(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. 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). 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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[ 413649, 9751]*) (*NotebookOutlinePosition[ 414361, 9776]*) (* CellTagsIndexPosition[ 414317, 9772]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{\( (*\ Preliminary\ \(Setup : \ Define\ Modules\)\ *) \), "\[IndentingNewLine]", RowBox[{\(Off[General::"\"]\), "\[IndentingNewLine]", RowBox[{\(CreateRules[EQ_, N_]\), ":=", RowBox[{"Module", "[", RowBox[{\({}\), ",", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"ToRules", "[", RowBox[{ SuperscriptBox["EQ", TagBox[\((k)\), Derivative], MultilineFunction->None], "[", 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p0}];\)\[IndentingNewLine]\[IndentingNewLine] qe[h] = Simplify[Series[q[s + h], {h, 0, i}] //. \[InvisibleSpace]R]\n pe[h] = Simplify[Series[ p[s + h], {h, 0, i}] //. \[InvisibleSpace]R]\)\)\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{"q0", "+", RowBox[{ RowBox[{ SuperscriptBox["H", TagBox[\((0, 1)\), Derivative], MultilineFunction->None], "[", \(q0, p0\), "]"}], " ", "h"}], "+", RowBox[{\(1\/2\), " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{ SuperscriptBox["H", TagBox[\((0, 2)\), Derivative], MultilineFunction->None], "[", \(q0, p0\), "]"}]}], " ", RowBox[{ SuperscriptBox["H", TagBox[\((1, 0)\), Derivative], MultilineFunction->None], "[", \(q0, p0\), "]"}]}], "+", RowBox[{ RowBox[{ SuperscriptBox["H", TagBox[\((0, 1)\), Derivative], MultilineFunction->None], "[", \(q0, p0\), "]"}], " ", RowBox[{ SuperscriptBox["H", TagBox[\((1, 1)\), Derivative], MultilineFunction->None], "[", \(q0, p0\), "]"}]}]}], ")"}], " ", \(h\^2\)}], "+", RowBox[{\(1\/6\), " ", 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