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For the function Abs(x*y) we suspect the non differentiability in the \
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0 g
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s
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F
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0 g
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Cell["\<\
We show \"peaks and valleys\". We suspect again that the limit does not \
exist.\
\>", "Text",
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}, Closed]],

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Cell["Numerical evaluation.", "Subsection",
  FontSize->24,
  FontColor->RGBColor[1, 0, 0],
  Background->RGBColor[1, 1, 0],
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Cell["\<\
We do a table of values of the functionin ponints in a neighbour of the \
origin.\
\>", "Text",
  FontSize->18],

Cell[BoxData[
    \(f[x_, y_] := \(x\ y\)\/\(x\^2 + y\^2\)\)], "Input",
  FontSize->18],

Cell["We declare the step and the points.", "Text",
  FontSize->18],

Cell[BoxData[
    \(n = 5; h = 0.1;\)], "Input",
  FontSize->18],

Cell[CellGroupData[{

Cell[BoxData[
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        0.3448275862068966`}, {0.3`, 0.4615384615384615`, 0.5`, 0.48`, 
        0.44117647058823534`}, {0.2352941176470588`, 0.39999999999999997`, 
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  FontSize->18]
}, Open  ]],

Cell[TextData[{
  "To visualize with ",
  ButtonBox["TableForm",
    ButtonStyle->"RefGuideLink"]
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  FontSize->18],

Cell[CellGroupData[{

Cell[BoxData[
    \(TableForm[
      Table[f[0 + j\ h, 0 + k\ h], {j, 1, n}, {k, 1, n}]]\)], "Input",
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Cell[BoxData[
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            "0.2352941176470588`", "0.1923076923076923`"},
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            "0.39999999999999997`", "0.3448275862068966`"},
          {"0.3`", "0.4615384615384615`", "0.5`", "0.48`", 
            "0.44117647058823534`"},
          {"0.2352941176470588`", "0.39999999999999997`", "0.48`", "0.5`", 
            "0.4878048780487805`"},
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Cell["Less step and more points.", "Text",
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Cell[BoxData[
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Cell[CellGroupData[{

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            "0.48000000000000004`", "0.49557522123893805`", "0.5`", 
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            "0.4245283018867924`", "0.46153846153846156`", 
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  " allow us the evaluation of the composition of two functions."
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                  Table[v1\[LeftDoubleBracket]k\[RightDoubleBracket] \[Rule] 
                      f2\[LeftDoubleBracket]k\[RightDoubleBracket], {k, 1, 
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                      f2\[LeftDoubleBracket]k\[RightDoubleBracket], {k, 1, 
                      Length[v1]}])\) . jacobiana[f2, v2] /. 
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                    Table[v1\[LeftDoubleBracket]
                          k\[RightDoubleBracket] \[Rule] 
                        f2\[LeftDoubleBracket]k\[RightDoubleBracket], {k, 1, 
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  "The temperature of a plate at any point (x,y) is given by the function \
T(x,y) = 25 + 4x",
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  " - 4xy+y",
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Will the alarm be triggered? "
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We use Lagrange multipliers. Define the function and the condition.\
\>", "Text",
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        y \[Rule] \(-\@5\)}, {\[Lambda] \[Rule] 0, x \[Rule] \(-\@5\), 
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Cell[BoxData[
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Cell["We evaluate the temperature in any point", "Text",
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Cell[CellGroupData[{

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Cell[CellGroupData[{

Cell[TextData[StyleBox["NEGATIVE  ASPECTS.",
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  FontColor->RGBColor[1, 0, 0]]], "Title",
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Cell[CellGroupData[{

Cell[TextData[StyleBox["Computational problems.",
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        eqns = {\[PartialD]\_x\ F[x, y] == 0, \[PartialD]\_y\ F[x, y] == 0, 
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a) astroid ",
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Cell[TextData[{
  "Remark:\nWe optimize ",
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Cell[BoxData[
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Cell[TextData[{
  "El punto es: (",
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Cell["\<\
Very complicated solutions.
Some interpretation: The origin is a point of the curve.\
\>", "Text",
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        y \[Rule] 0, \[Lambda] \[Rule] 
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Cell["No solutions found.", "Text",
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Cell[CellGroupData[{

Cell[TextData[StyleBox["SURPRISING  RESULTS.",
  FontSize->48,
  FontColor->RGBColor[1, 0, 0]]], "Title",
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Cell[CellGroupData[{

Cell[TextData[StyleBox["BUGS",
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  TextJustification->0,
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Cell[CellGroupData[{

Cell[TextData[StyleBox["Gamma function.",
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Cell[TextData[{
  "We define a function ",
  StyleBox["identically cero ",
    Background->RGBColor[0, 1, 1]],
  "(It is the main property of gamma function). But  ",
  StyleBox["surprise!",
    Background->RGBColor[1, 1, 0]]
}], "Text",
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Cell[BoxData[
    \(h[p_] := Gamma[p + 1] - p\ Gamma[p]\)], "Input",
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Cell[CellGroupData[{

Cell[BoxData[
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  FontSize->20],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[TextData[StyleBox["APPROXIMATING Pi.",
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Cell[CellGroupData[{

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Cell["Exact aritmetic", "Text",
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell["Approximation:", "Text",
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \(3.1415926535897932384626433833`18\)], "Output"]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["ONE SIDE LIMITS.",
  FontColor->RGBColor[1, 0, 0]]], "Title"],

Cell[TextData[{
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " has some options to evaluate limits of functions, approaching from the \
left ( with the option Direction\[Rule]1)  and from the right (with the \
option Direction\[Rule]-1). But if the limits are no equal and therefore the \
limit does not exist we try to find the limit and the ",
  StyleBox["Mathematica ",
    FontSlant->"Italic"],
  "answer is the same that the limit from the right."
}], "Text",
  FontSize->20],

Cell[CellGroupData[{

Cell[BoxData[
    \(Limit[\(1 + \[ExponentialE]\^\(1\/x\)\)\/\(1 - \
\[ExponentialE]\^\(1\/x\)\), x -> 0, Direction -> 1]\)], "Input",
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Cell[BoxData[
    \(1\)], "Output",
  FontSize->20]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Limit[\(1 + \[ExponentialE]\^\(1\/x\)\)\/\(1 - \
\[ExponentialE]\^\(1\/x\)\), x -> 0, Direction -> \(-1\)]\)], "Input",
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Cell[BoxData[
    \(\(-1\)\)], "Output",
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Cell[CellGroupData[{

Cell[BoxData[
    \(Limit[\(1 + \[ExponentialE]\^\(1\/x\)\)\/\(1 - \
\[ExponentialE]\^\(1\/x\)\), x -> 0]\)], "Input",
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Cell[BoxData[
    \(\(-1\)\)], "Output",
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Cell[TextData[StyleBox["PIECEWISE FUNCTIONS.",
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Cell[TextData[{
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  " offers the possiblity to define piecewiese functions with If or Which. ",
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  " find the limit and otther things ",
  StyleBox["INCORRECTLY.",
    Background->RGBColor[1, 1, 0]],
  " "
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  FontSize->20],

Cell["The function", "Text",
  FontSize->20],

Cell[BoxData[
    \(f[x_] := If[x <= 0, x, Sin[x]]\)], "Input",
  FontSize->20],

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Cell[CellGroupData[{

Cell[BoxData[
    \(Limit[f[x], x -> 0]\)], "Input",
  FontSize->20],

Cell[BoxData[
    \(Limit[If[x \[LessEqual] 0, x, Sin[x]], x \[Rule] 0]\)], "Output",
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Cell[CellGroupData[{

Cell[BoxData[
    \(Limit[f[x], x -> 0, Direction -> 1]\)], "Input",
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Cell[BoxData[
    \(Limit[If[x \[LessEqual] 0, x, Sin[x]], x \[Rule] 0, 
      Direction \[Rule] 1]\)], "Output",
  FontSize->18]
}, Open  ]],

Cell["Derivative.", "Text",
  FontSize->20],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(f'\)[x]\)], "Input",
  FontSize->20],

Cell[BoxData[
    \(If[x \[LessEqual] 0, 1, Cos[x]]\)], "Output",
  FontSize->18]
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Cell[TextData[{
  StyleBox["Mathematica",
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  " ",
  StyleBox["forgets the point 0",
    Background->RGBColor[1, 1, 0]],
  ", when the rule of definition is changed."
}], "Text",
  FontSize->20]
}, Closed]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["LIMITATIONS.",
  FontFamily->"Arial",
  FontSize->50,
  FontColor->RGBColor[0, 0, 0.500008]]], "Title",
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  TextJustification->0,
  FontSize->35],

Cell[CellGroupData[{

Cell[TextData[StyleBox["DIFFICULT CALCULATIONS",
  FontColor->RGBColor[1, 0, 0]]], "Title"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["a) Some derivatives",
  FontColor->RGBColor[1, 0, 0]]], "Title"],

Cell[TextData[{
  "If we try to evaluate derivatives of high orders ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " ",
  "can\.b4t do it",
  "."
}], "Text",
  FontSize->20],

Cell["For example for the function:", "Text",
  FontSize->20],

Cell[BoxData[
    \(f[x_] := Sin[x]*Log[x]/\((x^2 + 2)\)\)], "Input"],

Cell["Some derivatives:", "Text",
  FontSize->20],

Cell[CellGroupData[{

Cell[BoxData[
    \(D[f[x], x]\)], "Input",
  FontSize->20],

Cell[BoxData[
    \(\(Cos[x]\ Log[x]\)\/\(2 + x\^2\) + 
      Sin[x]\/\(x\ \((2 + x\^2)\)\) - \(2\ x\ Log[x]\ Sin[x]\)\/\((2 + \
x\^2)\)\^2\)], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(D[f[x], {x, 8}]\)], "Input",
  FontSize->20],

Cell[BoxData[
    \(\(-8\)\ Cos[
          x]\ \((1\/\(x\ \((2 + x\^2)\)\) - \(2\ x\ Log[x]\)\/\((2 + \
x\^2)\)\^2)\) + 
      8\ Cos[x]\ \((1680\/\(x\^5\ \((2 + x\^2)\)\^2\) + 
            720\/\(x\^7\ \((2 + x\^2)\)\) + \(7\ \((\(46080\ x\^6\)\/\((2 + x\
\^2)\)\^7 - \(57600\ x\^4\)\/\((2 + x\^2)\)\^6 + \(17280\ x\^2\)\/\((2 + \
x\^2)\)\^5 - 720\/\((2 + x\^2)\)\^4)\)\)\/x - \(21\ \((\(-\(\(3840\ \
x\^5\)\/\((2 + x\^2)\)\^6\)\) + \(3840\ x\^3\)\/\((2 + x\^2)\)\^5 - \(720\ \
x\)\/\((2 + x\^2)\)\^4)\)\)\/x\^2 + \(70\ \((\(384\ x\^4\)\/\((2 + x\^2)\)\^5 \
- \(288\ x\^2\)\/\((2 + x\^2)\)\^4 + 24\/\((2 + x\^2)\)\^3)\)\)\/x\^3 - \(210\
\ \((\(-\(\(48\ x\^3\)\/\((2 + x\^2)\)\^4\)\) + \(24\ x\)\/\((2 + x\^2)\)\^3)\
\)\)\/x\^4 + \(504\ \((\(8\ x\^2\)\/\((2 + x\^2)\)\^3 - 2\/\((2 + x\^2)\)\^2)\
\)\)\/x\^5 + \((\(-\(\(645120\ x\^7\)\/\((2 + x\^2)\)\^8\)\) + \(967680\ x\^5\
\)\/\((2 + x\^2)\)\^7 - \(403200\ x\^3\)\/\((2 + x\^2)\)\^6 + \(40320\ \
x\)\/\((2 + x\^2)\)\^5)\)\ Log[x])\) - 
      56\ Cos[x]\ \((60\/\(x\^3\ \((2 + x\^2)\)\^2\) + 
            24\/\(x\^5\ \((2 + x\^2)\)\) + \(5\ \((\(384\ x\^4\)\/\((2 + \
x\^2)\)\^5 - \(288\ x\^2\)\/\((2 + x\^2)\)\^4 + 24\/\((2 + x\^2)\)\^3)\)\)\/x \
- \(10\ \((\(-\(\(48\ x\^3\)\/\((2 + x\^2)\)\^4\)\) + \(24\ x\)\/\((2 + x\^2)\
\)\^3)\)\)\/x\^2 + \(20\ \((\(8\ x\^2\)\/\((2 + x\^2)\)\^3 - 2\/\((2 + \
x\^2)\)\^2)\)\)\/x\^3 + \((\(-\(\(3840\ x\^5\)\/\((2 + x\^2)\)\^6\)\) + \
\(3840\ x\^3\)\/\((2 + x\^2)\)\^5 - \(720\ x\)\/\((2 + x\^2)\)\^4)\)\ Log[
                x])\) + 
      56\ Cos[x]\ \((6\/\(x\ \((2 + x\^2)\)\^2\) + 
            2\/\(x\^3\ \((2 + x\^2)\)\) + \(3\ \((\(8\ x\^2\)\/\((2 + x\^2)\)\
\^3 - 2\/\((2 + x\^2)\)\^2)\)\)\/x + \((\(-\(\(48\ x\^3\)\/\((2 + \
x\^2)\)\^4\)\) + \(24\ x\)\/\((2 + x\^2)\)\^3)\)\ Log[
                x])\) + \(Log[x]\ Sin[x]\)\/\(2 + x\^2\) + \((\(-\(11520\/\(x\
\^6\ \((2 + x\^2)\)\^2\)\)\) - 
            5040\/\(x\^8\ \((2 + x\^2)\)\) + \(8\ \((\(-\(\(645120\ \
x\^7\)\/\((2 + x\^2)\)\^8\)\) + \(967680\ x\^5\)\/\((2 + x\^2)\)\^7 - \
\(403200\ x\^3\)\/\((2 + x\^2)\)\^6 + \(40320\ x\)\/\((2 + x\^2)\)\^5)\)\)\/x \
- \(28\ \((\(46080\ x\^6\)\/\((2 + x\^2)\)\^7 - \(57600\ x\^4\)\/\((2 + x\^2)\
\)\^6 + \(17280\ x\^2\)\/\((2 + x\^2)\)\^5 - 720\/\((2 + \
x\^2)\)\^4)\)\)\/x\^2 + \(112\ \((\(-\(\(3840\ x\^5\)\/\((2 + x\^2)\)\^6\)\) \
+ \(3840\ x\^3\)\/\((2 + x\^2)\)\^5 - \(720\ x\)\/\((2 + \
x\^2)\)\^4)\)\)\/x\^3 - \(420\ \((\(384\ x\^4\)\/\((2 + x\^2)\)\^5 - \(288\ x\
\^2\)\/\((2 + x\^2)\)\^4 + 24\/\((2 + x\^2)\)\^3)\)\)\/x\^4 + \(1344\ \
\((\(-\(\(48\ x\^3\)\/\((2 + x\^2)\)\^4\)\) + \(24\ x\)\/\((2 + x\^2)\)\^3)\)\
\)\/x\^5 - \(3360\ \((\(8\ x\^2\)\/\((2 + x\^2)\)\^3 - 2\/\((2 + \
x\^2)\)\^2)\)\)\/x\^6 + \((\(10321920\ x\^8\)\/\((2 + x\^2)\)\^9 - \(18063360\
\ x\^6\)\/\((2 + x\^2)\)\^8 + \(9676800\ x\^4\)\/\((2 + x\^2)\)\^7 - \
\(1612800\ x\^2\)\/\((2 + x\^2)\)\^6 + 40320\/\((2 + x\^2)\)\^5)\)\ Log[
                x])\)\ Sin[x] - 
      28\ \((\(-\(288\/\(x\^4\ \((2 + x\^2)\)\^2\)\)\) - 
            120\/\(x\^6\ \((2 + x\^2)\)\) + \(6\ \((\(-\(\(3840\ x\^5\)\/\((2 \
+ x\^2)\)\^6\)\) + \(3840\ x\^3\)\/\((2 + x\^2)\)\^5 - \(720\ x\)\/\((2 + \
x\^2)\)\^4)\)\)\/x - \(15\ \((\(384\ x\^4\)\/\((2 + x\^2)\)\^5 - \(288\ \
x\^2\)\/\((2 + x\^2)\)\^4 + 24\/\((2 + x\^2)\)\^3)\)\)\/x\^2 + \(40\ \((\(-\(\
\(48\ x\^3\)\/\((2 + x\^2)\)\^4\)\) + \(24\ x\)\/\((2 + x\^2)\)\^3)\)\)\/x\^3 \
- \(90\ \((\(8\ x\^2\)\/\((2 + x\^2)\)\^3 - 2\/\((2 + x\^2)\)\^2)\)\)\/x\^4 + \
\((\(46080\ x\^6\)\/\((2 + x\^2)\)\^7 - \(57600\ x\^4\)\/\((2 + x\^2)\)\^6 + \
\(17280\ x\^2\)\/\((2 + x\^2)\)\^5 - 720\/\((2 + x\^2)\)\^4)\)\ Log[
                x])\)\ Sin[x] + 
      70\ \((\(-\(16\/\(x\^2\ \((2 + x\^2)\)\^2\)\)\) - 
            6\/\(x\^4\ \((2 + x\^2)\)\) + \(4\ \((\(-\(\(48\ x\^3\)\/\((2 + x\
\^2)\)\^4\)\) + \(24\ x\)\/\((2 + x\^2)\)\^3)\)\)\/x - \(6\ \((\(8\ \
x\^2\)\/\((2 + x\^2)\)\^3 - 2\/\((2 + x\^2)\)\^2)\)\)\/x\^2 + \((\(384\ \
x\^4\)\/\((2 + x\^2)\)\^5 - \(288\ x\^2\)\/\((2 + x\^2)\)\^4 + 
                  24\/\((2 + x\^2)\)\^3)\)\ Log[x])\)\ Sin[x] - 
      28\ \((\(-\(4\/\((2 + x\^2)\)\^2\)\) - 
            1\/\(x\^2\ \((2 + x\^2)\)\) + \((\(8\ x\^2\)\/\((2 + x\^2)\)\^3 - 
                  2\/\((2 + x\^2)\)\^2)\)\ Log[x])\)\ Sin[x]\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "If we try to evaluate derivatives of very high orders ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " can\.b4t do it."
}], "Text",
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[TextData[StyleBox["b) Some limits",
  FontColor->RGBColor[1, 0, 0]]], "Title"],

Cell[TextData[{
  "If we try to evaluate elementary limits, using another type of arguments, \
",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " spent a lot of time."
}], "Text",
  FontSize->20],

Cell[TextData[StyleBox["For example Sin(x) and x are equivalents for  x \
small.",
  FontSize->24,
  FontColor->RGBColor[1, 0, 1]]], "Title",
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Cell["But we spent a lot of time for large powers.", "Text",
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    \({20.529`\ Second, 1}\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(Timing[Limit[Sin[x]\^20\/x\^20, x -> 0]]\)], "Input",
  FontSize->20],

Cell[BoxData[
    \(Timing[Limit[Sin[x]\^30\/x\^30, x -> 0]]\)], "Input",
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Cell[BoxData[
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Cell[BoxData[
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}, Closed]]
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Cell[CellGroupData[{

Cell[TextData[StyleBox["SIMPLIFICATIONS",
  FontColor->RGBColor[1, 0, 0]]], "Title"],

Cell["The matrix ", "Text",
  FontSize->20],

Cell[BoxData[
    RowBox[{\(h[a_]\), ":=", 
      RowBox[{"(", GridBox[{
            {"a", "a", "a"},
            {"a", "a", "a"},
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Cell[CellGroupData[{

Cell[BoxData[
    \(NullSpace[h[a]]\)], "Input",
  FontSize->20],

Cell[BoxData[
    \({{\(-1\), 0, 1}, {\(-1\), 1, 0}}\)], "Output",
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Cell[TextData[{
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " ",
  StyleBox["forgets the case a=0",
    Background->RGBColor[1, 1, 0]],
  "."
}], "Text",
  FontSize->20]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["UNEXPECTED RESULTS.",
  FontFamily->"Arial",
  FontSize->50,
  FontColor->RGBColor[0, 0, 0.500008]]], "Title",
  TextAlignment->Center,
  TextJustification->0,
  FontSize->35],

Cell[CellGroupData[{

Cell[TextData[StyleBox["REAL AND COMPLEX DOMAINS.",
  FontColor->RGBColor[1, 0, 0]]], "Title"],

Cell["The function", "Text",
  FontSize->20],

Cell[BoxData[
    \(h[x_] := Exp[\(-1\)/Log[x]]\)], "Input",
  FontSize->20],

Cell["The one side limits in 0.", "Text",
  FontSize->20],

Cell[CellGroupData[{

Cell[BoxData[
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  FontSize->20],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell["We evaluate the function in a negative number:", "Text",
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Cell[BoxData[
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Cell[BoxData[
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              StyleBox[ 
                AdjustmentBox[ 
                "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, 
                  BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", 
              AdjustmentBox[ 
              "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 
                0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", 
        "MMA"->"Mathematica"},
    LanguageCategory->"NaturalLanguage",
    CounterIncrements->"Subsection",
    CounterAssignments->{{"Subsubsection", 0}},
    FontFamily->"Times",
    FontSize->14,
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsection", "Presentation"],
    CellMargins->{{36, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontSize->22],
  
  Cell[StyleData["Subsection", "Condensed"],
    CellMargins->{{16, Inherited}, {6, 12}},
    FontSize->12],
  
  Cell[StyleData["Subsection", "Printout"],
    CellMargins->{{9, 0}, {7, 22}},
    FontSize->12]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsubsection"],
    CellDingbat->"\[FilledSmallSquare]",
    CellMargins->{{22, Inherited}, {8, 18}},
    CellGroupingRules->{"SectionGrouping", 50},
    PageBreakBelow->False,
    DefaultNewInlineCellStyle->"None",
    InputAutoReplacements->{"TeX"->StyleBox[ 
            RowBox[ {"T", 
              AdjustmentBox[ 
              "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 
                0.5], "X"}]], "LaTeX"->StyleBox[ 
            RowBox[ {"L", 
              StyleBox[ 
                AdjustmentBox[ 
                "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, 
                  BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", 
              AdjustmentBox[ 
              "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 
                0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", 
        "MMA"->"Mathematica"},
    LanguageCategory->"NaturalLanguage",
    CounterIncrements->"Subsubsection",
    FontFamily->"Times",
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsubsection", "Presentation"],
    CellMargins->{{34, 10}, {11, 26}},
    LineSpacing->{1, 0},
    FontSize->18],
  
  Cell[StyleData["Subsubsection", "Condensed"],
    CellMargins->{{17, Inherited}, {6, 12}},
    FontSize->10],
  
  Cell[StyleData["Subsubsection", "Printout"],
    CellMargins->{{9, 0}, {7, 14}},
    FontSize->11]
  }, Closed]]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Body Text", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Text"],
    CellMargins->{{12, 10}, {7, 7}},
    InputAutoReplacements->{"TeX"->StyleBox[ 
            RowBox[ {"T", 
              AdjustmentBox[ 
              "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 
                0.5], "X"}]], "LaTeX"->StyleBox[ 
            RowBox[ {"L", 
              StyleBox[ 
                AdjustmentBox[ 
                "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, 
                  BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", 
              AdjustmentBox[ 
              "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 
                0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", 
        "MMA"->"Mathematica"},
    Hyphenation->True,
    LineSpacing->{1, 3},
    CounterIncrements->"Text"],
  
  Cell[StyleData["Text", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["Text", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["Text", "Printout"],
    CellMargins->{{2, 2}, {6, 6}},
    TextJustification->0.5,
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SmallText"],
    CellMargins->{{12, 10}, {6, 6}},
    DefaultNewInlineCellStyle->"None",
    Hyphenation->True,
    LineSpacing->{1, 3},
    LanguageCategory->"NaturalLanguage",
    CounterIncrements->"SmallText",
    FontFamily->"Helvetica",
    FontSize->9],
  
  Cell[StyleData["SmallText", "Presentation"],
    CellMargins->{{24, 10}, {8, 8}},
    LineSpacing->{1, 5},
    FontSize->12],
  
  Cell[StyleData["SmallText", "Condensed"],
    CellMargins->{{8, 10}, {5, 5}},
    LineSpacing->{1, 2},
    FontSize->9],
  
  Cell[StyleData["SmallText", "Printout"],
    CellMargins->{{2, 2}, {5, 5}},
    TextJustification->0.5,
    FontSize->7]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Input/Output", "Section"],
  
  Cell["\<\
The cells in this section define styles used for input and output to the \
kernel.  Be careful when modifying, renaming, or removing these styles, \
because the front end associates special meanings with these style names. \
Some attributes for these styles are actually set in FormatType Styles (in \
the last section of this stylesheet). \
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Input"],
    CellMargins->{{45, 10}, {5, 7}},
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    DefaultFormatType->DefaultInputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    AutoItalicWords->{},
    LanguageCategory->"Formula",
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    LinebreakAdjustments->{0.85, 2, 10, 0, 1},
    CounterIncrements->"Input",
    FontWeight->"Bold"],
  
  Cell[StyleData["Input", "Presentation"],
    CellMargins->{{72, Inherited}, {8, 10}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Input", "Condensed"],
    CellMargins->{{40, 10}, {2, 3}},
    FontSize->11],
  
  Cell[StyleData["Input", "Printout"],
    CellMargins->{{39, 0}, {4, 6}},
    LinebreakAdjustments->{0.85, 2, 10, 1, 1},
    FontSize->9]
  }, Closed]],
  
  Cell[StyleData["InputOnly"],
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    AutoItalicWords->{},
    LanguageCategory->"Formula",
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    LinebreakAdjustments->{0.85, 2, 10, 0, 1},
    CounterIncrements->"Input",
    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Output"],
    CellMargins->{{47, 10}, {7, 5}},
    CellEditDuplicate->True,
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    DefaultFormatType->DefaultOutputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    AutoItalicWords->{},
    LanguageCategory->"Formula",
    FormatType->InputForm,
    CounterIncrements->"Output"],
  
  Cell[StyleData["Output", "Presentation"],
    CellMargins->{{72, Inherited}, {10, 8}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Output", "Condensed"],
    CellMargins->{{41, Inherited}, {3, 2}},
    FontSize->11],
  
  Cell[StyleData["Output", "Printout"],
    CellMargins->{{39, 0}, {6, 4}},
    FontSize->9]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Message"],
    CellMargins->{{45, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"OutputGrouping",
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Message",
    StyleMenuListing->None,
    FontSize->11,
    FontColor->RGBColor[0, 0, 1]],
  
  Cell[StyleData["Message", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Message", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontSize->11],
  
  Cell[StyleData["Message", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->7,
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Print"],
    CellMargins->{{45, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Print",
    StyleMenuListing->None],
  
  Cell[StyleData["Print", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Print", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontSize->11],
  
  Cell[StyleData["Print", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Graphics"],
    CellMargins->{{4, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"GraphicsGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    LanguageCategory->None,
    FormatType->InputForm,
    CounterIncrements->"Graphics",
    ImageMargins->{{43, Inherited}, {Inherited, 0}},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->10],
  
  Cell[StyleData["Graphics", "Presentation"],
    ImageMargins->{{62, Inherited}, {Inherited, 0}}],
  
  Cell[StyleData["Graphics", "Condensed"],
    ImageMargins->{{38, Inherited}, {Inherited, 0}},
    Magnification->0.6],
  
  Cell[StyleData["Graphics", "Printout"],
    ImageMargins->{{30, Inherited}, {Inherited, 0}},
    Magnification->0.8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["CellLabel"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->9,
    FontColor->RGBColor[0, 0, 1]],
  
  Cell[StyleData["CellLabel", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["CellLabel", "Condensed"],
    FontSize->9],
  
  Cell[StyleData["CellLabel", "Printout"],
    FontFamily->"Courier",
    FontSize->8,
    FontSlant->"Italic",
    FontColor->GrayLevel[0]]
  }, Closed]]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell["Inline Formatting", "Section"],
  
  Cell["\<\
These styles are for modifying individual words or letters in a cell \
exclusive of the cell tag.\
\>", "Text"],
  
  Cell[StyleData["RM"],
    StyleMenuListing->None,
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["BF"],
    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[StyleData["IT"],
    StyleMenuListing->None,
    FontSlant->"Italic"],
  
  Cell[StyleData["TR"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["TI"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["TB"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["TBI"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[StyleData["MR"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["MO"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["MB"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["MBO"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[StyleData["SR"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["SO"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SB"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["SBO"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SO10"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->10,
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SO10", "Printout"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->7,
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SO10", "EnhancedPrintout"],
    StyleMenuListing->None,
    FontFamily->"Futura",
    FontSize->7,
    FontWeight->"Plain",
    FontSlant->"Italic"]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Formulas and Programming", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["InlineFormula"],
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    LanguageCategory->"Formula",
    ScriptLevel->1,
    SingleLetterItalics->True],
  
  Cell[StyleData["InlineFormula", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["InlineFormula", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["InlineFormula", "Printout"],
    CellMargins->{{2, 0}, {6, 6}},
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["DisplayFormula"],
    CellMargins->{{42, Inherited}, {Inherited, Inherited}},
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"},
    LanguageCategory->"Formula",
    ScriptLevel->0,
    SingleLetterItalics->True,
    UnderoverscriptBoxOptions->{LimitsPositioning->True}],
  
  Cell[StyleData["DisplayFormula", "Presentation"],
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["DisplayFormula", "Condensed"],
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["DisplayFormula", "Printout"],
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Program"],
    CellFrame->{{0, 0}, {0.5, 0.5}},
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    Hyphenation->False,
    LanguageCategory->"Formula",
    ScriptLevel->1,
    FontFamily->"Courier"],
  
  Cell[StyleData["Program", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["Program", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["Program", "Printout"],
    CellMargins->{{2, 0}, {6, 6}},
    FontSize->9]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Hyperlink Styles", "Section"],
  
  Cell["\<\
The cells below define styles useful for making hypertext ButtonBoxes.  The \
\"Hyperlink\" style is for links within the same Notebook, or between \
Notebooks.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Hyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonNote->ButtonData}],
  
  Cell[StyleData["Hyperlink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["Hyperlink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["Hyperlink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell["\<\
The following styles are for linking automatically to the on-line help \
system.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MainBookLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["MainBookLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["MainBookLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["MainBookLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["AddOnsLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["AddOnsLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["AddOnsLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["AddOnsLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["RefGuideLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["RefGuideLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["GettingStartedLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["OtherInformationLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["OtherInformationLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["OtherInformationLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["OtherInformationLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Headers and Footers", "Section"],
  
  Cell[StyleData["Header"],
    CellMargins->{{0, 0}, {4, 1}},
    DefaultNewInlineCellStyle->"None",
    LanguageCategory->"NaturalLanguage",
    StyleMenuListing->None,
    FontSize->10,
    FontSlant->"Italic"],
  
  Cell[StyleData["Footer"],
    CellMargins->{{0, 0}, {0, 4}},
    DefaultNewInlineCellStyle->"None",
    LanguageCategory->"NaturalLanguage",
    StyleMenuListing->None,
    FontSize->9,
    FontSlant->"Italic"],
  
  Cell[StyleData["PageNumber"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Palette Styles", "Section"],
  
  Cell["\<\
The cells below define styles that define standard ButtonFunctions, for use \
in palette buttons.\
\>", "Text"],
  
  Cell[StyleData["Paste"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, After]}]&)}],
  
  Cell[StyleData["Evaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["EvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionMove[ 
          FrontEnd`InputNotebook[ ], All, Cell, 1], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
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Cached data follows.  If you edit this Notebook file directly, not
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Cell[CellGroupData[{
Cell[606867, 13715, 64, 2, 37, "Input"],
Cell[606934, 13719, 51, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[607022, 13725, 64, 2, 37, "Input"],
Cell[607089, 13729, 51, 1, 29, "Output"]
}, Open  ]],
Cell[607155, 13733, 79, 1, 40, "Text"],

Cell[CellGroupData[{
Cell[607259, 13738, 67, 2, 37, "Input"],
Cell[607329, 13742, 54, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[607420, 13748, 67, 2, 37, "Input"],
Cell[607490, 13752, 86, 1, 29, "Output"]
}, Open  ]],
Cell[607591, 13756, 45, 1, 40, "Text"],

Cell[CellGroupData[{
Cell[607661, 13761, 65, 2, 37, "Input"],
Cell[607729, 13765, 57, 1, 29, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[607823, 13771, 65, 2, 37, "Input"],
Cell[607891, 13775, 35, 1, 29, "Output"]
}, Open  ]],
Cell[607941, 13779, 45, 1, 40, "Text"]
}, Open  ]]
}, Closed]]
}, Closed]]
}, Closed]]
}
]
*)



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