(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 4.0,
MathReader 4.0, or any compatible application. The data for the notebook 
starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do one of 
the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the 
word CacheID, otherwise Mathematica-compatible applications may try to 
use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
***********************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[    129910,       3932]*)
(*NotebookOutlinePosition[    130887,       3962]*)
(*  CellTagsIndexPosition[    130843,       3958]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell[TextData[StyleBox["Nuclear Matter Paper: CR Equation Checks",
  FontSize->18]], "Title",
  Evaluatable->False,
  TextAlignment->Center,
  AspectRatioFixed->True],

Cell[TextData[{
  StyleBox["Overview:\nIn this notebook, we check equations for the nuclear \
matter perturbative matching paper and generate numbers for the figures.  We \
do cutoff regularization (CR) here.\n\nPlan:\nTry to make the equations and \
solutions as general as possible so that we can expand\n\n",
    Evaluatable->False,
    AspectRatioFixed->True],
  StyleBox["Mathematica",
    Evaluatable->False,
    AspectRatioFixed->True,
    FontSlant->"Italic"],
  StyleBox["  strategy:\n",
    Evaluatable->False,
    AspectRatioFixed->True],
  "Write equations as they appear in the notes, using := to define lhs's.  \
Then the evaluation of the rhs is not performed until the lhs is actually \
used somewhere else. This avoids the mess of having explicit arguments for \
everything.\n",
  StyleBox["\n",
    Evaluatable->False,
    AspectRatioFixed->True]
}], "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell["Clear symbols", "Section",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
In order to avoid interference from symbols defined in other \
notebooks, we first Clear all symbols.  We assume that the relevant symbols \
are in the Global` context.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(Clear["\<Global`*\>"]\)], "Input",
  AspectRatioFixed->True],

Cell["\<\
Suppress spelling warnings (only do this after the notebook is \
debugged!).\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(\(\(\ \)\(Off[General::"\<spell1\>", 
      General::"\<spell\>"]\)\(\ \ \)\)\)], "Input",
  AspectRatioFixed->True]
}, Open  ]],

Cell[CellGroupData[{

Cell["Date", "Section",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(\((date = 
        Date[\(-4\)]; \[IndentingNewLine]Print["\<Notebook run on: \>", 
        date[\([2]\)], "\</\>", date[\([3]\)], "\</\>", 
        date[\([1]\)], "\< at \>", date[\([4]\)], "\<:\>", 
        date[\([5]\)]])\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[\("Notebook run on: \
"\[InvisibleSpace]3\[InvisibleSpace]"/"\[InvisibleSpace]22\[InvisibleSpace]"/\
"\[InvisibleSpace]2000\[InvisibleSpace]" at "\[InvisibleSpace]22\
\[InvisibleSpace]":"\[InvisibleSpace]37\),
      SequenceForm[ 
      "Notebook run on: ", 3, "/", 22, "/", 2000, " at ", 22, ":", 37],
      Editable->False]], "Print"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Define potentials and find free-space constants", "Section",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell["True Potential", "Subsection"],

Cell["\<\
Define the forward matrix element of the separable S-wave \
potential:\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(V0[k_]\  := \ 4\ Pi\ m/M\ \ alpha\ m^2\ /\((k^2 + m^2)\)^2\)], "Input"],

Cell[BoxData[
    \(kcotdel0[k_]\  := \ \(-4\)\ Pi\ /\ \((M\ V0[k])\)\  + \ 
        I0[k]\)], "Input"],

Cell["\<\
Since the potential is separable, we can analytically solve for k \
cot \[Delta].\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(I0[k_]\  := \ \((k^2 - m^2)\)/\((2  m)\)\)], "Input"],

Cell["\<\
Define the forward K matrix.  We should solve this more generally \
using the CR technology so that we can use different potentials, including \
multiple terms.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(Kmat\  = \ \(-4\)\ Pi/M\ \ \ 1/kcotdel0[p]\)], "Input"],

Cell[BoxData[
    \(\(-\(\(4\ \[Pi]\)\/\(M\ \((\(\(-m\^2\) + p\^2\)\/\(2\ m\) - \((m\^2 + p\
\^2)\)\^2\/\(alpha\ m\^3\))\)\)\)\)\)], "Output"]
}, Open  ]],

Cell["Effective range expansion (stops at k^4 here!):", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(s1\  = \ Series[kcotdel0[k], {k, 0, 8}]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\((\(-\(m\/2\)\) - m\/alpha)\), 
        "+", \(\((1\/\(2\ m\) - 2\/\(alpha\ m\))\)\ k\^2\), 
        "-", \(k\^4\/\(alpha\ m\^3\)\), "+", 
        InterpretationBox[\(O[k]\^9\),
          SeriesData[ k, 0, {}, 0, 9, 1]]}],
      SeriesData[ k, 0, {
        Plus[ 
          Times[ 
            Rational[ -1, 2], m], 
          Times[ -1, 
            Power[ alpha, -1], m]], 0, 
        Plus[ 
          Times[ 
            Rational[ 1, 2], 
            Power[ m, -1]], 
          Times[ -2, 
            Power[ alpha, -1], 
            Power[ m, -1]]], 0, 
        Times[ -1, 
          Power[ alpha, -1], 
          Power[ m, -3]]}, 0, 9, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(ERexpansion\  = \ \((Solve[{\(-1\)/as, 1/2\ r0, \ r1}\  == \ 
              CoefficientList[s1, k^2], {as, r0, r1}])\)[\([1]\)]\)], "Input"],

Cell[BoxData[
    \({r0 \[Rule] \(-\(\(4 - alpha\)\/\(alpha\ m\)\)\), 
      r1 \[Rule] \(-\(1\/\(alpha\ m\^3\)\)\), 
      as \[Rule] \(2\ alpha\)\/\(\((2 + alpha)\)\ m\)}\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["CR Potential", "Subsection"],

Cell["Define the forward CR potential:", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(V0cr[
        k_]\  := \ \((C0cr\  + \ C2cr\ k^2\  + \ C4cr\ k^4)\)\ Exp[\(-k^2\)/
            Lambdac^2]\)], "Input"],

Cell["Define integrals needed to solve for the K matrix:", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
CRintegral[p_, n_] := 
  Simplify[Integrate[(k^(3 + 2*n))/
     (p^2 - k^2), {k, 0, Lc}, PrincipalValue -> True, 
    Assumptions -> 
     {Im[p] == 0, p > 0, Re[Lc^2] > 0, n >= 0}],
     Lc>0]\
\>", "Input"],

Cell[CellGroupData[{

Cell["I2cr = FullSimplify[CRintegral[p, 0],{Lc>0,p>0,Lc>p}]", "Input"],

Cell[BoxData[
    \(1\/2\ \((\(-Lc\^2\) + 2\ p\^2\ Log[p] - 
          p\^2\ Log[Lc\^2 - p\^2])\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(FullSimplify[Series[I2cr, {p, 0, 2}], Lc > 0]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(-\(Lc\^2\/2\)\), "+", \(Log[p\/Lc]\ p\^2\), "+", 
        InterpretationBox[\(O[p]\^3\),
          SeriesData[ p, 0, {}, 0, 3, 1]]}],
      SeriesData[ p, 0, {
        Times[ 
          Rational[ -1, 2], 
          Power[ Lc, 2]], 0, 
        Log[ 
          Times[ 
            Power[ Lc, -1], p]]}, 0, 3, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell["I4cr = FullSimplify[CRintegral[p, 1],{Lc>0,p>0,Lc>p}]", "Input"],

Cell[BoxData[
    \(1\/2\ \((\(-Lc\^2\) + 2\ p\^2\ Log[p] - 
          p\^2\ Log[Lc\^2 - p\^2])\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(I6cr = \ 
      FullSimplify[CRintegral[p, 2], {Lc > 0, p > 0, Lc > p}]\)], "Input"],

Cell[BoxData[
    \(1\/4\ \((\(-Lc\^4\) - 2\ Lc\^2\ p\^2 - 
          2\ p\^4\ \((\(-2\)\ Log[p] + Log[Lc\^2 - p\^2])\))\)\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(I8cr = \ 
      FullSimplify[CRintegral[p, 3], {Lc > 0, p > 0, Lc > p}]\)], "Input"],

Cell[BoxData[
    \(I10cr = \ 
      FullSimplify[CRintegral[p, 4], {Lc > 0, p > 0, Lc > p}]\)], "Input"],

Cell[BoxData[
    \(\(betacr\  = \ {\ {\ \ \ C0, \ \ \ \ \ \ C2/2, \ \ \ \ \ \ C4/4 + 
              C4t/4}, \n\t\t\ \ \ \ \ {C2/2, \ \ \ C4/2 - 
              C4t/2, \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ }, \n\t\ \ \ \ \ \ \ \ \ \ \
\ \ \ \ {C4/4 + 
              C4t/4, \ \ \ \ \ \ \ \ 0, \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ \
}\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ }\ ;\)\)], "Input"],

Cell[BoxData[
    \(\(betacr4\  = \ {\ {\ \ \ 0, \ \ \ \ \ \ 0, \ \ \ \ \ \ C4t/
              4}, \n\t\t\ \ \ \ \ {0, \ \ \ \(-C4t\)/
              2, \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ }, \n\t\ \ \ \ \ \ \ \ \ \ \ \ \
\ \ {\(+C4t\)/
              4, \ \ \ \ \ \ \ \ 0, \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ }\
\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ }\ ;\)\)], "Input"],

Cell["Green's function matrix:", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Gmatcr = M/(2*Pi^2)*{{I2cr, I4cr, I6cr }, 
                     {I4cr, I6cr, I8cr },
                     {I6cr, I8cr, I10cr}}; \
\>", "Input"],

Cell[BoxData[
    \(\(gcr\  = \ 
        Exp[\(-p^2\)/\((2  Lc^2)\)]\ \ \ {1, \ p^2\ , p^4\ }\ ;\)\)], "Input"],

Cell["Check the potential:", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(Vmatcr\  = \ Simplify[\ gcr\  . \ betacr\  . gcr\ ]\)], "Input"],

Cell[BoxData[
    \(\[ExponentialE]\^\(-\(p\^2\/Lc\^2\)\)\ \((C0 + C2\ p\^2 + 
          C4\ p\^4)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Vmatcr4\  = \ Simplify[\ gcr\  . \ betacr4\  . gcr\ ]\)], "Input"],

Cell[BoxData[
    \(0\)], "Output"]
}, Open  ]],

Cell["Calculate the K matrix:", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(\(Kmatcr\  = \ 
        gcr . \ \((\ 
            Inverse[\ IdentityMatrix[3]\  - \ betacr\  . \ Gmatcr\ ] . \ 
              betacr\ \ )\)\  . \ gcr\ ;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(Kmatcr4\)\(\ \)\(=\)\(\ \)\(Simplify[
        gcr . \ \((\ 
            Inverse[\ IdentityMatrix[3]\  - \ betacr4\  . \ Gmatcr\ ] . \ 
              betacr4\ \ )\)\  . \ gcr]\)\(\ \)\)\)], "Input"],

Cell[BoxData[
    \(\(-\(\((4\ C4t\^2\ Lc\^3\ M\ \[Pi]\^\(3/2\)\ \((\(-3\)\ C4t\ Lc\^7\ M\ \
\((15\ Lc\^4 - 20\ Lc\^2\ p\^2 + 4\ p\^4)\) + 
                16\ \((105\ Lc\^6 - 90\ Lc\^4\ p\^2 + 36\ Lc\^2\ p\^4 - 
                      8\ p\^6)\)\ \[Pi]\^\(3/2\))\))\)/\((2\ \
\[ExponentialE]\^\(p\^2\/Lc\^2\)\ \((3\ C4t\^3\ Lc\^11\ M\^3\ \((4\ Lc\^4 - 
                        9\ Lc\^2\ p\^2 + 2\ p\^4)\) - 
                  16\ C4t\^2\ Lc\^4\ M\^2\ \((36\ Lc\^6 - 39\ Lc\^4\ p\^2 + 
                        16\ Lc\^2\ p\^4 - 4\ p\^6)\)\ \[Pi]\^\(3/2\) + 
                  32768\ \[Pi]\^\(9/2\))\) + 
            C4t\^2\ Lc\^3\ M\^2\ p\ \@\[Pi]\ \((\(-3\)\ C4t\ Lc\^7\ M\ \((15\ \
Lc\^4 - 20\ Lc\^2\ p\^2 + 4\ p\^4)\) + 
                  16\ \((105\ Lc\^6 - 90\ Lc\^4\ p\^2 + 36\ Lc\^2\ p\^4 - 
                        8\ p\^6)\)\ \[Pi]\^\(3/2\))\)\ Erfi[
                p\/Lc])\)\)\)\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(kcotdelCR[
          k_]\  := \ \(-\((4  Pi/M)\)\)\ \ Series[1/Kmatcr, {p, 0, 4}]\  /. \ 
          p \[Rule] k;\)\)], "Input"],

Cell[BoxData[
    \(\(\(\ \)\(kcotdCR1\  = \ 
        Simplify[\ \(-\((4  Pi/M)\)\)\ \ Series[
                  1/Kmatcr, {p, 0, 0}]\ \  /. \ {C2 -> 0, \ 
                C4 -> \ 0}]\  /. \ p \[Rule] k;\)\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(kcotdCR2\  = \ 
      Simplify[\ \ \(-\((4  Pi/M)\)\)\ \ Series[
                1/Kmatcr, {p, 0, 2}]\  /. \ {\ C4 -> \ 0, 
              C4t \[Rule] 
                0}]\  /. \ \(\(p\)\(\[Rule]\)\(k\)\(\ \)\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(-\(\((8\ \((3\ C4t\^3\ Lc\^15\ M\^3 - 
                    144\ C4t\^2\ Lc\^10\ M\^2\ \[Pi]\^\(3/2\) - 
                    64\ C4t\ Lc\^6\ \((2\ C0 + 
                          3\ C2\ Lc\^2)\)\ M\^2\ \[Pi]\^\(3/2\) + 
                    64\ \((\(-C2\^2\)\ Lc\^6\ M\^2\ \[Pi]\^\(3/2\) + 
                          16\ C2\ Lc\^3\ M\ \[Pi]\^3 + 
                          32\ \[Pi]\^3\ \((C0\ Lc\ M + 
                                4\ \[Pi]\^\(3/2\))\))\))\))\)/\((M\ \@\[Pi]\ \
\((45\ C4t\^3\ Lc\^14\ M\^2 - 1680\ C4t\^2\ Lc\^9\ M\ \[Pi]\^\(3/2\) - 
                    384\ C4t\ Lc\^5\ \((4\ C0 + 
                          5\ C2\ Lc\^2)\)\ M\ \[Pi]\^\(3/2\) + 
                    256\ \((\(-3\)\ C2\^2\ Lc\^5\ M\ \[Pi]\^\(3/2\) + 
                          64\ C0\ \[Pi]\^3)\))\))\)\)\), 
        "+", \(\((8\ \((495\ C4t\^6\ Lc\^29\ M\^5 - 
                  31680\ C4t\^5\ Lc\^24\ M\^4\ \[Pi]\^\(3/2\) + 
                  192\ C4t\^4\ Lc\^19\ M\^3\ \[Pi]\^\(3/2\)\ \((\(-154\)\ C0\ \
Lc\ M - 165\ C2\ Lc\^3\ M + 2700\ \[Pi]\^\(3/2\))\) - 
                  192\ C4t\^3\ Lc\^14\ M\^2\ \[Pi]\^\(3/2\)\ \((77\ C2\^2\ Lc\
\^6\ M\^2 - 6208\ C0\ Lc\ M\ \[Pi]\^\(3/2\) - 
                        4896\ C2\ Lc\^3\ M\ \[Pi]\^\(3/2\) + 
                        4480\ \[Pi]\^3)\) + 
                  16384\ \[Pi]\^3\ \((7\ C2\^4\ Lc\^11\ M\^3 + 
                        112\ C2\^3\ Lc\^8\ M\^2\ \[Pi]\^\(3/2\) - 
                        2048\ C0\ \[Pi]\^3\ \((\(-C0\)\ Lc\ M + 
                              4\ \[Pi]\^\(3/2\))\) + 
                        1024\ C2\ Lc\^2\ \[Pi]\^3\ \((\(-C0\)\ Lc\ M + 
                              8\ \[Pi]\^\(3/2\))\) + 
                        32\ C2\^2\ Lc\^5\ M\ \[Pi]\^\(3/2\)\ \((\(-7\)\ C0\ \
Lc\ M + 52\ \[Pi]\^\(3/2\))\))\) + 
                  8192\ C4t\ Lc\^5\ M\ \[Pi]\^3\ \((\(-896\)\ C0\^2\ Lc\ M\ \
\[Pi]\^\(3/2\) + 8\ C0\ \((7\ C2\^2\ Lc\^6\ M\^2 - 
                              84\ C2\ Lc\^3\ M\ \[Pi]\^\(3/2\) + 
                              320\ \[Pi]\^3)\) + 
                        3\ C2\ Lc\^2\ \((21\ C2\^2\ Lc\^6\ M\^2 + 
                              112\ C2\ Lc\^3\ M\ \[Pi]\^\(3/2\) + 
                              640\ \[Pi]\^3)\))\) + 
                  1024\ C4t\^2\ Lc\^9\ M\ \[Pi]\^3\ \((448\ C0\^2\ Lc\^2\ \
M\^2 + 336\ C0\ Lc\ M\ \((3\ C2\ Lc\^3\ M - 22\ \[Pi]\^\(3/2\))\) + 
                        3\ \((359\ C2\^2\ Lc\^6\ M\^2 + 
                              1392\ C2\ Lc\^3\ M\ \[Pi]\^\(3/2\) + 
                              8320\ \[Pi]\^3)\))\))\)\ k\^2)\)/\((Lc\^2\ M\ \
\@\[Pi]\ \((45\ C4t\^3\ Lc\^14\ M\^2 - 
                    1680\ C4t\^2\ Lc\^9\ M\ \[Pi]\^\(3/2\) - 
                    384\ C4t\ Lc\^5\ \((4\ C0 + 
                          5\ C2\ Lc\^2)\)\ M\ \[Pi]\^\(3/2\) + 
                    256\ \((\(-3\)\ C2\^2\ Lc\^5\ M\ \[Pi]\^\(3/2\) + 
                          64\ C0\ \[Pi]\^3)\))\)^2)\)\), "+", 
        InterpretationBox[\(O[k]\^3\),
          SeriesData[ k, 0, {}, 0, 3, 1]]}],
      SeriesData[ k, 0, {
        Times[ -8, 
          Power[ M, -1], 
          Power[ Pi, 
            Rational[ -1, 2]], 
          Power[ 
            Plus[ 
              Times[ 45, 
                Power[ C4t, 3], 
                Power[ Lc, 14], 
                Power[ M, 2]], 
              Times[ -1680, 
                Power[ C4t, 2], 
                Power[ Lc, 9], M, 
                Power[ Pi, 
                  Rational[ 3, 2]]], 
              Times[ -384, C4t, 
                Power[ Lc, 5], 
                Plus[ 
                  Times[ 4, C0], 
                  Times[ 5, C2, 
                    Power[ Lc, 2]]], M, 
                Power[ Pi, 
                  Rational[ 3, 2]]], 
              Times[ 256, 
                Plus[ 
                  Times[ -3, 
                    Power[ C2, 2], 
                    Power[ Lc, 5], M, 
                    Power[ Pi, 
                      Rational[ 3, 2]]], 
                  Times[ 64, C0, 
                    Power[ Pi, 3]]]]], -1], 
          Plus[ 
            Times[ 3, 
              Power[ C4t, 3], 
              Power[ Lc, 15], 
              Power[ M, 3]], 
            Times[ -144, 
              Power[ C4t, 2], 
              Power[ Lc, 10], 
              Power[ M, 2], 
              Power[ Pi, 
                Rational[ 3, 2]]], 
            Times[ -64, C4t, 
              Power[ Lc, 6], 
              Plus[ 
                Times[ 2, C0], 
                Times[ 3, C2, 
                  Power[ Lc, 2]]], 
              Power[ M, 2], 
              Power[ Pi, 
                Rational[ 3, 2]]], 
            Times[ 64, 
              Plus[ 
                Times[ -1, 
                  Power[ C2, 2], 
                  Power[ Lc, 6], 
                  Power[ M, 2], 
                  Power[ Pi, 
                    Rational[ 3, 2]]], 
                Times[ 16, C2, 
                  Power[ Lc, 3], M, 
                  Power[ Pi, 3]], 
                Times[ 32, 
                  Power[ Pi, 3], 
                  Plus[ 
                    Times[ C0, Lc, M], 
                    Times[ 4, 
                      Power[ Pi, 
                        Rational[ 3, 2]]]]]]]]], 0, 
        Times[ 8, 
          Power[ Lc, -2], 
          Power[ M, -1], 
          Power[ Pi, 
            Rational[ -1, 2]], 
          Power[ 
            Plus[ 
              Times[ 45, 
                Power[ C4t, 3], 
                Power[ Lc, 14], 
                Power[ M, 2]], 
              Times[ -1680, 
                Power[ C4t, 2], 
                Power[ Lc, 9], M, 
                Power[ Pi, 
                  Rational[ 3, 2]]], 
              Times[ -384, C4t, 
                Power[ Lc, 5], 
                Plus[ 
                  Times[ 4, C0], 
                  Times[ 5, C2, 
                    Power[ Lc, 2]]], M, 
                Power[ Pi, 
                  Rational[ 3, 2]]], 
              Times[ 256, 
                Plus[ 
                  Times[ -3, 
                    Power[ C2, 2], 
                    Power[ Lc, 5], M, 
                    Power[ Pi, 
                      Rational[ 3, 2]]], 
                  Times[ 64, C0, 
                    Power[ Pi, 3]]]]], -2], 
          Plus[ 
            Times[ 495, 
              Power[ C4t, 6], 
              Power[ Lc, 29], 
              Power[ M, 5]], 
            Times[ -31680, 
              Power[ C4t, 5], 
              Power[ Lc, 24], 
              Power[ M, 4], 
              Power[ Pi, 
                Rational[ 3, 2]]], 
            Times[ 192, 
              Power[ C4t, 4], 
              Power[ Lc, 19], 
              Power[ M, 3], 
              Power[ Pi, 
                Rational[ 3, 2]], 
              Plus[ 
                Times[ -154, C0, Lc, M], 
                Times[ -165, C2, 
                  Power[ Lc, 3], M], 
                Times[ 2700, 
                  Power[ Pi, 
                    Rational[ 3, 2]]]]], 
            Times[ -192, 
              Power[ C4t, 3], 
              Power[ Lc, 14], 
              Power[ M, 2], 
              Power[ Pi, 
                Rational[ 3, 2]], 
              Plus[ 
                Times[ 77, 
                  Power[ C2, 2], 
                  Power[ Lc, 6], 
                  Power[ M, 2]], 
                Times[ -6208, C0, Lc, M, 
                  Power[ Pi, 
                    Rational[ 3, 2]]], 
                Times[ -4896, C2, 
                  Power[ Lc, 3], M, 
                  Power[ Pi, 
                    Rational[ 3, 2]]], 
                Times[ 4480, 
                  Power[ Pi, 3]]]], 
            Times[ 16384, 
              Power[ Pi, 3], 
              Plus[ 
                Times[ 7, 
                  Power[ C2, 4], 
                  Power[ Lc, 11], 
                  Power[ M, 3]], 
                Times[ 112, 
                  Power[ C2, 3], 
                  Power[ Lc, 8], 
                  Power[ M, 2], 
                  Power[ Pi, 
                    Rational[ 3, 2]]], 
                Times[ -2048, C0, 
                  Power[ Pi, 3], 
                  Plus[ 
                    Times[ -1, C0, Lc, M], 
                    Times[ 4, 
                      Power[ Pi, 
                        Rational[ 3, 2]]]]], 
                Times[ 1024, C2, 
                  Power[ Lc, 2], 
                  Power[ Pi, 3], 
                  Plus[ 
                    Times[ -1, C0, Lc, M], 
                    Times[ 8, 
                      Power[ Pi, 
                        Rational[ 3, 2]]]]], 
                Times[ 32, 
                  Power[ C2, 2], 
                  Power[ Lc, 5], M, 
                  Power[ Pi, 
                    Rational[ 3, 2]], 
                  Plus[ 
                    Times[ -7, C0, Lc, M], 
                    Times[ 52, 
                      Power[ Pi, 
                        Rational[ 3, 2]]]]]]], 
            Times[ 8192, C4t, 
              Power[ Lc, 5], M, 
              Power[ Pi, 3], 
              Plus[ 
                Times[ -896, 
                  Power[ C0, 2], Lc, M, 
                  Power[ Pi, 
                    Rational[ 3, 2]]], 
                Times[ 8, C0, 
                  Plus[ 
                    Times[ 7, 
                      Power[ C2, 2], 
                      Power[ Lc, 6], 
                      Power[ M, 2]], 
                    Times[ -84, C2, 
                      Power[ Lc, 3], M, 
                      Power[ Pi, 
                        Rational[ 3, 2]]], 
                    Times[ 320, 
                      Power[ Pi, 3]]]], 
                Times[ 3, C2, 
                  Power[ Lc, 2], 
                  Plus[ 
                    Times[ 21, 
                      Power[ C2, 2], 
                      Power[ Lc, 6], 
                      Power[ M, 2]], 
                    Times[ 112, C2, 
                      Power[ Lc, 3], M, 
                      Power[ Pi, 
                        Rational[ 3, 2]]], 
                    Times[ 640, 
                      Power[ Pi, 3]]]]]], 
            Times[ 1024, 
              Power[ C4t, 2], 
              Power[ Lc, 9], M, 
              Power[ Pi, 3], 
              Plus[ 
                Times[ 448, 
                  Power[ C0, 2], 
                  Power[ Lc, 2], 
                  Power[ M, 2]], 
                Times[ 336, C0, Lc, M, 
                  Plus[ 
                    Times[ 3, C2, 
                      Power[ Lc, 3], M], 
                    Times[ -22, 
                      Power[ Pi, 
                        Rational[ 3, 2]]]]], 
                Times[ 3, 
                  Plus[ 
                    Times[ 359, 
                      Power[ C2, 2], 
                      Power[ Lc, 6], 
                      Power[ M, 2]], 
                    Times[ 1392, C2, 
                      Power[ Lc, 3], M, 
                      Power[ Pi, 
                        Rational[ 3, 2]]], 
                    Times[ 8320, 
                      Power[ Pi, 3]]]]]]]]}, 0, 3, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(kcotdCR3\  = \ 
      Simplify[\ \ \(-\((4  Pi/M)\)\)\ \ Series[1/Kmatcr, {p, 0, 4}]\  /. \ 
          p \[Rule] k\ ]\)], "Input"],

Cell[BoxData[
    \($Aborted\)], "Output"]
}, Open  ]],

Cell["With one constant we can solve for it directly:", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(a1cr\  = \ \(Simplify[\ 
          Solve[s1 \[Equal] kcotdCR1, {C0}]]\)[\([1]\)]\)], "Input"],

Cell[BoxData[
    \({C0 \[Rule] \(8\ alpha\ \[Pi]\^\(3/2\)\)\/\(\(-2\)\ alpha\ Lc\ M + 2\ m\
\ M\ \@\[Pi] + alpha\ m\ M\ \@\[Pi]\)}\)], "Output"]
}, Open  ]],

Cell["Too hard for two or three constants.", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \( (*\ a2cr\  = \ \(Simplify[\ 
            Solve[s1 \[Equal] kcotdCR2, {C2}]]\)[\([1]\)]\ \ *) \)], "Input"],

Cell[BoxData[
    \( (*\ a3cr\  = \ \(Simplify[
            Solve[s1 \[Equal] kcotdCR3, {C0, C2, 
                C4}]]\)[\([1]\)]\ \ *) \)], "Input"],

Cell[BoxData[
    \( (*\ {C00cr, C01cr, C02cr}\  = \ 
        CoefficientList[\ Simplify[Series[C0 /. a1cr, {alpha, 0, 2}]], \ 
          alpha]\ *) \)], "Input"],

Cell["\<\
Expand V + VGV out to p^0 for both the true and CR \
potentials:\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(\(\(\ \)\(vgv1\  = 
        Simplify[
          Series[Series[
                Kmat, {alpha, 0, 
                  2}]\ , \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {p, 0, 0}\ ]\  /. \ 
            p \[Rule] k];\)\)\)], "Input"],

Cell[BoxData[
    \(\(\(\ \)\(vgvCR1\  = \ \ Simplify[
          Series[Series[
                Kmatcr /. {C0 \[Rule] C01cr\ alpha\  + \ C02cr\ alpha^2, 
                    C2 -> 0, \ C4 -> \ 0}, {alpha, 0, 
                  2}]\ , \[IndentingNewLine]{p, 0, 0}\ ]\  /. \ 
            p \[Rule] k];\)\)\)], "Input"],

Cell["\<\
Solve for the CR constants C01 and C02:\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(w1cr\  = \ \(ExpandAll[
          Simplify[\ 
            Solve[vgv1 \[Equal] vgvCR1, {C01cr, 
                C02cr}]]]\)[\([1]\)]\)], "Input"],

Cell[BoxData[
    \({C02cr \[Rule] \(4\ Lc\ \@\[Pi]\)\/\(m\^2\ M\) - \(2\ \[Pi]\)\/\(m\ \
M\), C01cr \[Rule] \(4\ \[Pi]\)\/\(m\ M\)}\)], "Output"]
}, Open  ]],

Cell["\<\
Check that V + VGV out to p^0 agree for the true and CR potentials:\
\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[vgv1\  - \ vgvCR1\  /. \ w1cr]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          InterpretationBox[\(O[k]\^1\),
            SeriesData[ k, 0, {}, 1, 1, 1]], " ", "alpha"}], "+", 
        RowBox[{
          InterpretationBox[\(O[k]\^1\),
            SeriesData[ k, 0, {}, 1, 1, 1]], " ", \(alpha\^2\)}], "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {}, 1, 1, 1], 
        SeriesData[ k, 0, {}, 1, 1, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(\ \)\(vgv2\  = 
        Simplify[
          Series[Series[Kmat, {alpha, 0, 2}]\ , \[IndentingNewLine]{p, 0, 
                2}\ ]\  /. \ p \[Rule] k];\)\)\)], "Input"],

Cell[BoxData[
    \(\(vgv2tot\  = \ 
        4\ Pi/M\ \((\ 
            alpha\ m^3/\((k^2 + m^2)\)^2\  + \ 
              alpha^2\ m^6/\((k^2 + 
                        m^2)\)^4\ \((\((k^2 - m^2)\)/\((2  m)\)\  - \ 
                    I\ k)\))\);\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Series[Series[vgv2tot - vgv2, {alpha, 0, 2}], {k, 0, 3}]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          InterpretationBox[\(O[k]\^3\),
            SeriesData[ k, 0, {}, 3, 3, 1]], " ", "alpha"}], "+", 
        RowBox[{
          RowBox[{"(", 
            InterpretationBox[
              
              RowBox[{\(-\(\(4\ \[ImaginaryI]\ \[Pi]\ k\)\/\(m\^2\ M\)\)\), 
                "+", 
                InterpretationBox[\(O[k]\^3\),
                  SeriesData[ k, 0, {}, 1, 3, 1]]}],
              SeriesData[ k, 0, {
                Times[ 
                  Complex[ 0, -4], 
                  Power[ m, -2], 
                  Power[ M, -1], Pi]}, 1, 3, 1]], ")"}], " ", \(alpha\^2\)}], 
        "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {}, 3, 3, 1], 
        SeriesData[ k, 0, {
          Times[ 
            Complex[ 0, -4], 
            Power[ m, -2], 
            Power[ M, -1], Pi]}, 1, 3, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(\ \)\(vgvCR2\  = \ \ Simplify[
          Series[Series[
                Kmatcr /. {C0 \[Rule] C01cr\ alpha\  + \ C02cr\ alpha^2, 
                    C2 \[Rule] C21cr\ alpha\  + \ C22cr\ alpha^2, \ 
                    C4 -> \ 0, \ C4t \[Rule] 0}, {alpha, 0, 
                  2}]\ , \[IndentingNewLine]{p, 0, 2}\ ]\  /. \ 
            p \[Rule] k];\)\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ExpandAll[
      Simplify[\(\(\(\((vgv2 - vgvCR2)\)/\((4\ Pi/\((m\ M)\))\)\)/\((k/
                      m)\)^2\  /. \ w1cr\)\  /. \ {C21cr \[Rule] 0, 
              C22cr \[Rule] 0}\) /. \ Lc \[Rule] Lambdac]]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          RowBox[{"(", 
            InterpretationBox[
              RowBox[{\((\(-2\) + m\^2\/Lambdac\^2)\), "+", 
                InterpretationBox[\(O[k]\^1\),
                  SeriesData[ k, 0, {}, 0, 1, 1]]}],
              SeriesData[ k, 0, {
                Plus[ -2, 
                  Times[ 
                    Power[ Lambdac, -2], 
                    Power[ m, 2]]]}, 0, 1, 1]], ")"}], " ", "alpha"}], "+", 
        RowBox[{
          RowBox[{"(", 
            InterpretationBox[
              
              RowBox[{\((5\/2 - 
                    m\^2\/\(2\ Lambdac\^2\) - \(2\ m\)\/\(Lambdac\ \@\[Pi]\))\
\), "+", 
                InterpretationBox[\(O[k]\^1\),
                  SeriesData[ k, 0, {}, 0, 1, 1]]}],
              SeriesData[ k, 0, {
                Plus[ 
                  Rational[ 5, 2], 
                  Times[ 
                    Rational[ -1, 2], 
                    Power[ Lambdac, -2], 
                    Power[ m, 2]], 
                  Times[ -2, 
                    Power[ Lambdac, -1], m, 
                    Power[ Pi, 
                      Rational[ -1, 2]]]]}, 0, 1, 1]], ")"}], 
          " ", \(alpha\^2\)}], "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {
          Plus[ -2, 
            Times[ 
              Power[ Lambdac, -2], 
              Power[ m, 2]]]}, 0, 1, 1], 
        SeriesData[ k, 0, {
          Plus[ 
            Rational[ 5, 2], 
            Times[ 
              Rational[ -1, 2], 
              Power[ Lambdac, -2], 
              Power[ m, 2]], 
            Times[ -2, 
              Power[ Lambdac, -1], m, 
              Power[ Pi, 
                Rational[ -1, 2]]]]}, 0, 1, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(w2cr\  = \ \(ExpandAll[
          Simplify[\ 
            Solve[vgv2 \[Equal] vgvCR2, {C01cr, C21cr, C02cr, 
                C22cr}]]]\)[\([1]\)]\)], "Input"],

Cell[BoxData[
    \({C22cr \[Rule] \(6\ Lc\^3\ \@\[Pi]\)\/\(m\^6\ M\) - \(22\ Lc\ \@\[Pi]\)\
\/\(m\^4\ M\) + \(3\ \@\[Pi]\)\/\(2\ Lc\ m\^2\ M\) + \(10\ \[Pi]\)\/\(m\^3\ M\
\) - \(2\ \[Pi]\)\/\(Lc\^2\ m\ M\), 
      C02cr \[Rule] \(3\ Lc\^5\ \@\[Pi]\)\/\(m\^6\ M\) - \(7\ Lc\^3\ \
\@\[Pi]\)\/\(m\^4\ M\) + \(27\ Lc\ \@\[Pi]\)\/\(4\ m\^2\ M\) - \(2\ \[Pi]\)\/\
\(m\ M\), C01cr \[Rule] \(4\ \[Pi]\)\/\(m\ M\), 
      C21cr \[Rule] \(-\(\(8\ \[Pi]\)\/\(m\^3\ M\)\)\) + \(4\ \
\[Pi]\)\/\(Lc\^2\ m\ M\)}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[vgv2\  - \ vgvCR2\  /. \ w2cr]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          InterpretationBox[\(O[k]\^3\),
            SeriesData[ k, 0, {}, 3, 3, 1]], " ", "alpha"}], "+", 
        RowBox[{
          InterpretationBox[\(O[k]\^3\),
            SeriesData[ k, 0, {}, 3, 3, 1]], " ", \(alpha\^2\)}], "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {}, 3, 3, 1], 
        SeriesData[ k, 0, {}, 3, 3, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(\ \)\(vgv3\  = 
        Simplify[
          Series[Series[Kmat, {alpha, 0, 2}]\ , \[IndentingNewLine]{p, 0, 
                4}\ ]\  /. \ p \[Rule] k];\)\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Series[Series[vgv2tot - vgv3, {alpha, 0, 2}], {k, 0, 4}]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          InterpretationBox[\(O[k]\^5\),
            SeriesData[ k, 0, {}, 5, 5, 1]], " ", "alpha"}], "+", 
        RowBox[{
          RowBox[{"(", 
            InterpretationBox[
              
              RowBox[{\(-\(\(4\ \[ImaginaryI]\ \[Pi]\ k\)\/\(m\^2\ M\)\)\), 
                "+", \(\(16\ \[ImaginaryI]\ \[Pi]\ k\^3\)\/\(m\^4\ M\)\), "+",
                 
                InterpretationBox[\(O[k]\^5\),
                  SeriesData[ k, 0, {}, 1, 5, 1]]}],
              SeriesData[ k, 0, {
                Times[ 
                  Complex[ 0, -4], 
                  Power[ m, -2], 
                  Power[ M, -1], Pi], 0, 
                Times[ 
                  Complex[ 0, 16], 
                  Power[ m, -4], 
                  Power[ M, -1], Pi]}, 1, 5, 1]], ")"}], " ", \(alpha\^2\)}], 
        "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {}, 5, 5, 1], 
        SeriesData[ k, 0, {
          Times[ 
            Complex[ 0, -4], 
            Power[ m, -2], 
            Power[ M, -1], Pi], 0, 
          Times[ 
            Complex[ 0, 16], 
            Power[ m, -4], 
            Power[ M, -1], Pi]}, 1, 5, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(\ \)\(vgvCR3\  = \ \ Simplify[
          Series[Series[
                Kmatcr /. {C0 \[Rule] C01cr\ alpha\  + \ C02cr\ alpha^2, 
                    C2 \[Rule] C21cr\ alpha\  + \ C22cr\ alpha^2, \ 
                    C4 -> \ C41cr\ alpha\  + \ C42cr\ alpha^2}, {alpha, 0, 
                  2}]\ , \[IndentingNewLine]{p, 0, 4}\ ]\  /. \ 
            p \[Rule] k];\)\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ExpandAll[
      Simplify[\(\(\(\((vgv3 - vgvCR3)\)/\((4\ Pi/\((m\ M)\))\)\)/\((k/
                      m)\)^4\  /. \ w2cr\)\  /. \ {C41cr \[Rule] 0, 
              C42cr \[Rule] 0}\) /. \ Lc \[Rule] Lambdac]]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          RowBox[{"(", 
            InterpretationBox[
              
              RowBox[{\((3 - \(2\ m\^2\)\/Lambdac\^2 + 
                    m\^4\/\(2\ Lambdac\^4\))\), "+", 
                InterpretationBox[\(O[k]\^1\),
                  SeriesData[ k, 0, {}, 0, 1, 1]]}],
              SeriesData[ k, 0, {
                Plus[ 3, 
                  Times[ -2, 
                    Power[ Lambdac, -2], 
                    Power[ m, 2]], 
                  Times[ 
                    Rational[ 1, 2], 
                    Power[ Lambdac, -4], 
                    Power[ m, 4]]]}, 0, 1, 1]], ")"}], " ", "alpha"}], "+", 
        RowBox[{
          RowBox[{"(", 
            InterpretationBox[
              
              RowBox[{\((\(-7\) + \(5\ m\^2\)\/\(2\ Lambdac\^2\) - 
                    m\^4\/\(4\ Lambdac\^4\) + \(4\ Lambdac\)\/\(m\ \@\[Pi]\) \
+ \(4\ m\)\/\(Lambdac\ \@\[Pi]\) - \(5\ m\^3\)\/\(3\ Lambdac\^3\ \@\[Pi]\))\),
                 "+", 
                InterpretationBox[\(O[k]\^1\),
                  SeriesData[ k, 0, {}, 0, 1, 1]]}],
              SeriesData[ k, 0, {
                Plus[ -7, 
                  Times[ 
                    Rational[ 5, 2], 
                    Power[ Lambdac, -2], 
                    Power[ m, 2]], 
                  Times[ 
                    Rational[ -1, 4], 
                    Power[ Lambdac, -4], 
                    Power[ m, 4]], 
                  Times[ 4, Lambdac, 
                    Power[ m, -1], 
                    Power[ Pi, 
                      Rational[ -1, 2]]], 
                  Times[ 4, 
                    Power[ Lambdac, -1], m, 
                    Power[ Pi, 
                      Rational[ -1, 2]]], 
                  Times[ 
                    Rational[ -5, 3], 
                    Power[ Lambdac, -3], 
                    Power[ m, 3], 
                    Power[ Pi, 
                      Rational[ -1, 2]]]]}, 0, 1, 1]], ")"}], 
          " ", \(alpha\^2\)}], "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {
          Plus[ 3, 
            Times[ -2, 
              Power[ Lambdac, -2], 
              Power[ m, 2]], 
            Times[ 
              Rational[ 1, 2], 
              Power[ Lambdac, -4], 
              Power[ m, 4]]]}, 0, 1, 1], 
        SeriesData[ k, 0, {
          Plus[ -7, 
            Times[ 
              Rational[ 5, 2], 
              Power[ Lambdac, -2], 
              Power[ m, 2]], 
            Times[ 
              Rational[ -1, 4], 
              Power[ Lambdac, -4], 
              Power[ m, 4]], 
            Times[ 4, Lambdac, 
              Power[ m, -1], 
              Power[ Pi, 
                Rational[ -1, 2]]], 
            Times[ 4, 
              Power[ Lambdac, -1], m, 
              Power[ Pi, 
                Rational[ -1, 2]]], 
            Times[ 
              Rational[ -5, 3], 
              Power[ Lambdac, -3], 
              Power[ m, 3], 
              Power[ Pi, 
                Rational[ -1, 2]]]]}, 0, 1, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(w3cr\  = \ \(ExpandAll[
          Simplify[\ 
            Solve[vgv3 \[Equal] vgvCR3, {C01cr, C21cr, C41cr, C02cr, C22cr, 
                C42cr}]]]\)[\([1]\)]\)], "Input"],

Cell[BoxData[
    \({C42cr \[Rule] \(297\ Lc\^5\ \@\[Pi]\)\/\(16\ m\^10\ M\) - \(183\ Lc\^3\
\ \@\[Pi]\)\/\(4\ m\^8\ M\) + \(1263\ Lc\ \@\[Pi]\)\/\(16\ m\^6\ M\) - \(117\ \
\@\[Pi]\)\/\(8\ Lc\ m\^4\ M\) - \(77\ \@\[Pi]\)\/\(192\ Lc\^3\ m\^2\ M\) - \
\(28\ \[Pi]\)\/\(m\^5\ M\) + \(10\ \[Pi]\)\/\(Lc\^2\ m\^3\ M\) - \
\[Pi]\/\(Lc\^4\ m\ M\), 
      C22cr \[Rule] \(675\ Lc\^7\ \@\[Pi]\)\/\(32\ m\^10\ M\) - \(369\ Lc\^5\ \
\@\[Pi]\)\/\(8\ m\^8\ M\) + \(1677\ Lc\^3\ \@\[Pi]\)\/\(32\ m\^6\ M\) - \(667\
\ Lc\ \@\[Pi]\)\/\(16\ m\^4\ M\) + \(651\ \@\[Pi]\)\/\(128\ Lc\ m\^2\ M\) + \
\(10\ \[Pi]\)\/\(m\^3\ M\) - \(2\ \[Pi]\)\/\(Lc\^2\ m\ M\), 
      C02cr \[Rule] \(945\ Lc\^9\ \@\[Pi]\)\/\(64\ m\^10\ M\) - \(495\ Lc\^7\ \
\@\[Pi]\)\/\(16\ m\^8\ M\) + \(2055\ Lc\^5\ \@\[Pi]\)\/\(64\ m\^6\ M\) - \
\(605\ Lc\^3\ \@\[Pi]\)\/\(32\ m\^4\ M\) + \(2265\ Lc\ \@\[Pi]\)\/\(256\ m\^2\
\ M\) - \(2\ \[Pi]\)\/\(m\ M\), C01cr \[Rule] \(4\ \[Pi]\)\/\(m\ M\), 
      C21cr \[Rule] \(-\(\(8\ \[Pi]\)\/\(m\^3\ M\)\)\) + \(4\ \
\[Pi]\)\/\(Lc\^2\ m\ M\), 
      C41cr \[Rule] \(12\ \[Pi]\)\/\(m\^5\ M\) - \(8\ \[Pi]\)\/\(Lc\^2\ m\^3\ \
M\) + \(2\ \[Pi]\)\/\(Lc\^4\ m\ M\)}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[vgv3\  - \ vgvCR3\  /. \ w3cr]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{
        RowBox[{
          InterpretationBox[\(O[k]\^5\),
            SeriesData[ k, 0, {}, 5, 5, 1]], " ", "alpha"}], "+", 
        RowBox[{
          InterpretationBox[\(O[k]\^5\),
            SeriesData[ k, 0, {}, 5, 5, 1]], " ", \(alpha\^2\)}], "+", 
        InterpretationBox[\(O[alpha]\^3\),
          SeriesData[ alpha, 0, {}, 1, 3, 1]]}],
      SeriesData[ alpha, 0, {
        SeriesData[ k, 0, {}, 5, 5, 1], 
        SeriesData[ k, 0, {}, 5, 5, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(C01crt\  = \ 4\ Pi/\((M\ m)\);\)\)], "Input"],

Cell[BoxData[
    \(\(C02crt\ \  = \ \(-4\)\ Pi/\((M\ m)\)\ \((1/2\  - \ 
              1/Sqrt[Pi]\ Lambdac/m)\);\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(C01crt\  - \ C01cr /. w1cr\)], "Input"],

Cell[BoxData[
    \(0\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(C02crt\  - \ C02cr /. w1cr\)\  /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    \(0\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(C21crt\  = \ \(-2\)/m^4\ 4\ Pi\ m/M\  + \ 
          C01crt/Lambdac^2;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(delC02crt\  = \ 
      Simplify[M/\((4\ Pi)\)\ Lambdac^3/
            Sqrt[Pi]\ *\ \((C01crt\ C21crt/2\  + \ 
              3/16\ C21crt^2\ Lambdac^2)\)]\)], "Input"],

Cell[BoxData[
    \(\(Lambdac\ \((12\ Lambdac\^4 - 28\ Lambdac\^2\ m\^2 + 11\ m\^4)\)\ \@\
\[Pi]\)\/\(4\ m\^6\ M\)\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(C22crt\  = \ 
        4  Pi/\((m\ M)\) \((5/\((2\ m^2)\))\)\  + \ 
          2\ M\ C01crt\ C21crt/\((4\ Pi)\)\ \((3\ Lambdac/\((4\ Sqrt[
                        Pi])\)\ )\)\  + \[IndentingNewLine]M\ C01crt^2/\((4\ \
Pi)\)\ \((\(-\ 3\)/\((Sqrt[
                      Pi]\ Lambdac)\))\)\  + \[IndentingNewLine]M\ \
C21crt^2/\((4\ Pi)\)\ 3\ Lambdac^3/\((16\ Sqrt[Pi])\)\  + \ \((C02crt + \ 
                delC02crt)\)/Lambdac^2;\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(delC02cr\  = \ 
      Simplify[\(C02cr\  - \ C02crt\  /. \ w2cr\)\  /. \ 
          Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    \(\(Lambdac\ \((12\ Lambdac\^4 - 28\ Lambdac\^2\ m\^2 + 11\ m\^4)\)\ \@\
\[Pi]\)\/\(4\ m\^6\ M\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(delC02crb\  = \ 
      Simplify[\((C02cr /. \ w2cr\ )\) - \ \((C02cr\  /. \ w1cr)\)\  /. \ 
          Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    \(\(Lambdac\ \((12\ Lambdac\^4 - 28\ Lambdac\^2\ m\^2 + 11\ m\^4)\)\ \@\
\[Pi]\)\/\(4\ m\^6\ M\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(C02crt + delC02crt\  - \ C02cr /. w2cr\)\  /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    \(0\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(C21crt\  - \ C21cr /. w2cr\)\  /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    \(0\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(C22crt\  - \ C22cr /. w2cr\)\  /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    \(0\)], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Free Space Error Plots", "Section",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(<< Graphics`\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(vgvtrue = \ 
      Simplify[Normal[Series[Kmat, {alpha, 0, 2}]]] /. p \[Rule] k\)], "Input"],

Cell[BoxData[
    \(\(2\ alpha\ m\^3\ \((2\ k\^4 + \((4 + alpha)\)\ k\^2\ m\^2 - \((\(-2\) \
+ alpha)\)\ m\^4)\)\ \[Pi]\)\/\(\((k\^2 + m\^2)\)\^4\ M\)\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(\ \)\(vgvCRtot1 = \ \ Simplify[
          Normal[\(Series[
                  Kmatcr /. {C0 \[Rule] C01cr\ alpha\  + \ C02cr\ alpha^2, 
                      C2 \[Rule] 0, \ C4 -> \ 0}, {alpha, 0, 2}]\ \  /. \ 
                w1cr\) /. \ p \[Rule] k]];\)\)\)], "Input"],

Cell[BoxData[""], "Input"],

Cell[BoxData[
    \(\(\(\ \)\(vgvCRtot2 = \ \ Simplify[
          Normal[\(Series[
                  Kmatcr /. {C0 \[Rule] C01cr\ alpha\  + \ C02cr\ alpha^2, 
                      C2 \[Rule] C21cr\ alpha\  + \ C22cr\ alpha^2, \ 
                      C4 -> \ 0}, {alpha, 0, 2}]\ \  /. \ w2cr\) /. \ 
              p \[Rule] k]];\)\)\)], "Input"],

Cell[BoxData[
    \(\(\(\ \)\(vgvCRtot3\  = \ \ Simplify[
          Normal[\(Series[
                  Kmatcr /. {C0 \[Rule] C01cr\ alpha\  + \ C02cr\ alpha^2, 
                      C2 \[Rule] C21cr\ alpha\  + \ C22cr\ alpha^2, \ 
                      C4 -> \ C41cr\ alpha\  + \ C42cr\ alpha^2}, {alpha, 0, 
                    2}]\ \  /. \ w3cr\) /. \ p \[Rule] k]];\)\)\)], "Input"],

Cell[BoxData[
    \(\(parameters\  = \ {alpha \[Rule] \(- .5\), \ m \[Rule] 600, \ 
          M \[Rule] 940, \ mu \[Rule] 600, \ g \[Rule] 4, \ 
          Lambdac \[Rule] 600, \ Lc \[Rule] 600};\)\)], "Input"],

Cell[BoxData[
    \(ximin\  = \  .001; \ \ ximax\  = \ 2; \ \ delxi\  = \ 1.2;\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(vgvtrue\  /. \ k \[Rule] m\ xi\)\  /. \ parameters\)], "Input"],

Cell[BoxData[
    \(\(-\(\(721897.8863568036`\ \((3.24`*^11 + 4.536`*^11\ xi\^2 + 
                259200000000\ xi\^4)\)\)\/\((360000 + 360000\ xi\^2)\)\^4\)\)\
\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(xip[i_]\  := \ ximin\ delxi^i\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(LogLogPlot[{Evaluate[\(Abs[vgvtrue - vgvCRtot1]*10^6 /. \ 
              k \[Rule] m\ xi\) /. \ 
            parameters], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ Evaluate[\(Abs[vgvtrue - vgvCRtot2]*10^6 /. \ 
              k \[Rule] m\ xi\)\  /. \ 
            parameters], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ Evaluate[\(Abs[vgvtrue - vgvCRtot3]*10^6 /. \ 
              k \[Rule] m\ xi\)\  /. \ 
            parameters]\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ }, \[IndentingNewLine]{xi,  .001, 
        2}, \[IndentingNewLine]PlotRange \[Rule] {{ .001, 
            1. }, {10^\((\(-8\))\), 10}}, 
      PlotStyle \[Rule] {Thickness[ .0015], GrayLevel[0]}]\)], "Input"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .61803 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10  scalefont  setfont
% Scaling calculations
1 0.333333 0.549364 0.0686704 [
[.23299 -0.0125 -17 -9.8125 ]
[.23299 -0.0125 17 0 ]
[.33333 -0.0125 -14 -9.8125 ]
[.33333 -0.0125 14 0 ]
[.56632 -0.0125 -14 -9.8125 ]
[.56632 -0.0125 14 0 ]
[.66667 -0.0125 -11 -9.8125 ]
[.66667 -0.0125 11 0 ]
[.89966 -0.0125 -11 -9.8125 ]
[.89966 -0.0125 11 0 ]
[1 -0.0125 -5 -9.8125 ]
[1 -0.0125 5 0 ]
[-0.0125 .13734 -47.1875 -6.0625 ]
[-0.0125 .13734 0 6.0625 ]
[-0.0125 .27468 -40 -4.90625 ]
[-0.0125 .27468 0 4.90625 ]
[-0.0125 .41202 -28 -4.90625 ]
[-0.0125 .41202 0 4.90625 ]
[-0.0125 .54936 -10 -4.90625 ]
[-0.0125 .54936 0 4.90625 ]
[ -0.0005 -0.0005 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.23299 0 m
.23299 .00625 L
s
gsave
.23299 -0.0125 -78 -13.8125 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.005) show
93.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.33333 0 m
.33333 .00625 L
s
gsave
.33333 -0.0125 -75 -13.8125 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.01) show
87.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.56632 0 m
.56632 .00625 L
s
gsave
.56632 -0.0125 -75 -13.8125 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.05) show
87.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.66667 0 m
.66667 .00625 L
s
gsave
.66667 -0.0125 -72 -13.8125 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.1) show
81.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.89966 0 m
.89966 .00625 L
s
gsave
.89966 -0.0125 -72 -13.8125 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.5) show
81.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
1 0 m
1 .00625 L
s
gsave
1 -0.0125 -66 -13.8125 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
69.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.001 w
.10034 0 m
.10034 .00375 L
s
.15904 0 m
.15904 .00375 L
s
.20069 0 m
.20069 .00375 L
s
.25938 0 m
.25938 .00375 L
s
.2817 0 m
.2817 .00375 L
s
.30103 0 m
.30103 .00375 L
s
.31808 0 m
.31808 .00375 L
s
.43368 0 m
.43368 .00375 L
s
.49237 0 m
.49237 .00375 L
s
.53402 0 m
.53402 .00375 L
s
.59272 0 m
.59272 .00375 L
s
.61503 0 m
.61503 .00375 L
s
.63436 0 m
.63436 .00375 L
s
.65141 0 m
.65141 .00375 L
s
.76701 0 m
.76701 .00375 L
s
.82571 0 m
.82571 .00375 L
s
.86735 0 m
.86735 .00375 L
s
.92605 0 m
.92605 .00375 L
s
.94837 0 m
.94837 .00375 L
s
.9677 0 m
.9677 .00375 L
s
.98475 0 m
.98475 .00375 L
s
.25 Mabswid
0 0 m
1 0 L
s
0 .13734 m
.00625 .13734 L
s
gsave
-0.0125 .13734 -108.188 -10.0625 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.125 translate 1 -1 scale
63.000 13.562 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 13.562 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1.) show
75.000 13.562 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
76.812 13.562 moveto
%%IncludeResource: font Math1Mono
%%IncludeFont: Math1Mono
/Math1Mono findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(\\264) show
84.625 13.562 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(10) show
96.625 9.375 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 7.125 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
96.625 9.375 moveto
%%IncludeResource: font Math1Mono
%%IncludeFont: Math1Mono
/Math1Mono findfont 7.125 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
100.875 9.375 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 7.125 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(6) show
105.125 9.375 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 7.125 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .27468 m
.00625 .27468 L
s
gsave
-0.0125 .27468 -101 -8.90625 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.0001) show
99.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .41202 m
.00625 .41202 L
s
gsave
-0.0125 .41202 -89 -8.90625 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0.01) show
87.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .54936 m
.00625 .54936 L
s
gsave
-0.0125 .54936 -71 -8.90625 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 17.8125 translate 1 -1 scale
63.000 11.250 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
%%BeginResource: font Courier-MISO
%%BeginFont: Courier-MISO
/Courier /Courier-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
69.000 11.250 moveto
%%IncludeResource: font Courier-MISO
%%IncludeFont: Courier-MISO
/Courier-MISO findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.001 w
0 .07411 m
.00375 .07411 L
s
0 .09351 m
.00375 .09351 L
s
0 .10517 m
.00375 .10517 L
s
0 .11353 m
.00375 .11353 L
s
0 .12005 m
.00375 .12005 L
s
0 .1254 m
.00375 .1254 L
s
0 .12993 m
.00375 .12993 L
s
0 .13387 m
.00375 .13387 L
s
0 .21145 m
.00375 .21145 L
s
0 .23085 m
.00375 .23085 L
s
0 .24251 m
.00375 .24251 L
s
0 .25087 m
.00375 .25087 L
s
0 .25739 m
.00375 .25739 L
s
0 .26274 m
.00375 .26274 L
s
0 .26727 m
.00375 .26727 L
s
0 .27121 m
.00375 .27121 L
s
0 .34879 m
.00375 .34879 L
s
0 .36819 m
.00375 .36819 L
s
0 .37985 m
.00375 .37985 L
s
0 .38821 m
.00375 .38821 L
s
0 .39473 m
.00375 .39473 L
s
0 .40008 m
.00375 .40008 L
s
0 .40461 m
.00375 .40461 L
s
0 .40855 m
.00375 .40855 L
s
0 .48613 m
.00375 .48613 L
s
0 .50553 m
.00375 .50553 L
s
0 .51719 m
.00375 .51719 L
s
0 .52555 m
.00375 .52555 L
s
0 .53207 m
.00375 .53207 L
s
0 .53742 m
.00375 .53742 L
s
0 .54195 m
.00375 .54195 L
s
0 .54589 m
.00375 .54589 L
s
.25 Mabswid
0 0 m
0 .61803 L
s
0 0 m
1 0 L
1 .61803 L
0 .61803 L
closepath
clip
newpath
.0015 w
1e-05 .22002 m
.6381 .48224 L
.74394 .52359 L
.80138 .54378 L
.84102 .55561 L
.85916 .56013 L
.8739 .56325 L
.88792 .56568 L
.89976 .56725 L
.90529 .56782 L
.91094 .56827 L
.91359 .56845 L
.91639 .5686 L
.91798 .56867 L
.91941 .56872 L
.92087 .56877 L
.92218 .5688 L
.92345 .56882 L
.92402 .56883 L
.92463 .56884 L
.92528 .56885 L
.92588 .56885 L
.92651 .56885 L
.92687 .56885 L
.92721 .56885 L
.9278 .56885 L
.92836 .56885 L
.92886 .56885 L
.92941 .56884 L
.93 .56883 L
.93062 .56882 L
.93173 .5688 L
.93291 .56877 L
.93418 .56873 L
.93645 .56864 L
.9391 .56849 L
.94148 .56833 L
.94588 .56796 L
.94985 .56752 L
.95848 .56624 L
.96653 .5646 L
.97348 .56281 L
.98738 .55802 L
.99961 .55225 L
s
.99961 .55225 m
1 .552 L
s
.5 Mabswid
.21972 0 m
.6381 .34432 L
.74394 .42933 L
.80138 .47328 L
.84102 .5016 L
.8739 .52308 L
.89976 .53818 L
.92296 .55004 L
.94227 .55851 L
.9587 .56463 L
.97434 .5695 L
.98795 .57294 L
.99994 .57534 L
s
.99994 .57534 m
1 .57535 L
s
.0015 w
.44418 0 m
.6381 .20301 L
.74394 .33177 L
.80138 .39965 L
.84102 .44469 L
.8739 .48026 L
.89976 .5067 L
.92296 .529 L
.94227 .54632 L
.9587 .56001 L
.97434 .57198 L
.98795 .58133 L
.99994 .58852 L
s
.99994 .58852 m
1 .58855 L
s
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{288, 177.938},
  ImageMargins->{{43, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40004P0000/A000`40O003h00Oogoo8Goo003oOolQ
Ool00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00
ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol005]oo`8000Aoo`03001oogoo00=o
o`8000Aoo`8000=oo`D000Aoo`03001oogoo00=oo`8000=oo`@0025oo`8000Aoo`03001oogoo00=o
o`8000=oo`<000Ioo`8000Aoo`03001oogoo009oo`@002Moo`8000Aoo`03001oogoo009oo`<000mo
o`@000Aoo`00FWoo00@007ooOol000Qoo`04001oogoo0002Ool01000Oomoo`0017oo0P0000=oo`00
Ool01goo00@007ooOol000Aoo`03001oogoo01moo`04001oogoo0008Ool01000Oomoo`001Goo00<0
07ooOol00Woo00@007ooOol000Yoo`03001oogoo02Eoo`04001oogoo000;Ool00`00Oomoo`0>Ool0
0`00Oomoo`03Ool005Yoo`04001oogoo0008Ool01000Oomoo`000Woo00@007ooOol000Aoo`800003
Ool007oo00Moo`04001oogoo0004Ool00`00Oomoo`0OOol01000Oomoo`0027oo00@007ooOol000Eo
o`03001oogoo009oo`04001oogoo000:Ool00`00Oomoo`0UOol01000Oomoo`002goo00<007ooOol0
3Woo00<007ooOol00goo001JOol01000Oomoo`0027oo00@007ooOol0009oo`04001oogoo0002Ool3
0002Ool00`00Oomoo`06Ool01000Oomoo`0017oo00<007ooOol07goo00@007ooOol000Qoo`04001o
ogoo0002Ool30005Ool01000Oomoo`002Woo00<007ooOol09Goo00@007ooOol000Qoo`<0015oo`03
001oogoo00=oo`00FWoo00@007ooOol000Qoo`04001oogoo0002Ool01000Oomoo`000Woo00<007oo
00000Woo00<007ooOol01Woo00@007ooOol000Aoo`03001oogoo01moo`04001oogoo0008Ool01000
Oomoo`000Woo00<007ooOol01Goo00@007ooOol000Yoo`03001oogoo02Eoo`04001oogoo0008Ool0
0`00Oomoo`0AOol00`00Oomoo`03Ool005Yoo`04001oogoo0008Ool01000Oomoo`000Woo00@007oo
Ool0009oo`03001oo`00009oo`03001oogoo00Ioo`04001oogoo0002Ool3000QOol01000Oomoo`00
27oo00@007ooOol0009oo`03001oogoo00Eoo`04001oogoo0008Ool3000WOol01000Oomoo`0027oo
00<007ooOol03goo0`001Goo001KOol2000:Ool20004Ool20003Ool5000:Ool20005Ool00`00Oomo
o`0POol2000:Ool20003Ool40005Ool2000;Ool00`00Oomoo`0VOol20009Ool4000@Ool00`00Oomo
o`03Ool00?moob5oo`00ogoo8Goo000bOooY0005Ool0039oo`03001oogoo01Aoo`03001oogoo00Yo
o`03001oogoo00Moo`03001oogoo00=oo`03001oo`0000Eoo`03001oogoo009oo`05001oogooOol0
0003Ool01@00Oomoogoo00005Woo00D007ooOomoo`0000Uoo`03001oogoo00Ioo`03001oogoo00Eo
o`03001oogoo00=oo`03001oogoo009oo`03001oogoo009oo`05001oogooOol00002Ool00`00Oomo
o`0DOol00`00Oomoo`0;Ool00`00Oomoo`07Ool00`00Oomoo`04Ool00`00Oomoo`03Ool00`00Oomo
o`03Ool01@00Oomoogoo00000goo00D007ooOomoo`0000Eoo`00<Woo00<007ooOol0<Woo0P00<Woo
00<007ooOol0PWoo000bOol00`00Oomoo`0dOol00`00Oomoo`0`Ool00`00Oomoo`21Ool0039oo`03
001oogoo03Eoo`03001oogoo031oo`03001oogoo081oo`00<Woo00<007ooOol0=Woo00<007ooOol0
<7oo00<007ooOol0Ogoo000bOol00`00Oomoo`0gOol00`00Oomoo`0`Ool00`00Oomoo`1nOol0039o
o`03001oogoo03Qoo`80035oo`03001oogoo07eoo`00<Woo00<007ooOol0>Woo00<007ooOol0;goo
00<007ooOol0O7oo000bOol00`00Oomoo`0kOol00`00Oomoo`0_Ool00`00Oomoo`1kOol0039oo`03
001oogoo03aoo`03001oogoo02moo`03001oogoo07Yoo`00<Woo00<007ooOol0?Goo00<007ooOol0
;goo00<007ooOol0NGoo000bOol00`00Oomoo`0nOol2000_Ool00`00Oomoo`1iOol0039oo`03001o
ogoo041oo`03001oogoo02eoo`03001oogoo07Qoo`00<Woo00<007ooOol0@Goo00<007ooOol0;Goo
00<007ooOol0Mgoo000bOol00`00Oomoo`12Ool00`00Oomoo`0]Ool00`00Oomoo`1fOol0039oo`03
001oogoo04=oo`8002ioo`03001oogoo07Eoo`00<Woo00<007ooOol0AGoo00<007ooOol0;7oo00<0
07ooOol0M7oo000bOol00`00Oomoo`16Ool00`00Oomoo`0/Ool00`00Oomoo`1cOol0039oo`03001o
ogoo04Moo`03001oogoo02aoo`03001oogoo079oo`00<Woo00<007ooOol0B7oo00<007ooOol0;7oo
00<007ooOol0LGoo000bOol00`00Oomoo`19Ool2000]Ool00`00Oomoo`1`Ool0039oo`03001oogoo
04]oo`03001oogoo02]oo`03001oogoo06moo`00<Woo00<007ooOol0C7oo00<007ooOol0:goo00<0
07ooOol0KWoo000bOol00`00Oomoo`1=Ool00`00Oomoo`0[Ool00`00Oomoo`1]Ool0039oo`03001o
ogoo04ioo`03001oogoo02]oo`03001oogoo06aoo`00<Woo00<007ooOol0Cgoo0P00;7oo00<007oo
Ool0Jgoo000bOol00`00Oomoo`1AOol00`00Oomoo`0ZOol00`00Oomoo`1ZOol0039oo`03001oogoo
059oo`03001oogoo02Yoo`03001oogoo06Uoo`000goo10000goo00<007ooOol00goo00D007ooOomo
o`0000=oo`@000=oo`80015oo`03001oogoo05=oo`03001oogoo02Yoo`03001oogoo06Qoo`001Goo
00<007ooOol02Goo00<007oo00001Woo00D007ooOomoo`00009oo`03001oogoo00ioo`03001oogoo
05Aoo`03001oogoo02Yoo`03001oogoo06Moo`001Goo00<007ooOol02Woo00<007ooOol01Goo00D0
07ooOomoo`00009oo`03001oogoo00ioo`03001oogoo05Eoo`8002]oo`03001oogoo06Ioo`001Goo
00<007ooOol02Goo00<007oo00001Woo00D007ooOomoo`00009oo`03001oogoo00ioo`8005Qoo`03
001oogoo02Uoo`03001oogoo06Eoo`001Goo00<007ooOol027oo00D007ooOomoo`0000Eoo`05001o
ogooOol00002Ool00`00Oomoo`04Ool20008Ool00`00Oomoo`1HOol00`00Oomoo`0YOol00`00Oomo
o`1TOol000=oo`<0019oo`<000=oo`04001oogoo0002Ool40002Ool00`00Oomoo`05Ool00`00Oomo
o`1IOol00`00Oomoo`0YOol00`00Oomoo`1SOol000Eoo`03001oogoo019oo`03001oogoo009oo`80
00Ioo`<000Qoo`03001oogoo05Yoo`8002Yoo`03001oogoo069oo`00:7oo0`001goo00<007ooOol0
G7oo00<007ooOol09goo00<007ooOol0HWoo000bOol00`00Oomoo`1MOol00`00Oomoo`0WOol00`00
Oomoo`1QOol0039oo`03001oogoo05ioo`03001oogoo02Moo`03001oogoo061oo`00<Woo00<007oo
Ool0Ggoo00<007ooOol09goo00<007ooOol0Ggoo000bOol00`00Oomoo`1POol2000XOol00`00Oomo
o`1NOol0039oo`03001oogoo069oo`03001oogoo02Ioo`03001oogoo05eoo`00<Woo00<007ooOol0
Hgoo00<007ooOol09Woo00<007ooOol0G7oo000bOol00`00Oomoo`1TOol00`00Oomoo`0VOol00`00
Oomoo`1KOol0039oo`03001oogoo06Eoo`03001oogoo02Ioo`03001oogoo05Yoo`00<Woo00<007oo
Ool0IWoo0P009goo00<007ooOol0FGoo000bOol00`00Oomoo`1XOol00`00Oomoo`0UOol00`00Oomo
o`1HOol0039oo`03001oogoo06Uoo`03001oogoo02Eoo`03001oogoo05Moo`00<Woo00<007ooOol0
JWoo00<007ooOol09Goo00<007ooOol0EWoo000bOol00`00Oomoo`1[Ool2000VOol00`00Oomoo`1E
Ool0039oo`03001oogoo06eoo`03001oogoo02=oo`03001oogoo05Eoo`00<Woo0P00Kgoo00<007oo
Ool08goo00<007ooOol0E7oo000bOol01000Ool00000KWoo00<007ooOol08goo00<007ooOol0Dgoo
000bOol01000Oomoogoo0`00K7oo00<007ooOol08goo00<007ooOol0DWoo000bOol00`00Oomoo`04
Ool2001[Ool2000TOol00`00Oomoo`1AOol0039oo`03001oogoo00Ioo`8006]oo`03001oogoo025o
o`03001oogoo055oo`00<Woo00<007ooOol027oo0`00JGoo00<007ooOol08Goo00<007ooOol0D7oo
000bOol00`00Oomoo`0;Ool2001XOol00`00Oomoo`0QOol00`00Oomoo`1?Ool0039oo`03001oogoo
00eoo`<006Ioo`03001oogoo025oo`03001oogoo04ioo`00<Woo00<007ooOol047oo0P00IGoo0P00
8Woo00<007ooOol0CGoo000bOol00`00Oomoo`0BOol3001TOol00`00Oomoo`0OOol00`00Oomoo`1=
Ool0039oo`03001oogoo01Eoo`8006=oo`03001oogoo01moo`03001oogoo04aoo`002goo0P0017oo
00<007ooOol00goo0P0017oo0P0017oo0P000goo10001Woo00<007ooOol05goo0P00HWoo00<007oo
Ool07goo00<007ooOol0Bgoo000:Ool01000Oomoo`0027oo00@007ooOol0009oo`04001oogoo0002
Ool01000Oomoo`0017oo00<007ooOol01Goo0P006Woo0`00H7oo00<007ooOol07goo00<007ooOol0
BWoo000:Ool01000Oomoo`0027oo00@007ooOol0009oo`04001oogoo0002Ool01000Oomoo`0017oo
00<007ooOol01Goo00<007ooOol077oo0P00Ggoo0P0087oo00<007ooOol0BGoo000:Ool01000Oomo
o`0027oo00@007ooOol0009oo`04001oogoo0002Ool01000Oomoo`0017oo00<007ooOol01Goo00<0
07ooOol07Woo0`00GWoo00<007ooOol07Goo00<007ooOol0BGoo000:Ool01000Oomoo`0027oo00@0
07ooOol0009oo`04001oogoo0002Ool01000Oomoo`0017oo00<007ooOol01Goo00<007ooOol08Goo
0P00GGoo00<007ooOol07Goo00<007ooOol0B7oo000:Ool01000Oomoo`0027oo00@007ooOol0009o
o`04001oogoo0002Ool01000Oomoo`000Woo0`001goo00<007ooOol08goo0`00Fgoo00<007ooOol0
7Goo00<007ooOol0Agoo000;Ool2000:Ool20004Ool20004Ool20005Ool00`00Oomoo`05Ool00`00
Oomoo`0VOol2001JOol2000NOol00`00Oomoo`16Ool0039oo`03001oogoo02Qoo`8005Yoo`03001o
ogoo01aoo`03001oogoo04Eoo`00<Woo00<007ooOol0:Woo0`00F7oo00<007ooOol06goo00<007oo
Ool0AGoo000bOol00`00Oomoo`0]Ool2001GOol00`00Oomoo`0KOol00`00Oomoo`14Ool0039oo`03
001oogoo02moo`<005Eoo`03001oogoo01]oo`03001oogoo04=oo`00<Woo00<007ooOol0<Woo0P00
E7oo0P0077oo00<007ooOol0@Woo000bOol00`00Oomoo`0dOol3001COol00`00Oomoo`0JOol00`00
Oomoo`11Ool0039oo`03001oogoo03Moo`80059oo`03001oogoo01Uoo`03001oogoo045oo`00<Woo
00<007ooOol0>Goo0P00DGoo00<007ooOol06Goo00<007ooOol0@7oo000bOol00`00Oomoo`0kOol3
001?Ool00`00Oomoo`0IOol00`00Oomoo`0oOol0039oo`03001oogoo03ioo`8004ioo`8001Yoo`03
001oogoo03ioo`00<Woo00<007ooOol0@7oo0`00CGoo00<007ooOol067oo00<007ooOol0?Goo000b
Ool00`00Oomoo`13Ool2001<Ool00`00Oomoo`0HOol00`00Oomoo`0lOol0039oo`03001oogoo04Eo
o`8004]oo`03001oogoo01Moo`03001oogoo03aoo`00<Woo00<007ooOol0Agoo0`00BGoo0P0067oo
00<007ooOol0>goo000bOol00`00Oomoo`1:Ool20019Ool00`00Oomoo`0FOol00`00Oomoo`0jOol0
039oo`03001oogoo04aoo`<004Moo`03001oogoo01Ioo`03001oogoo03Uoo`00<Woo00<007ooOol0
Cgoo0P00AWoo00<007ooOol05Woo00<007ooOol0>7oo000bOol00`00Oomoo`1AOol30014Ool2000G
Ool00`00Oomoo`0gOol0039oo`03001oogoo05Aoo`8004Aoo`03001oogoo01Eoo`03001oogoo03Io
o`00<Woo00<007ooOol0EWoo0P00@goo00<007ooOol05Goo00<007ooOol0=Goo000bOol00`00Oomo
o`1HOol30011Ool00`00Oomoo`0DOol00`00Oomoo`0eOol0039oo`03001oogoo05]oo`80041oo`80
01Eoo`03001oogoo03Aoo`00<Woo00<007ooOol0GGoo0`00?goo00<007ooOol04goo00<007ooOol0
<goo000bOol00`00Oomoo`1POol2000nOol00`00Oomoo`0COol00`00Oomoo`0bOol0039oo`03001o
ogoo069oo`<003aoo`8001Aoo`03001oogoo035oo`005goo0P0017oo00<007ooOol00goo0P000goo
10001Woo00<007ooOol0IGoo0P00?7oo00<007ooOol04Woo00<007ooOol0<7oo000FOol01000Oomo
o`0027oo00@007ooOol000Aoo`03001oogoo00Eoo`8006Qoo`8003]oo`03001oogoo019oo`03001o
ogoo02moo`005Woo00@007ooOol000Qoo`04001oogoo0004Ool00`00Oomoo`05Ool00`00Oomoo`1Y
Ool3000iOol00`00Oomoo`0BOol00`00Oomoo`0^Ool001Ioo`04001oogoo0008Ool01000Oomoo`00
17oo00<007ooOol01Goo00<007ooOol0K7oo0P00>7oo0P004goo00<007ooOol0;Goo000FOol01000
Oomoo`0027oo00@007ooOol000Aoo`03001oogoo00Eoo`03001oogoo06ioo`<003Moo`03001oogoo
011oo`03001oogoo02eoo`005Woo00@007ooOol000Qoo`04001oogoo0002Ool30007Ool00`00Oomo
o`1aOol2000fOol00`00Oomoo`0@Ool00`00Oomoo`0/Ool001Moo`8000Yoo`8000Eoo`03001oogoo
00Eoo`03001oogoo07=oo`<003Aoo`03001oogoo011oo`03001oogoo02]oo`00<Woo00<007ooOol0
MWoo0P00<goo0P004Goo00<007ooOol0:Woo000bOol00`00Oomoo`1hOol2000cOol00`00Oomoo`0?
Ool00`00Oomoo`0YOol0039oo`03001oogoo07Yoo`<0035oo`03001oogoo00moo`03001oogoo02Qo
o`00<Woo00<007ooOol0OGoo0P00<7oo0P0047oo00<007ooOol09goo000bOol00`00Oomoo`1oOol3
000_Ool00`00Oomoo`0>Ool00`00Oomoo`0VOol0039oo`03001oogoo089oo`8002ioo`03001oogoo
00ioo`03001oogoo02Eoo`00<Woo00<007ooOol0Q7oo0`00;7oo0P003Woo00<007ooOol09Goo000b
Ool00`00Oomoo`27Ool2000/Ool00`00Oomoo`0<Ool00`00Oomoo`0TOol0039oo`03001oogoo08Uo
o`8002]oo`03001oogoo00aoo`03001oogoo02=oo`00<Woo00<007ooOol0Rgoo0`00:Goo0P003Goo
00<007ooOol08Woo000bOol00`00Oomoo`2>Ool2000YOol00`00Oomoo`0;Ool00`00Oomoo`0QOol0
039oo`03001oogoo091oo`<002Moo`03001oogoo00]oo`03001oogoo021oo`00<Woo00<007ooOol0
Tgoo0P009Woo0P0037oo00<007ooOol07goo000bOol00`00Oomoo`2EOol3000UOol00`00Oomoo`0:
Ool00`00Oomoo`0NOol0039oo`03001oogoo09Qoo`<002=oo`8000]oo`03001oogoo01eoo`00<Woo
00<007ooOol0Vgoo0P008goo00<007ooOol02Goo00<007ooOol077oo000bOol00`00Oomoo`2MOol3
000QOol2000:Ool00`00Oomoo`0KOol0039oo`03001oogoo0:1oo`<0021oo`03001oogoo00Qoo`03
001oogoo01Yoo`00<Woo00<007ooOol0Xgoo0P007goo00<007ooOol027oo00<007ooOol06Goo000b
Ool00`00Oomoo`2UOol3000MOol20009Ool2000IOol0039oo`03001oogoo0:Qoo`<001aoo`03001o
ogoo00Qoo`03001oogoo01Ioo`00<Woo00<007ooOol0Zgoo0P006goo0P002Goo00<007ooOol05Goo
000bOol00`00Oomoo`2]Ool3000JOol00`00Oomoo`07Ool00`00Oomoo`0DOol0039oo`03001oogoo
0;1oo`<001Qoo`8000Qoo`03001oogoo01=oo`00<Woo00<007ooOol0/goo0P0067oo0P001goo00<0
07ooOol04Woo000XOol40006Ool00`00Oomoo`2eOol3000GOol30005Ool00`00Oomoo`0AOol002Yo
o`03001oogoo00Eoo`800;Uoo`<001Moo`8000Aoo`03001oogoo011oo`00:Woo00<007ooOol01Goo
00<007ooOol0^goo10005Goo0P000goo00<007ooOol01goo0`001Goo000ZOol00`00Oomoo`05Ool0
0`00Oomoo`2oOol3000DOol20002Ool00`00Oomoo`03Ool30008Ool002Yoo`03001oogoo00Eoo`03
001oogoo0<9oo`L000moo`800004Ool007ooOol2000;Ool002Qoo`<000Moo`03001oogoo0<Uoo`L0
00Qoo`H000eoo`00:Woo00<007ooOol01Goo00<007ooOol0d7oo20001Goo10002Woo000bOol00`00
Oomoo`3POol60005Ool0039oo`03001oogoo0>5oo`03001oogoo00Moo`00<Woo00<007ooOol0hWoo
00<007ooOol01Woo000bOol00`00Oomoo`3SOol30005Ool0039oo`03001oogoo0>]oo`00<Woo00<0
07ooOol0jgoo000bOol00`00Oomoo`3[Ool0039oo`03001oogoo0>]oo`00<Woo00<007ooOol0jgoo
000bOol00`00Oomoo`3[Ool0039oo`03001oogoo0>]oo`00ogoo8Goo003oOolQOol00?moob5oo`00
ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo0000\
\>"],
  ImageRangeCache->{{{91.5625, 320.938}, {291.75, 150.438}} -> {-5.13101, \
2.3701, 0.0129515, 0.0628679}}],

Cell[BoxData[
    TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
      False,
      Editable->False]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(\[IndentingNewLine]\)\(TableForm[
      Table[{xip[
            i], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
FortranForm[\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(Abs[
                    vgvtrue - vgvCRtot1]*10^6\  /. \ k \[Rule] m\ xip[i]\) /. 
              parameters\ ], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ FortranForm[\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\(Abs[vgvtrue - vgvCRtot2]*10^6 /. \ k \[Rule] m\ xip[i]\) /. 
              parameters], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ FortranForm[\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(Abs[
                    vgvtrue - vgvCRtot3]*10^6 /. \ k \[Rule] m\ xip[i]\) /. 
              parameters]}, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ {i, 0, 
          Log[ximax/ximin]/
            Log[delxi]}], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ TableSpacing \[Rule] {0, 1}]\)\)\)], "Input"],

Cell[BoxData[
    TagBox[GridBox[{
          {"0.001`", 
            InterpretationBox[
              StyleBox["0.000015995446639308422",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.5995446639308422*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(2.3271383192864648  e - 11\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.3271383192864648*^-11],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0],
              Editable->True,
              AutoDelete->True]},
          {"0.0012`", 
            InterpretationBox[
              StyleBox["0.000023033408330880387",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.3033408330880387*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(4.824699667560495  e - 11\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 4.8246996675604947*^-11],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(6.776263578034403  e - 15\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 6.7762635780344027*^-15],
              Editable->True,
              AutoDelete->True]},
          {"0.0014399999999999999`", 
            InterpretationBox[
              StyleBox["0.00003316803577193346",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.3168035771933462*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.0003797920252189  e - 10\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.0003797920252189*^-10],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(8.470329472543003  e - 15\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 8.4703294725430034*^-15],
              Editable->True,
              AutoDelete->True]},
          {"0.0017279999999999997`", 
            InterpretationBox[
              StyleBox["0.00004776182175487162",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 4.776182175487162*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(2.0744006284847266  e - 10\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.0744006284847266*^-10],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(3.3881317890172014  e - 15\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.3881317890172014*^-15],
              Editable->True,
              AutoDelete->True]},
          {"0.0020736`", 
            InterpretationBox[
              StyleBox["0.00006877671276258831",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 6.877671276258831*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(4.301419653405733  e - 10\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 4.3014196534057331*^-10],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.6940658945086007  e - 15\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.6940658945086007*^-15],
              Editable->True,
              AutoDelete->True]},
          {"0.0024883199999999996`", 
            InterpretationBox[
              StyleBox["0.00009903782240716663",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 9.9037822407166626*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(8.919307756564618  e - 10\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 8.9193077565646178*^-10],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(6.776263578034403  e - 15\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 6.7762635780344027*^-15],
              Editable->True,
              AutoDelete->True]},
          {"0.0029859839999999993`", 
            InterpretationBox[
              StyleBox["0.00014261312893588702",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00014261312893588702],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.8494947462638703  e - 9\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.8494947462638703*^-09],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.8634724839594607  e - 14\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.8634724839594607*^-14],
              Editable->True,
              AutoDelete->True]},
          {"0.0035831807999999995`", 
            InterpretationBox[
              StyleBox["0.00020536013678351564",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00020536013678351564],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(3.835050088911093  e - 9\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.8350500889110933*^-09],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(5.929230630780102  e - 14\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.9292306307801024*^-14],
              Editable->True,
              AutoDelete->True]},
          {"0.0042998169599999985`", 
            InterpretationBox[
              StyleBox["0.0002957128555408959",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00029571285554089589],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(7.952194336509864  e - 9\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 7.9521943365098643*^-09],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.9651164376299768  e - 13\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.9651164376299768*^-13],
              Editable->True,
              AutoDelete->True]},
          {"0.005159780351999999`", 
            InterpretationBox[
              StyleBox["0.00042581460684984007",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00042581460684984007],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.6489227653649144  e - 8\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.6489227653649144*^-08],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(5.675120746603812  e - 13\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.6751207466038123*^-13],
              Editable->True,
              AutoDelete->True]},
          {"0.006191736422399998`", 
            InterpretationBox[
              StyleBox["0.0006131483484611897",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00061314834846118969],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(3.41907102266838  e - 8\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.4190710226683803*^-08],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.6940658945086007  e - 12\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.6940658945086007*^-12],
              Editable->True,
              AutoDelete->True]},
          {"0.007430083706879997`", 
            InterpretationBox[
              StyleBox["0.0008828824372449892",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00088288243724498922],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(7.089382690107521  e - 8\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 7.0893826901075215*^-08],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(5.0720332881587504  e - 12\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.0720332881587504*^-12],
              Editable->True,
              AutoDelete->True]},
          {"0.008916100448255996`", 
            InterpretationBox[
              StyleBox["0.0012712445826373008",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0012712445826373008],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.4699340648762632  e - 7\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.4699340648762632*^-07],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.5148337228695907  e - 11\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.5148337228695907*^-11],
              Editable->True,
              AutoDelete->True]},
          {"0.010699320537907194`", 
            InterpretationBox[
              StyleBox["0.0018303721617919586",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0018303721617919586],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(3.0476959152171083  e - 7\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.0476959152171083*^-07],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(4.525019410821923  e - 11\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 4.5250194108219233*^-11],
              Editable->True,
              AutoDelete->True]},
          {"0.012839184645488633`", 
            InterpretationBox[
              StyleBox["0.002635279726520014",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0026352797265200142],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(6.318629633731386  e - 7\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 6.318629633731386*^-07],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.3509667288937738  e - 10\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.3509667288937738*^-10],
              Editable->True,
              AutoDelete->True]},
          {"0.01540702157458636`", 
            InterpretationBox[
              StyleBox["0.003793857104820246",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0037938571048202461],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.3099108826981638  e - 6\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.3099108826981638*^-06],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(4.032774683854559  e - 10\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 4.0327746838545592*^-10],
              Editable->True,
              AutoDelete->True]},
          {"0.01848842588950363`", 
            InterpretationBox[
              StyleBox["0.005461193961542839",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0054611939615428389],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(2.715275542996003  e - 6\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.7152755429960028*^-06],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.2037862839788666  e - 9\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.2037862839788666*^-09],
              Editable->True,
              AutoDelete->True]},
          {"0.022186111067404354`", 
            InterpretationBox[
              StyleBox["0.007860056689242896",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0078600566892428961],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(5.627543332861144  e - 6\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.6275433328611436*^-06],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(3.5928020541281525  e - 9\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.5928020541281525*^-09],
              Editable->True,
              AutoDelete->True]},
          {"0.026623333280885227`", 
            InterpretationBox[
              StyleBox["0.011310063954753492",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.011310063954753492],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00001166076458482268",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.166076458482268*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(1.0720724912742334  e - 8\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.0720724912742334*^-08],
              Editable->True,
              AutoDelete->True]},
          {"0.03194799993706227`", 
            InterpretationBox[
              StyleBox["0.016269056767760554",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.016269056767760554],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.000024154381968822863",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.4154381968822863*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(3.198049125323864  e - 8\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.1980491253238638*^-08],
              Editable->True,
              AutoDelete->True]},
          {"0.038337599924474726`", 
            InterpretationBox[
              StyleBox["0.023391346186372883",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.023391346186372883],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00005001086877791123",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.0010868777911228*^-05],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(9.535826616454291  e - 8\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 9.5358266164542911*^-08],
              Editable->True,
              AutoDelete->True]},
          {"0.04600511990936966`", 
            InterpretationBox[
              StyleBox["0.0336088645193455",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.033608864519345499],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00010347716107434704",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00010347716107434704],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(2.84159331739235  e - 7\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.8415933173923501*^-07],
              Editable->True,
              AutoDelete->True]},
          {"0.0552061438912436`", 
            InterpretationBox[
              StyleBox["0.04824243795535693",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.048242437955356932],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00021389956820339453",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00021389956820339453],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(8.460146289985182  e - 7\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 8.4601462899851817*^-07],
              Editable->True,
              AutoDelete->True]},
          {"0.06624737266949232`", 
            InterpretationBox[
              StyleBox["0.0691506343449029",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0691506343449029],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.0004415493541494285",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00044154935414942849],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(2.5155732209883883  e - 6\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.5155732209883883*^-06],
              Editable->True,
              AutoDelete->True]},
          {"0.07949684720339077`", 
            InterpretationBox[
              StyleBox["0.09892107438463683",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.098921074384636834],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.0009096882530162118",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00090968825301621179],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox[\(7.466154957667492  e - 6\),
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 7.4661549576674922*^-06],
              Editable->True,
              AutoDelete->True]},
          {"0.09539621664406893`", 
            InterpretationBox[
              StyleBox["0.1410998542375198",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.14109985423751981],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00186886541725178",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0018688654172517799],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00002210101360209933",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.210101360209933*^-05],
              Editable->True,
              AutoDelete->True]},
          {"0.11447545997288272`", 
            InterpretationBox[
              StyleBox["0.20043128048428663",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.20043128048428663],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.003823887731568601",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.003823887731568601],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.00006517645682021839",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 6.5176456820218386*^-05],
              Editable->True,
              AutoDelete->True]},
          {"0.13737055196745926`", 
            InterpretationBox[
              StyleBox["0.28302910287041483",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.28302910287041483],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.007778940461557147",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0077789404615571473],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.0001911776191489882",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00019117761914898821],
              Editable->True,
              AutoDelete->True]},
          {"0.16484466236095108`", 
            InterpretationBox[
              StyleBox["0.3963013479600583",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.39630134796005828],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.015694959644203012",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.015694959644203012],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.0005565125784077237",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.00055651257840772374],
              Editable->True,
              AutoDelete->True]},
          {"0.1978135948331413`", 
            InterpretationBox[
              StyleBox["0.5482809739475205",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.54828097394752051],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.031299371209459775",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.031299371209459775],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.0016026938018043947",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0016026938018043947],
              Editable->True,
              AutoDelete->True]},
          {"0.23737631379976953`", 
            InterpretationBox[
              StyleBox["0.7457745228704359",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.74577452287043589],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.061402970284594106",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.061402970284594106],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.004546914378302966",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.0045469143783029662],
              Editable->True,
              AutoDelete->True]},
          {"0.28485157655972343`", 
            InterpretationBox[
              StyleBox["0.9905295840536009",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.99052958405360092],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.11774187103332535",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.11774187103332535],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.012636145600198895",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.012636145600198895],
              Editable->True,
              AutoDelete->True]},
          {"0.3418218918716681`", 
            InterpretationBox[
              StyleBox["1.272787145744614",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.272787145744614],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.21881523572756978",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.21881523572756978],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.03414938110101345",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.034149381101013447],
              Editable->True,
              AutoDelete->True]},
          {"0.4101862702460017`", 
            InterpretationBox[
              StyleBox["1.562878155755935",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.562878155755935],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.38991172242000066",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.38991172242000066],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.08895123985660967",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.088951239856609673],
              Editable->True,
              AutoDelete->True]},
          {"0.4922235242952021`", 
            InterpretationBox[
              StyleBox["1.8048346223143388",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.8048346223143388],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.6577527023091547",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.65775270230915472],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.2210406717493039",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.22104067174930389],
              Editable->True,
              AutoDelete->True]},
          {"0.5906682291542424`", 
            InterpretationBox[
              StyleBox["1.9207459963379057",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.9207459963379057],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["1.0362425034677063",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.0362425034677063],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["0.5181787663780755",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.51817876637807547],
              Editable->True,
              AutoDelete->True]},
          {"0.708801874985091`", 
            InterpretationBox[
              StyleBox["1.8357532147731186",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.8357532147731186],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["1.5063918759249193",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.5063918759249193],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["1.1311238279718654",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.1311238279718654],
              Editable->True,
              AutoDelete->True]},
          {"0.850562249982109`", 
            InterpretationBox[
              StyleBox["1.5218726298830907",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.5218726298830907],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["2.0051291038278443",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.0051291038278443],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["2.25262125006956",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.2526212500695602],
              Editable->True,
              AutoDelete->True]},
          {"1.0206746999785308`", 
            InterpretationBox[
              StyleBox["1.033771514172054",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.033771514172054],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["2.4304520855261162",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.4304520855261162],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["3.926259272780848",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.9262592727808481],
              Editable->True,
              AutoDelete->True]},
          {"1.224809639974237`", 
            InterpretationBox[
              StyleBox["0.4984206921562448",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.49842069215624479],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["2.630949064058176",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.6309490640581759],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["5.52523186469588",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.52523186469588],
              Editable->True,
              AutoDelete->True]},
          {"1.4697715679690841`", 
            InterpretationBox[
              StyleBox["0.057205529337204984",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.057205529337204984],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["2.396967784399853",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 2.3969677843998531],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["5.528544306813207",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 5.528544306813207],
              Editable->True,
              AutoDelete->True]},
          {"1.763725881562901`", 
            InterpretationBox[
              StyleBox["0.1938883962047421",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 0.1938883962047421],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["1.6637443936405485",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 1.6637443936405485],
              Editable->True,
              AutoDelete->True], 
            InterpretationBox[
              StyleBox["3.4046984986780626",
                ShowStringCharacters->True,
                NumberMarks->True],
              FortranForm[ 3.4046984986780626],
              Editable->True,
              AutoDelete->True]}
          },
        RowSpacings->0,
        ColumnSpacings->1,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      (TableForm[ #, TableSpacing -> {0, 1}]&)]], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Nuclear Matter Energy/A", "Section",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
General definitions of dimensionless variable \[Xi] and density 
\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(kf\  := \ xi\ m\)], "Input"],

Cell[BoxData[
    \(rho\  := \ g\ kf^3/\((6\ Pi^2)\)\)], "Input"],

Cell[BoxData[
    \(EoverA\  := \ EoverA1\ \  + \ EoverA2\)], "Input"],

Cell[BoxData[
    \(EoverA1\  := \ g \((g - 1)\)/\((Pi^4\ rho)\)\ m^4\ J\)], "Input"],

Cell[BoxData[
    \(EoverA2\  := \ g \((g - 1)\)/\((Pi^4\ rho)\)\ m^4\ Jp\)], "Input"],

Cell[BoxData[
    \(EoverA2p\  := \ 
      g \((g - 1)\) 
        alpha^2\ m^5/\((6\ Pi^3\ M\ rho)\)\ *\ \((\[IndentingNewLine]\ 
          Log[1 + xi^2]\  - \ 
            xi^2 \((2 + xi^2)\)/\((2\ \((1 + xi^2)\))\)\  - \ 
            Tp1)\)\)], "Input"],

Cell[BoxData[
    \(Tp1\  := \ 
      2/\((35\ Pi)\)\ \((xi^7 \((\(-11\)\  + \ 2  Log[2])\)\  - \ 
            4/9\ xi^9\ \((\(-167\)/3 + 8\ Log[2])\)\ )\)\)], "Input"],

Cell[BoxData[
    \(Jp\  := \ \(\(J1\)\(\ \)\(-\)\(\ \)\(J2\)\(\ \)\)\)], "Input"],

Cell[BoxData[
    \(J\  := \ 
      alpha\ \((2\ Pi\ m/\((3\ M)\))\)\ \((\ 
          xi^2\  + \ 
            xi^3\ ArcTan[
                xi]\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \  - \ \((1\  + \ 
                  3/2\ xi^2)\)\ Log[1 + xi^2]\ )\)\)], "Input"],

Cell[BoxData[
    \(J1\  := \ 
      alpha^2\ \((Pi\ m/\((6\ M)\))\)\ \((Log[1 + xi^2]\  - \ 
            xi^2 \((2 + xi^2)\)/\((2\ \((1 + xi^2)\))\)\ )\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Series[
      J1/\((alpha^2\ \((Pi\ m/\((6\ M)\))\))\), {xi, 0, 20}]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(-\(xi\^6\/6\)\), "+", \(xi\^8\/4\), 
        "-", \(\(3\ xi\^10\)\/10\), "+", \(xi\^12\/3\), 
        "-", \(\(5\ xi\^14\)\/14\), "+", \(\(3\ xi\^16\)\/8\), 
        "-", \(\(7\ xi\^18\)\/18\), "+", \(\(2\ xi\^20\)\/5\), "+", 
        InterpretationBox[\(O[xi]\^21\),
          SeriesData[ xi, 0, {}, 6, 21, 1]]}],
      SeriesData[ xi, 0, {
        Rational[ -1, 6], 0, 
        Rational[ 1, 4], 0, 
        Rational[ -3, 10], 0, 
        Rational[ 1, 3], 0, 
        Rational[ -5, 14], 0, 
        Rational[ 3, 8], 0, 
        Rational[ -7, 18], 0, 
        Rational[ 2, 5]}, 6, 21, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(J2\  := \ 
      alpha^2 \((m/\((105\ M)\))\)\ \((xi^7 \((\(-11\)\  + \ 
                  2\ Log[2])\)\  - \ 
            4/9\ xi^9\ \((\(-167\)/3\  + \ 8  Log[2])\)\ )\)\)], "Input"],

Cell[BoxData[
    \(EoverAcr\  := \ EoverA1cr\  + \ EoverA2cr\)], "Input"],

Cell[BoxData[
    \(EoverA1cr\  := \ \((g - 
            1)\)\ alpha\ \((m^2/\((3\ Pi\ M)\))\)\ \((M\ m/\((4\ Pi)\))\)\ *\ \
\((\[IndentingNewLine]C01p\ xi^3\  + \ 
            3/10\ m^2\ \((C21p - C01p/Lambdac^2)\)\ xi^5\ \ )\)\)], "Input"],

Cell[BoxData[
    \(EoverA2crp\  := \ 
      3\ \((g - 1)\)\ alpha^2\ M\ m^4\ xi^4/
          Pi^4\ \((I1nt - I2nt)\)\)], "Input"],

Cell[BoxData[
    \(I1nt\  := \ \(-Sqrt[Pi]\) 
          m/Lambdac\ 1/xi\ \((\ 
            1/144\ \((C01p^2\  + \ 
                    1/2\ C01p\ C21p\ Lambdac^2)\)\ \[IndentingNewLine] + \ 
              Lambdac^4/
                  384\ \((1/
                      2\ C21p^2)\)\ )\)\  - \ \(\(xi\)\(\ \)\(m\)\(\ \)\(Sqrt[
              Pi]/Lambdac\)\(\ \)\((1/
                  160 \((\(-C01p^2\)\  + \ C01p\ C21p\ Lambdac^2/2)\)\  + \ 
              Lambdac^4/284\ 1/2\ \ C21^2\ )\)\(\ \)\)\)], "Input"],

Cell[BoxData[
    \(I2nt\  := \ 
      C01p^2\ 1/840\ \((\(-11\)\  + \ 2  Log[2])\)\  - \ 
        1/2\ \((1/840)\)\ \((4/9\ \((167/3 - 8\ Log[2])\))\) 
          m^2 \((C01p\ C21p\  - \ 
              C01p^2/Lambdac^2)\)\ \(\(xi^2\)\(\ \)\)\)], "Input"],

Cell[BoxData[
    \(EoverA2cr\  := \ \(-\((g - 
              1)\)\)\ alpha^2\ m^2\ /\ \((6\ Pi\ M)\)\ *\ \((M\ m/\((4\ \
Pi)\))\)^2\ *\[IndentingNewLine]\ \((\ \[IndentingNewLine]\((\ 
                Lambdac/\((Sqrt[Pi]\ m)\) \((2\ C01p^2\  + \ 
                        C01p\ C21p\ Lambdac^2\  + \ 
                        3/8\ C21p^2\ Lambdac^4)\)\[IndentingNewLine]\  - \ 
                  8\ Pi/\((M\ m)\)\ \((C02p\  + \ 
                        delC02p)\)\ )\)\ xi^3\[IndentingNewLine] - \ 
            C01p^2\ 12 \((11 - \ 
                    2\ Log[2])\)/\((35\ Pi)\)\ xi^4\[IndentingNewLine] + \ 
            9/10 \((\ 
                m/\((Sqrt[Pi]\ Lambdac)\)\ \((\(-2\)\ C01p^2\  + \ 
                        C01p\ C21p\ Lambdac^2\  + \ 
                        1/8\ C21p^2\ Lambdac^4)\)\[IndentingNewLine]\ \ \ \ \ \
\ \ \ \ \  - \ 8\ Pi\ m/\((3\ M)\)\ \((C22p\  - \ \((C02p\  + \ delC02p)\)/
                          Lambdac^2)\)\ )\) xi^5\[IndentingNewLine] - \ 
            m^2\ \((C01p\ C21p\  - \ 
                  C01p^2/Lambdac^2)\)\ 8 \((167/3 - 
                    8\ Log[2])\)/\((105\ Pi)\)\ \
xi^6\[IndentingNewLine])\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf1\  = \ 
      Series[EoverA1, {xi, 0, 15}]/\((\ \((g - 1)\) 
            alpha\ m^2/\((3\ Pi\ M)\)\ )\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), "-", \(\(3\ xi\^5\)\/5\), "+", \(\(27\ xi\^7\)\/70\),
         "-", \(\(4\ xi\^9\)\/15\), "+", \(\(15\ xi\^11\)\/77\), 
        "-", \(\(27\ xi\^13\)\/182\), "+", \(\(7\ xi\^15\)\/60\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 3, 16, 1]]}],
      SeriesData[ xi, 0, {1, 0, 
        Rational[ -3, 5], 0, 
        Rational[ 27, 70], 0, 
        Rational[ -4, 15], 0, 
        Rational[ 15, 77], 0, 
        Rational[ -27, 182], 0, 
        Rational[ 7, 60]}, 3, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf2cr\  = \ 
      Series[EoverA1cr, {xi, 0, 15}]/\((\ \((g - 1)\) 
            alpha\ m^2/\((3\ Pi\ M)\)\ )\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\(C01p\ m\ M\ xi\^3\)\/\(4\ \[Pi]\)\), 
        "+", \(\(3\ \((C21p - 
                  C01p\/Lambdac\^2)\)\ m\^3\ M\ xi\^5\)\/\(40\ \[Pi]\)\), "+",
         
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 3, 16, 1]]}],
      SeriesData[ xi, 0, {
        Times[ 
          Rational[ 1, 4], C01p, m, M, 
          Power[ Pi, -1]], 0, 
        Times[ 
          Rational[ 3, 40], 
          Plus[ C21p, 
            Times[ -1, C01p, 
              Power[ Lambdac, -2]]], 
          Power[ m, 3], M, 
          Power[ Pi, -1]]}, 3, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\ \(sf1 - sf2cr\  /. \ {C01p \[Rule] C01cr, C21p \[Rule] 0, 
            C41p \[Rule] 0}\)\  /. \ w1cr]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(3\/10\ \((\(-2\) + m\^2\/Lambdac\^2)\)\ xi\^5\), 
        "+", \(\(27\ xi\^7\)\/70\), "-", \(\(4\ xi\^9\)\/15\), 
        "+", \(\(15\ xi\^11\)\/77\), "-", \(\(27\ xi\^13\)\/182\), 
        "+", \(\(7\ xi\^15\)\/60\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 5, 16, 1]]}],
      SeriesData[ xi, 0, {
        Times[ 
          Rational[ 3, 10], 
          Plus[ -2, 
            Times[ 
              Power[ Lambdac, -2], 
              Power[ m, 2]]]], 0, 
        Rational[ 27, 70], 0, 
        Rational[ -4, 15], 0, 
        Rational[ 15, 77], 0, 
        Rational[ -27, 182], 0, 
        Rational[ 7, 60]}, 5, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\ \(\(sf1 - sf2cr\  /. \ {C01p \[Rule] C01cr, 
              C21p \[Rule] C21cr, C41p \[Rule] 0}\)\  /. \ w2cr\) /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\(27\ xi\^7\)\/70\), "-", \(\(4\ xi\^9\)\/15\), 
        "+", \(\(15\ xi\^11\)\/77\), "-", \(\(27\ xi\^13\)\/182\), 
        "+", \(\(7\ xi\^15\)\/60\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 7, 16, 1]]}],
      SeriesData[ xi, 0, {
        Rational[ 27, 70], 0, 
        Rational[ -4, 15], 0, 
        Rational[ 15, 77], 0, 
        Rational[ -27, 182], 0, 
        Rational[ 7, 60]}, 7, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf3\  = \ 
      Simplify[Series[
            EoverA2, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), 
        "+", \(\(12\ \((\(-11\) + Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\)\), 
        "-", \(\(3\ xi\^5\)\/2\), 
        "-", \(\(16\ \((\(-167\) + 24\ Log[2])\)\ xi\^6\)\/\(315\ \[Pi]\)\), 
        "+", \(\(9\ xi\^7\)\/5\), "-", \(2\ xi\^9\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {1, 
        Times[ 
          Rational[ 12, 35], 
          Power[ Pi, -1], 
          Plus[ -11, 
            Log[ 4]]], 
        Rational[ -3, 2], 
        Times[ 
          Rational[ -16, 315], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Rational[ 9, 5], 0, -2}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf3p = \ 
      Simplify[Series[
            EoverA2p, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), 
        "+", \(\(12\ \((\(-11\) + Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\)\), 
        "-", \(\(3\ xi\^5\)\/2\), 
        "-", \(\(16\ \((\(-167\) + 24\ Log[2])\)\ xi\^6\)\/\(315\ \[Pi]\)\), 
        "+", \(\(9\ xi\^7\)\/5\), "-", \(2\ xi\^9\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {1, 
        Times[ 
          Rational[ 12, 35], 
          Power[ Pi, -1], 
          Plus[ -11, 
            Log[ 4]]], 
        Rational[ -3, 2], 
        Times[ 
          Rational[ -16, 315], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Rational[ 9, 5], 0, -2}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[sf3 - sf3p]\)], "Input"],

Cell[BoxData[
    InterpretationBox[\(O[xi]\^10\),
      SeriesData[ xi, 0, {}, 10, 10, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(sf4cr\  = \ 
        Simplify[
          Series[EoverA2cr, {xi, 0, 15}]/\((\ \(-\((g - 1)\)\) 
                alpha^2\ m^2/\((6\ Pi\ M)\)\ )\)];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(\(sf3 - sf4cr\  /. \ {C01p \[Rule] C01cr, 
              C02p \[Rule] C02cr, delC02p \[Rule] 0, C21p \[Rule] 0, 
              C22p \[Rule] 0, C41p \[Rule] 0, C42p \[Rule] 0}\)\  /. \ 
          w1cr\)\  /. \ Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(3\/10\ \((\(-5\) + 
              m\^2\/Lambdac\^2 + \(4\ m\)\/\(Lambdac\ \@\[Pi]\))\)\ xi\^5\), 
        "-", \(\(8\ \((\((2\ Lambdac\^2 - m\^2)\)\ \((\(-167\) + 
                      24\ Log[
                          2])\))\)\ xi\^6\)\/\(315\ \((Lambdac\^2\ \[Pi])\)\)\
\), "+", \(\(9\ xi\^7\)\/5\), "-", \(2\ xi\^9\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 5, 10, 1]]}],
      SeriesData[ xi, 0, {
        Times[ 
          Rational[ 3, 10], 
          Plus[ -5, 
            Times[ 
              Power[ Lambdac, -2], 
              Power[ m, 2]], 
            Times[ 4, 
              Power[ Lambdac, -1], m, 
              Power[ Pi, 
                Rational[ -1, 2]]]]], 
        Times[ 
          Rational[ -8, 315], 
          Power[ Lambdac, -2], 
          Plus[ 
            Times[ 2, 
              Power[ Lambdac, 2]], 
            Times[ -1, 
              Power[ m, 2]]], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Rational[ 9, 5], 0, -2}, 5, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(\(sf4cr\  /. \ {C01p \[Rule] C01cr, C02p \[Rule] C02cr, 
              delC02p \[Rule] 0, C21p \[Rule] 0, C22p \[Rule] 0, 
              C41p \[Rule] 0, C42p \[Rule] 0}\)\  /. \ w1cr\)\  /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), 
        "+", \(\(12\ \((\(-11\) + Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\)\), 
        "-", \(\(3\ \((m\ \((m + \(4\ Lambdac\)\/\@\[Pi])\))\)\ xi\^5\)\/\(10\
\ Lambdac\^2\)\), 
        "-", \(\(8\ \((m\^2\ \((\(-167\) + 
                      24\ Log[
                          2])\))\)\ xi\^6\)\/\(315\ \((Lambdac\^2\ \[Pi])\)\)\
\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 3, 16, 1]]}],
      SeriesData[ xi, 0, {1, 
        Times[ 
          Rational[ 12, 35], 
          Power[ Pi, -1], 
          Plus[ -11, 
            Log[ 4]]], 
        Times[ 
          Rational[ -3, 10], 
          Power[ Lambdac, -2], m, 
          Plus[ m, 
            Times[ 4, Lambdac, 
              Power[ Pi, 
                Rational[ -1, 2]]]]], 
        Times[ 
          Rational[ -8, 315], 
          Power[ Lambdac, -2], 
          Power[ m, 2], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]]}, 3, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(\(sf3 - sf4cr\  /. \ {C01p \[Rule] C01cr, 
              C02p \[Rule] C02cr, delC02p \[Rule] 0, C21p \[Rule] C21cr, 
              C22p \[Rule] C22cr, C41p \[Rule] 0, C42p \[Rule] 0}\)\  /. \ 
          w2cr\)\  /. \ Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\(9\ xi\^7\)\/5\), "-", \(2\ xi\^9\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 7, 10, 1]]}],
      SeriesData[ xi, 0, {
        Rational[ 9, 5], 0, -2}, 7, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(\(sf4cr\  /. \ {C01p \[Rule] C01cr, C02p \[Rule] C02cr, 
              delC02p \[Rule] 0, C21p \[Rule] C21cr, C22p \[Rule] C22cr, 
              C41p \[Rule] 0, C42p \[Rule] 0}\)\  /. \ w2cr\)\  /. \ 
        Lc \[Rule] Lambdac]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), 
        "+", \(\(12\ \((\(-11\) + Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\)\), 
        "-", \(\(3\ xi\^5\)\/2\), 
        "-", \(\(16\ \((\(-167\) + 24\ Log[2])\)\ xi\^6\)\/\(315\ \[Pi]\)\), 
        "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 3, 16, 1]]}],
      SeriesData[ xi, 0, {1, 
        Times[ 
          Rational[ 12, 35], 
          Power[ Pi, -1], 
          Plus[ -11, 
            Log[ 4]]], 
        Rational[ -3, 2], 
        Times[ 
          Rational[ -16, 315], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]]}, 3, 16, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(sfmaxt1cr[imax_]\  := \ 
      Normal[\ Simplify[\ 
          Series[\((EoverA - EoverAcr)\)/\((\ \((g - 1)\) 
                    alpha\ m^2/\((3\ Pi\ M)\)\ )\), {xi, 0, 
                imax}]\  /. \ {C01p \[Rule] C01cr, C02p \[Rule] C02cr, 
              C21p \[Rule] 0, C22p \[Rule] 0, C41p \[Rule] 0, 
              C42p \[Rule] 0}]\ ]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(sfmaxt1cr[5]\)], "Input"],

Cell[BoxData[
    \(\(\(1\/\(16\ \[Pi]\^\(5/2\)\)\)\((\((4\ \[Pi]\^\(3/2\)\ \((\(-C01cr\)\ \
m\ M + 4\ \[Pi])\) + 
              alpha\ \((C01cr\^2\ Lambdac\ m\ M\^2 - 
                    4\ \[Pi]\^\(3/2\)\ \((C02cr\ m\ M + delC02p\ m\ M + 
                          2\ \[Pi])\))\))\)\ xi\^3)\)\) + \(\(1\/\(160\ \
Lambdac\^2\ \[Pi]\^\(5/2\)\)\)\((3\ \((4\ \[Pi]\^\(3/2\)\ \((C01cr\ m\^3\ M - 
                    8\ Lambdac\^2\ \[Pi])\) + 
              alpha\ \((\(-3\)\ C01cr\^2\ Lambdac\ m\^3\ M\^2 + 
                    4\ \[Pi]\^\(3/2\)\ \((C02cr\ m\^3\ M + delC02p\ m\^3\ M + 
                          10\ Lambdac\^2\ \[Pi])\))\))\)\ xi\^5)\)\) - \(3\ \
alpha\ \((\(-C01cr\^2\)\ m\^2\ M\^2 + 16\ \[Pi]\^2)\)\ xi\^4\ \((\(-11\) + \
Log[4])\)\)\/\(280\ \[Pi]\^3\)\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(<< Graphics`\)], "Input"],

Cell[BoxData[
    \(\(parameters\  = \ {alpha \[Rule] \(- .5\), \ m \[Rule] 600, \ 
          M \[Rule] 939, \ mu \[Rule] 600, \ g \[Rule] 4};\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(factor\  = \ \((\ \((g - 1)\) alpha\ m^2/\((3\ Pi\ M)\)\ )\)\  /. \ 
        parameters\)], "Input"],

Cell[BoxData[
    \(\(-61.01786955599821`\)\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(ximin\  = \  .001; \ \ ximax\  = \ 2; \ \ delxi\  = \ 1.2;\)], "Input"],

Cell[BoxData[
    \(xip[i_]\  := \ ximin\ delxi^i\)], "Input"],

Cell["\<\
To extract this table for use in xmgr or xmgrace, first select it \
(clicking on the bar on the right) and then do Cell->Convert to OutputForm.  \
This gets rid of spaces in the exponent.  Then do Edit->Copy As Plain Text, \
which puts it in the copy buffer.  Open up a new nedit window
or emacs window and you should be able to just \"paste\" the result in \
(ctrl-v or Paste from the Edit menu in Nedit).\
\>", "Text"]
}, Open  ]]
}, Open  ]]
},
FrontEndVersion->"4.0 for X",
ScreenRectangle->{{0, 1280}, {0, 1024}},
WindowSize->{663, 853},
WindowMargins->{{65, Automatic}, {Automatic, 62}},
PrintingPageRange->{Automatic, Automatic},
PrintingOptions->{"PaperSize"->{612, 792},
"PaperOrientation"->"Portrait",
"PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "home", \
"furnstah", "Research", "papers", "nuclear_matter_paper", "Mathematica"}, \
"CR_check.nb.ps", CharacterEncoding -> "ISO8859-1"],
"Magnification"->1}
]


(***********************************************************************
Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of 
the file.  The cache data will then be recreated when you save this file 
from within Mathematica.
***********************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{

Cell[CellGroupData[{
Cell[1739, 51, 166, 4, 83, "Title",
  Evaluatable->False],
Cell[1908, 57, 924, 23, 230, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[2857, 84, 80, 2, 54, "Section",
  Evaluatable->False],
Cell[2940, 88, 240, 6, 50, "Text",
  Evaluatable->False],
Cell[3183, 96, 80, 2, 27, "Input"],
Cell[3266, 100, 148, 5, 32, "Text",
  Evaluatable->False],
Cell[3417, 107, 136, 3, 27, "Input"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3590, 115, 71, 2, 54, "Section",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[3686, 121, 259, 5, 59, "Input"],
Cell[3948, 128, 372, 7, 23, "Print"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[4369, 141, 114, 2, 54, "Section",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[4508, 147, 36, 0, 45, "Subsection"],
Cell[4547, 149, 142, 5, 32, "Text",
  Evaluatable->False],
Cell[4692, 156, 91, 1, 27, "Input"],
Cell[4786, 159, 103, 2, 27, "Input"],
Cell[4892, 163, 153, 5, 32, "Text",
  Evaluatable->False],
Cell[5048, 170, 73, 1, 27, "Input"],
Cell[5124, 173, 232, 6, 50, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[5381, 183, 75, 1, 27, "Input"],
Cell[5459, 186, 142, 2, 59, "Output"]
}, Open  ]],
Cell[5616, 191, 111, 2, 32, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[5752, 197, 72, 1, 27, "Input"],
Cell[5827, 200, 708, 22, 49, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[6572, 227, 160, 2, 43, "Input"],
Cell[6735, 231, 186, 3, 47, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[6970, 240, 34, 0, 45, "Subsection"],
Cell[7007, 242, 96, 2, 32, "Text",
  Evaluatable->False],
Cell[7106, 246, 138, 3, 27, "Input"],
Cell[7247, 251, 114, 2, 32, "Text",
  Evaluatable->False],
Cell[7364, 255, 218, 7, 102, "Input"],

Cell[CellGroupData[{
Cell[7607, 266, 70, 0, 27, "Input"],
Cell[7680, 268, 111, 2, 44, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[7828, 275, 78, 1, 27, "Input"],
Cell[7909, 278, 375, 11, 46, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[8321, 294, 70, 0, 27, "Input"],
Cell[8394, 296, 111, 2, 44, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[8542, 303, 104, 2, 27, "Input"],
Cell[8649, 307, 136, 2, 44, "Output"]
}, Open  ]],
Cell[8800, 312, 104, 2, 27, "Input"],
Cell[8907, 316, 105, 2, 27, "Input"],
Cell[9015, 320, 386, 6, 75, "Input"],
Cell[9404, 328, 369, 6, 75, "Input"],
Cell[9776, 336, 88, 2, 32, "Text",
  Evaluatable->False],
Cell[9867, 340, 153, 4, 57, "Input"],
Cell[10023, 346, 111, 2, 27, "Input"],
Cell[10137, 350, 84, 2, 32, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[10246, 356, 84, 1, 27, "Input"],
Cell[10333, 359, 114, 2, 42, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[10484, 366, 86, 1, 27, "Input"],
Cell[10573, 369, 35, 1, 27, "Output"]
}, Open  ]],
Cell[10623, 373, 87, 2, 32, "Text",
  Evaluatable->False],
Cell[10713, 377, 187, 4, 27, "Input"],

Cell[CellGroupData[{
Cell[10925, 385, 221, 4, 43, "Input"],
Cell[11149, 391, 902, 14, 199, "Output"]
}, Open  ]],
Cell[12066, 408, 149, 3, 27, "Input"],
Cell[12218, 413, 220, 4, 59, "Input"],

Cell[CellGroupData[{
Cell[12463, 421, 242, 5, 59, "Input"],
Cell[12708, 428, 11059, 297, 328, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[23804, 730, 150, 3, 27, "Input"],
Cell[23957, 735, 42, 1, 27, "Output"]
}, Open  ]],
Cell[24014, 739, 111, 2, 32, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[24150, 745, 113, 2, 27, "Input"],
Cell[24266, 749, 145, 2, 52, "Output"]
}, Open  ]],
Cell[24426, 754, 100, 2, 32, "Text",
  Evaluatable->False],
Cell[24529, 758, 127, 2, 27, "Input"],
Cell[24659, 762, 150, 3, 27, "Input"],
Cell[24812, 767, 162, 3, 43, "Input"],
Cell[24977, 772, 136, 5, 32, "Text",
  Evaluatable->False],
Cell[25116, 779, 292, 7, 43, "Input"],
Cell[25411, 788, 316, 6, 91, "Input"],
Cell[25730, 796, 111, 4, 32, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[25866, 804, 164, 4, 27, "Input"],
Cell[26033, 810, 146, 2, 47, "Output"]
}, Open  ]],
Cell[26194, 815, 141, 5, 32, "Text",
  Evaluatable->False],

Cell[CellGroupData[{
Cell[26360, 824, 72, 1, 27, "Input"],
Cell[26435, 827, 532, 13, 29, "Output"]
}, Open  ]],
Cell[26982, 843, 192, 4, 43, "Input"],
Cell[27177, 849, 262, 6, 75, "Input"],

Cell[CellGroupData[{
Cell[27464, 859, 89, 1, 27, "Input"],
Cell[27556, 862, 1016, 28, 44, "Output"]
}, Open  ]],
Cell[28587, 893, 391, 7, 107, "Input"],

Cell[CellGroupData[{
Cell[29003, 904, 243, 4, 75, "Input"],
Cell[29249, 910, 1865, 53, 96, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[31151, 968, 178, 4, 43, "Input"],
Cell[31332, 974, 511, 8, 125, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[31880, 987, 72, 1, 27, "Input"],
Cell[31955, 990, 532, 13, 29, "Output"]
}, Open  ]],
Cell[32502, 1006, 192, 4, 43, "Input"],

Cell[CellGroupData[{
Cell[32719, 1014, 89, 1, 27, "Input"],
Cell[32811, 1017, 1339, 37, 51, "Output"]
}, Open  ]],
Cell[34165, 1057, 406, 7, 123, "Input"],

Cell[CellGroupData[{
Cell[34596, 1068, 243, 4, 75, "Input"],
Cell[34842, 1074, 3194, 90, 140, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[38073, 1169, 192, 4, 75, "Input"],
Cell[38268, 1175, 1166, 17, 248, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[39471, 1197, 72, 1, 27, "Input"],
Cell[39546, 1200, 532, 13, 29, "Output"]
}, Open  ]],
Cell[40093, 1216, 67, 1, 27, "Input"],
Cell[40163, 1219, 128, 2, 27, "Input"],

Cell[CellGroupData[{
Cell[40316, 1225, 59, 1, 27, "Input"],
Cell[40378, 1228, 35, 1, 27, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[40450, 1234, 108, 2, 27, "Input"],
Cell[40561, 1238, 35, 1, 27, "Output"]
}, Open  ]],
Cell[40611, 1242, 107, 2, 27, "Input"],

Cell[CellGroupData[{
Cell[40743, 1248, 186, 4, 59, "Input"],
Cell[40932, 1254, 128, 2, 47, "Output"]
}, Open  ]],
Cell[41075, 1259, 464, 8, 91, "Input"],

Cell[CellGroupData[{
Cell[41564, 1271, 136, 3, 27, "Input"],
Cell[41703, 1276, 128, 2, 47, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[41868, 1283, 154, 3, 27, "Input"],
Cell[42025, 1288, 128, 2, 47, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[42190, 1295, 120, 2, 27, "Input"],
Cell[42313, 1299, 35, 1, 27, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[42385, 1305, 108, 2, 27, "Input"],
Cell[42496, 1309, 35, 1, 27, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[42568, 1315, 108, 2, 27, "Input"],
Cell[42679, 1319, 35, 1, 27, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[42775, 1327, 89, 2, 54, "Section",
  Evaluatable->False],
Cell[42867, 1331, 45, 1, 27, "Input"],

Cell[CellGroupData[{
Cell[42937, 1336, 112, 2, 27, "Input"],
Cell[43052, 1340, 164, 2, 49, "Output"]
}, Open  ]],
Cell[43231, 1345, 293, 5, 91, "Input"],
Cell[43527, 1352, 26, 0, 27, "Input"],
Cell[43556, 1354, 346, 6, 107, "Input"],
Cell[43905, 1362, 386, 6, 107, "Input"],
Cell[44294, 1370, 209, 3, 43, "Input"],
Cell[44506, 1375, 91, 1, 27, "Input"],

Cell[CellGroupData[{
Cell[44622, 1380, 85, 1, 27, "Input"],
Cell[44710, 1383, 176, 3, 50, "Output"]
}, Open  ]],
Cell[44901, 1389, 62, 1, 27, "Input"],

Cell[CellGroupData[{
Cell[44988, 1394, 771, 13, 123, "Input"],
Cell[45762, 1409, 29401, 1035, 186, 17568, 885, "GraphicsData", "PostScript", \
"Graphics"],
Cell[75166, 2446, 130, 3, 27, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[75333, 2454, 1016, 16, 171, "Input"],
Cell[76352, 2472, 36317, 931, 532, "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{
Cell[112718, 3409, 90, 2, 54, "Section",
  Evaluatable->False],
Cell[112811, 3413, 137, 5, 50, "Text",
  Evaluatable->False],
Cell[112951, 3420, 48, 1, 27, "Input"],
Cell[113002, 3423, 65, 1, 27, "Input"],
Cell[113070, 3426, 70, 1, 27, "Input"],
Cell[113143, 3429, 85, 1, 27, "Input"],
Cell[113231, 3432, 86, 1, 27, "Input"],
Cell[113320, 3435, 255, 6, 43, "Input"],
Cell[113578, 3443, 168, 3, 27, "Input"],
Cell[113749, 3448, 82, 1, 27, "Input"],
Cell[113834, 3451, 262, 6, 43, "Input"],
Cell[114099, 3459, 167, 3, 27, "Input"],

Cell[CellGroupData[{
Cell[114291, 3466, 101, 2, 27, "Input"],
Cell[114395, 3470, 653, 16, 46, "Output"]
}, Open  ]],
Cell[115063, 3489, 204, 4, 27, "Input"],
Cell[115270, 3495, 74, 1, 27, "Input"],
Cell[115347, 3498, 241, 4, 43, "Input"],
Cell[115591, 3504, 130, 3, 27, "Input"],
Cell[115724, 3509, 508, 10, 107, "Input"],
Cell[116235, 3521, 254, 5, 43, "Input"],
Cell[116492, 3528, 1161, 20, 203, "Input"],

Cell[CellGroupData[{
Cell[117678, 3552, 139, 3, 27, "Input"],
Cell[117820, 3557, 580, 13, 46, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[118437, 3575, 143, 3, 27, "Input"],
Cell[118583, 3580, 629, 18, 51, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[119249, 3603, 145, 2, 27, "Input"],
Cell[119397, 3607, 724, 19, 51, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[120158, 3631, 188, 3, 43, "Input"],
Cell[120349, 3636, 502, 12, 46, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[120888, 3653, 166, 4, 27, "Input"],
Cell[121057, 3659, 775, 22, 84, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[121869, 3686, 166, 4, 27, "Input"],
Cell[122038, 3692, 775, 22, 84, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[122850, 3719, 53, 1, 27, "Input"],
Cell[122906, 3722, 103, 2, 29, "Output"]
}, Open  ]],
Cell[123024, 3727, 182, 4, 27, "Input"],

Cell[CellGroupData[{
Cell[123231, 3735, 272, 4, 59, "Input"],
Cell[123506, 3741, 1142, 33, 94, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[124685, 3779, 264, 4, 59, "Input"],
Cell[124952, 3785, 1059, 32, 112, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[126048, 3822, 280, 4, 59, "Input"],
Cell[126331, 3828, 267, 6, 46, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[126635, 3839, 272, 4, 59, "Input"],
Cell[126910, 3845, 697, 21, 46, "Output"]
}, Open  ]],
Cell[127622, 3869, 373, 7, 91, "Input"],

Cell[CellGroupData[{
Cell[128020, 3880, 45, 1, 27, "Input"],
Cell[128068, 3883, 785, 12, 155, "Output"]
}, Open  ]],
Cell[128868, 3898, 45, 1, 27, "Input"],
Cell[128916, 3901, 157, 2, 27, "Input"],

Cell[CellGroupData[{
Cell[129098, 3907, 120, 2, 27, "Input"],
Cell[129221, 3911, 57, 1, 27, "Output"]
}, Open  ]],
Cell[129293, 3915, 91, 1, 27, "Input"],
Cell[129387, 3918, 62, 1, 27, "Input"],
Cell[129452, 3921, 430, 7, 86, "Text"]
}, Open  ]]
}, Open  ]]
}
]
*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)