb08355-9ad1-4257-9f97-e394177d7e32"],
+Cell[37007, 889, 274, 8, 25, "Output",ExpressionUUID->"87e29f54-9d68-4261-96d4-95d24dcdc36a"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[29133, 692, 1441, 27, 71, "Input",ExpressionUUID->"e61ed118-a102-4290-8440-cba17b87145b"],
-Cell[30577, 721, 10038, 212, 275, "Output",ExpressionUUID->"6cada30c-d260-4892-8f67-49af9e1c1a05"]
+Cell[37318, 902, 1542, 27, 55, "Input",ExpressionUUID->"e61ed118-a102-4290-8440-cba17b87145b"],
+Cell[38863, 931, 12321, 270, 180, "Output",ExpressionUUID->"2e45389f-59c7-4eaf-9b3a-270214fa013e"]
 }, Open  ]],
-Cell[40630, 936, 175, 3, 29, "Input",ExpressionUUID->"0f87aa05-2cc9-472a-ab27-39ee15777442"],
-Cell[40808, 941, 356, 7, 29, "Input",ExpressionUUID->"627c17e0-e2d8-4347-8fe9-812183a42941"],
+Cell[51199, 1204, 175, 3, 22, "Input",ExpressionUUID->"0f87aa05-2cc9-472a-ab27-39ee15777442"],
+Cell[51377, 1209, 356, 7, 24, "Input",ExpressionUUID->"627c17e0-e2d8-4347-8fe9-812183a42941"],
 Cell[CellGroupData[{
-Cell[41189, 952, 176, 2, 29, "Input",ExpressionUUID->"f32c32be-7fcb-4660-bf43-cbc119acda96"],
-Cell[41368, 956, 2097, 65, 58, "Output",ExpressionUUID->"01b48fb7-d8c9-4012-92f6-488cf7e7087c"]
+Cell[51758, 1220, 176, 2, 22, "Input",ExpressionUUID->"f32c32be-7fcb-4660-bf43-cbc119acda96"],
+Cell[51937, 1224, 2097, 65, 61, "Output",ExpressionUUID->"01b48fb7-d8c9-4012-92f6-488cf7e7087c"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[43502, 1026, 860, 24, 32, "Input",ExpressionUUID->"bfa6a31f-5eb9-4063-b798-e45ab1e3b53a"],
-Cell[44365, 1052, 1944, 57, 77, "Output",ExpressionUUID->"0ca79efb-1867-4b1f-96fc-4a691d54b72e"]
+Cell[54071, 1294, 860, 24, 24, "Input",ExpressionUUID->"bfa6a31f-5eb9-4063-b798-e45ab1e3b53a"],
+Cell[54934, 1320, 1944, 57, 60, "Output",ExpressionUUID->"0ca79efb-1867-4b1f-96fc-4a691d54b72e"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[46346, 1114, 2622, 77, 122, "Input",ExpressionUUID->"242aacdf-e4c7-423c-a26a-12188ba2476e"],
-Cell[48971, 1193, 21838, 439, 241, "Output",ExpressionUUID->"073d831e-11a6-4203-90ce-0df429c1a3f0"]
+Cell[56915, 1382, 2622, 77, 93, "Input",ExpressionUUID->"242aacdf-e4c7-423c-a26a-12188ba2476e"],
+Cell[59540, 1461, 21838, 439, 180, "Output",ExpressionUUID->"073d831e-11a6-4203-90ce-0df429c1a3f0"]
 }, Open  ]],
-Cell[70824, 1635, 725, 15, 29, "Input",ExpressionUUID->"80c6c675-eade-40e1-8d0f-13a6578b30ff"],
-Cell[71552, 1652, 764, 21, 29, "Input",ExpressionUUID->"d8847f2e-21fe-4fb7-84ae-676f83acdf5a"],
+Cell[81393, 1903, 725, 15, 24, "Input",ExpressionUUID->"80c6c675-eade-40e1-8d0f-13a6578b30ff"],
+Cell[82121, 1920, 764, 21, 22, "Input",ExpressionUUID->"d8847f2e-21fe-4fb7-84ae-676f83acdf5a"],
 Cell[CellGroupData[{
-Cell[72341, 1677, 679, 17, 50, "Input",ExpressionUUID->"15d60f60-2f87-40da-a2c6-66d640111d75"],
-Cell[73023, 1696, 1298, 32, 36, "Output",ExpressionUUID->"6f1d902a-0431-4a99-adc2-97eb3c423317"]
+Cell[82910, 1945, 679, 17, 40, "Input",ExpressionUUID->"15d60f60-2f87-40da-a2c6-66d640111d75"],
+Cell[83592, 1964, 1298, 32, 44, "Output",ExpressionUUID->"6f1d902a-0431-4a99-adc2-97eb3c423317"]
 }, Open  ]],
 Cell[CellGroupData[{
-Cell[74358, 1733, 736, 18, 71, "Input",ExpressionUUID->"bec4c929-c1a6-4fd0-be18-caf3643ba3a4"],
-Cell[75097, 1753, 14613, 314, 239, "Output",ExpressionUUID->"b48c9c3b-23cc-4864-8ea2-6e98855eb77d"]
+Cell[84927, 2001, 736, 18, 57, "Input",ExpressionUUID->"bec4c929-c1a6-4fd0-be18-caf3643ba3a4"],
+Cell[85666, 2021, 14613, 314, 179, "Output",ExpressionUUID->"b48c9c3b-23cc-4864-8ea2-6e98855eb77d"]
 }, Open  ]]
 }
 ]