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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[ 37270, 1150]*) (*NotebookOutlinePosition[ 38458, 1188]*) (* CellTagsIndexPosition[ 38414, 1184]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Arno's nonconjugable map", "Section", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(var5 = Array[x\_#&, {5}]; \)\)], "Input"], Cell[BoxData[ \(\(arno = {x\_1 + x\_2\ x\_5\^2, \n\t\t x\_2 + \(x\_1\^2\) x\_5 - \(x\_4\) x\_5\^2, \n\t\t x\_3 + \(x\_2\^2\) x\_5, \n\t\t x\_4 + 2 \( x\_1\) \(x\_2\) x\_5 - \(x\_3\) x\_5\^2, \n\t\tx\_5}; \)\)], "Input", AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell["Inverse", "Section", Evaluatable->False, AspectRatioFixed->True], Cell["The inverse of Arno's map:", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(arnoinversa = Array[x\_#&, {5}] /. \n\t\t\t \(Solve[arno == Array[y\_#&, {5}], \n\t\t\t\tArray[x\_#&, {5}]] \)\[LeftDoubleBracket]1\[RightDoubleBracket] // Expand\)], "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ \(arnoinversa\)], "Input"], Cell[BoxData[ \({y\_1 - y\_2\ y\_5\%2 + y\_1\%2\ y\_5\%3 - y\_4\ y\_5\%4 - y\_3\ y\_5\%6, y\_2 - y\_1\%2\ y\_5 + y\_4\ y\_5\%2 + y\_3\ y\_5\%4, y\_3 - y\_2\%2\ y\_5 + 2\ y\_1\%2\ y\_2\ y\_5\%2 - y\_1\%4\ y\_5\%3 - 2\ y\_2\ y\_4\ y\_5\%3 + 2\ y\_1\%2\ y\_4\ y\_5\%4 - 2\ y\_2\ y\_3\ y\_5\%5 - y\_4\%2\ y\_5\%5 + 2\ y\_1\%2\ y\_3\ y\_5\%6 - 2\ y\_3\ y\_4\ y\_5\%7 - y\_3\%2\ y\_5\%9, y\_4 - 2\ y\_1\ y\_2\ y\_5 + 2\ y\_1\%3\ y\_5\%2 + y\_3\ y\_5\%2 + y\_2\%2\ y\_5\%3 - 2\ y\_1\ y\_4\ y\_5\%3 - 2\ y\_1\%2\ y\_2\ y\_5\%4 + y\_1\%4\ y\_5\%5 - 2\ y\_1\ y\_3\ y\_5\%5 + 2\ y\_2\ y\_4\ y\_5\%5 - 2\ y\_1\%2\ y\_4\ y\_5\%6 + 2\ y\_2\ y\_3\ y\_5\%7 + y\_4\%2\ y\_5\%7 - 2\ y\_1\%2\ y\_3\ y\_5\%8 + 2\ y\_3\ y\_4\ y\_5\%9 + y\_3\%2\ y\_5\%11, y\_5}\)], "Output"] }, Open ]], Cell["Collecting terms with respect to degree:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Collect[arnoinversa /. y\_i_ \[RuleDelayed] t\ y\_i, t]\)], "Input"], Cell[BoxData[ \({t\ y\_1 - t\^3\ y\_2\ y\_5\%2 - t\^7\ y\_3\ y\_5\%6 + t\^5\ \((y\_1\%2\ y\_5\%3 - y\_4\ y\_5\%4)\), t\ y\_2 + t\^5\ y\_3\ y\_5\%4 + t\^3\ \((\(-y\_1\%2\)\ y\_5 + y\_4\ y\_5\%2)\), t\ y\_3 - t\^3\ y\_2\%2\ y\_5 - t\^11\ y\_3\%2\ y\_5\%9 + t\^5\ \((2\ y\_1\%2\ y\_2\ y\_5\%2 - 2\ y\_2\ y\_4\ y\_5\%3)\) + t\^7\ \(( \(-y\_1\%4\)\ y\_5\%3 + 2\ y\_1\%2\ y\_4\ y\_5\%4 - 2\ y\_2\ y\_3\ y\_5\%5 - y\_4\%2\ y\_5\%5)\) + t\^9\ \((2\ y\_1\%2\ y\_3\ y\_5\%6 - 2\ y\_3\ y\_4\ y\_5\%7)\), t\ y\_4 + t\^13\ y\_3\%2\ y\_5\%11 + t\^3\ \((\(-2\)\ y\_1\ y\_2\ y\_5 + y\_3\ y\_5\%2)\) + t\^5\ \(( 2\ y\_1\%3\ y\_5\%2 + y\_2\%2\ y\_5\%3 - 2\ y\_1\ y\_4\ y\_5\%3) \) + t\^7\ \(( \(-2\)\ y\_1\%2\ y\_2\ y\_5\%4 - 2\ y\_1\ y\_3\ y\_5\%5 + 2\ y\_2\ y\_4\ y\_5\%5)\) + t\^9\ \(( y\_1\%4\ y\_5\%5 - 2\ y\_1\%2\ y\_4\ y\_5\%6 + 2\ y\_2\ y\_3\ y\_5\%7 + y\_4\%2\ y\_5\%7)\) + t\^11\ \((\(-2\)\ y\_1\%2\ y\_3\ y\_5\%8 + 2\ y\_3\ y\_4\ y\_5\%9)\), t\ y\_5}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Exponent[%, t]\)], "Input"], Cell[BoxData[ \({7, 5, 11, 13, 1}\)], "Output"] }, Open ]], Cell["Separation of the degrees:", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(inversagrado[n_] := Coefficient[Collect[arnoinversa /. y\_i_ \[RuleDelayed] t\ y\_i, t], t\^n]; 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