From 36c174b5b3ec9a4d5435a27128bc7e1c1fa4f118 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 23 Dec 2020 11:24:29 +0100
Subject: Got the basic matching working!

---
 new_schofield.nb | 7668 +++++++++++++++++++++++++++++++++++++++++++++++++-----
 schofield.wl     |   30 +-
 2 files changed, 7037 insertions(+), 661 deletions(-)

diff --git a/new_schofield.nb b/new_schofield.nb
index 7aafe40..b73ca0d 100644
--- a/new_schofield.nb
+++ b/new_schofield.nb
@@ -10,10 +10,10 @@
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+  AxesLabel->{None, None},
+  AxesOrigin->{0, 0},
+  DisplayFunction->Identity,
+  FrameLabel->{{None, None}, {None, None}},
+  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
+  GridLinesStyle->Directive[
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+  ImagePadding->All,
+  Method->{
+   "DefaultGraphicsInteraction" -> {
+     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
+      "Effects" -> {
+       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
+        "Droplines" -> {
+         "freeformCursorMode" -> True, 
+          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "ScalingFunctions" -> 
+    None},
+  PlotRange->{{-0.9999999658982575, 
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+  PlotRangeClipping->True,
+  PlotRangePadding->{{
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+     Scaled[0.05]}, {
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+     Scaled[0.05]}},
+  Ticks->{Automatic, Automatic}]], "Output",
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+      Axes->{True, True},
+      AxesLabel->{None, None},
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+      FrameLabel->{{None, None}, {None, None}},
+      FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
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diff --git a/schofield.wl b/schofield.wl
index 7597891..0d18848 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -31,31 +31,29 @@ $Assumptions = {θc > 0, θc > 1, gC[_] ∈ Reals, B > 0, γ > 0}
 ]
 
 Δ[D_:2] := β[D] δ[D]
+t[θ_] := (θ)^2 - 1
+h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
 
-f[θ_] := θ^2 - 1
-g[gC_:gC, θc_:θc][n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
+RFf[y_] := π^-1 y Exp[1/y] ExpIntegralEi[-1/y]
+RF[n_][θ_] := A (RFf[B(θc-θ)] + RFf[B(θc+θ)]) + Sum[FC[i] θ^(2i) , {i, 0, n}]
 
-I\[ScriptCapitalM]f[y_] := (1 + 1 / x) Exp[-1/x]
-R\[ScriptCapitalM]f[y_] := (1 - y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)
+ruleB[g_] := π / (2 1.3578383417066) (- g'[θc] / t[θc]^Δ[2])
 
-R\[ScriptCapitalM][2][B_, θc_, M0_][θ_] := - M0 (R\[ScriptCapitalM]f[B(θc - θ)] - R\[ScriptCapitalM]f[B(θc + θ)])
-
-ruleB[2][f_, g_] := π / (2 1.3578383417066) (Δ g[θc] f[θc]^(-Δ[2]-1) f'[θc] - g'[θc] / f[θc]^Δ[2])
-
-eqLow[D_:2][f_, g_][m_] := SeriesCoefficient[
-  R\[ScriptCapitalM][D][B, θc, M0][θ] + f[θ]^β[D] Gl'[g[θ] / f[θ]^Δ[D]],
+eqLow[F_, h_][m_] := SeriesCoefficient[
+  F[θ] - t[θ]^2 (Gl[h[θ] t[θ]^-Δ[2]] + Log[t[θ]^2]/(8 π)),
   {θ, θc, m},
   Assumptions -> Join[$Assumptions, {θ < θc, θ > 1}]
 ]
 
-eqHigh[D_:2][f_, g_][m_] := SeriesCoefficient[
-  R\[ScriptCapitalM][D][B, θc, M0][θ] + (-f[θ])^β[D] Gh'[g[θ] / (-f[θ])^Δ[D]],
+eqHigh[F_, h_][m_] := SeriesCoefficient[
+  F[θ] - (-t[θ])^2 (Gh[h[θ] (-t[θ])^-Δ[2]] + Log[(-t[θ])^2]/(8 π)),
   {θ, 0, m},
   Assumptions -> Join[$Assumptions, {θ > 0, θ < 1}]
 ]
 
-eqMid[D_:2][f_, g_][m_] := SeriesCoefficient[
-  R\[ScriptCapitalM][D][B, θc, M0][θ] + g[θ]^(1/δ[D]) ((2 - α[D]) Φ'[η] - η Φ'[η]) / Δ[D] /. η -> f[θ] / g[θ]^(1 / Δ[D]),
+eqMid[F_, h_][m_] := SeriesCoefficient[
+  F[θ] - t[θ]^2 Log[h[θ]^2]/(8 Δ[2]π) - h[θ]^((2-α[2])/Δ[2]) Φ[η]
+    /. η -> t[θ] / h[θ]^(1 / Δ[2]),
   {θ, 1, m},
   Assumptions -> Join[$Assumptions, {θ > 0, θ < θc}]
 ]
@@ -103,9 +101,9 @@ dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)!
 GlRules = MapIndexed[dRule[Gl], Gls];
 GhRules = MapIndexed[dRule[Gh], Ghs];
 
-rules[f_, g_] := Join[{B -> ruleB[2][f, g]}, ΦRules, GlRules, GhRules]
+rules[g_] := Join[{B -> ruleB[g]}, ΦRules, GlRules, GhRules]
 
-eq[D_:2][f_, g_][m_] := Select[Flatten[{eqLow[D][f, g][#], eqMid[D][f, g][#], eqHigh[D][f, g][#]} & /@ Range[0, m]] /. rules[f, g], # != 0 &]
+eq[F_, g_][m_] := Select[Flatten[{eqLow[F, g][#], eqMid[F, g][#], eqHigh[F, g][#]} & /@ Range[0, m]] /. rules[g], !(# === 0) &]
 
 EndPackage[]
 
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