(*********************************************************************** 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[ 17660, 556]*) (*NotebookOutlinePosition[ 18481, 586]*) (* CellTagsIndexPosition[ 18398, 580]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["SplittingFunction", "Subsection", CellTags->"SplittingFunction"], Cell[CellGroupData[{ Cell["Description", "Subsubsection"], Cell[TextData[{ "SplittingFunction[pxy] is a database of splitting functions in the ", Cell[BoxData[ \(TraditionalForm\`MS\&_\)]], " scheme." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[SplittingFunction]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{Polarization \[Rule] 1}\)], "Output"] }, Open ]], Cell[TextData[{ "See also: ", " ", ButtonBox["AnomalousDimension", ButtonData:>"AnomalousDimension", ButtonStyle->"Hyperlink", ButtonNote->"AnomalousDimension"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Examples", "Subsubsection"], Cell["Unpolarized case:", "Text"], Cell[BoxData[ \(SetOptions[SplittingFunction, Polarization \[Rule] 0]; \)], "Input"], Cell["\<\ In general the argument should be a string, but if the variables \ Pqq, etc. have no value, you can omit the \"\".\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pqq]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(C\_F\), " ", RowBox[{"(", RowBox[{\(\(-4\)\ x\), "+", RowBox[{"6", " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(8\ \(\((1\/\(1 - x\))\)\_+\)\), "-", "4"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pqg]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`T\_f\ \((16\ x\^2 - 16\ x + 8)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pgq]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`C\_F\ \((4\ x - 8 + 8\/x)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pgg]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"8", " ", \(C\_A\), " ", RowBox[{"(", RowBox[{\(-x\^2\), "+", "x", "+", RowBox[{\(11\/12\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\((1\/\(1 - x\))\)\_+\), "-", "2", "+", \(1\/x\)}], ")"}]}], "-", RowBox[{\(8\/3\), " ", \(N\_f\), " ", \(T\_f\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[aqq]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(C\_F\), " ", RowBox[{"(", RowBox[{\(2\ x\), "+", RowBox[{\((7 - 4\ \(\[Zeta](2)\))\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\((2\ x + 2)\)\ \(log(\((1 - x)\)\ x)\)\), "-", \(4\ \((\(log(x)\)\/\(1 - x\) + \(\((\(log(1 - x)\)\/\(1 - x\ \))\)\_+\))\)\), "-", "4"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[agq]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`C\_F\ \((\(-2\)\ x + \((\(-2\)\ x + 4 - 4\/x)\)\ \(log(\((1 - x)\)\ x)\) + 2 - 4\/x)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[aqg]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`T\_f\ \((\((\(-8\)\ x\^2 + 8\ x - 4)\)\ \(log(\((1 - x)\)\ x)\) - 4)\)\)], "Output"] }, Open ]], Cell[BoxData[ \(SplittingFunction[agg]\)], "Input"], Cell["Polarized case:", "Text"], Cell[BoxData[ \(SetOptions[SplittingFunction, Polarization \[Rule] 1]; \)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pqq]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(C\_F\), " ", RowBox[{"(", RowBox[{\(\(-4\)\ x\), "+", RowBox[{"6", " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(8\ \(\((1\/\(1 - x\))\)\_+\)\), "-", "4"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pqg]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`T\_f\ \((16\ x - 8)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pgq]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`C\_F\ \((8 - 4\ x)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[Pgg]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{\(C\_A\), " ", RowBox[{"(", RowBox[{\(\(-16\)\ x\), "+", RowBox[{\(22\/3\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(8\ \(\((1\/\(1 - x\))\)\_+\)\), "+", "8"}], ")"}]}], "-", RowBox[{\(8\/3\), " ", \(N\_f\), " ", \(T\_f\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[aqq]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{\(C\_F\), " ", RowBox[{"(", RowBox[{\(8\ \((1 - x)\)\), "+", \(2\ x\), "+", RowBox[{\((7 - 4\ \(\[Zeta](2)\))\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\((2\ x + 2)\)\ \(log(\((1 - x)\)\ x)\)\), "-", \(4\ \(log(x)\)\ \(\((1\/\(1 - x\))\)\_+\)\), "-", \(4\ \(\((\(log(1 - x)\)\/\(1 - x\))\)\_+\)\), "-", "4"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[agq]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`C\_F\ \((\(-4\)\ x + \((2\ x - 4)\)\ \(log(\((1 - x)\)\ x)\) + 2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[agqd]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`C\_F\ \((\((2\ x - 4)\)\ \(log(\((1 - x)\)\ x)\) - 2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[aqg]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`T\_f\ \((\((4 - 8\ x)\)\ \(log(\((1 - x)\)\ x)\) - 4)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[aqgd]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`T\_f\ \((\((4 - 8\ x)\)\ \(log(\((1 - x)\)\ x)\) - 4)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[agg]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{\(C\_A\), " ", RowBox[{"(", RowBox[{ RowBox[{\((67\/9 - 4\ \(\[Zeta](2)\))\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\((8\ x - 4)\)\ \(log(\((1 - x)\)\ x)\)\), "-", \(4\ \((\(log(x)\)\/\(1 - x\) + \(\((\(log(1 - x)\)\/\(1 - \ x\))\)\_+\))\)\), "+", "2"}], ")"}]}], "-", RowBox[{\(20\/9\), " ", \(T\_f\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[aggd]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{\(C\_A\), " ", RowBox[{"(", RowBox[{ RowBox[{\((67\/9 - 4\ \(\[Zeta](2)\))\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\((8\ x - 4)\)\ \(log(\((1 - x)\)\ x)\)\), "-", \(4\ \((\(log(x)\)\/\(1 - x\) + \(\((\(log(1 - x)\)\/\(1 - \ x\))\)\_+\))\)\), "+", "2"}], ")"}]}], "-", RowBox[{\(20\/9\), " ", \(T\_f\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[PQQS]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`C\_F\ T\_f\ \((\(-16\)\ \((x + 1)\)\ \(\(log\^2\)( x)\) + \((48\ x - 16)\)\ \(log(x)\) + 16\ \((1 - x)\))\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[PQQNS]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{\(\(-4\)\ \((x + 1)\)\ \(\(log\^2\)(x)\)\), "-", \(8\ \((2\ x + 3\/\(1 - x\))\)\ \(log(x)\)\), "-", \(\(16\ \((x\^2 + 1)\)\ \(log(1 - x)\)\ \(log( x)\)\)\/\(1 - x\)\), "-", \(40\ \((1 - x)\)\), "+", RowBox[{ RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}], " ", RowBox[{"(", RowBox[{\(\(-24\)\ \(\[Zeta](2)\)\), "+", RowBox[{"48", " ", TagBox[ RowBox[{"\[Zeta]", "(", TagBox["3", (Editable -> True)], ")"}], InterpretTemplate[ Zeta[ #]&]]}], "+", "3"}], ")"}]}]}], ")"}], " ", \(C\_F\%2\)}], "+", RowBox[{\(N\_f\), " ", RowBox[{"(", RowBox[{\(\(88\ x\)\/9\), "+", RowBox[{\((\(-\(\(16\ \(\[Zeta](2)\)\)\/3\)\) - 2\/3)\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "-", \(\(8\ \((x\^2 + 1)\)\ \(log(x)\)\)\/\(3\ \((1 - x)\)\)\), "-", \(80\/9\ \(\((1\/\(1 - x\))\)\_+\)\), "-", \(8\/9\)}], ")"}], " ", \(C\_F\)}], "-", \(8\ \((C\_F - C\_A\/2)\)\ \((4\ \((1 - x)\) + 2\ \((x + 1)\)\ \(log( x)\) + \(\((x\^2 + 1)\)\ \((\(log\^2\)(x) - 4\ \(log(x + 1)\ \)\ \(log(x)\) - 2\ \(\[Zeta](2)\) - 4\ \(\(Li\_2\)(\(-x\))\))\)\)\/\(x + \ 1\))\)\ C\_F\), "+", RowBox[{\(C\_A\), " ", RowBox[{"(", RowBox[{\(\(4\ \((x\^2 + 1)\)\ \(\(log\^2\)(x)\)\)\/\(1 - x\)\), "-", \(4\/3\ \((5\ x - 22\/\(1 - x\) + 5)\)\ \(log(x)\)\), "+", \(4\/9\ \((53 - 187\ x)\)\), "+", \(8\ \((x + 1)\)\ \(\[Zeta](2)\)\), "+", \(\((536\/9 - 16\ \(\[Zeta](2)\))\)\ \(\((1\/\(1 - x\))\)\_+\)\), "+", RowBox[{ RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}], " ", RowBox[{"(", RowBox[{\(\(88\ \(\[Zeta](2)\)\)\/3\), "-", RowBox[{"24", " ", TagBox[ RowBox[{"\[Zeta]", "(", TagBox["3", (Editable -> True)], ")"}], InterpretTemplate[ Zeta[ #]&]]}], "+", \(17\/3\)}], ")"}]}]}], ")"}], " ", \(C\_F\)}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[PQG]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`4\ C\_F\ T\_f\ \((\((8\ x - 4)\)\ \(\(log\^2\)( 1 - x)\) + \((16 - 16\ x)\)\ \(log( 1 - x)\) + \((8 - 16\ x)\)\ \(log(x)\)\ \(log( 1 - x)\) + \((4\ x - 2)\)\ \(\(log\^2\)(x)\) + 54\ x - 16\ x\ \(\[Zeta](2)\) + 8\ \(\[Zeta](2)\) - 18\ \(log(x)\) - 44)\) + 4\ C\_A\ T\_f\ \((\((4 - 8\ x)\)\ \(\(log\^2\)( 1 - x)\) + \((16\ x - 16)\)\ \(log( 1 - x)\) + \((\(-8\)\ x - 4)\)\ \(\(log\^2\)(x)\) - 44\ x - 8\ \(\[Zeta](2)\) + \((32\ x + 4)\)\ \(log( x)\) + \((\(-16\)\ x - 8)\)\ \(log(x)\)\ \(log( x + 1)\) + \((\(-16\)\ x - 8)\)\ \(\(Li\_2\)(\(-x\))\) + 48)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[PGQ]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`\((C\_A\ C\_F)\) . \((\((16 - 8\ x)\)\ \(\(log\^2\)( 1 - x)\) + \((\(8\ x\)\/3 + 80\/3)\)\ \(log( 1 - x)\) + \((16\ x - 32)\)\ \(log(x)\)\ \(log( 1 - x)\) + \((8\ x + 16)\)\ \(\(log\^2\)( x)\) + \(280\ x\)\/9 + 16\ x\ \(\[Zeta](2)\) + \((32 - 104\ x)\)\ \(log( x)\) + \((16\ x + 32)\)\ \(log(x)\)\ \(log( x + 1)\) + \((16\ x + 32)\)\ \(\(Li\_2\)(\(-x\))\) + 328\/9)\) + C\_F\%2 . \((\((8\ x - 16)\)\ \(\(log\^2\)( 1 - x)\) + \((\(-8\)\ x - 16)\)\ \(log( 1 - x)\) + \((8 - 4\ x)\)\ \(\(log\^2\)(x)\) + 32\ x - \((32\ x + 64)\)\ \(log(x)\) + \((36\ x + 48)\)\ \(log( x)\) - 68)\) + \((C\_F\ T\_f)\) . \((\(-\(\(32\ x\)\/9\)\) + \ \((\(32\ x\)\/3 - 64\/3)\)\ \(log(1 - x)\) - 128\/9)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplittingFunction[PGG]\)], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{\(\((\(-\(8\/\(x + 1\)\)\) + 32 + 8\/\(1 - x\))\)\ \(\(log\^2\)(x)\)\), "+", \(\((232\/3 - \(536\ x\)\/3)\)\ \(log(x)\)\), "+", \(\((64\ x - 32\/\(1 - x\) - 32)\)\ \(log(1 - x)\)\ \(log( x)\)\), "+", \(\((64\ x + 32\/\(x + 1\) + 32)\)\ \(log(x + 1)\)\ \(log( x)\)\), "-", \(\(388\ x\)\/9\), "+", RowBox[{\(64\/3\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\(\[Zeta]( 2)\)\ \((64\ x - 16\ \(\((1\/\(1 - x\))\)\_+\) + 16\/\(x + 1\))\)\), "+", \(536\/9\ \(\((1\/\(1 - x\))\)\_+\)\), "+", \(\((64\ x + 32\/\(x + 1\) + 32)\)\ \(\(Li\_2\)(\(-x\))\)\), "+", RowBox[{"24", " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}], " ", TagBox[ RowBox[{"\[Zeta]", "(", TagBox["3", (Editable -> True)], ")"}], InterpretTemplate[ Zeta[ #]&]]}], "-", \(148\/9\)}], ")"}], " ", \(C\_A\%2\)}], "+", RowBox[{\(T\_f\), " ", RowBox[{"(", RowBox[{\(\(608\ x\)\/9\), "-", RowBox[{\(32\/3\), " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "+", \(\((\(-\(\(32\ x\)\/3\)\) - 32\/3)\)\ \(log(x)\)\), "-", \(160\/9\ \(\((1\/\(1 - x\))\)\_+\)\), "-", \(448\/9\)}], ")"}], " ", \(C\_A\)}], "+", RowBox[{\(C\_F\), " ", \(T\_f\), " ", RowBox[{"(", RowBox[{\(\((\(-16\)\ x - 16)\)\ \(\(log\^2\)(x)\)\), "+", \(\((16\ x - 80)\)\ \(log(x)\)\), "+", \(80\ x\), "-", RowBox[{"8", " ", RowBox[{"\[Delta]", "(", FormBox[\(1 - x\), "TraditionalForm"], ")"}]}], "-", "80"}], ")"}]}]}], TraditionalForm]], "Output"] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"4.0 for X", ScreenRectangle->{{0, 1024}, {0, 768}}, WindowSize->{520, 485}, WindowMargins->{{Automatic, 244}, {114, Automatic}}, StyleDefinitions -> "Demo.nb" ] (*********************************************************************** 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->{ "SplittingFunction"->{ Cell[1739, 51, 72, 1, 40, "Subsection", CellTags->"SplittingFunction"]} } *) (*CellTagsIndex CellTagsIndex->{ {"SplittingFunction", 18290, 573} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1739, 51, 72, 1, 40, "Subsection", CellTags->"SplittingFunction"], Cell[CellGroupData[{ Cell[1836, 56, 36, 0, 36, "Subsubsection"], Cell[1875, 58, 165, 5, 31, "Text"], Cell[CellGroupData[{ Cell[2065, 67, 59, 1, 31, "Input"], Cell[2127, 70, 75, 1, 47, "Output"] }, Open ]], Cell[2217, 74, 197, 8, 29, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[2451, 87, 33, 0, 36, "Subsubsection"], Cell[2487, 89, 33, 0, 29, "Text"], Cell[2523, 91, 88, 1, 31, "Input"], Cell[2614, 94, 138, 3, 43, "Text"], Cell[CellGroupData[{ Cell[2777, 101, 55, 1, 31, "Input"], Cell[2835, 104, 379, 10, 65, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3251, 119, 55, 1, 70, "Input"], Cell[3309, 122, 83, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3429, 128, 55, 1, 70, "Input"], Cell[3487, 131, 78, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3602, 137, 55, 1, 70, "Input"], Cell[3660, 140, 627, 15, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4324, 160, 55, 1, 70, "Input"], Cell[4382, 163, 499, 11, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4918, 179, 55, 1, 70, "Input"], Cell[4976, 182, 154, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5167, 189, 55, 1, 70, "Input"], Cell[5225, 192, 138, 2, 70, "Output"] }, Open ]], Cell[5378, 197, 55, 1, 70, "Input"], Cell[5436, 200, 31, 0, 70, "Text"], Cell[5470, 202, 88, 1, 70, "Input"], Cell[CellGroupData[{ Cell[5583, 207, 55, 1, 70, "Input"], Cell[5641, 210, 379, 10, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6057, 225, 55, 1, 70, "Input"], Cell[6115, 228, 72, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6224, 234, 55, 1, 70, "Input"], Cell[6282, 237, 71, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6390, 243, 55, 1, 70, "Input"], Cell[6448, 246, 599, 15, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7084, 266, 55, 1, 70, "Input"], Cell[7142, 269, 567, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7746, 286, 55, 1, 70, "Input"], Cell[7804, 289, 135, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7976, 296, 56, 1, 70, "Input"], Cell[8035, 299, 117, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8189, 306, 55, 1, 70, "Input"], Cell[8247, 309, 117, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8401, 316, 56, 1, 70, "Input"], Cell[8460, 319, 117, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8614, 326, 55, 1, 70, "Input"], Cell[8672, 329, 687, 16, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9396, 350, 56, 1, 70, "Input"], Cell[9455, 353, 687, 16, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10179, 374, 56, 1, 70, "Input"], Cell[10238, 377, 183, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10458, 385, 57, 1, 70, "Input"], Cell[10518, 388, 2798, 60, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13353, 453, 55, 1, 70, "Input"], Cell[13411, 456, 768, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14216, 473, 55, 1, 70, "Input"], Cell[14274, 476, 923, 15, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15234, 496, 55, 1, 70, "Input"], Cell[15292, 499, 2328, 52, 70, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)