(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' 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). 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[ 7079, 267]*) (*NotebookOutlinePosition[ 8229, 304]*) (* CellTagsIndexPosition[ 8101, 297]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ "Liebe Mathematica-Fans\nVielen Dank f\[UDoubleDot]r die vielen Anregungen \ und Hilfen zu meiner Frage. Sie sei nochmals etwas pr\[ADoubleDot]ziser \ gestellt: Gesucht ist eine Funktion sigma, welche die Menge Q der rationalen \ Zahlen vereinigt mit \n{a+ b ", Cell[BoxData[ \(\@5\)]], ", a,b rational} permutiert.\nJede rationale Zahl geht in sich \ \[UDoubleDot]ber, und a+ b ", Cell[BoxData[ \(\@5\)]], " geht \[UDoubleDot]ber in a- b ", Cell[BoxData[ \(\@5\)]], "." }], "Text"], Cell["\<\ Ich habe wieder einiges gelernt. so weiss ich jetzt, dass dasSymbol \"_.\"im \ Zusammenhang mit x_+y_. den Defaultwert 0 erh\[ADoubleDot]lt.\ \>", "Text"], Cell["\<\ Die L\[ODoubleDot]sung von Thomas Hahn ist sehr elegant: \ \>", "Text"], Cell[BoxData[ \(u = a1 + b1\ \@5; v = a2 + b2\ \@5;\)], "Input"], Cell[BoxData[ \(Clear[\[Sigma]]\)], "Input"], Cell[BoxData[ \(\[Sigma][x_] := Apply[\((#1 - #2\ \@5)\)\ &, CoefficientList[x, \@5]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][3 + 4\ \@5]\)], "Input"], Cell[BoxData[ \(3 - 4\ \@5\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][u + v]\)], "Input"], Cell[BoxData[ \(a1 + a2 - \@5\ \((b1 + b2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][u\ v]\)], "Input"], Cell[BoxData[ \(a1\ a2 + 5\ b1\ b2 - \@5\ \((a2\ b1 + a1\ b2)\)\)], "Output"] }, Open ]], Cell["\<\ Insbesondere lassen sich damit \[Sigma][u+v]==\[Sigma][u]+\[Sigma][v] und \[Sigma][u v]==\[Sigma][u] \ \[Sigma][v] nacgweisen. Leider ist sie f\[UDoubleDot]r rationale Zahlen nicht \ brauchbar:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][3]\)], "Input"], Cell[BoxData[ RowBox[{\(Function::"slotn"\), \(\(:\)\(\ \)\), "\<\"Slot number \ \\!\\(2\\) in \\!\\(\\(\\(#1 - \\(\\(#2\\\\ \\@5\\)\\)\\)\\) &\\) cannot be \ filled from \\!\\(\\(\\((\\(\\(\\(#1 - \\(\\(#2\\\\ \\@5\\)\\)\\)\\) &\\))\\)\ \\)[3]\\). \\!\\(\\*ButtonBox[\\\"Mehr\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"Function::slotn\\\"]\\)\"\>"}]], "Message"], Cell[BoxData[ \(3 - \@5\ #2\)], "Output"] }, Open ]], Cell["\<\ Die L\[ODoubleDot]sung von Jens-Peer Kuska l\[ODoubleDot]st dieses Problem, \ allerdings ist die Kritik von Thomas Hahn bez\[UDoubleDot]glich \"Kopieren\" \ und \"Einf\[UDoubleDot]gen\" schwerwiegend.\ \>", "Text"], Cell[BoxData[{ \(Clear[\[Sigma]]\), "\n", \(\[InvisiblePrefixScriptBase]\[Sigma][a_ + b_\ . \@5] := \[Sigma][a] - b\ \@5\), "\n", \(\[Sigma][a_] := a\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?\[Sigma]\)\)], "Input"], Cell["Global`\[Sigma]", "Print", CellTags->"Info3369029533-8148559"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(\[Sigma][a_] := a\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "\[Sigma]"], Editable->False]], "Print", CellTags->"Info3369029533-8148559"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][3 + 4 \@\(\(\ \)\(5\)\)]\)], "Input"], Cell[BoxData[ \(3 + 4\ \@5\)], "Output"] }, Open ]], Cell["\<\ Ich vermute, dass dieses Fehlverhalten mit den fehlenden Trennzeichen \";\" \ zu tun hat. Die folgende Version funktioniert jedenfalls einwandfrei (auch \ mit Kopieren).\ \>", "Text"], Cell[BoxData[{ \(\(Clear[\[Sigma]];\)\), "\[IndentingNewLine]", \(\[Sigma][a_ + b_. \@\(\(\ \)\(5\)\)] := \[Sigma][a] - b\ \@5; \[Sigma][ a_] := a\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?\[Sigma]\)\)], "Input"], Cell["Global`\[Sigma]", "Print", CellTags->"Info3369029542-1911593"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(\[Sigma][\@5\ b_. + a_] := \[Sigma][a] - b\ \@5\)}, {" "}, {\(\[Sigma][a_] := a\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ "\[Sigma]"], Editable->False]], "Print", CellTags->"Info3369029542-1911593"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][3]\)], "Input"], Cell[BoxData[ \(3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][3 + 4 \@\(\(\ \)\(5\)\)]\)], "Input"], Cell[BoxData[ \(3 - 4\ \@5\)], "Output"] }, Open ]], Cell[BoxData[ \(u = a1 + b1\ \@5; v = a2 + b2\ \@5;\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][u + v]\)], "Input"], Cell[BoxData[ \(a1 + a2 - \@5\ b1 - \@5\ b2\)], "Output"] }, Open ]], Cell["Leider versagt sie bei der Multiplikation", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sigma][u\ v]\)], "Input"], Cell[BoxData[ \(\((a1 + \@5\ b1)\)\ \((a2 + \@5\ b2)\)\)], "Output"] }, Open ]], Cell["\<\ Vielleicht findet jaemand eine L\[ODoubleDot]sung, die alle meine Bed\ \[UDoubleDot]rfnisse befriedigt.\ \>", "Text"] }, FrontEndVersion->"5.2 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 685}}, WindowSize->{495, 561}, WindowMargins->{{Automatic, 147}, {Automatic, 6}}, ShowSelection->True ] (******************************************************************* Cached data follows. 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