(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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[ 1387460, 36480]*) (*NotebookOutlinePosition[ 1388734, 36525]*) (* CellTagsIndexPosition[ 1388591, 36517]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Mathematische Anwendersysteme Sommersemester 1999 Prof. Dr. Heinz Spindler\ \>", "Subtitle", TextAlignment->Center, FontColor->GrayLevel[0]], Cell[TextData[ "Fachbereich Mathematik/Informatik\nder Universit\[ADoubleDot]t Osnabr\ \[UDoubleDot]ck"], "Subsubtitle", TextAlignment->Center, FontColor->GrayLevel[0]], Cell["\<\ ...Nun will ich nicht bestreiten, da\[SZ] es sinnvoll ist, das Einmaleins zu \ beherrschen und zu wissen, wie man einfache Dreisatz- und Bruchrechnungen \ auszuf\[UDoubleDot]hren hat. Aber mit mathematischem Denken hat das alle \ nichts zu tun. Es ist so, als w\[UDoubleDot]rde man Menschen in die Musik \ einf\[UDoubleDot]hren, indem man sie jahrelang Tonleitern \[UDoubleDot]ben l\ \[ADoubleDot]\[SZ]t. Das Resultat w\[ADoubleDot]re vermutlich lebenslanger Ha\ \[SZ] auf diese Kunst. - Hans Magnus Enzensberger\ \>", "ItemizedTextNote", FontSlant->"Italic"], Cell[CellGroupData[{ Cell["Vorwort", "Subsubsection"], Cell[TextData[{ "In dieser Veranstaltung wird eine Einf\[UDoubleDot]hrung in moderne \ Computeralgebrasysteme (CAS) gegeben. Unter den vielen existierenden \ Produkten sind wohl zur Zeit ", ButtonBox["Maple", ButtonData:>{ URL[ "http://www.maplesoft.com/"], None}, ButtonStyle->"Hyperlink"], " und ", ButtonBox["Mathematica", ButtonData:>{ URL[ "http://www.wolfram.co.uk"], None}, ButtonStyle->"Hyperlink"], " am bekanntesten. Allerdings werden diese Systeme zur Zeit noch recht \ wenig in der Schule eingesetzt (siehe: ", ButtonBox["Maths & Fun", ButtonData:>{ URL[ "http://www.mathsnfun.ac.at"], None}, ButtonStyle->"Hyperlink"], ", ", ButtonBox["Vergleich von Computeralgebrasystemen", ButtonData:>{ URL[ "http://www.ikg.rt.bw.schule.de/leucas/"], None}, ButtonStyle->"Hyperlink"], "), obwohl meiner Meinung nach sowohl ", StyleBox["Mathematica", FontSlant->"Italic"], " als auch ", StyleBox["Maple", FontSlant->"Italic"], " ideal dazu geeignet sind. Der Einsatz von Computeralgbrasystemen in der \ Schule k\[ODoubleDot]nnte den Mathematikunterricht revolutionieren! Er macht \ es m\[ODoubleDot]glich, auch komplexere Beispiele, die nicht mehr mit Papier \ und Bleistift zu berechnen sind, zu behandeln. Er sch\[ADoubleDot]rft den \ Blick daf\[UDoubleDot]r, was konstruktive Verfahren sind, die maschinell \ durchf\[UDoubleDot]hrbar sind. Das mathematische Denken wird geschult, denn \ die erfolgreiche Behandlung eines komplexen mathematischen Problems mit \ Computeralgebra setzt das theoretische Verst\[ADoubleDot]ndnis des Problems \ voraus und f\[UDoubleDot]hrt zu umso besseren Ergebnissen, je besser man das \ Problem mathematisch beherrscht. Au\[SZ]erdem wird stumpfsinnige Rechnerei \ jetzt vom CAS \[UDoubleDot]bernommen. Termumformungen \ durchf\[UDoubleDot]hren, Wertetabellen erstellen, Funktionsgraphen zeichnen, \ Gleichungen l\[ODoubleDot]sen, Grenzwerte, Ableitungen und Integrale \ berechnen, halt all das, was man so t\[ADoubleDot]glich in der Schule \ insbesondere die Sch\[UDoubleDot]ler, die vorgeben in Mathe nicht \ durchzublicken, im Matheunterricht tun l\[ADoubleDot]\[SZ]t, \ geh\[ODoubleDot]rt mehr zu den einfachen Dingen, die jedes CAS beherrscht. \ Nat\[UDoubleDot]rlich gibt es auch hier Grenzen! Der Trend, da\[SZ] einfach \ nur Rezepte zum L\[ODoubleDot]sen standardisierter Aufgaben eingesetzt werden \ und deren Benutzung intensiv ge\[UDoubleDot]bt wird, dagegen die Herleitung \ und Entwicklung dieser Rezepte nicht ausf\[UDoubleDot]hrlich genug behandelt \ wird, k\[ODoubleDot]nnte gestoppt werden. Die Herausforderung und das \ Faszinierende bei der Behandlung einer mathematischen Aufgabe besteht darin, \ ihre Struktur zu erkennen, zum Beispiel die Variablen \ aufzusp\[UDoubleDot]ren, die zwischen diesen bestehenden Beziehungen etwa in \ Gleichungen auszudr\[UDoubleDot]cken, zu analysieren, an welcher Stelle man \ Computeralgebra einsetzen kann. Das schafft eine ungeheuere Erweiterung der M\ \[ODoubleDot]glichkeiten. Dinge, von denen man fr\[UDoubleDot]her nur tr\ \[ADoubleDot]umte, sind jetzt im Unterricht realisierbar. Der altmodische \ Taschenrechner, der einmal den Rechenschieber abl\[ODoubleDot]ste, wird jetzt \ abgel\[ODoubleDot]st durch das Notebook, auf dem ein CAS installiert ist. " }], "Text"], Cell[TextData[{ "Wir beschr\[ADoubleDot]nken uns in dieser Veranstaltung auf ", StyleBox["Mathematica", FontSlant->"Italic"], ". Hat man ein CAS kennengelernt, so kann man sich auch m\[UDoubleDot]helos \ in ein anderes System einarbeiten." }], "Text"], Cell[TextData[StyleBox[ "Die mathematischen Grundvorlesungen Lineare Algebra, Einf\[UDoubleDot]hrung \ in die Algebra, Analysis 1 und Analysis 2 werden voraugesetzt. Kenntnisse in \ Geometrie, Funktionentheorie, Zahlentheorie sind n\[UDoubleDot]tzlich."]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Links zu allgemeinen ", ButtonBox["Computeralgebrasystemen", ButtonData:>{ URL[ "http://math-www.uni-paderborn.de/CAIN/"], None}, ButtonStyle->"Hyperlink"] }], "Subsubsection"], Cell[TextData[ButtonBox["Mathematica", ButtonData:>{ URL[ "http://www.wolfram.co.uk"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Maple", ButtonData:>{ URL[ "http://www.maplesoft.com/"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Reduce", ButtonData:>{ URL[ "http://www.rrz.uni-koeln.de/REDUCE/"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Axiom", ButtonData:>{ URL[ "http://www.nag.co.uk:70/"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Macsyma", ButtonData:>{ URL[ "http://www.macsyma.com"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Mathcad", ButtonData:>{ URL[ "http://www.mathsoft.com/mathcad/"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Mupad ", ButtonData:>{ URL[ "http://www.mupad.de"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Derive", ButtonData:>{ URL[ "http://www.derive.com/"], None}, ButtonStyle->"Hyperlink"]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Links zu speziellen Computeralgebrasystemen", "Subsubsection"], Cell[TextData[StyleBox["CoCoA", FontWeight->"Bold"]], "Text"], Cell[TextData[StyleBox["Macaulay", FontWeight->"Bold"]], "Text"], Cell[TextData[ButtonBox["Macaulay2", ButtonData:>{ URL[ "http://www.math.uiuc.edu/Macaulay2/"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[{ "Dieses System ist am Fachbereich installiert. Wie man es aufruft und \ weitere Informationen findet man unter ", ButtonBox["www.mathematik.uni-osnabrueck.de/neuigkeiten", ButtonData:>{ URL[ "http://www.mathematik.uni-osnabrueck.de/neuigkeiten/"], None}, ButtonStyle->"Hyperlink"] }], "Text"], Cell[TextData[ButtonBox["Singular", ButtonData:>{ URL[ "http://www.mathematik.uni-kl.de/~zca/Singular/"], None}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Gap", ButtonData:>{ URL[ "http://www.math.rwth-aachen.de/LDFM/GAP/"], None}, ButtonStyle->"Hyperlink"]], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Die kleine ", StyleBox["Mathematica", FontSlant->"Italic"], "-Fibel" }], "Title"], Cell["\<\ Version 1.0 Datum: 15. 2. 99\ \>", "Caption"], Cell[CellGroupData[{ Cell["Einleitung", "Section"], Cell[TextData[{ StyleBox[ "Mathematica is a system for doing mathematics by computer. \n \ - Stephen Wolfram", FontWeight->"Light", FontColor->RGBColor[0, 0, 0.500008]], "\n " }], "ItemizedTextNote", FontSlant->"Italic"], Cell[TextData[{ "Dieses Mathematica-Notebook soll helfen, sich mit dem \ Computeralgebrasystem ", StyleBox["Mathematica", FontSlant->"Italic"], " vertraut zu machen. Beim Durcharbeiten dieser Fibel, sollte man ", StyleBox["Mathematica", FontSlant->"Italic"], " gestartet haben und alle vorgestellten Befehle selbst ausprobieren. Nur \ durch aktives Mitarbeiten lernt man den Umgang mit ", StyleBox["Mathematica.", FontSlant->"Italic"], " Beachtet man einige wichtige Syntaxregeln, so ist das Arbeiten mit ", StyleBox["Mathematica", FontSlant->"Italic"], " nach einer relativ kurzen Einarbeitungszeit ein Kinderspiel. \nAbschnitt \ 1 (Getting Started) gibt einige erste Orientierungshilfen. In Abschnitt 2 \ (Einf\[UDoubleDot]hrung in ", StyleBox["Mathematica", FontSlant->"Italic"], ") wird dann an mehr oder weniger willk\[UDoubleDot]rlich \ zusammengestellten Beispielen vorgef\[UDoubleDot]hrt, wie man mit ", StyleBox["Mathematica", FontSlant->"Italic"], " arbeitet. Dabei habe ich manchmal die verwendeten Befehle mit Absicht \ nicht im Detail erkl\[ADoubleDot]rt. Vielmehr sollte durch Betrachten des \ Outputs oder Variation des Inputs ihre Wirkungsweise klar werden. Bleibt \ etwas unklar, so kann man immer auf den Help Browser \ zur\[UDoubleDot]ckgreifen. Sehr zu empfehlen ist auch das ", StyleBox["Mathematica", FontSlant->"Italic"], "-Buch von Wolfram, die Bibel des ", StyleBox["Mathematica", FontSlant->"Italic"], "-Benutzers. Das Buch ist auch in deutscher Sprache erschienen. (N\ \[ADoubleDot]here Informationen dazu findet man unter ", ButtonBox["www.wolfram.com", ButtonData:>{"http//:www.cup.cam.ac.uk", None}, ButtonStyle->"Hyperlink"], ". Deutschsprachige B\[UDoubleDot]cher zu ", StyleBox["Mathematica", FontSlant->"Italic"], " findet man unter ", ButtonBox["www.mathematica.ch", ButtonData:>{ URL[ "http://www.mathematica.ch"], None}, ButtonStyle->"Hyperlink"], ".)\nDie folgenden Abschnitte behandeln dann etwas systematischer den \ Einsatz von ", StyleBox["Mathematica", FontSlant->"Italic"], " bei der Behandlung von Themen aus verschiedenen Gebieten der Mathematik \ und Physik. Dabei habe ich darauf wert gelegt, da\[SZ] die \ ausgew\[ADoubleDot]hlten Themen auch f\[UDoubleDot]r die Schule interessant \ sein k\[ODoubleDot]nnten, etwa f\[UDoubleDot]r Projekte in der Informatik \ oder den Leistungskursen in Mathematik\nJeder Abschnitt endet mit einem \ Aufgabenteil. Es werden Aufgaben von verschiedenem Schwierigkeitsgrad und \ Umfang gestellt. Die mit \[HappySmiley] versehenen Aufgaben dienen nur zum \ Ein\[UDoubleDot]ben der eingef\[UDoubleDot]hrten Befehle und enthalten nichts \ Tiefsinniges.\nVom Leser dieser Fibel wird erwartet, da\[SZ] er schon \ Erfahrungen mit dem PC besitzt, wei\[SZ] wie man sich mit der Maus unter \ Windows bewegt und schon einmal ein Textverarbeitungsprogramm wie Word \ benutzt hat. " }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Literatur", "Section"], Cell[TextData[{ "[1] Kevin R. Coombes et al.: The ", StyleBox["Mathematica", FontSlant->"Italic"], "-Primer, Cambridge University Press 1998 (ISBN 0-521-63715-5)" }], "Text"], Cell[TextData[{ "[2] Roman E. Maeder: Informatik f\[UDoubleDot]r Mathematiker und \ Naturwissenschaftler, Eine Einf\[UDoubleDot]hrung mit ", StyleBox["Mathematica", FontSlant->"Italic"], ", Addison-Wesley 1993 (ISBN 3-89319-519-X)" }], "Text"], Cell[TextData[{ "[3] Wolfram, S: The ", StyleBox["Mathematica", FontSlant->"Italic"], "-Book, 3rd edition, Wolfram Media/Cambridge University Press 1996 " }], "Text"], Cell[TextData[{ "[4] Wolfram, S.: Das ", StyleBox["Mathematica", FontSlant->"Italic"], "-Buch, Addison-Wesley 1998 (ISBN 3-8273-1338-4)" }], "Text"], Cell["Weiterf\[UDoubleDot]hrende Literatur:", "Text"], Cell[TextData[{ "[5] Roman Maeder: The ", StyleBox["Mathematica", FontSlant->"Italic"], " Programmer, Academic Press 1994" }], "Text"], Cell[TextData[{ "[6] Richard Gass: ", StyleBox["Mathematica", FontSlant->"Italic"], " for Scientists and Engineers Using ", StyleBox["Mathematica", FontSlant->"Italic"], " to do Science, Prentice Hall 1998" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["1. Getting Started", "Section"], Cell[CellGroupData[{ Cell["Programmstart", "Subsection"], Cell[TextData[{ "Auf den NT-Rechnern im PC-Raum 31/149 startet man ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0 \[UDoubleDot]ber " }], "Text"], Cell[TextData[{ " ", StyleBox[ "Start \[DoubleRightArrow] Programme \[DoubleRightArrow] Mathematik & \ Statistik \[DoubleRightArrow] Mathematica", FontWeight->"Bold"] }], "ItemizedText"], Cell[TextData[{ "Im LAN Mathematik startet man ", StyleBox["Mathematica", FontSlant->"Italic"], " unter X-Windows etwa auf dem Rechner ", StyleBox["rowan", FontWeight->"Bold"], " mit dem Befehl " }], "Text"], Cell[TextData[StyleBox[" mathematica30", FontWeight->"Bold"]], "Text"], Cell[TextData[{ StyleBox["Das "], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[ "-Programm ben\[ODoubleDot]tigt sehr viel 'Memory'. \nEs ist deshalb \ ratsam, alle anderen Anwendungen zu schlie\[SZ]en."] }], "Caption", Background->GrayLevel[0.900008]], Cell["\<\ Das Notebook-Interface wird gestartet. Es erscheint ein \ Men\[UDoubleDot]balken, ein Notebook-Fenster mit dem Namen \"Untitled-1\" und \ eine Palette f\[UDoubleDot]r einige mathematische Symbole. \ \>", "Text"], Cell[TextData[{ "Man startet nun den ", StyleBox["Mathematica", FontSlant->"Italic"], "-Kern \[UDoubleDot]ber das ", StyleBox["Mathematica", FontSlant->"Italic"], "-Men\[UDoubleDot] durch " }], "Text"], Cell[TextData[{ " ", StyleBox["Kernel \[Implies] Start Kernel \[Implies] Local.", FontWeight->"Bold"] }], "ItemizedText"] }, Open ]], Cell[CellGroupData[{ Cell["Schreiben im Notebook", "Subsection"], Cell["\<\ Zun\[ADoubleDot]chst klickt man in das Notebook-Fenster, um das Fenster zu \ aktivieren.\ \>", "Text"], Cell[TextData[{ "Man kann dann wie in einem Textverarbeitungsprogramm arbeiten. Gibt man \ etwa ", StyleBox["37+13", "Input"], " ein, und dr\[UDoubleDot]ckt anschlie\[SZ]end ", Cell[BoxData[ FormBox[ FrameBox["Shift", BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], StyleBox["+", FontWeight->"Bold"], Cell[BoxData[ FormBox[ FrameBox["Return", BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " oder auch ", Cell[BoxData[ FormBox[ FrameBox["Enter", BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], ", so erscheint im Fenster folgendes" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(37 + 13\)], "Input", CellLabel->"In[1]:="], Cell[BoxData[ \(50\)], "Output", CellLabel->"Out[1]="] }, Open ]], Cell[TextData[{ "Tippt man ", StyleBox["Plot[", "Input"], Cell[BoxData[ \(TraditionalForm\`x\^2\)], "Input"], StyleBox[",{x,-1.2,1.2}]", "Input"], ", so erh\[ADoubleDot]lt man ein Bild der Normalparabel im Bereich ", Cell[BoxData[ \(TraditionalForm\`\(-1.2\) \[LessEqual] x \[LessEqual] 1.2\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ 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Dazu klickt man auf das \ Feld ", Cell[BoxData[ FormBox[ FrameBox[\(\ \ \[FilledSmallSquare]\^\[Placeholder]\ \ \), BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " und tippt dann nacheinander x \[TabKey] 2 und dann, um die Zeile des \ Exponenten wieder zu verlassen, gleichzeitig \[ControlKey]+\[SpaceKey]. \ Statt ", Cell[BoxData[ \(TraditionalForm\`x\^2\)]], " kann man aber auch (ohne Palettenbenutzung) einfach x^2 \[UDoubleDot]ber \ die Tastatur eingeben." }], "Text"], Cell[TextData[{ "W\[ADoubleDot]hlt man nun im Men\[UDoubleDot] ", StyleBox["Format", FontWeight->"Bold"], " den ", StyleBox["Style Text ", FontWeight->"Bold"], "aus, so befindet man sich in einer Textzelle und kann normalen Text \ eingeben, den ", StyleBox["Mathematica", FontSlant->"Italic"], " nicht auswertet. (siehe Abschnitt 2 ", ButtonBox["Input und Output", ButtonData:>"input und output", ButtonStyle->"Hyperlink"], " ) Befindet man sich im Textmodus, so gibt es einen kleinen Unterschied \ beim Eingeben von \"zweidimensionalen\" Ausdr\[UDoubleDot]cken wie ", Cell[BoxData[ \(TraditionalForm\`x\^2\)]], ". Durch Eingeben des Feldes ", Cell[BoxData[ FormBox[ FrameBox[\(\ \ \[FilledSmallSquare]\^\[Placeholder]\ \ \), BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " wird innerhalb des Textes eine Grafikzelle (vergleichbar dem \ mathematischen Modus bei Tex ) erzeugt. Man geht dann zun\[ADoubleDot]chst \ wie oben beschrieben vor. Um dann die Grafikzelle zu verlassen, mu\[SZ] man \ nocheinmal die Kombination \[ControlKey]+\[SpaceKey] dr\[UDoubleDot]cken." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Speichern des Notebooks", "Subsection"], Cell[TextData[{ "Man w\[ADoubleDot]hlt im ", StyleBox["Mathematica", FontSlant->"Italic"], "-Men\[UDoubleDot]: ", StyleBox["File \[Implies] Save As ", FontWeight->"Bold"], ". Dann erscheint ein neues Fenster, in dem man wie gewohnt fortf\ \[ADoubleDot]hrt. Der Filename sollte die Endung \".nb\" besitzen. Nennen wir \ das Notebook etwa \"Mein erstes Notebook.nb\" Dann kann man es schlie\[SZ]en, \ ohne die ", StyleBox["Mathematica", FontSlant->"Italic"], "-Sitzung zu verlassen, indem man ", StyleBox["File \[Implies] Close", FontWeight->"Bold"], " w\[ADoubleDot]hlt (oder die bekannten Windows- Mausklicks ausf\ \[UDoubleDot]hrt)." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\[CapitalODoubleDot]ffnen eines Notebooks", "Subsection"], Cell[TextData[{ "\[CapitalUDoubleDot]ber ", StyleBox["File \[Implies] Open ", FontWeight->"Bold"], " kann man das vorher gespeicherte und geschlossene Notebook wieder \ \[ODoubleDot]ffnen. Es erscheint ein neues Notebook-Fenster mit dem Namen \ \"Mein erstes Notebook.nb\". Jetzt kann man \[CapitalADoubleDot]nderungen \ vornehmen oder weitere Befehle ausf\[UDoubleDot]hren lassen. Mit ", StyleBox["File \[Implies] Save ", FontWeight->"Bold"], "werden die \[CapitalADoubleDot]nderungen gespeichert." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Der Help Browser ", "Subsection"], Cell[TextData[{ StyleBox["W\[ADoubleDot]hlen Sie "], StyleBox["Help\[Implies]Help", FontWeight->"Bold"], StyleBox[" aus dem "], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[ "-Men\[UDoubleDot]. Der Help Browser wird ge\[ODoubleDot]ffnet. Er bietet \ sehr umfangreiche Informationsm\[ODoubleDot]glichkeiten. Zum Beispiel ist das \ komplette "], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[ "-Buch (allerdings nur in englischer Sprache) zug\[ADoubleDot]nglich. \nUm \ einen kleinen Eindruck zu gewinnen, beginnen Sie etwa mit \n"], StyleBox[ "Getting Started/Demos \[Implies] Demos \[Implies] Notebook-Demos \ \[Implies] Calculating Pi", FontWeight->"Bold"], StyleBox[ ". \nSie werden etwas \[UDoubleDot]ber die Kreiszahl \[Pi] erfahren. Um die \ Zellen zu \[ODoubleDot]ffnen, mu\[SZ] man nur an die \[ADoubleDot]u\[SZ]eren \ Zellenklammern doppelklicken.\nVersuchen Sie dann:\n"], StyleBox[ "Getting Started/Demos \[Implies] GraphicsGallery \[Implies] Animations\n", FontWeight->"Bold"], StyleBox[ "Sie erhalten eine Liste von Animationen. Klicken Sie zum Beispiel auf \ \"Rolling Square\". Es erscheint ein Bild. Klicken Sie nun auf die \ \[ADoubleDot]u\[SZ]ere rechte senkrechte blaue Linie. Sie wird fett-schwarz. \ Jetzt k\[ODoubleDot]nnen Sie einfach die Tastenkombination \[ControlKey]+Y dr\ \[UDoubleDot]cken (Sie k\[ODoubleDot]nnen auch mit der Maus im Men\ \[UDoubleDot] "], StyleBox["Cell", FontWeight->"Bold"], StyleBox[" nach "], StyleBox["Animate Selected Graphics", FontWeight->"Bold"], StyleBox[ " suchen oder noch einfacher einfach in das Bild doppelklicken) und so die \ Animation starten."] }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Beenden der ", StyleBox["Mathematica", FontSlant->"Italic"], "-Sitzung" }], "Subsection", CellDingbat->"\[FilledSquare]"], Cell[TextData[{ "Man beendet eine ", StyleBox["Mathematica", FontSlant->"Italic"], "-Sitzung mit ", StyleBox["File \[Implies] Exit", FontWeight->"Bold"], " " }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Aufgaben zu Abschnitt 1", "Section"], Cell[TextData[{ "\[HappySmiley] 1. Stellen Sie ein Notebook mit einer oder mehreren \ Textzellen (seihe Men\[UDoubleDot] Format), einer Inputzelle und der \ ausgewerteten Outputzelle (Enter dr\[UDoubleDot]cken!) her. Speichern Sie das \ Notebook unter einem selbsterdachten Namen mit der Extension ", StyleBox[".nb ", FontWeight->"Bold"], "Schlie\[SZ]en Sie das Notebook. \[CapitalODoubleDot]ffnen Sie das Notebook \ wieder. F\[UDoubleDot]gen Sie etwas hinzu, z.B eine Grafik mit dem Befehl ", StyleBox["Plot", "Input"], ". Speichern Sie die \[CapitalADoubleDot]nderungen." }], "Text"], Cell[TextData[{ "\[HappySmiley] 2. Informieren Sie sich \[UDoubleDot]ber den Befehl ", StyleBox["Plot", "Input"], " mit Hilfe der verschiedenen M\[ODoubleDot]glichkeiten im Help Browser. \ Plotten Sie die \"Funktion\" ", Cell[BoxData[ \(TraditionalForm\`x\^3 - x\)]], " im Intervall ", Cell[BoxData[ \(TraditionalForm\`\([\(-2\), 2]\)\)]], "." }], "Text"], Cell[TextData[{ StyleBox["\[HappySmiley] 3. Machen Sie sich mit dem Men\[UDoubleDot] "], StyleBox["Edit", FontWeight->"Bold"], StyleBox[ " vertraut. Kopieren Sie Text von einem Notebookfenster in ein anderes(\ \[ControlKey]C und \[ControlKey]V). \[CapitalODoubleDot]ffnen Sie dazu zun\ \[ADoubleDot]chst ein neues Fenster mit "], StyleBox["File \[Implies] New", FontWeight->"Bold"], StyleBox["."], StyleBox[" ", FontWeight->"Bold"], StyleBox["Es funktioniert wie in einem Standardtextverarbeitungsprogramm."] }], "Text"], Cell[TextData[{ "\[HappySmiley] 4. Folgen Sie dem folgenden Link im Help Browser: ", StyleBox[ "Other Information \[Implies] Contact Information \[Implies] World Wide Web \ ", FontWeight->"Bold"], " . Man schaue zum Beispiel unter ", StyleBox["MathSource.", FontSlant->"Italic"], " Gibt es dort Programme zu den Themen Geometry, Calculus, Linear Algebra?" }], "Text"], Cell[TextData[{ "\[HappySmiley] 5. Berechnen Sie nacheinander ", Cell[BoxData[ \(TraditionalForm\`2\^64\)]], ", ", Cell[BoxData[ \(TraditionalForm\`\((23 + 567)\)\^3\)]], ",", Cell[BoxData[ \(TraditionalForm\`\@12345\%3\)]], ", ", Cell[BoxData[ \(TraditionalForm\`\[Sum]\+\(k = 1\)\%100 k\)]], ". (Benutzen Sie die Palette ", StyleBox["Basic Input) ", FontWeight->"Bold"] }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "2. ", StyleBox["Mathematica", FontSlant->"Italic"], "-Einf\[UDoubleDot]hrung" }], "Section"], Cell[CellGroupData[{ Cell["Input und Output", "Subsection", CellTags->"input und output"], Cell[TextData[{ "Ein ", StyleBox["Mathematica-", FontSlant->"Italic"], "Notebook besteht aus verschiedenen Zellen. Es gibt im wesentlichen drei \ Typen von Zellen: Input-Zellen, Output-Zellen und Text-Zellen. Am rechten \ Rand des Fensters werden Zellen-Klammern angezeigt. Bewegt man die Maus in \ eine Zelle, so bekommt der Mauszeiger die Gestalt eines senkrechten Balkens. \ Zieht man die Maus zwischen zwei Zellen oder ans Ende des Notebooks, so \ bekommt der Mauszeiger die Form eines waagerechten Balkens. Klickt man dann \ auf die linke Maustaste, so entsteht eine durchgezogene waagerechte Linie, \ und man kann eine neue Zelle beginnen. Mit \[AltKey]+7 wechselt man zum \ Textmodus. Der Zelleninhalt einer Text-Zelle wird von ", StyleBox["Mathematica", FontSlant->"Italic"], " nicht ausgewertet. Die Default-Einstellung f\[UDoubleDot]r das Format \ einer Zelle ist Input. Eine Input-Zelle wird, wenn sie aktiv ist, durch \ gleichzeitiges Dr\[UDoubleDot]cken von \[ShiftKey]+\[ReturnKey] oder von ", Cell[BoxData[ FormBox[ FrameBox[ StyleBox["Enter", "Caption"], BoxMargins->{{0.2, 0.2}, {0.4, 0.4}}], TraditionalForm]]], " (ganz rechts auf der Tastatur) ausgewertet. Eine Zelle ist aktiv, wenn \ sich der Mauszeiger in der Zelle befindet, oder wenn die Zellen-Klammer \ fett-schwarz ist." }], "Text"], Cell[TextData[{ "Beispiel: Man tippe ", Cell[BoxData[ \(TraditionalForm\`\((a + b)\)\^3\)]], " und werte dies dann wie oben beschrieben aus. Das Ergebnis sollte so \ aussehen: " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((a + b)\)\^3\)], "Input", CellLabel->"In[3]:="], Cell[BoxData[ \(\((a + b)\)\^3\)], "Output", CellLabel->"Out[3]="] }, Open ]], Cell[TextData[{ "Schade! ", StyleBox["Mathematica", FontSlant->"Italic"], " beherrscht die binomischen Formeln nicht. Dem ist nat\[UDoubleDot]rlich \ nicht so. Wir sollten ", Cell[BoxData[ \(TraditionalForm\`Expand[\((a + b)\)\^3]\)]], " tippen. Dann ergibt Auswerten das gew\[UDoubleDot]nschte Ergebnis:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[\((a + b)\)\^3]\)], "Input", CellLabel->"In[4]:="], Cell[BoxData[ \(a\^3 + 3\ a\^2\ b + 3\ a\ b\^2 + b\^3\)], "Output", CellLabel->"Out[4]="] }, Open ]], Cell["\<\ Wir sehen, da\[SZ] wir schon 4 Eingaben gemacht haben. Manchmal wird man \ Fehler machen. Dann wird eine Fehlermeldung ausgegeben, und man hat die M\ \[ODoubleDot]glichkeit, die Eingabe zu korrigieren. Ein Beispiel:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Expand[b \((a + b)\)\^3\))\)\)], "Input", CellLabel->"In[5]:="], Cell[BoxData[ \(Syntax::"bktmop" \( : \ \) "Expression \"\!\(Expand[\(b \((a + b)\)\^3\))\)\" has no opening \ \"\!\(\"(\"\)\".\!\(\"\"\)"\)], "Message"], Cell[BoxData[ StyleBox[ ErrorBox[\(\(Expand[b \((a + b)\)\^3\))\)], ShowStringCharacters->True]], "Message"] }, Open ]], Cell["\<\ Man kann mit der Maus in die fehlerhafte Input-Zelle gehen und den Fehler \ verbessern.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[b \((a + b)\)\^3]\)], "Input", CellLabel->"In[5]:="], Cell[BoxData[ \(a\^3\ b + 3\ a\^2\ b\^2 + 3\ a\ b\^3 + b\^4\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell[TextData[{ "Strebt man an, Text und Input in der \[UDoubleDot]blichen mathematischen \ Notation zu schreiben, so es ist es ratsam, die Paletten zu benutzen. Dazu \ gehe man zum Men\[UDoubleDot] ", StyleBox[" File \[Implies]Palettes. ", FontWeight->"Bold"], "Neben ", StyleBox["Basic Input", FontWeight->"Bold"], " ist die Palette", StyleBox[" Complete Characters ", FontWeight->"Bold"], "wichtig. Die Bedienung ist selbsterkl\[ADoubleDot]rend. Mit der Palette ", StyleBox["Basic Input", FontWeight->"Bold"], " kann man zum Beispiel ein bestimmtes Integral in der \[UDoubleDot]blichen \ Form eingeben. Dabei werden nach und nach die Eintr\[ADoubleDot]ge in die \ geschw\[ADoubleDot]rzten Felder vorgenommen. Man springt mit der \ Tabulatortaste \[TabKey] von einem Feld zum n\[ADoubleDot]chsten." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_1\%2\( 1\/\(1 + x\^2\)\) \[DifferentialD]x\)], "Input", CellLabel->"In[6]:="], Cell[BoxData[ \(\(-\(\[Pi]\/4\)\) + ArcTan[2]\)], "Output", CellLabel->"Out[6]="] }, Open ]], Cell[TextData[{ "Man versuche es nachzumachen! Falls es nicht klappt, informiere man sich \ im Help Browser unter ", StyleBox["Getting Started \[Implies] Tour of ", FontWeight->"Bold"], StyleBox["Mathematica", FontWeight->"Bold", FontSlant->"Italic"], StyleBox[" \[Implies] Palettes and Buttons", FontWeight->"Bold"], "." }], "Text"], Cell[TextData[{ "Man kann das bestimmte Integral auch \[UDoubleDot]ber die Tastatur \ eingeben. Um zu sehen wie, schaue man sich die InputForm an. Damit nichts \ berechnet wird, wende man au\[SZ]erdem ", StyleBox["Hold", "Input"], " an:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Hold[InputForm[\[Integral]\_1\%2\( 1\/\(1 + x\^2\)\) \[DifferentialD]x]] \)], "Input", CellLabel->"In[7]:="], Cell[BoxData[ RowBox[{"Hold", "[", InterpretationBox[ StyleBox[\(Integrate[1/\((1\ + \ x^2)\), \ {x, \ 1, \ 2}]\), ShowStringCharacters->True, NumberMarks->True], InputForm[ Integrate[ Times[ 1, Power[ Plus[ 1, Power[ x, 2]], -1]], {x, 1, 2}]], Editable->True, AutoDelete->True], "]"}]], "Output", CellLabel->"Out[7]="] }, Open ]], Cell["Der Befehl lautet also in InputForm:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Integrate[1/\((1 + x^2)\), {x, 1, 2}]\)], "Input", CellLabel->"In[8]:="], Cell[BoxData[ \(\(-\(\[Pi]\/4\)\) + ArcTan[2]\)], "Output", CellLabel->"Out[8]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Zahlen", "Subsection"], Cell[CellGroupData[{ Cell["Ganze Zahlen", "Subsubsection"], Cell["\<\ Man kann in gewohnter Weise mit ganzen Zahlen rechnen. Das Malzeichen * kann \ man durch ein Blank ersetzen. Beispiel:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((200 - 302)\) 123\ - 1 + 2\^10\)], "Input", CellLabel->"In[9]:="], Cell[BoxData[ \(\(-11523\)\)], "Output", CellLabel->"Out[9]="] }, Open ]], Cell["Die Summe der ersten 10 nat\[UDoubleDot]rlichen Zahlen:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(k = 1\)\%10 k\)], "Input", CellLabel->"In[10]:="], Cell[BoxData[ \(55\)], "Output", CellLabel->"Out[10]="] }, Open ]], Cell["Die Summe der ersten 10 Quadratzahlen:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(j = 1\)\%10 j\^2\)], "Input", CellLabel->"In[11]:="], Cell[BoxData[ \(385\)], "Output", CellLabel->"Out[11]="] }, Open ]], Cell["Die Primfaktorzerlegung einer ganzen Zahl:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(FactorInteger[12121212]\)], "Input", CellLabel->"In[12]:="], Cell[BoxData[ \({{2, 2}, {3, 1}, {73, 1}, {101, 1}, {137, 1}}\)], "Output", CellLabel->"Out[12]="] }, Open ]], Cell[TextData[{ "Mit dem Befehl ", StyleBox["Head", "Input"], " erf\[ADoubleDot]hrt man etwas \[UDoubleDot]ber den Typ eines Ausdrucks. \ Der Kopf einer ganzen Zahl ist ", StyleBox["Integer", "Input"], ". Beispiel:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Head[1234501]\)], "Input", CellLabel->"In[13]:="], Cell[BoxData[ \(Integer\)], "Output", CellLabel->"Out[13]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Rationale Zahlen", "Subsubsection"], Cell["\<\ Gibt man einen Bruch ein, so wird seine gek\[UDoubleDot]rzte Form bestimmt. \ Beispiel:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(24\/36\)], "Input", CellLabel->"In[14]:="], Cell[BoxData[ \(2\/3\)], "Output", CellLabel->"Out[14]="] }, Open ]], Cell["\<\ Die Arithmetik mit rationalen Zahlen ergibt stets exakte Werte. Als Beispiel \ berechnen wir eine harmonische Zahl:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(k = 1\)\%10 1\/k\)], "Input", CellLabel->"In[15]:="], Cell[BoxData[ \(7381\/2520\)], "Output", CellLabel->"Out[15]="] }, Open ]], Cell[TextData[{ "Der Kopf eines Bruches, der nicht ganz ist, ist ", StyleBox["Rational", "Input"], ". Beispiele:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Head[1\/2]\)], "Input", CellLabel->"In[16]:="], Cell[BoxData[ \(Rational\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Head[4\/2]\)], "Input", CellLabel->"In[17]:="], Cell[BoxData[ \(Integer\)], "Output", CellLabel->"Out[17]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Reelle Zahlen ", "Subsubsection"], Cell["\<\ Reelle Zahlen werden als Dezimalbr\[UDoubleDot]che eingegeben. Nat\ \[UDoubleDot]rlich kann man nur endliche Dezimalbr\[UDoubleDot]che eingeben. \ Das Komma wird dabei als Punkt notiert. Auch eine ganze oder eine rationale \ Zahl kann als reelle Zahl dargestellt werden. Beispiele:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({Head[2123], Head[2123.0], Head[2123. ]}\)], "Input", CellLabel->"In[18]:="], Cell[BoxData[ \({Integer, Real, Real}\)], "Output", CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Head[1\/2. ]\)], "Input", CellLabel->"In[19]:="], Cell[BoxData[ \(Real\)], "Output", CellLabel->"Out[19]="] }, Open ]], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\@2\)]], " wird als formaler Ausdruck ", StyleBox["Power[2,", "Input"], StyleBox[Cell[BoxData[ \(TraditionalForm\`1\/2\)], "Input"], "Input"], StyleBox["]", "Input"], " aufgefa\[SZ]t und nicht als reelle Zahl. Demzufolge ergibt sich:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Head[\@2]\)], "Input", CellLabel->"In[20]:="], Cell[BoxData[ \(Power\)], "Output", CellLabel->"Out[20]="] }, Open ]], Cell[TextData[{ "Man kann aber mit dem Befehl ", StyleBox["N", "Input"], " zu einem reellen Wert \[UDoubleDot]bergehen. Hier der Wert von ", Cell[BoxData[ \(TraditionalForm\`\@2\)]], " auf 12 Dezimalstellen genau (Die Ziffern vor dem Komma werden nat\ \[UDoubleDot]rlich mitgez\[ADoubleDot]hlt!):" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[\@2, 12]\)], "Input", CellLabel->"In[21]:="], Cell[BoxData[ StyleBox["1.4142135623730951`", StyleBoxAutoDelete->True, PrintPrecision->12]], "Output", CellLabel->"Out[21]="] }, Open ]], Cell["Eine andere M\[ODoubleDot]glichkeit:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\@2. \)], "Input", CellLabel->"In[22]:="], Cell[BoxData[ \(1.4142135623730951`\)], "Output", CellLabel->"Out[22]="] }, Open ]], Cell[TextData[{ "Die Gau\[SZ]klammer ", Cell[BoxData[ \(TraditionalForm\`\[LeftFloor]x\[RightFloor]\)]], " ist die gr\[ODoubleDot]\[SZ]te ganze Zahl, die kleiner oder gleich ", Cell[BoxData[ \(TraditionalForm\`x\)]], " ist. Man kann auch ", StyleBox["Floor", "Input"], " verwenden. " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({\[LeftFloor]123.4\[RightFloor], Floor[123.4], Floor[\@2], Floor[345\/57]}\)], "Input", CellLabel->"In[23]:="], Cell[BoxData[ \({123, 123, 1, 6}\)], "Output", CellLabel->"Out[23]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Komplexe Zahlen", "Subsubsection"], Cell[TextData[{ "Die letzte Stufe in der Hierarchie des Zahlensystems sind die komplexen \ Zahlen. Die Zahl ", Cell[BoxData[ \(TraditionalForm\`\@\(-1\)\)]], " wird in ", StyleBox["Mathematica", FontSlant->"Italic"], " mit dem festen Symbol ", StyleBox["I", "Input"], " bezeichnet. Beispiele:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((3 + 4 I)\) \((2 - I)\)\)], "Input", CellLabel->"In[24]:="], Cell[BoxData[ \(10 + 5\ I\)], "Output", CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Head[3 + 4 I]\)], "Input", CellLabel->"In[25]:="], Cell[BoxData[ \(Complex\)], "Output", CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Head[3. + 4. \ I]\)], "Input", CellLabel->"In[26]:="], Cell[BoxData[ \(Complex\)], "Output", CellLabel->"Out[26]="] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Algebraische Terme", "Subsection"], Cell[TextData[{ "Ein Buchstabe oder ein Wort wird von ", StyleBox["Mathematica", FontSlant->"Italic"], " als ein Symbol oder eine Variable betrachtet. Aus solchen Symbolen kann \ man durch arithmetische Operationen, Verschachteln mit Klammern neue Ausdr\ \[UDoubleDot]cke bilden. Einige Beispiele:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Head[a]\)], "Input", CellLabel->"In[27]:="], Cell[BoxData[ \(Symbol\)], "Output", CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\((a + b)\) \((a + b)\) \((a - b)\) \((a - 3)\)\)], "Input", CellLabel->"In[28]:="], Cell[BoxData[ \(\((\(-3\) + a)\)\ \((a - b)\)\ \((a + b)\)\^2\)], "Output", CellLabel->"Out[28]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[%]\)], "Input", CellLabel->"In[29]:="], Cell[BoxData[ \(\(-3\)\ a\^3 + a\^4 - 3\ a\^2\ b + a\^3\ b + 3\ a\ b\^2 - a\^2\ b\^2 + 3\ b\^3 - a\ b\^3\)], "Output", CellLabel->"Out[29]="] }, Open ]], Cell[TextData[{ "Mit ", StyleBox["%", "Input"], " bezeichnet man den vorhergehenden Output. Man sollte dieses Zeichen m\ \[ODoubleDot]glichst nicht verwenden. " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Factor[%]\)], "Input", CellLabel->"In[30]:="], Cell[BoxData[ \(\((\(-3\) + a)\)\ \((a - b)\)\ \((a + b)\)\^2\)], "Output", CellLabel->"Out[30]="] }, Open ]], Cell[TextData[{ "Im folgenden Term tauchen drei Variable auf: ", StyleBox["a,b", "Input"], " und ", StyleBox["ab", "Input"], ". Dabei wird ", StyleBox["ab ", "Input"], "nicht etwa als Produkt von ", StyleBox["a", "Input"], " und ", StyleBox["b", "Input"], " gelesen, sondern als ein einziges Symbol mit dem Namen ", StyleBox["ab", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a\ b\^2 - ab\^2\)], "Input", CellLabel->"In[31]:="], Cell[BoxData[ \(\(-ab\^2\) + a\ b\^2\)], "Output", CellLabel->"Out[31]="] }, Open ]], Cell[TextData[{ "Das kann man mit dem Befehl ", StyleBox["Variables", "Input"], " abfragen." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Variables[%]\)], "Input", CellLabel->"In[32]:="], Cell[BoxData[ \({a, ab, b}\)], "Output", CellLabel->"Out[32]="] }, Open ]], Cell["\<\ Die Namen von Variablen k\[ODoubleDot]nnen beliebig lang sein, \ d\[UDoubleDot]rfen aber keine Blanks enthalten, weil ein Blank als Malzeichen \ gelesen wird. Ein weiteres Bespiel:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[\((variablea + variableb)\)\^2]\)], "Input", CellLabel->"In[33]:="], Cell[BoxData[ \(General::"spell1" \( : \ \) "Possible spelling error: new symbol name \"\!\(variableb\)\" is \ similar to existing symbol \"\!\(variablea\)\"."\)], "Message"], Cell[BoxData[ \(variablea\^2 + 2\ variablea\ variableb + variableb\^2\)], "Output", CellLabel->"Out[33]="] }, Open ]], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " hat eine Fehlermeldung ausgegeben, die darauf aufmerksam macht, da\[SZ] \ wir uns eventuell verschrieben haben. Das ist hier nicht der Fall. Also k\ \[ODoubleDot]nnen wir, ohne die Fehlermeldung zu beachten, fortfahren." }], "Text"], Cell[TextData[{ "In der Palette ", StyleBox["Algebraic Manipulation ", FontWeight->"Bold"], "findet man viele weitere Befehle zum Vereinfachen oder Umformen \ algebraischer Ausdr\[UDoubleDot]cke. Hier illustrieren wir noch die Wirkung \ von ", StyleBox["Simplify", "Input"], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\(x\^3 - y\^3\)\/\(x - y\)]\)], "Input", CellLabel->"In[34]:="], Cell[BoxData[ \(x\^2 + x\ y + y\^2\)], "Output", CellLabel->"Out[34]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\(x\^4 - y\^4\)\/\(x - y\)]\)], "Input", CellLabel->"In[35]:="], Cell[BoxData[ \(x\^3 + x\^2\ y + x\ y\^2 + y\^3\)], "Output", CellLabel->"Out[35]="] }, Open ]], Cell["\<\ Beim n\[ADoubleDot]chsten Beispiel ist der Term nach dem K\[UDoubleDot]rzen \ zu lang, deshalb bleibt der Ausdruck unver\[ADoubleDot]ndert.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\(x\^5 - y\^5\)\/\(x - y\)]\)], "Input", CellLabel->"In[36]:="], Cell[BoxData[ \(\(x\^5 - y\^5\)\/\(x - y\)\)], "Output", CellLabel->"Out[36]="] }, Open ]], Cell["\<\ Manchmal bringt Ausmultiplizieren eine Vereinfachung. Beispiel:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\((1 + x + x\^2)\) \((1 - x + x\^2)\)]\)], "Input", CellLabel->"In[37]:="], Cell[BoxData[ \(1 + x\^2 + x\^4\)], "Output", CellLabel->"Out[37]="] }, Open ]], Cell["oft aber auch nicht:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\((1 + 2 x + 6 x\^2)\) \((3 - x + x\^2)\)]\)], "Input", CellLabel->"In[38]:="], Cell[BoxData[ \(\((3 - x + x\^2)\)\ \((1 + 2\ x + 6\ x\^2)\)\)], "Output", CellLabel->"Out[38]="] }, Open ]], Cell["\<\ Manchmal liefert umgekehrt Faktorisieren eine Vereinfachung. Beispiel:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\((1 + 2 x + x\^2)\) \((9 - 6 x + x\^2)\)]\)], "Input", CellLabel->"In[39]:="], Cell[BoxData[ \(\((\(-3\) + x)\)\^2\ \((1 + x)\)\^2\)], "Output", CellLabel->"Out[39]="] }, Open ]], Cell["Ein letztes Beispiel:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((1 - x)\) \(\[Sum]\+\(k = 0\)\%7 x\^k\)\)], "Input", CellLabel->"In[40]:="], Cell[BoxData[ \(\((1 - x)\)\ \((1 + x + x\^2 + x\^3 + x\^4 + x\^5 + x\^6 + x\^7)\)\)], "Output", CellLabel->"Out[40]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[%]\)], "Input", CellLabel->"In[41]:="], Cell[BoxData[ \(1 - x\^8\)], "Output", CellLabel->"Out[41]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Hilfe", "Subsection"], Cell[TextData[{ "Will man Informationen zu einem Befehl, etwa ", StyleBox["Expand", "Input"], " haben, so tippt man \n", StyleBox["?Expand oder ??Expand", "Input"], ". Kennt man den Namen des Befehls, nach dem man sucht nicht genau, so kann \ man auch den Stern * verwenden. Es werden dann alle dazu passenden Befehle \ angezeigt. Einige Beispiele:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?*pand\)\)], "Input", CellLabel->"In[42]:="], Cell[TextData[StyleBox[ "ComplexExpand LogicalExpand\nExpand PowerExpand\nFunctionExpand \ TrigExpand"]], "Print", CellLabel->"From In[42]:="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?Si*\)\)], "Input", CellLabel->"In[43]:="], Cell[TextData[StyleBox[ "Sign\nSignature\nSignPadding\nSimplify\nSin\nSingleLetterItalics\n\ SingularityDepth\nSingularValues\nSinh\nSinhIntegral\nSinIntegral\n\ SixJSymbol"]], "Print", CellLabel->"From In[43]:="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?Exp*\)\)], "Input", CellLabel->"In[44]:="], Cell[TextData[StyleBox[ "Exp\nExpand\nExpandable\nExpandAll\nExpandDenominator\nExpandNumerator\n\ ExpIntegralE\nExpIntegralEi\nExponent\nExponentFunction\nExponentStep\n\ Expression\nExpressionPacket\nExpToTrig"]], "Print", CellLabel->"From In[44]:="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(?? Expand\)], "Input", CellLabel->"In[45]:="], Cell[BoxData[ \("Expand[expr] expands out products and positive integer powers in expr. \ Expand[expr, patt] leaves unexpanded any parts of expr that are free of the \ pattern patt."\)], "Print"], Cell[BoxData[ InterpretationBox[ StyleBox[\(Attributes[Expand]\ = \ {Protected}\n\ \n Options[Expand]\ = \ {Modulus\ -> \ 0, \ Trig\ -> \ False}\), ShowStringCharacters->True, NumberMarks->True], InputForm[ Definition[ Expand]], Editable->True, AutoDelete->True]], "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Optionen", "Subsection"], Cell[TextData[{ "Viele ", StyleBox["Mathematica-", FontSlant->"Italic"], "Befehle besitzen Optionen, die verschiedene Werte annehmen \ k\[ODoubleDot]nnen. Eine Option wird festgelegt nach dem Schema (den Pfeil \ entnimmt der Palette Basis Input oder man kombiniert ihn aus den Zeichen ", StyleBox["- ", "Input"], "und ", StyleBox["> ", "Input"], ") ", StyleBox["Optionsname\[Rule]Optionswert", "Input"], "." }], "Text"], Cell["Einige Beispiele:", "Text"], Cell[TextData[{ StyleBox["1", FontWeight->"Bold"], ". In den folgenden Beispielen werden in der binomischen Formel die \ Binomialkoeffizienten modulo 2, 3 und schlie\[SZ]lich modulo 5 reduziert." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[\((x + y)\)\^5, Modulus \[Rule] 2]\)], "Input", CellLabel->"In[46]:="], Cell[BoxData[ \(x\^5 + x\^4\ y + x\ y\^4 + y\^5\)], "Output", CellLabel->"Out[46]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[\((x + y)\)\^5, Modulus \[Rule] 3]\)], "Input", CellLabel->"In[47]:="], Cell[BoxData[ \(x\^5 + 2\ x\^4\ y + x\^3\ y\^2 + x\^2\ y\^3 + 2\ x\ y\^4 + y\^5\)], "Output", CellLabel->"Out[47]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[\((x + y)\)\^5, Modulus \[Rule] 5]\)], "Input", CellLabel->"In[48]:="], Cell[BoxData[ \(x\^5 + y\^5\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["2", FontWeight->"Bold"], ". Der Befehl ", StyleBox["Plot", "Input"], " besitzt eine F\[UDoubleDot]lle von Optionen. Welche und mit welchen \ aktuellen Werten, kann man mit dem Befehl ", StyleBox["Options", "Input"], " feststellen." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[Plot]\)], "Input", CellLabel->"In[49]:="], Cell[BoxData[ \({AspectRatio \[Rule] 1\/GoldenRatio, Axes \[Rule] Automatic, AxesLabel \[Rule] None, AxesOrigin \[Rule] Automatic, AxesStyle \[Rule] Automatic, Background \[Rule] Automatic, ColorOutput \[Rule] Automatic, Compiled \[Rule] True, DefaultColor \[Rule] Automatic, Epilog \[Rule] {}, Frame \[Rule] False, FrameLabel \[Rule] None, FrameStyle \[Rule] Automatic, FrameTicks \[Rule] Automatic, GridLines \[Rule] None, ImageSize \[Rule] Automatic, MaxBend \[Rule] 10.`, PlotDivision \[Rule] 30.`, PlotLabel \[Rule] None, PlotPoints \[Rule] 25, PlotRange \[Rule] Automatic, PlotRegion \[Rule] Automatic, PlotStyle \[Rule] Automatic, Prolog \[Rule] {}, RotateLabel \[Rule] True, Ticks \[Rule] Automatic, DefaultFont \[RuleDelayed] $DefaultFont, DisplayFunction \[RuleDelayed] $DisplayFunction, FormatType \[RuleDelayed] $FormatType, TextStyle \[RuleDelayed] $TextStyle}\)], "Output", CellLabel->"Out[49]="] }, Open ]], Cell[TextData[{ "Man kann die Werte \[ADoubleDot]ndern. Hier einige Beispiele:\na) Die \ Normalparabel in der Farbe ", StyleBox["Hue[0.56]", "Input"], ". Die Farbtafeln zu ", StyleBox["Hue", "Input"], " findet man im ", StyleBox["Mathematica", FontSlant->"Italic"], "-Buch unter ", ButtonBox["G.2.43", ButtonData:>{ "C:\\Programme\\Wolfram \ Research\\Mathematica\\3.0\\Documentation\\English\\MainBook\\ColorCharts.nb", "G.2.43"}, ButtonStyle->"Hyperlink"], ". Zum Aufruf ", StyleBox["Plot[", "Input"], Cell[BoxData[ FormBox[ StyleBox[\(x\^2\), "Input"], TraditionalForm]]], StyleBox[",{x,-1.2,1.2}]", "Input"], "haben wir die Optionen ", StyleBox["Axes,DefaultColor,Background,PlotLabel,TextStyle", "Input"], " mit neuen Werten hinzugef\[UDoubleDot]gt. Etwas schwierig ist es \ allerdings, herauszubekommen, welche Werte f\[UDoubleDot]r eine gegebene \ Option m\[ODoubleDot]glich sind. " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[x\^2, {x, \(-1.2\), 1.2}, Axes \[Rule] False, DefaultColor \[Rule] Hue[0.56], Background \[Rule] GrayLevel[0.9], PlotLabel \[Rule] "\", TextStyle \[Rule] {FontFamily \[Rule] Helvetica, FontSize \[Rule] 10}] \)], "Input", CellLabel->"In[50]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Background color .9 g MFill % Scaling calculations 0.5 0.396825 0.0147151 0.408753 [ [.5 .63053 -19.0625 0 ] [.5 .63053 19.0625 11.1875 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 .64 1 r gsave .5 .63053 -80.0625 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 20 translate 1 -1 scale gsave 0.000000 0.000000 0.000000 setrgbcolor 1.000000 setlinewidth gsave newpath 61.000000 15.187500 moveto 558.000000 15.187500 lineto 558.000000 4.000000 lineto 61.000000 4.000000 lineto 61.000000 15.187500 lineto closepath clip newpath 63.000000 12.125000 moveto %%IncludeResource: font Helvetica %%IncludeFont: Helvetica /Helvetica findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.639994 1.000000 setrgbcolor 0.000000 0.000000 rmoveto 63.000000 12.125000 moveto %%IncludeResource: font Helvetica %%IncludeFont: Helvetica /Helvetica findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.639994 1.000000 setrgbcolor (Parabel) show 97.125000 12.125000 moveto %%IncludeResource: font Helvetica %%IncludeFont: Helvetica /Helvetica findfont 10.000000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000000 0.639994 1.000000 setrgbcolor 0.000000 0.000000 rmoveto 1.000000 setlinewidth grestore grestore %%DocumentNeededResources: font Helvetica %%DocumentSuppliedResources: %%DocumentNeededFonts: Helvetica %%DocumentSuppliedFonts: %%DocumentFonts: font Helvetica grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid [ ] 0 setdash .02381 .60332 m .06244 .51168 L .10458 .42058 L .14415 .34341 L .18221 .27686 L .22272 .21429 L .26171 .16211 L .30316 .11529 L .34309 .07863 L .3815 .05117 L .40095 .04018 L .42237 .03036 L .44268 .02324 L .45178 .02075 L .46172 .01852 L .4671 .01752 L .4721 .01674 L .47727 .01606 L .48196 .01556 L .48658 .01518 L .4887 .01505 L .49093 .01493 L .49332 .01483 L .49438 .0148 L .49552 .01477 L .49675 .01474 L .49789 .01473 L .49859 .01472 L .49925 .01472 L .50049 .01472 L .50163 .01472 L .50286 .01474 L .50401 .01476 L .50508 .01478 L .50754 .01486 L .51014 .01498 L .51268 .01513 L .51504 .0153 L .5204 .0158 L .5293 .01694 L .53882 .01863 L .54906 .02096 L .56016 .02411 L .58032 .03146 L .60019 .04077 L .62123 .05287 L .65912 .08044 L .69946 .11799 L .73829 .1621 L .77956 .21759 L Mistroke .81932 .2794 L .85757 .34659 L .89827 .42644 L .93745 .51144 L .97619 .60332 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgI03>IIIS>IVC>Ic3>Ioc?<03?<[ZjWAdM:NWYj0Pl=WIfJj^[WMgMl30`>OWifm_Kh000820P000P28R8X20 0020P4:JY`0g?02001YOI`00kUDJRj>SXhb"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.37565, -0.0360077, 0.00958644, 0.0093067}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output", CellLabel->"Out[50]="] }, Open ]], Cell[TextData[{ "b) Die Normalparabel mit einem zus\[ADoubleDot]tzlich durch ", StyleBox["Epilog\[Rule]", "Input"], StyleBox["Grafikobjekt", "Input", FontSlant->"Italic"], " eingef\[UDoubleDot]gten Grafikobjekt, hier: eine Kreisscheibe und eine \ Kreislinie. 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" }], "Text"], Cell[TextData[{ StyleBox["3", FontWeight->"Bold"], ". Mit dem Befehl ", StyleBox["Factor", "Input"], " kann man zum Beispiel Polynome in irreduzible Faktoren zerlegen. \ Bekanntlich kommt es dabei auch auf den Grundk\[ODoubleDot]rper an. Mit der \ Option ", StyleBox["Extension", "Input"], " kann man vom K\[ODoubleDot]rper \[DoubleStruckCapitalQ] der rationalen \ Zahlen zu einem geeigneten Erweiterungsk\[ODoubleDot]rper \ \[UDoubleDot]bergehen." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[Factor]\)], "Input", CellLabel->"In[52]:="], Cell[BoxData[ \({Extension \[Rule] None, GaussianIntegers \[Rule] False, Modulus \[Rule] 0, Trig \[Rule] False}\)], "Output", CellLabel->"Out[52]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Factor[x\^2 - 2]\)], "Input", CellLabel->"In[53]:="], Cell[BoxData[ \(\(-2\) + x\^2\)], "Output", CellLabel->"Out[53]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Factor[x\^2 - 2, Extension \[Rule] \@2]\)], "Input", CellLabel->"In[54]:="], Cell[BoxData[ \(\(-\((\@2 - x)\)\)\ \((\@2 + x)\)\)], "Output", CellLabel->"Out[54]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Factor[x\^4 - 2, Extension \[Rule] {I \@ 2, \@2\%4}]\)], "Input", CellLabel->"In[55]:="], Cell[BoxData[ \(\(-\((2\^\(1/4\) - x)\)\)\ \((2\^\(1/4\) - I\ x)\)\ \((2\^\(1/4\) + I\ x)\)\ \((2\^\(1/4\) + x)\)\)], "Output", CellLabel->"Out[55]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Namen und Zuweisungen", "Subsection"], Cell["\<\ Einem Symbol kann man mit Hilfe eines einfachen Gleichheitszeichen einen Wert \ zuweisen. 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So vermeidet man Fehler im sp\[ADoubleDot]teren Verlauf \ einer ", StyleBox["Mathematica", FontSlant->"Italic"], "-Sitzung. Beispielsweise erh\[ADoubleDot]lt man mit den jetztigen Werten \ von ", StyleBox["b,c", "Input"], " ein merkw\[UDoubleDot]rdiges Ergebnis:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(d = \((b + c)\)\^2\)], "Input", CellLabel->"In[71]:="], Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{\(-4\), "-", \(x\^2\), "+", "y", "+", \(f[x]\), "+", RowBox[{"(", TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], ")"}]}], ")"}], "2"]], "Output", CellLabel->"Out[71]="] }, Open ]], Cell["Wir l\[ODoubleDot]schen die Werte:", "Text"], Cell[BoxData[ \(Clear[a, b, c, f, d]\)], "Input", CellLabel->"In[72]:="], Cell[TextData[{ "Wir erfragen die bisher in der ", StyleBox["Mathematica", FontSlant->"Italic"], "-Sitzung eingef\[UDoubleDot]hrten Namen. Sie haben den Kontext ", StyleBox["Global", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Names["\"]\)], "Input", CellLabel->"In[73]:="], Cell[BoxData[ \({"a", "ab", "b", "c", "d", "f", "Helvetica", "j", "k", "variablea", "variableb", "x", "y"}\)], "Output", CellLabel->"Out[73]="] }, Open ]], Cell["Wir entfernen alle Namen:", "Text"], Cell[BoxData[ \(\(Map[Remove, Names["\"]]; \)\)], "Input", CellLabel->"In[74]:="], Cell["Jetzt gibt es keine Namen mehr:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Names["\"]\)], "Input", CellLabel->"In[75]:="], Cell[BoxData[ \({}\)], "Output", CellLabel->"Out[75]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Gleichungen", "Subsection"], Cell[TextData[{ "Eine Gleichung ist eine Aussageform der Bauart ", StyleBox["linkeseite==rechteseite", "Input"], ". Das Gleichheitszeichen in einer Gleichung besteht also aus zwei \ nebeneinanderstehenden Gleichheitszeichen ", StyleBox["==", "Input"], ". Sind konkrete Werte, etwa Zahlen, gegeben, so besitzt eine Gleichung \ einen der beiden Wahrheitswerte ", StyleBox["True", "Input"], " oder ", StyleBox["False", "Input"], ". Einige Beispiele:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(2 == 3\)], "Input", CellLabel->"In[76]:="], Cell[BoxData[ \(False\)], "Output", CellLabel->"Out[76]="] }, Open ]], Cell[TextData[{ "Dasselbe leistet (", StyleBox["==", "Input"], " ist das Infixzeichen f\[UDoubleDot]r den Operator ", StyleBox["Equal", "Input"], ")" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Equal[2, 3]\)], "Input", CellLabel->"In[77]:="], Cell[BoxData[ \(False\)], "Output", CellLabel->"Out[77]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(2 + 2 == 4\)], "Input", CellLabel->"In[78]:="], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[78]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(n = 1\)\%\[Infinity] 1\/n\^2 == \[Pi]\^2\/6\)], "Input", CellLabel->"In[79]:="], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[79]="] }, Open ]], Cell["\<\ Kommen unbestimmte Symbole vor, so wird die Gleichung nicht ausgewertet. \ Beispiele:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(x + 2 == 3\)], "Input", CellLabel->"In[80]:="], Cell[BoxData[ \(2 + x == 3\)], "Output", CellLabel->"Out[80]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(gleichungssystem = {3 x + 4 y == 3, 6 x + 9 y == \(-4\)}\)], "Input",\ CellLabel->"In[81]:="], Cell[BoxData[ \({3\ x + 4\ y == 3, 6\ x + 9\ y == \(-4\)}\)], "Output", CellLabel->"Out[81]="] }, Open ]], Cell[TextData[{ "Mit dem Befehl ", StyleBox["Solve", "Input"], " kann man Gleichungen und Gleichungssysteme l\[ODoubleDot]sen. ", StyleBox["Solve[gl,t]", "Input"], " l\[ODoubleDot]st die Gleichung ", StyleBox["gl", "Input"], " nach ", StyleBox["t", "Input"], " auf. ", StyleBox["gl", "Input"], " darf auch eine Liste von Gleichungen und ", StyleBox["t", "Input"], " darf eine ", ButtonBox["Liste", ButtonData:>"liste", ButtonStyle->"Hyperlink"], " von Variablen sein. F\[UDoubleDot]r unsere beiden Beispiele ergibt sich:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[x + 2 == 3, x]\)], "Input", CellLabel->"In[82]:="], Cell[BoxData[ \({{x \[Rule] 1}}\)], "Output", CellLabel->"Out[82]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[gleichungssystem, {x, y}]\)], "Input", CellLabel->"In[83]:="], Cell[BoxData[ \({{x \[Rule] 43\/3, y \[Rule] \(-10\)}}\)], "Output", CellLabel->"Out[83]="] }, Open ]], Cell[TextData[{ "Die L\[ODoubleDot]sungen werden in der Form von Einsetzungsregeln \ angegeben. Das ist auf den ersten Blick vielleicht etwas aufwendig, erweist \ sich aber als sehr praktisch. \nMan kann die L\[ODoubleDot]sungen durch \ Einsetzen mit Hilfe des Befehls ", StyleBox["/.", "Input"], " (ReplaceAll) erhalten:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(x /. x \[Rule] z\)], "Input", CellLabel->"In[84]:="], Cell[BoxData[ \(z\)], "Output", CellLabel->"Out[84]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(x /. Solve[x + 2 == 3, x]\)], "Input", CellLabel->"In[85]:="], Cell[BoxData[ \({1}\)], "Output", CellLabel->"Out[85]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({x, y} /. Solve[gleichungssystem, {x, y}]\)], "Input", CellLabel->"In[86]:="], Cell[BoxData[ \({{43\/3, \(-10\)}}\)], "Output", CellLabel->"Out[86]="] }, Open ]], Cell["\<\ Nat\[UDoubleDot]rlich gibt es kompliziertere Gleichungen, die man nicht \ symbolisch aufl\[ODoubleDot]sen kann! Einige Beispiele m\[ODoubleDot]gen dies \ illustrieren:\ \>", "Text"], Cell["\<\ 1. Wenn nicht nur Polynome in der Gleichung vorkommen, klappt die Berechnung \ in der Regel nicht:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[Sin[x] - x\^2 + \@x == 2, x]\)], "Input", CellLabel->"In[87]:="], Cell[BoxData[ \(Solve::"tdep" \( : \ \) "The equations appear to involve transcendental functions of the \ variables in an essentially non-algebraic way."\)], "Message"], Cell[BoxData[ \(Solve[\@x - x\^2 + Sin[x] == 2, x]\)], "Output", CellLabel->"Out[87]="] }, Open ]], Cell["Manchmal wenigstens teilweise:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[Sin[x] == Cos[x], x]\)], "Input", CellLabel->"In[88]:="], Cell[BoxData[ \(Solve::"ifun" \( : \ \) "Inverse functions are being used by \!\(Solve\), so some solutions may \ not be found."\)], "Message"], Cell[BoxData[ \({{x \[Rule] \(-\(\(3\ \[Pi]\)\/4\)\)}, {x \[Rule] \[Pi]\/4}}\)], "Output", CellLabel->"Out[88]="] }, Open ]], Cell["\<\ 2. Bekanntlich kann man Polynomgleichungen vom Grad gr\[ODoubleDot]\[SZ]er \ als vier im allgemeinen nicht durch Wurzeln l\[ODoubleDot]sen:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[x\^5 + 2 x\^3 - x == 1, x]\)], "Input", CellLabel->"In[89]:="], Cell[BoxData[ \({{x \[Rule] Root[\(-1\) - #1 + 2\ #1\^3 + #1\^5&, 1]}, { x \[Rule] Root[\(-1\) - #1 + 2\ #1\^3 + #1\^5&, 2]}, { x \[Rule] Root[\(-1\) - #1 + 2\ #1\^3 + #1\^5&, 3]}, { x \[Rule] Root[\(-1\) - #1 + 2\ #1\^3 + #1\^5&, 4]}, { x \[Rule] Root[\(-1\) - #1 + 2\ #1\^3 + #1\^5&, 5]}}\)], "Output", CellLabel->"Out[89]="] }, Open ]], Cell["In speziellen F\[ADoubleDot]llen geht es doch:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[\(-1\) + 5\ x - 10\ x\^2 + 10\ x\^3 - 5\ x\^4 + x\^5 == 1, x]\)], "Input", CellLabel->"In[90]:="], Cell[BoxData[ \({{x \[Rule] 2}, { x \[Rule] 3\/4 - \@5\/4 - 1\/2\ I\ \@\(5\/2 - \@5\/2\)}, { x \[Rule] 3\/4 - \@5\/4 + 1\/2\ I\ \@\(5\/2 - \@5\/2\)}, { x \[Rule] 3\/4 + \@5\/4 - 1\/2\ I\ \@\(5\/2 + \@5\/2\)}, { x \[Rule] 3\/4 + \@5\/4 + 1\/2\ I\ \@\(5\/2 + \@5\/2\)}}\)], "Output",\ CellLabel->"Out[90]="] }, Open ]], Cell[TextData[ "3. F\[UDoubleDot]r Polynome vom Grad \[LessEqual]4 gibt es stets L\ \[ODoubleDot]sungen durch Radikale:"], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[x\^4 - x\^2 + 12 x - 36 == 0, x]\)], "Input", CellLabel->"In[91]:="], Cell[BoxData[ \({{x \[Rule] \(-3\)}, {x \[Rule] 2}, { x \[Rule] 1\/2\ \((1 - I\ \@23)\)}, { x \[Rule] 1\/2\ \((1 + I\ \@23)\)}}\)], "Output", CellLabel->"Out[91]="] }, Open ]], Cell["\<\ Sie k\[ODoubleDot]nnen allerdings sehr kompliziert sein. Ersetzt man etwa in \ obiger Gleichung 12x durch 10x, so sind die L\[ODoubleDot]sungen sehr \ komplizierte Ausdr\[UDoubleDot]cke. Wir geben die erste der vier L\ \[ODoubleDot]sungen an:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(a = x /. \(Solve[x\^4 - x\^2 + 10 x - 36 == 0, x]\)[\([1]\)]\)], "Input", CellLabel->"In[92]:="], Cell[BoxData[ \(\(-\(1\/2\)\)\ \[Sqrt]\(( 2\/3 - 431\/\(3\ \((53 + 30\ \@88962)\)\^\(1/3\)\) + 1\/3\ \((53 + 30\ \@88962)\)\^\(1/3\))\) - 1\/2\ \[Sqrt]\(( 4\/3 + 431\/\(3\ \((53 + 30\ \@88962)\)\^\(1/3\)\) - 1\/3\ \((53 + 30\ \@88962)\)\^\(1/3\) + 20/\((\[Sqrt]\(( 2\/3 - 431\/\(3\ \((53 + 30\ \@88962)\)\^\(1/3\)\) + 1\/3\ \((53 + 30\ \@88962)\)\^\(1/3\))\))\))\)\)], "Output", CellLabel->"Out[92]="] }, Open ]], Cell["\<\ Man kann das Ergebnis auch in traditioneller Form aufschreiben:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(TraditionalForm[a]\)], "Input", CellLabel->"In[93]:="], Cell[BoxData[ \(TraditionalForm \`\(-\(1\/2\)\)\ \@\(2\/3 - 431\/\(3\ \@\(53 + 30\ \@88962\)\%3\) + 1\/3\ \@\(53 + 30\ \@88962\)\%3\) - 1\/2\ \[Sqrt]\(( 4\/3 + 431\/\(3\ \@\(53 + 30\ \@88962\)\%3\) - 1\/3\ \@\(53 + 30\ \@88962\)\%3 + 20\/\@\(2\/3 - 431\/\(3\ \@\(53 + 30\ \@88962\)\%3\) + 1\/3\ \@\(53 + 30\ \@88962\)\%3\))\)\)], "Output", CellLabel->"Out[93]//TraditionalForm="] }, Open ]], Cell[TextData[{ "Die L\[ODoubleDot]sung ist zwar durch Wurzeln beschrieben, man sieht aber \ nicht ann\[ADoubleDot]hernd, welchen numerischen Wert sie hat. Doch daf\ \[UDoubleDot]r haben wir ja den Befehl ", StyleBox["N", "Input"], ". Es ergibt sich:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[a]\)], "Input", CellLabel->"In[94]:="], Cell[BoxData[ \(\(-2.93217277278032497`\)\)], "Output", CellLabel->"Out[94]="] }, Open ]], Cell[BoxData[ \(Clear[a]\)], "Input", CellLabel->"In[95]:="], Cell[TextData[{ "Mit dem Befehl ", StyleBox["NSolve", "Input"], " kann man stets numerische L\[ODoubleDot]sungen bestimmen" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(NSolve[x\^5 + 2 x\^3 - x == 1, x]\)], "Input", CellLabel->"In[96]:="], Cell[BoxData[ \({{x \[Rule] \(-0.509940932812616942`\) - 0.452053410974865776`\ I}, { x \[Rule] \(-0.509940932812616942`\) + 0.452053410974865776`\ I}, { x \[Rule] \(0.070746612138446796`\[InvisibleSpace]\) - 1.56412143209462817`\ I}, { x \[Rule] \(0.070746612138446796`\[InvisibleSpace]\) + 1.56412143209462817`\ I}, {x \[Rule] 0.87838864134834047`}}\)], "Output", CellLabel->"Out[96]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Eingebaute Funktionen", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " kennt alle wichtigen mathematischen Funktionen. Wir begn\[UDoubleDot]gen \ uns mit einigen Beispielen. Die vollst\[ADoubleDot]ndige Liste und ausf\ \[UDoubleDot]hrliche Informationen erh\[ADoubleDot]lt man im Help Browser \ unter\n", StyleBox["Built-in Functions", FontWeight->"Bold"], "." }], "Text"], Cell[TextData[{ "Zun\[ADoubleDot]chst laden wir mit dem Befehl ", StyleBox["Get", "Input"], " oder kurz ", StyleBox["<<", "Input"], " die Pakete ", StyleBox["Graphics`Colors`", "Input"], " und ", StyleBox["Graphics`Legend`", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?Get\)\)], "Input", CellLabel->"In[97]:="], Cell[BoxData[ \("<"In[98]:="], Cell[BoxData[ \(\(<< Graphics`Legend`\ \)\)], "Input", CellLabel->"In[99]:="], Cell[TextData[{ "Jetzt hat man die M\[ODoubleDot]glichkeit eine Grafik mit einer Legende zu \ versehen. Mehr zur Struktur des Befehls Plot findet man im Abschnitt ", ButtonBox["Grafik mit Plot", ButtonData:>"plot", ButtonStyle->"Hyperlink"], " " }], "Text"], Cell[TextData[{ StyleBox["Die", FontWeight->"Bold"], " ", StyleBox["trigonometrischen Funktionen", FontWeight->"Bold"], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[{Sin[x], Cos[x], Tan[x], Cot[x], Sec[x], Csc[x]}, {x, 0, 2 Pi}, AspectRatio \[Rule] Automatic, PlotRange \[Rule] {\(-4\), 4}, PlotStyle \[Rule] {DeepPink, CadmiumLemon, DodgerBlue, PermanentGreen, Oak, Ultramarine}, Background \[Rule] Titanium, PlotLegend \[Rule] {"\", "\", "\", "\", "\", "\"}]\)], "Input", CellLabel->"In[100]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.21665 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % 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.68338 .765 L .68646 .766 L .68974 .76702 L .6929 .76798 L .69593 .76886 L .69916 .76978 L .70227 .77063 L .70557 .7715 L .70876 .77231 L .71182 .77307 L .71508 .77385 L .71821 .77457 L .72155 .77531 L .72476 .77599 L .72785 .77663 L .73114 .77729 L .73431 .7779 L .73735 .77846 L .74059 .77904 L .74371 .77958 L .74703 .78013 L .75022 .78064 L .75329 .78112 L .75656 .7816 L .75971 .78205 L .76274 .78247 L .76596 .7829 L .76906 .7833 L .77236 .78371 L .77554 .78409 L .7786 .78444 L .78185 .7848 L .78498 .78513 L .78831 .78547 L .79151 .78579 L .7946 .78608 L .79788 .78638 L .80104 .78666 L .80407 .78691 L .80731 .78718 L .81042 .78742 L .81373 .78767 L .81692 .7879 L Mistroke .81998 .78812 L .82325 .78834 L .82639 .78854 L .82973 .78875 L .83294 .78894 L .83604 .78912 L .83933 .7893 L .8425 .78947 L .84555 .78962 L .84879 .78978 L .85192 .78993 L .85524 .79008 L .85844 .79022 L .86151 .79035 L .86479 .79048 L .86794 .7906 L .87097 .79072 L .8742 .79083 L .87731 .79094 L .88061 .79105 L .88379 .79115 L .88685 .79124 L .89011 .79134 L .89324 .79143 L .89657 .79152 L .89978 .7916 L .90287 .79168 L .90615 .79176 L .90932 .79183 L .91236 .7919 L .9156 .79197 L .91872 .79204 L .92203 .7921 L .92522 .79216 L .92829 .79222 L .93156 .79228 L .9347 .79233 L .93805 .79238 L .94127 .79243 L .94437 .79248 L .94766 .79253 L .95084 .79257 L .95389 .79261 L .95714 .79265 L .96027 .79269 L .96359 .79273 L .9668 .79277 L .96988 .7928 L .97316 .79284 L .97619 .79287 L Mistroke Mfstroke .529 .808 .922 r .02381 .4754 m .02691 .47537 L .03029 .47533 L .03347 .4753 L .03652 .47526 L .03978 .47523 L .04291 .47519 L .04623 .47514 L .04944 .4751 L .05252 .47506 L .0558 .47501 L .05896 .47496 L .062 .47491 L .06523 .47486 L .06834 .47481 L .07165 .47475 L .07484 .47469 L .0779 .47463 L .08117 .47456 L .08431 .4745 L .08765 .47442 L .09086 .47435 L .09396 .47427 L .09725 .47419 L .10042 .47411 L .10346 .47403 L .10671 .47394 L .10983 .47385 L .11315 .47375 L .11635 .47364 L .11943 .47354 L .1227 .47343 L .12585 .47332 L .12888 .47321 L .13211 .47308 L .13521 .47295 L .13852 .47282 L .1417 .47268 L .14476 .47254 L .14801 .47238 L .15115 .47223 L .15448 .47205 L .15769 .47188 L .16077 .47171 L .16406 .47152 L .16722 .47132 L .17026 .47113 L .1735 .47092 L .17662 .4707 L .17993 .47046 L Mistroke .18312 .47022 L .18619 .46998 L .18946 .46972 L .1926 .46945 L .19594 .46915 L .19916 .46886 L .20226 .46856 L .20556 .46822 L .20873 .46789 L .21178 .46756 L .21503 .46719 L .21816 .46681 L .22149 .4664 L .22469 .46598 L .22777 .46557 L .23105 .4651 L .2342 .46464 L .23724 .46417 L .24047 .46365 L .24358 .46313 L .24688 .46255 L .25007 .46196 L .25313 .46138 L .25639 .46073 L .25953 .46007 L .26286 .45934 L .26608 .45861 L .26917 .45787 L .27246 .45705 L .27563 .45622 L .27867 .45539 L .28191 .45446 L .28503 .45353 L .28835 .45249 L .29155 .45144 L .29462 .45038 L .29789 .4492 L .30104 .44801 L .30407 .44682 L .30729 .44548 L .3104 .44413 L .31369 .44263 L .31687 .44111 L .31993 .43957 L .32318 .43785 L .32631 .43611 L .32964 .43417 L .33285 .4322 L .33593 .4302 L .33922 .42796 L Mistroke .34238 .42569 L .34541 .4234 L .34865 .42082 L .35176 .4182 L .35507 .41525 L .35826 .41225 L .36133 .4092 L .36459 .40576 L .36774 .40225 L .37108 .3983 L .37429 .39424 L .37739 .3901 L .38068 .38541 L .38385 .38059 L .3869 .37566 L .39015 .37006 L .39327 .3643 L .3966 .35773 L .3998 .35094 L .40287 .34392 L .40615 .33588 L .4093 .32753 L .41233 .31888 L .41556 .3089 L .41867 .29848 L .42197 .28641 L .42516 .2737 L .42822 .26032 L .43147 .24469 L .43461 .22806 L .43794 .20845 L .44115 .18734 L .44424 .16462 L .44753 .13739 L .45069 .10761 L .45373 .075 L .45697 .03506 L Mfstroke .45697 .03506 m .45942 0 L s .49995 0 m .49995 1.26984 L s .54058 1.26984 m .54323 1.23205 L .54632 1.19418 L .54961 1.15921 L .55278 1.12978 L .55582 1.10474 L .55906 1.08102 L .56218 1.06063 L .5655 1.04118 L .56869 1.02432 L .57177 1.0096 L .57504 .99535 L .57818 .98283 L .58121 .97178 L .58443 .96095 L .58754 .95135 L .59083 .94193 L .59401 .93355 L .59707 .92606 L .60032 .91865 L .60345 .91202 L .60678 .90545 L .60998 .89954 L .61307 .89423 L .61635 .88893 L .61951 .88416 L .62254 .87983 L .62578 .87551 L .62889 .87158 L .6322 .86766 L .63539 .8641 L .63845 .86086 L .64172 .85761 L .64486 .85465 L .6482 .85168 L .65141 .84897 L .65451 .84651 L .6578 .84402 L .66097 .84175 L .66402 .83967 L .66726 .83757 L .67039 .83565 L .67371 .83371 L .67691 .83194 L .67999 .83032 L .68326 .82867 L .68641 .82716 L .68944 .82578 L .69267 .82438 L .69578 .82309 L Mistroke .69908 .82178 L .70226 .82058 L .70532 .81948 L .70858 .81836 L .71171 .81733 L .71504 .81629 L .71825 .81533 L .72134 .81445 L .72463 .81355 L .72779 .81273 L .73083 .81197 L .73407 .8112 L .73719 .81049 L .7405 .80976 L .74369 .8091 L .74676 .80848 L .75003 .80786 L .75318 .80728 L .75652 .8067 L .75974 .80616 L .76284 .80566 L .76613 .80515 L .76931 .80469 L .77236 .80426 L .77561 .80382 L .77874 .80341 L .78206 .803 L .78527 .80262 L .78835 .80227 L .79163 .80191 L .79478 .80158 L .79782 .80128 L .80105 .80097 L .80416 .80068 L .80747 .80039 L .81065 .80012 L .81372 .79987 L .81698 .79961 L .82011 .79938 L .82345 .79914 L .82666 .79891 L .82976 .79871 L .83305 .7985 L .83621 .79831 L .83926 .79813 L .8425 .79795 L .84562 .79778 L .84894 .79761 L .85214 .79745 L .85521 .79731 L Mistroke .85848 .79716 L .86163 .79702 L .86466 .79689 L .86789 .79676 L .87099 .79664 L .87429 .79652 L .87747 .7964 L .88053 .7963 L .88378 .79619 L .88691 .79609 L .89024 .79599 L .89345 .7959 L .89653 .79581 L .89982 .79572 L .90298 .79564 L .90602 .79557 L .90925 .79549 L .91237 .79542 L .91568 .79535 L .91887 .79528 L .92194 .79522 L .9252 .79515 L .92834 .7951 L .93168 .79504 L .9349 .79498 L .938 .79493 L .94129 .79488 L .94446 .79483 L .94751 .79478 L .95076 .79474 L .95389 .7947 L .95721 .79465 L .96041 .79461 L .96349 .79458 L .96676 .79454 L .96992 .7945 L .97295 .79447 L .97618 .79444 L .97619 .79444 L Mfstroke .07 .04 .56 r .02381 .65069 m .02691 .651 L .03029 .65134 L .03347 .65167 L .03652 .65199 L .03978 .65235 L .04291 .65269 L .04623 .65306 L .04944 .65343 L .05252 .65379 L .0558 .65418 L .05896 .65457 L .062 .65494 L .06523 .65535 L .06834 .65575 L .07165 .65619 L .07484 .65662 L .0779 .65704 L .08117 .65749 L .08431 .65794 L .08765 .65842 L .09086 .6589 L .09396 .65936 L .09725 .65987 L .10042 .66036 L .10346 .66085 L .10671 .66138 L .10983 .6619 L .11315 .66246 L .11635 .66301 L .11943 .66355 L .1227 .66414 L .12585 .66471 L .12888 .66528 L .13211 .66589 L .13521 .66649 L .13852 .66714 L .1417 .66778 L .14476 .6684 L .14801 .66908 L .15115 .66974 L .15448 .67046 L .15769 .67117 L .16077 .67186 L .16406 .67262 L .16722 .67335 L .17026 .67407 L .1735 .67485 L .17662 .67562 L .17993 .67645 L Mistroke .18312 .67726 L .18619 .67806 L .18946 .67892 L .1926 .67976 L .19594 .68068 L .19916 .68157 L .20226 .68245 L .20556 .6834 L .20873 .68433 L .21178 .68524 L .21503 .68623 L .21816 .68719 L .22149 .68824 L .22469 .68926 L .22777 .69026 L .23105 .69134 L .2342 .69239 L .23724 .69343 L .24047 .69454 L .24358 .69563 L .24688 .69681 L .25007 .69796 L .25313 .69909 L .25639 .7003 L .25953 .70149 L .26286 .70277 L .26608 .70402 L .26917 .70524 L .27246 .70655 L .27563 .70784 L .27867 .70909 L .28191 .71043 L .28503 .71175 L .28835 .71316 L .29155 .71454 L .29462 .71588 L .29789 .71732 L .30104 .71873 L .30407 .72009 L .30729 .72156 L .3104 .72299 L .31369 .72452 L .31687 .726 L .31993 .72745 L .32318 .72899 L .32631 .73049 L .32964 .7321 L .33285 .73366 L .33593 .73516 L .33922 .73677 L Mistroke .34238 .73833 L .34541 .73984 L .34865 .74144 L .35176 .743 L .35507 .74465 L .35826 .74624 L .36133 .74778 L .36459 .74941 L .36774 .75098 L .37108 .75264 L .37429 .75424 L .37739 .75577 L .38068 .75739 L .38385 .75894 L .3869 .76042 L .39015 .76199 L .39327 .76348 L .3966 .76505 L .3998 .76654 L .40287 .76796 L .40615 .76944 L .4093 .77085 L .41233 .77218 L .41556 .77357 L .41867 .77487 L .42197 .77623 L .42516 .7775 L .42822 .7787 L .43147 .77993 L .43461 .78107 L .43794 .78225 L .44115 .78333 L .44424 .78434 L .44753 .78536 L .45069 .78629 L .45373 .78714 L .45697 .78799 L .46009 .78876 L .46341 .78952 L .4666 .7902 L .46967 .7908 L .47294 .79137 L .47609 .79187 L .47943 .79233 L .48265 .79271 L .48575 .79301 L .48905 .79327 L .49069 .79338 L .49222 .79346 L .49379 .79353 L Mistroke .49528 .79358 L .49606 .7936 L .49692 .79362 L .49769 .79363 L .49841 .79364 L .49878 .79365 L .49899 .79365 L .49918 .79365 L .49936 .79365 L .49946 .79365 L .49956 .79365 L .49966 .79365 L .49974 .79365 L .49983 .79365 L .49991 .79365 L .50001 .79365 L .50011 .79365 L .50016 .79365 L .50022 .79365 L .50032 .79365 L .50043 .79365 L .50052 .79365 L .5007 .79365 L .50092 .79365 L .50112 .79365 L .50156 .79364 L .50194 .79364 L .50234 .79363 L .50306 .79362 L .50392 .7936 L .50472 .79358 L .50623 .79353 L .5079 .79345 L .51115 .79326 L .51428 .79301 L .51761 .79268 L .52082 .79229 L .52391 .79187 L .52719 .79135 L .53035 .79079 L .53339 .7902 L .53663 .78952 L .53975 .7888 L .54306 .78798 L .54625 .78714 L .54932 .78629 L .55258 .78532 L .55573 .78435 L .55907 .78326 L .56229 .78217 L Mistroke .56538 .78107 L .56868 .77987 L .57185 .77867 L .5749 .77748 L .57815 .77618 L .58128 .7749 L .5846 .7735 L .5878 .77212 L .59088 .77077 L .59416 .76931 L .59731 .76787 L .60035 .76648 L .60358 .76497 L .60669 .7635 L .60999 .76192 L .61317 .76039 L .61624 .7589 L .6195 .7573 L .62263 .75576 L .62597 .75411 L .62918 .75251 L .63227 .75097 L .63556 .74933 L .63872 .74775 L .64177 .74623 L .64501 .74461 L .64813 .74305 L .65144 .7414 L .65464 .73981 L .65771 .73829 L .66098 .73668 L .66413 .73513 L .66716 .73365 L .67038 .73209 L .67348 .73059 L .67678 .72901 L .67996 .7275 L .68301 .72606 L .68627 .72454 L .6894 .72308 L .69272 .72155 L .69593 .7201 L .69901 .71871 L .70229 .71724 L .70545 .71585 L .70849 .71452 L .71173 .71313 L .71484 .7118 L .71815 .71041 L .72134 .70908 L Mistroke .7244 .70782 L .72766 .7065 L .73081 .70525 L .73414 .70393 L .73736 .70268 L .74046 .70149 L .74375 .70025 L .74692 .69907 L .74997 .69795 L .75321 .69678 L .75634 .69566 L .75966 .6945 L .76286 .69339 L .76593 .69235 L .76921 .69125 L .77236 .69022 L .77539 .68923 L .77862 .6882 L .78172 .68723 L .78503 .68621 L .78821 .68525 L .79127 .68433 L .79452 .68338 L .79766 .68248 L .80099 .68153 L .8042 .68064 L .80729 .67979 L .81057 .67891 L .81374 .67808 L .81678 .67729 L .82002 .67646 L .82313 .67568 L .82645 .67487 L .82964 .6741 L .83271 .67337 L .83598 .67261 L .83912 .67189 L .84246 .67114 L .84569 .67043 L .84878 .66976 L .85208 .66906 L .85526 .6684 L .85831 .66778 L .86156 .66712 L .86469 .66651 L .86801 .66587 L .87121 .66526 L .87429 .66469 L .87757 .66409 L .88073 .66352 L Mistroke .88376 .66299 L .887 .66243 L .89011 .66191 L .89341 .66136 L .8966 .66084 L .89966 .66035 L .90292 .65984 L .90606 .65936 L .9094 .65886 L .91261 .65838 L .9157 .65794 L .91899 .65747 L .92216 .65703 L .92521 .65661 L .92845 .65618 L .93157 .65577 L .93489 .65534 L .93809 .65493 L .94116 .65455 L .94443 .65416 L .94758 .65378 L .95061 .65343 L .95383 .65306 L .95694 .65271 L .96024 .65234 L .96342 .652 L .96647 .65168 L .96973 .65134 L .97286 .65102 L .97619 .65069 L .97619 .65069 L Mfstroke 0 0 1 r .02381 .61908 m .02691 .61876 L .03029 .61841 L .03347 .61808 L .03652 .61775 L .03978 .61739 L .04291 .61704 L .04623 .61666 L .04944 .61628 L .05252 .61591 L .0558 .61551 L .05896 .61512 L .062 .61474 L .06523 .61432 L .06834 .61391 L .07165 .61346 L .07484 .61302 L .0779 .61259 L .08117 .61212 L .08431 .61166 L .08765 .61116 L .09086 .61067 L .09396 .61018 L .09725 .60966 L .10042 .60914 L .10346 .60864 L .10671 .60809 L .10983 .60755 L .11315 .60696 L .11635 .60638 L .11943 .60581 L .1227 .60519 L .12585 .60459 L .12888 .60399 L .13211 .60334 L .13521 .60271 L .13852 .60202 L .1417 .60134 L .14476 .60067 L .14801 .59994 L .15115 .59923 L .15448 .59845 L .15769 .59769 L .16077 .59693 L .16406 .59612 L .16722 .59531 L .17026 .59452 L .1735 .59366 L .17662 .59282 L .17993 .5919 L Mistroke .18312 .59099 L .18619 .5901 L .18946 .58913 L .1926 .58817 L .19594 .58713 L .19916 .58611 L .20226 .5851 L .20556 .58401 L .20873 .58292 L .21178 .58186 L .21503 .5807 L .21816 .57956 L .22149 .57832 L .22469 .57709 L .22777 .57588 L .23105 .57456 L .2342 .57326 L .23724 .57199 L .24047 .57059 L .24358 .56921 L .24688 .56771 L .25007 .56623 L .25313 .56477 L .25639 .56317 L .25953 .56159 L .26286 .55987 L .26608 .55817 L .26917 .55649 L .27246 .55465 L .27563 .55283 L .27867 .55104 L .28191 .54907 L .28503 .54712 L .28835 .545 L .29155 .54289 L .29462 .5408 L .29789 .53851 L .30104 .53623 L .30407 .53399 L .30729 .53152 L .3104 .52907 L .31369 .52638 L .31687 .5237 L .31993 .52105 L .32318 .51813 L .32631 .51522 L .32964 .51202 L .33285 .50882 L .33593 .50564 L .33922 .50212 L Mistroke .34238 .49861 L .34541 .49511 L .34865 .49123 L .35176 .48736 L .35507 .48307 L .35826 .47876 L .36133 .47444 L .36459 .46964 L .36774 .46481 L .37108 .45943 L .37429 .454 L .37739 .44853 L .38068 .44241 L .38385 .43621 L .3869 .42993 L .39015 .4229 L .39327 .41574 L .3966 .40768 L .3998 .39944 L .40287 .39102 L .40615 .38149 L .4093 .37169 L .41233 .36163 L .41556 .35015 L .41867 .33828 L .42197 .32466 L .42516 .31044 L .42822 .29562 L .43147 .27843 L .43461 .2603 L .43794 .23909 L .44115 .21643 L .44424 .19222 L .44753 .16339 L .45069 .13207 L .45373 .09797 L .45697 .05644 L .46009 .01018 L Mfstroke .46009 .01018 m .46068 0 L s .49995 0 m .49995 1.26984 L s .53933 1.26984 m .54002 1.25787 L .54323 1.21057 L .54632 1.17118 L .54961 1.13461 L .55278 1.10363 L .55582 1.07711 L .55906 1.05182 L .56218 1.02993 L .5655 1.00889 L .56869 .9905 L .57177 .97432 L .57504 .95851 L .57818 .94451 L .58121 .93203 L .58443 .9197 L .58754 .90866 L .59083 .89772 L .59401 .88787 L .59707 .87899 L .60032 .8701 L .60345 .86205 L .60678 .85398 L .60998 .84665 L .61307 .83997 L .61635 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.8612 .63258 .84975 Metetra .587 .64 .87 r .63258 .84975 .64006 .8612 .66007 .86007 .65261 .84813 Metetra .581 .629 .864 r .65261 .84813 .66007 .86007 .68026 .85941 .6728 .84693 Metetra .574 .617 .858 r .6728 .84693 .68026 .85941 .70062 .85928 .69318 .84622 Metetra .566 .605 .851 r .69318 .84622 .70062 .85928 .72118 .85976 .71373 .84603 Metetra .558 .592 .843 r .71373 .84603 .72118 .85976 .74195 .86091 .73449 .84645 Metetra .55 .578 .835 r .73449 .84645 .74195 .86091 .76295 .86281 .75547 .84755 Metetra .541 .563 .826 r .75547 .84755 .76295 .86281 .78419 .86557 .77667 .8494 Metetra .532 .548 .817 r .77667 .8494 .78419 .86557 .8057 .86929 .79813 .85211 Metetra .522 .532 .807 r .79813 .85211 .8057 .86929 .8275 .87408 .81986 .85578 Metetra .512 .515 .796 r .81986 .85578 .8275 .87408 .84962 .88009 .84189 .86053 Metetra .502 .498 .785 r .84189 .86053 .84962 .88009 .87209 .88747 .86425 .86651 Metetra .492 .481 .773 r .86425 .86651 .87209 .88747 .89496 .8964 .88698 .87385 Metetra .482 .464 .762 r .88698 .87385 .89496 .8964 .91826 .90706 .9101 .88274 Metetra .471 .447 .75 r .9101 .88274 .91826 .90706 .94206 .91971 .93368 .89339 Metetra .461 .43 .738 r .93368 .89339 .94206 .91971 .9664 .93458 .95776 .90602 Metetra .451 .414 .726 r .95776 .90602 .9664 .93458 .99136 .952 .9824 .92089 Metetra .632 .682 .879 r .4697 .86327 .4775 .87322 .49643 .86955 .48868 .85926 Metetra .629 .675 .874 r .48868 .85926 .49643 .86955 .51549 .86604 .50777 .85537 Metetra .626 .667 .87 r .50777 .85537 .51549 .86604 .53466 .86271 .52698 .85163 Metetra .623 .659 .864 r .52698 .85163 .53466 .86271 .55397 .85958 .54632 .84806 Metetra .62 .65 .858 r .54632 .84806 .55397 .85958 .57341 .8567 .56578 .84467 Metetra .616 .641 .852 r .56578 .84467 .57341 .8567 .59299 .85407 .58538 .84149 Metetra .613 .631 .845 r .58538 .84149 .59299 .85407 .61271 .85174 .60512 .83855 Metetra .608 .621 .838 r .60512 .83855 .61271 .85174 .63258 .84975 .625 .83588 Metetra .604 .609 .83 r .625 .83588 .63258 .84975 .65261 .84813 .64503 .83351 Metetra .599 .598 .822 r .64503 .83351 .65261 .84813 .6728 .84693 .66522 .83148 Metetra .594 .586 .813 r .66522 .83148 .6728 .84693 .69318 .84622 .68558 .82984 Metetra .589 .573 .804 r .68558 .82984 .69318 .84622 .71373 .84603 .70611 .82863 Metetra .583 .56 .794 r .70611 .82863 .71373 .84603 .73449 .84645 .72682 .82791 Metetra .578 .547 .784 r .72682 .82791 .73449 .84645 .75547 .84755 .74773 .82773 Metetra .572 .533 .773 r .74773 .82773 .75547 .84755 .77667 .8494 .76885 .82817 Metetra .566 .519 .763 r .76885 .82817 .77667 .8494 .79813 .85211 .79021 .82929 Metetra .559 .506 .752 r .79021 .82929 .79813 .85211 .81986 .85578 .8118 .8312 Metetra .553 .492 .741 r .8118 .8312 .81986 .85578 .84189 .86053 .83367 .83398 Metetra .547 .479 .73 r .83367 .83398 .84189 .86053 .86425 .86651 .85582 .83774 Metetra .541 .465 .72 r .85582 .83774 .86425 .86651 .88698 .87385 .87829 .8426 Metetra .535 .453 .709 r .87829 .8426 .88698 .87385 .9101 .88274 .90112 .84872 Metetra .529 .44 .699 r .90112 .84872 .9101 .88274 .93368 .89339 .92433 .85624 Metetra .524 .428 .689 r .92433 .85624 .93368 .89339 .95776 .90602 .94797 .86534 Metetra .518 .417 .679 r .94797 .86534 .95776 .90602 .9824 .92089 .97209 .87624 Metetra .639 .668 .862 r .46187 .85243 .4697 .86327 .48868 .85926 .48088 .84799 Metetra .637 .66 .856 r .48088 .84799 .48868 .85926 .50777 .85537 .50001 .84362 Metetra .634 .652 .85 r .50001 .84362 .50777 .85537 .52698 .85163 .51925 .83936 Metetra .632 .643 .843 r .51925 .83936 .52698 .85163 .54632 .84806 .53862 .8352 Metetra .629 .634 .836 r .53862 .8352 .54632 .84806 .56578 .84467 .55811 .83117 Metetra .626 .624 .828 r .55811 .83117 .56578 .84467 .58538 .84149 .57772 .82728 Metetra .623 .613 .82 r .57772 .82728 .58538 .84149 .60512 .83855 .59747 .82355 Metetra .62 .603 .811 r .59747 .82355 .60512 .83855 .625 .83588 .61735 .82001 Metetra .616 .591 .802 r .61735 .82001 .625 .83588 .64503 .83351 .63737 .81667 Metetra .613 .58 .793 r .63737 .81667 .64503 .83351 .66522 .83148 .65754 .81357 Metetra .609 .568 .783 r .65754 .81357 .66522 .83148 .68558 .82984 .67786 .81074 Metetra .604 .556 .773 r .67786 .81074 .68558 .82984 .70611 .82863 .69834 .8082 Metetra .6 .543 .763 r .69834 .8082 .70611 .82863 .72682 .82791 .71898 .806 Metetra .596 .531 .752 r .71898 .806 .72682 .82791 .74773 .82773 .7398 .80418 Metetra .591 .519 .742 r .7398 .80418 .74773 .82773 .76885 .82817 .76081 .80279 Metetra .587 .507 .731 r .76081 .80279 .76885 .82817 .79021 .82929 .78201 .80188 Metetra .582 .495 .721 r .78201 .80188 .79021 .82929 .8118 .8312 .80342 .80152 Metetra .577 .483 .711 r .80342 .80152 .8118 .8312 .83367 .83398 .82506 .80176 Metetra .573 .471 .701 r .82506 .80176 .83367 .83398 .85582 .83774 .84694 .80268 Metetra .569 .46 .691 r .84694 .80268 .85582 .83774 .87829 .8426 .86908 .80438 Metetra .564 .45 .681 r .86908 .80438 .87829 .8426 .90112 .84872 .89151 .80693 Metetra .56 .44 .672 r .89151 .80693 .90112 .84872 .92433 .85624 .91425 .81047 Metetra .556 .43 .664 r .91425 .81047 .92433 .85624 .94797 .86534 .93733 .8151 Metetra .552 .421 .656 r .93733 .8151 .94797 .86534 .97209 .87624 .96078 .82096 Metetra .645 .66 .85 r .45401 .84093 .46187 .85243 .48088 .84799 .47306 .83598 Metetra .644 .652 .843 r .47306 .83598 .48088 .84799 .50001 .84362 .49222 .83107 Metetra .642 .643 .836 r .49222 .83107 .50001 .84362 .51925 .83936 .51149 .8262 Metetra .64 .634 .828 r .51149 .8262 .51925 .83936 .53862 .8352 .53088 .82137 Metetra .638 .624 .82 r .53088 .82137 .53862 .8352 .55811 .83117 .55039 .81659 Metetra .636 .614 .812 r .55039 .81659 .55811 .83117 .57772 .82728 .57002 .81188 Metetra .633 .604 .803 r .57002 .81188 .57772 .82728 .59747 .82355 .58977 .80724 Metetra .63 .593 .794 r .58977 .80724 .59747 .82355 .61735 .82001 .60965 .80268 Metetra .627 .582 .784 r .60965 .80268 .61735 .82001 .63737 .81667 .62965 .79823 Metetra .624 .571 .774 r .62965 .79823 .63737 .81667 .65754 .81357 .64979 .79388 Metetra .621 .56 .764 r .64979 .79388 .65754 .81357 .67786 .81074 .67006 .78967 Metetra .618 .548 .754 r .67006 .78967 .67786 .81074 .69834 .8082 .69048 .7856 Metetra .614 .537 .744 r .69048 .7856 .69834 .8082 .71898 .806 .71104 .7817 Metetra .611 .525 .733 r .71104 .7817 .71898 .806 .7398 .80418 .73174 .77799 Metetra .607 .514 .723 r .73174 .77799 .7398 .80418 .76081 .80279 .75261 .77449 Metetra .603 .503 .713 r .75261 .77449 .76081 .80279 .78201 .80188 .77363 .77124 Metetra .599 .492 .703 r .77363 .77124 .78201 .80188 .80342 .80152 .79483 .76826 Metetra .596 .482 .693 r .79483 .76826 .80342 .80152 .82506 .80176 .81621 .76559 Metetra .592 .471 .684 r .81621 .76559 .82506 .80176 .84694 .80268 .83777 .76327 Metetra .589 .462 .675 r .83777 .76327 .84694 .80268 .86908 .80438 .85954 .76135 Metetra .585 .453 .666 r .85954 .76135 .86908 .80438 .89151 .80693 .88151 .75987 Metetra .582 .444 .658 r .88151 .75987 .89151 .80693 .91425 .81047 .90371 .75888 Metetra .579 .436 .65 r .90371 .75888 .91425 .81047 .93733 .8151 .92616 .75846 Metetra .576 .428 .643 r .92616 .75846 .93733 .8151 .96078 .82096 .94886 .75867 Metetra .652 .657 .842 r .4461 .82904 .45401 .84093 .47306 .83598 .46519 .82355 Metetra .651 .649 .835 r .46519 .82355 .47306 .83598 .49222 .83107 .48439 .81805 Metetra .65 .64 .827 r .48439 .81805 .49222 .83107 .51149 .8262 .50369 .81252 Metetra .648 .631 .819 r .50369 .81252 .51149 .8262 .53088 .82137 .52311 .80697 Metetra .647 .622 .811 r .52311 .80697 .53088 .82137 .55039 .81659 .54264 .80139 Metetra .645 .612 .802 r .54264 .80139 .55039 .81659 .57002 .81188 .56228 .7958 Metetra .643 .602 .793 r .56228 .7958 .57002 .81188 .58977 .80724 .58203 .79018 Metetra .641 .591 .783 r .58203 .79018 .58977 .80724 .60965 .80268 .6019 .78454 Metetra .638 .581 .774 r .6019 .78454 .60965 .80268 .62965 .79823 .62189 .77888 Metetra .636 .57 .764 r .62189 .77888 .62965 .79823 .64979 .79388 .642 .77321 Metetra .633 .559 .754 r .642 .77321 .64979 .79388 .67006 .78967 .66222 .76752 Metetra .63 .548 .743 r .66222 .76752 .67006 .78967 .69048 .7856 .68257 .76181 Metetra .627 .537 .733 r .68257 .76181 .69048 .7856 .71104 .7817 .70304 .7561 Metetra .624 .527 .723 r .70304 .7561 .71104 .7817 .73174 .77799 .72363 .75037 Metetra .621 .516 .713 r .72363 .75037 .73174 .77799 .75261 .77449 .74434 .74464 Metetra .618 .506 .703 r .74434 .74464 .75261 .77449 .77363 .77124 .76519 .7389 Metetra .615 .496 .694 r .76519 .7389 .77363 .77124 .79483 .76826 .78616 .73316 Metetra .612 .486 .684 r .78616 .73316 .79483 .76826 .81621 .76559 .80726 .72742 Metetra .609 .477 .676 r .80726 .72742 .81621 .76559 .83777 .76327 .8285 .72169 Metetra .606 .468 .667 r .8285 .72169 .83777 .76327 .85954 .76135 .84987 .71596 Metetra .603 .459 .659 r .84987 .71596 .85954 .76135 .88151 .75987 .87137 .71025 Metetra .601 .451 .651 r .87137 .71025 .88151 .75987 .90371 .75888 .89302 .70457 Metetra .598 .444 .644 r .89302 .70457 .90371 .75888 .92616 .75846 .91481 .69891 Metetra .596 .437 .637 r .91481 .69891 .92616 .75846 .94886 .75867 .93675 .69328 Metetra .659 .659 .839 r .43816 .81704 .4461 .82904 .46519 .82355 .45728 .81102 Metetra .658 .651 .832 r .45728 .81102 .46519 .82355 .48439 .81805 .47652 .80491 Metetra .658 .643 .824 r .47652 .80491 .48439 .81805 .50369 .81252 .49585 .79873 Metetra .657 .634 .816 r .49585 .79873 .50369 .81252 .52311 .80697 .5153 .79245 Metetra .656 .625 .807 r .5153 .79245 .52311 .80697 .54264 .80139 .53485 .78607 Metetra .654 .616 .798 r .53485 .78607 .54264 .80139 .56228 .7958 .55451 .77958 Metetra .653 .606 .789 r .55451 .77958 .56228 .7958 .58203 .79018 .57427 .77298 Metetra .651 .596 .78 r .57427 .77298 .58203 .79018 .6019 .78454 .59414 .76626 Metetra .649 .586 .77 r .59414 .76626 .6019 .78454 .62189 .77888 .61411 .7594 Metetra .647 .576 .76 r .61411 .7594 .62189 .77888 .642 .77321 .63419 .75239 Metetra .645 .565 .75 r .63419 .75239 .642 .77321 .66222 .76752 .65437 .74522 Metetra .643 .555 .74 r .65437 .74522 .66222 .76752 .68257 .76181 .67465 .73789 Metetra .641 .544 .73 r .67465 .73789 .68257 .76181 .70304 .7561 .69503 .73036 Metetra .638 .534 .72 r .69503 .73036 .70304 .7561 .72363 .75037 .71551 .72263 Metetra .636 .524 .71 r .71551 .72263 .72363 .75037 .74434 .74464 .73609 .71467 Metetra .633 .514 .7 r .73609 .71467 .74434 .74464 .76519 .7389 .75676 .70647 Metetra .631 .505 .691 r .75676 .70647 .76519 .7389 .78616 .73316 .77751 .698 Metetra .628 .496 .682 r .77751 .698 .78616 .73316 .80726 .72742 .79835 .68923 Metetra .626 .487 .673 r .79835 .68923 .80726 .72742 .8285 .72169 .81927 .68014 Metetra .623 .478 .664 r .81927 .68014 .8285 .72169 .84987 .71596 .84027 .6707 Metetra .621 .47 .656 r .84027 .6707 .84987 .71596 .87137 .71025 .86133 .66087 Metetra .618 .463 .649 r .86133 .66087 .87137 .71025 .89302 .70457 .88244 .65061 Metetra .616 .455 .641 r .88244 .65061 .89302 .70457 .91481 .69891 .90361 .63989 Metetra .614 .449 .635 r .90361 .63989 .91481 .69891 .93675 .69328 .92481 .62865 Metetra .666 .666 .84 r .43016 .80523 .43816 .81704 .45728 .81102 .44933 .79869 Metetra .666 .659 .833 r .44933 .79869 .45728 .81102 .47652 .80491 .4686 .79203 Metetra .666 .651 .825 r .4686 .79203 .47652 .80491 .49585 .79873 .48797 .78522 Metetra .666 .643 .817 r .48797 .78522 .49585 .79873 .5153 .79245 .50745 .77825 Metetra .665 .634 .809 r .50745 .77825 .5153 .79245 .53485 .78607 .52703 .77111 Metetra .664 .625 .8 r .52703 .77111 .53485 .78607 .55451 .77958 .5467 .76379 Metetra .664 .616 .791 r .5467 .76379 .55451 .77958 .57427 .77298 .56648 .75626 Metetra .663 .607 .782 r .56648 .75626 .57427 .77298 .59414 .76626 .58635 .74851 Metetra .662 .597 .772 r .58635 .74851 .59414 .76626 .61411 .7594 .60632 .74052 Metetra .66 .587 .762 r .60632 .74052 .61411 .7594 .63419 .75239 .62638 .73226 Metetra .659 .577 .752 r .62638 .73226 .63419 .75239 .65437 .74522 .64653 .72371 Metetra .657 .568 .742 r .64653 .72371 .65437 .74522 .67465 .73789 .66676 .71485 Metetra .655 .558 .732 r .66676 .71485 .67465 .73789 .69503 .73036 .68707 .70563 Metetra .654 .548 .722 r .68707 .70563 .69503 .73036 .71551 .72263 .70746 .69603 Metetra .652 .538 .713 r .70746 .69603 .71551 .72263 .73609 .71467 .72791 .686 Metetra .65 .529 .703 r .72791 .686 .73609 .71467 .75676 .70647 .74843 .67551 Metetra .648 .52 .693 r .74843 .67551 .75676 .70647 .77751 .698 .76899 .66451 Metetra .646 .511 .684 r .76899 .66451 .77751 .698 .79835 .68923 .7896 .65295 Metetra .643 .502 .675 r .7896 .65295 .79835 .68923 .81927 .68014 .81025 .64078 Metetra .641 .494 .667 r .81025 .64078 .81927 .68014 .84027 .6707 .8309 .62792 Metetra .639 .486 .659 r .8309 .62792 .84027 .6707 .86133 .66087 .85157 .61433 Metetra .637 .478 .651 r .85157 .61433 .86133 .66087 .88244 .65061 .87221 .59991 Metetra .635 .471 .643 r .87221 .59991 .88244 .65061 .90361 .63989 .89283 .5846 Metetra .633 .465 .636 r .89283 .5846 .90361 .63989 .92481 .62865 .91339 .5683 Metetra .673 .677 .846 r .4221 .79388 .43016 .80523 .44933 .79869 .44132 .78689 Metetra .674 .671 .839 r .44132 .78689 .44933 .79869 .4686 .79203 .46063 .77973 Metetra .674 .664 .832 r .46063 .77973 .4686 .79203 .48797 .78522 .48004 .77236 Metetra .675 .657 .824 r .48004 .77236 .48797 .78522 .50745 .77825 .49956 .76479 Metetra .675 .649 .816 r .49956 .76479 .50745 .77825 .52703 .77111 .51917 .75698 Metetra .675 .641 .808 r .51917 .75698 .52703 .77111 .5467 .76379 .53887 .74892 Metetra .675 .633 .799 r .53887 .74892 .5467 .76379 .56648 .75626 .55867 .74058 Metetra .675 .624 .79 r .55867 .74058 .56648 .75626 .58635 .74851 .57856 .73193 Metetra .675 .615 .781 r .57856 .73193 .58635 .74851 .60632 .74052 .59853 .72295 Metetra .674 .606 .771 r .59853 .72295 .60632 .74052 .62638 .73226 .61858 .7136 Metetra .674 .597 .761 r .61858 .7136 .62638 .73226 .64653 .72371 .63871 .70385 Metetra .673 .588 .752 r .63871 .70385 .64653 .72371 .66676 .71485 .65891 .69365 Metetra .672 .578 .742 r .65891 .69365 .66676 .71485 .68707 .70563 .67918 .68296 Metetra .671 .569 .732 r .67918 .68296 .68707 .70563 .70746 .69603 .6995 .67173 Metetra .67 .56 .722 r .6995 .67173 .70746 .69603 .72791 .686 .71986 .65992 Metetra .668 .55 .712 r .71986 .65992 .72791 .686 .74843 .67551 .74026 .64745 Metetra .667 .541 .702 r .74026 .64745 .74843 .67551 .76899 .66451 .76068 .63427 Metetra .665 .533 .693 r .76068 .63427 .76899 .66451 .7896 .65295 .78111 .62031 Metetra .664 .524 .684 r .78111 .62031 .7896 .65295 .81025 .64078 .80153 .60549 Metetra .662 .516 .675 r .80153 .60549 .81025 .64078 .8309 .62792 .82192 .58972 Metetra .661 .508 .666 r .82192 .58972 .8309 .62792 .85157 .61433 .84226 .57292 Metetra .659 .5 .658 r .84226 .57292 .85157 .61433 .87221 .59991 .86253 .55498 Metetra .657 .493 .65 r .86253 .55498 .87221 .59991 .89283 .5846 .8827 .53579 Metetra .656 .486 .643 r .8827 .53579 .89283 .5846 .91339 .5683 .90273 .51525 Metetra .68 .693 .855 r .41397 .78324 .4221 .79388 .44132 .78689 .43324 .77588 Metetra .682 .688 .849 r .43324 .77588 .44132 .78689 .46063 .77973 .4526 .76831 Metetra .683 .682 .843 r .4526 .76831 .46063 .77973 .48004 .77236 .47206 .7605 Metetra .684 .676 .836 r .47206 .7605 .48004 .77236 .49956 .76479 .49161 .75244 Metetra .686 .67 .829 r .49161 .75244 .49956 .76479 .51917 .75698 .51126 .74409 Metetra .687 .663 .821 r .51126 .74409 .51917 .75698 .53887 .74892 .531 .73544 Metetra .688 .656 .813 r .531 .73544 .53887 .74892 .55867 .74058 .55083 .72644 Metetra .689 .649 .805 r .55083 .72644 .55867 .74058 .57856 .73193 .57075 .71708 Metetra .69 .641 .796 r .57075 .71708 .57856 .73193 .59853 .72295 .59074 .7073 Metetra .69 .633 .787 r .59074 .7073 .59853 .72295 .61858 .7136 .6108 .69708 Metetra .691 .625 .778 r .6108 .69708 .61858 .7136 .63871 .70385 .63094 .68637 Metetra .691 .616 .768 r .63094 .68637 .63871 .70385 .65891 .69365 .65113 .67511 Metetra .691 .608 .758 r .65113 .67511 .65891 .69365 .67918 .68296 .67137 .66325 Metetra .691 .599 .748 r .67137 .66325 .67918 .68296 .6995 .67173 .69166 .65074 Metetra .691 .591 .738 r .69166 .65074 .6995 .67173 .71986 .65992 .71197 .63751 Metetra .691 .582 .728 r .71197 .63751 .71986 .65992 .74026 .64745 .7323 .62349 Metetra .69 .573 .719 r .7323 .62349 .74026 .64745 .76068 .63427 .75263 .6086 Metetra .69 .565 .709 r .75263 .6086 .76068 .63427 .78111 .62031 .77293 .59276 Metetra .689 .556 .699 r .77293 .59276 .78111 .62031 .80153 .60549 .7932 .57587 Metetra .688 .548 .69 r .7932 .57587 .80153 .60549 .82192 .58972 .81341 .55783 Metetra .688 .54 .681 r .81341 .55783 .82192 .58972 .84226 .57292 .83353 .53854 Metetra .687 .533 .672 r .83353 .53854 .84226 .57292 .86253 .55498 .85353 .51787 Metetra .686 .525 .663 r .85353 .51787 .86253 .55498 .8827 .53579 .87338 .4957 Metetra .685 .518 .655 r .87338 .4957 .8827 .53579 .90273 .51525 .89304 .4719 Metetra .687 .714 .869 r .40576 .77349 .41397 .78324 .43324 .77588 .42508 .76587 Metetra .689 .71 .864 r .42508 .76587 .43324 .77588 .4526 .76831 .44449 .75801 Metetra .691 .706 .859 r .44449 .75801 .4526 .76831 .47206 .7605 .464 .74989 Metetra .694 .702 .854 r .464 .74989 .47206 .7605 .49161 .75244 .4836 .74148 Metetra .696 .698 .848 r .4836 .74148 .49161 .75244 .51126 .74409 .5033 .73275 Metetra .698 .693 .841 r .5033 .73275 .51126 .74409 .531 .73544 .52309 .72368 Metetra .701 .688 .834 r .52309 .72368 .531 .73544 .55083 .72644 .54296 .71424 Metetra .703 .682 .827 r .54296 .71424 .55083 .72644 .57075 .71708 .56291 .70437 Metetra .705 .676 .819 r .56291 .70437 .57075 .71708 .59074 .7073 .58294 .69405 Metetra .708 .67 .811 r .58294 .69405 .59074 .7073 .6108 .69708 .60304 .68323 Metetra .71 .664 .803 r .60304 .68323 .6108 .69708 .63094 .68637 .6232 .67185 Metetra .712 .657 .794 r .6232 .67185 .63094 .68637 .65113 .67511 .64341 .65987 Metetra .714 .65 .785 r .64341 .65987 .65113 .67511 .67137 .66325 .66367 .64722 Metetra .716 .643 .775 r .66367 .64722 .67137 .66325 .69166 .65074 .68395 .63383 Metetra .717 .636 .766 r .68395 .63383 .69166 .65074 .71197 .63751 .70426 .61964 Metetra .719 .628 .756 r .70426 .61964 .71197 .63751 .7323 .62349 .72457 .60456 Metetra .72 .621 .746 r .72457 .60456 .7323 .62349 .75263 .6086 .74486 .58852 Metetra .722 .613 .736 r .74486 .58852 .75263 .6086 .77293 .59276 .76512 .5714 Metetra .723 .606 .726 r .76512 .5714 .77293 .59276 .7932 .57587 .78532 .55312 Metetra .723 .598 .716 r .78532 .55312 .7932 .57587 .81341 .55783 .80543 .53356 Metetra .724 .591 .706 r .80543 .53356 .81341 .55783 .83353 .53854 .82544 .51261 Metetra .725 .583 .696 r .82544 .51261 .83353 .53854 .85353 .51787 .84529 .49012 Metetra .725 .576 .687 r .84529 .49012 .85353 .51787 .87338 .4957 .86497 .46598 Metetra .725 .569 .678 r .86497 .46598 .87338 .4957 .89304 .4719 .88442 .44002 Metetra .691 .738 .887 r .39746 .76477 .40576 .77349 .42508 .76587 .41683 .75701 Metetra .695 .737 .884 r .41683 .75701 .42508 .76587 .44449 .75801 .4363 .74899 Metetra .698 .736 .88 r .4363 .74899 .44449 .75801 .464 .74989 .45586 .7407 Metetra .701 .734 .876 r .45586 .7407 .464 .74989 .4836 .74148 .47552 .73211 Metetra .705 .732 .872 r .47552 .73211 .4836 .74148 .5033 .73275 .49527 .72319 Metetra .709 .73 .867 r .49527 .72319 .5033 .73275 .52309 .72368 .51511 .71391 Metetra .713 .728 .862 r .51511 .71391 .52309 .72368 .54296 .71424 .53504 .70423 Metetra .717 .726 .857 r .53504 .70423 .54296 .71424 .56291 .70437 .55505 .69411 Metetra .721 .723 .851 r .55505 .69411 .56291 .70437 .58294 .69405 .57513 .68352 Metetra .726 .721 .845 r .57513 .68352 .58294 .69405 .60304 .68323 .59528 .6724 Metetra .731 .718 .839 r .59528 .6724 .60304 .68323 .6232 .67185 .61549 .66069 Metetra .735 .715 .832 r .61549 .66069 .6232 .67185 .64341 .65987 .63575 .64836 Metetra .74 .711 .824 r .63575 .64836 .64341 .65987 .66367 .64722 .65605 .63532 Metetra .745 .708 .816 r .65605 .63532 .66367 .64722 .68395 .63383 .67638 .62151 Metetra .75 .704 .808 r .67638 .62151 .68395 .63383 .70426 .61964 .69672 .60686 Metetra .755 .7 .799 r .69672 .60686 .70426 .61964 .72457 .60456 .71707 .59129 Metetra .76 .695 .79 r .71707 .59129 .72457 .60456 .74486 .58852 .73739 .57469 Metetra .765 .691 .781 r .73739 .57469 .74486 .58852 .76512 .5714 .75767 .55698 Metetra .769 .686 .771 r .75767 .55698 .76512 .5714 .78532 .55312 .77789 .53805 Metetra .774 .681 .761 r .77789 .53805 .78532 .55312 .80543 .53356 .79801 .51778 Metetra .778 .676 .751 r .79801 .51778 .80543 .53356 .82544 .51261 .81802 .49606 Metetra .783 .671 .74 r .81802 .49606 .82544 .51261 .84529 .49012 .83786 .47273 Metetra .787 .665 .73 r .83786 .47273 .84529 .49012 .86497 .46598 .85751 .44768 Metetra .791 .66 .719 r .85751 .44768 .86497 .46598 .88442 .44002 .87693 .42073 Metetra .693 .766 .907 r .38906 .75714 .39746 .76477 .41683 .75701 .40848 .74936 Metetra .697 .768 .906 r .40848 .74936 .41683 .75701 .4363 .74899 .428 .74132 Metetra .701 .769 .905 r .428 .74132 .4363 .74899 .45586 .7407 .44763 .73302 Metetra .706 .771 .903 r .44763 .73302 .45586 .7407 .47552 .73211 .46735 .72442 Metetra .71 .773 .902 r .46735 .72442 .47552 .73211 .49527 .72319 .48716 .7155 Metetra .715 .776 .9 r .48716 .7155 .49527 .72319 .51511 .71391 .50707 .70621 Metetra .721 .778 .898 r .50707 .70621 .51511 .71391 .53504 .70423 .52706 .69654 Metetra .727 .781 .895 r .52706 .69654 .53504 .70423 .55505 .69411 .54713 .68643 Metetra .734 .784 .893 r .54713 .68643 .55505 .69411 .57513 .68352 .56728 .67585 Metetra .741 .787 .89 r .56728 .67585 .57513 .68352 .59528 .6724 .5875 .66475 Metetra .749 .79 .886 r .5875 .66475 .59528 .6724 .61549 .66069 .60779 .65308 Metetra .757 .794 .883 r .60779 .65308 .61549 .66069 .63575 .64836 .62813 .64078 Metetra .766 .798 .879 r .62813 .64078 .63575 .64836 .65605 .63532 .64851 .62778 Metetra .775 .802 .874 r .64851 .62778 .65605 .63532 .67638 .62151 .66892 .61403 Metetra .785 .806 .869 r .66892 .61403 .67638 .62151 .69672 .60686 .68935 .59945 Metetra .795 .81 .864 r .68935 .59945 .69672 .60686 .71707 .59129 .70978 .58394 Metetra .807 .815 .858 r .70978 .58394 .71707 .59129 .73739 .57469 .7302 .56744 Metetra .818 .82 .851 r .7302 .56744 .73739 .57469 .75767 .55698 .75058 .54983 Metetra .831 .825 .843 r .75058 .54983 .75767 .55698 .77789 .53805 .7709 .53102 Metetra .843 .83 .834 r .7709 .53102 .77789 .53805 .79801 .51778 .79113 .51088 Metetra .856 .835 .824 r .79113 .51088 .79801 .51778 .81802 .49606 .81125 .48931 Metetra .87 .84 .813 r .81125 .48931 .81802 .49606 .83786 .47273 .83122 .46616 Metetra .883 .844 .801 r .83122 .46616 .83786 .47273 .85751 .44768 .851 .44129 Metetra .897 .849 .787 r .851 .44129 .85751 .44768 .87693 .42073 .87054 .41456 Metetra .691 .795 .929 r .38054 .75058 .38906 .75714 .40848 .74936 .40003 .74291 Metetra .695 .8 .93 r .40003 .74291 .40848 .74936 .428 .74132 .41961 .735 Metetra .699 .806 .931 r .41961 .735 .428 .74132 .44763 .73302 .43929 .72684 Metetra .703 .812 .932 r .43929 .72684 .44763 .73302 .46735 .72442 .45908 .7184 Metetra .708 .818 .934 r .45908 .7184 .46735 .72442 .48716 .7155 .47896 .70966 Metetra .713 .826 .935 r .47896 .70966 .48716 .7155 .50707 .70621 .49893 .70059 Metetra .719 .834 .936 r .49893 .70059 .50707 .70621 .52706 .69654 .519 .69115 Metetra .726 .844 .937 r .519 .69115 .52706 .69654 .54713 .68643 .53915 .68131 Metetra .733 .854 .938 r .53915 .68131 .54713 .68643 .56728 .67585 .55939 .67103 Metetra .741 .865 .938 r .55939 .67103 .56728 .67585 .5875 .66475 .5797 .66026 Metetra .749 .878 .938 r .5797 .66026 .5875 .66475 .60779 .65308 .60008 .64897 Metetra .758 .891 .938 r .60008 .64897 .60779 .65308 .62813 .64078 .62052 .63709 Metetra .767 .906 .936 r .62052 .63709 .62813 .64078 .64851 .62778 .64101 .62457 Metetra .777 .922 .933 r .64101 .62457 .64851 .62778 .66892 .61403 .66154 .61134 Metetra .786 .938 .928 r .66154 .61134 .66892 .61403 .68935 .59945 .6821 .59734 Metetra .795 .955 .92 r .6821 .59734 .68935 .59945 .70978 .58394 .70268 .58249 Metetra .802 .971 .908 r .70268 .58249 .70978 .58394 .7302 .56744 .72325 .5667 Metetra .807 .985 .889 r .72325 .5667 .7302 .56744 .75058 .54983 .7438 .54989 Metetra .808 .995 .863 r .7438 .54989 .75058 .54983 .7709 .53102 .76431 .53196 Metetra .802 1 .827 r .76431 .53196 .7709 .53102 .79113 .51088 .78475 .5128 Metetra .788 .995 .778 r .78475 .5128 .79113 .51088 .81125 .48931 .80509 .49229 Metetra .763 .978 .715 r .80509 .49229 .81125 .48931 .83122 .46616 .8253 .47032 Metetra .724 .945 .638 r .8253 .47032 .83122 .46616 .851 .44129 .84536 .44674 Metetra .673 .897 .547 r .84536 .44674 .851 .44129 .87054 .41456 .86521 .42141 Metetra .682 .823 .951 r .37192 .74502 .38054 .75058 .40003 .74291 .39146 .73756 Metetra .685 .831 .953 r .39146 .73756 .40003 .74291 .41961 .735 .4111 .72991 Metetra .687 .84 .957 r .4111 .72991 .41961 .735 .43929 .72684 .43085 .72203 Metetra .69 .85 .96 r .43085 .72203 .43929 .72684 .45908 .7184 .4507 .71391 Metetra .693 .862 .963 r .4507 .71391 .45908 .7184 .47896 .70966 .47065 .70553 Metetra .695 .874 .965 r .47065 .70553 .47896 .70966 .49893 .70059 .49071 .69687 Metetra .697 .888 .968 r .49071 .69687 .49893 .70059 .519 .69115 .51085 .68788 Metetra .698 .902 .969 r .51085 .68788 .519 .69115 .53915 .68131 .5311 .67855 Metetra .698 .918 .968 r .5311 .67855 .53915 .68131 .55939 .67103 .55143 .66884 Metetra .697 .933 .965 r .55143 .66884 .55939 .67103 .5797 .66026 .57184 .6587 Metetra .692 .948 .958 r .57184 .6587 .5797 .66026 .60008 .64897 .59234 .64811 Metetra .682 .96 .943 r .59234 .64811 .60008 .64897 .62052 .63709 .6129 .63702 Metetra .665 .967 .919 r .6129 .63702 .62052 .63709 .64101 .62457 .63353 .62537 Metetra .638 .965 .882 r .63353 .62537 .64101 .62457 .66154 .61134 .65422 .61311 Metetra .599 .949 .827 r .65422 .61311 .66154 .61134 .6821 .59734 .67495 .60019 Metetra .544 .915 .75 r .67495 .60019 .6821 .59734 .70268 .58249 .69571 .58652 Metetra .473 .859 .652 r .69571 .58652 .70268 .58249 .72325 .5667 .71649 .57206 Metetra .71649 .57206 .72325 .5667 .7438 .54989 .73727 .5567 Metetra .73727 .5567 .7438 .54989 .76431 .53196 .75804 .54037 Metetra .75804 .54037 .76431 .53196 .78475 .5128 .77877 .52298 Metetra .77877 .52298 .78475 .5128 .80509 .49229 .79944 .50442 Metetra .79944 .50442 .80509 .49229 .8253 .47032 .82002 .48459 Metetra .016 0 .021 r .82002 .48459 .8253 .47032 .84536 .44674 .84049 .46335 Metetra .072 0 .097 r .84049 .46335 .84536 .44674 .86521 .42141 .8608 .44059 Metetra .667 .846 .968 r .36318 .74029 .37192 .74502 .39146 .73756 .38277 .73316 Metetra .666 .856 .972 r .38277 .73316 .39146 .73756 .4111 .72991 .40248 .72586 Metetra .665 .868 .976 r .40248 .72586 .4111 .72991 .43085 .72203 .42229 .7184 Metetra .663 .881 .979 r .42229 .7184 .43085 .72203 .4507 .71391 .44221 .71074 Metetra .659 .894 .981 r .44221 .71074 .4507 .71391 .47065 .70553 .46224 .70287 Metetra .652 .907 .981 r .46224 .70287 .47065 .70553 .49071 .69687 .48237 .69477 Metetra .642 .92 .977 r .48237 .69477 .49071 .69687 .51085 .68788 .50261 .68643 Metetra .627 .931 .968 r .50261 .68643 .51085 .68788 .5311 .67855 .52294 .67781 Metetra .605 .937 .951 r .52294 .67781 .5311 .67855 .55143 .66884 .54338 .6689 Metetra .572 .936 .92 r .54338 .6689 .55143 .66884 .57184 .6587 .56391 .65966 Metetra .527 .921 .873 r .56391 .65966 .57184 .6587 .59234 .64811 .58453 .65006 Metetra .465 .887 .803 r .58453 .65006 .59234 .64811 .6129 .63702 .60524 .64006 Metetra .388 .832 .709 r .60524 .64006 .6129 .63702 .63353 .62537 .62603 .62964 Metetra .62603 .62964 .63353 .62537 .65422 .61311 .64689 .61874 Metetra .64689 .61874 .65422 .61311 .67495 .60019 .66782 .60732 Metetra .66782 .60732 .67495 .60019 .69571 .58652 .68881 .59532 Metetra .68881 .59532 .69571 .58652 .71649 .57206 .70985 .5827 Metetra .063 0 0 r .70985 .5827 .71649 .57206 .73727 .5567 .73092 .56939 Metetra .128 0 .003 r .73092 .56939 .73727 .5567 .75804 .54037 .75201 .55533 Metetra .182 0 .084 r .75201 .55533 .75804 .54037 .77877 .52298 .77311 .54042 Metetra .227 0 .152 r .77311 .54042 .77877 .52298 .79944 .50442 .79419 .52461 Metetra .264 0 .208 r .79419 .52461 .79944 .50442 .82002 .48459 .81524 .5078 Metetra .294 0 .255 r .81524 .5078 .82002 .48459 .84049 .46335 .83624 .48989 Metetra .319 .022 .294 r .83624 .48989 .84049 .46335 .8608 .44059 .85715 .47077 Metetra .646 .861 .981 r .35432 .73618 .36318 .74029 .38277 .73316 .37397 .72945 Metetra .64 .872 .985 r .37397 .72945 .38277 .73316 .40248 .72586 .39374 .72261 Metetra .633 .884 .987 r .39374 .72261 .40248 .72586 .42229 .7184 .41362 .71564 Metetra .622 .896 .987 r .41362 .71564 .42229 .7184 .44221 .71074 .43361 .70855 Metetra .607 .907 .984 r .43361 .70855 .44221 .71074 .46224 .70287 .45371 .70131 Metetra .586 .914 .974 r .45371 .70131 .46224 .70287 .48237 .69477 .47393 .69392 Metetra .556 .917 .955 r .47393 .69392 .48237 .69477 .50261 .68643 .49425 .68636 Metetra .514 .909 .922 r .49425 .68636 .50261 .68643 .52294 .67781 .51469 .67862 Metetra .458 .887 .87 r .51469 .67862 .52294 .67781 .54338 .6689 .53523 .67069 Metetra .385 .844 .793 r .53523 .67069 .54338 .6689 .56391 .65966 .55589 .66254 Metetra .297 .778 .692 r .55589 .66254 .56391 .65966 .58453 .65006 .57665 .65415 Metetra .57665 .65415 .58453 .65006 .60524 .64006 .59751 .64551 Metetra .59751 .64551 .60524 .64006 .62603 .62964 .61847 .63659 Metetra .61847 .63659 .62603 .62964 .64689 .61874 .63953 .62736 Metetra .085 0 0 r .63953 .62736 .64689 .61874 .66782 .60732 .66069 .61779 Metetra .158 0 0 r .66069 .61779 .66782 .60732 .68881 .59532 .68193 .60786 Metetra .218 0 .027 r .68193 .60786 .68881 .59532 .70985 .5827 .70325 .59752 Metetra .266 0 .106 r .70325 .59752 .70985 .5827 .73092 .56939 .72464 .58674 Metetra .306 0 .17 r .72464 .58674 .73092 .56939 .75201 .55533 .74611 .57547 Metetra .338 0 .224 r .74611 .57547 .75201 .55533 .77311 .54042 .76763 .56366 Metetra .364 .036 .269 r .76763 .56366 .77311 .54042 .79419 .52461 .7892 .55127 Metetra .386 .072 .306 r .7892 .55127 .79419 .52461 .81524 .5078 .8108 .53824 Metetra .403 .103 .337 r .8108 .53824 .81524 .5078 .83624 .48989 .83242 .5245 Metetra .418 .129 .364 r .83242 .5245 .83624 .48989 .85715 .47077 .85404 .50998 Metetra .622 .867 .989 r .34536 .73244 .35432 .73618 .37397 .72945 .36507 .72616 Metetra .611 .877 .991 r .36507 .72616 .37397 .72945 .39374 .72261 .38489 .71982 Metetra .597 .887 .991 r .38489 .71982 .39374 .72261 .41362 .71564 .40483 .71341 Metetra .577 .896 .986 r .40483 .71341 .41362 .71564 .43361 .70855 .42489 .70695 Metetra .549 .9 .975 r .42489 .70695 .43361 .70855 .45371 .70131 .44507 .70042 Metetra .512 .898 .952 r .44507 .70042 .45371 .70131 .47393 .69392 .46537 .69382 Metetra .461 .884 .914 r .46537 .69382 .47393 .69392 .49425 .68636 .48578 .68714 Metetra .394 .852 .855 r .48578 .68714 .49425 .68636 .51469 .67862 .50632 .68039 Metetra .311 .799 .77 r .50632 .68039 .51469 .67862 .53523 .67069 .52698 .67355 Metetra .52698 .67355 .53523 .67069 .55589 .66254 .54776 .66662 Metetra .54776 .66662 .55589 .66254 .57665 .65415 .56866 .6596 Metetra .56866 .6596 .57665 .65415 .59751 .64551 .58968 .65248 Metetra .086 0 0 r .58968 .65248 .59751 .64551 .61847 .63659 .61082 .64525 Metetra .166 0 0 r .61082 .64525 .61847 .63659 .63953 .62736 .63209 .6379 Metetra .233 0 0 r .63209 .6379 .63953 .62736 .66069 .61779 .65347 .63043 Metetra .287 0 .056 r .65347 .63043 .66069 .61779 .68193 .60786 .67498 .62282 Metetra .33 0 .13 r .67498 .62282 .68193 .60786 .70325 .59752 .69661 .61507 Metetra .365 0 .191 r .69661 .61507 .70325 .59752 .72464 .58674 .71836 .60716 Metetra .393 .039 .241 r .71836 .60716 .72464 .58674 .74611 .57547 .74022 .59908 Metetra .416 .078 .283 r .74022 .59908 .74611 .57547 .76763 .56366 .7622 .59082 Metetra .434 .112 .318 r .7622 .59082 .76763 .56366 .7892 .55127 .78429 .58236 Metetra .449 .14 .348 r .78429 .58236 .7892 .55127 .8108 .53824 .8065 .57368 Metetra .462 .164 .372 r .8065 .57368 .8108 .53824 .83242 .5245 .82881 .56476 Metetra .473 .184 .394 r .82881 .56476 .83242 .5245 .85404 .50998 .85122 .55558 Metetra .601 .864 .993 r .3363 .72878 .34536 .73244 .36507 .72616 .35606 .72296 Metetra .586 .873 .994 r .35606 .72296 .36507 .72616 .38489 .71982 .37595 .71714 Metetra .566 .881 .992 r .37595 .71714 .38489 .71982 .40483 .71341 .39595 .71132 Metetra .539 .886 .984 r .39595 .71132 .40483 .71341 .42489 .70695 .41607 .70551 Metetra .502 .884 .967 r .41607 .70551 .42489 .70695 .44507 .70042 .43632 .69971 Metetra .453 .873 .936 r .43632 .69971 .44507 .70042 .46537 .69382 .4567 .69393 Metetra .388 .847 .886 r .4567 .69393 .46537 .69382 .48578 .68714 .4772 .68817 Metetra .307 .8 .811 r .4772 .68817 .48578 .68714 .50632 .68039 .49784 .68244 Metetra .211 .729 .71 r .49784 .68244 .50632 .68039 .52698 .67355 .5186 .67674 Metetra .5186 .67674 .52698 .67355 .54776 .66662 .5395 .67109 Metetra .5395 .67109 .54776 .66662 .56866 .6596 .56054 .6655 Metetra .099 0 0 r .56054 .6655 .56866 .6596 .58968 .65248 .58172 .65996 Metetra .184 0 0 r .58172 .65996 .58968 .65248 .61082 .64525 .60305 .6545 Metetra .254 0 0 r .60305 .6545 .61082 .64525 .63209 .6379 .62452 .64913 Metetra .311 0 .024 r .62452 .64913 .63209 .6379 .65347 .63043 .64614 .64386 Metetra .356 0 .103 r .64614 .64386 .65347 .63043 .67498 .62282 .66792 .63871 Metetra .392 0 .169 r .66792 .63871 .67498 .62282 .69661 .61507 .68985 .63369 Metetra .421 .048 .223 r .68985 .63369 .69661 .61507 .71836 .60716 .71195 .62883 Metetra .444 .089 .268 r .71195 .62883 .71836 .60716 .74022 .59908 .73423 .62414 Metetra .463 .124 .305 r .73423 .62414 .74022 .59908 .7622 .59082 .75668 .61966 Metetra .478 .153 .337 r .75668 .61966 .7622 .59082 .78429 .58236 .77931 .6154 Metetra .491 .178 .363 r .77931 .6154 .78429 .58236 .8065 .57368 .80214 .6114 Metetra .501 .199 .386 r .80214 .6114 .8065 .57368 .82881 .56476 .82517 .6077 Metetra .51 .217 .405 r .82517 .6077 .82881 .56476 .85122 .55558 .84842 .60433 Metetra .587 .855 .994 r .32716 .72488 .3363 .72878 .35606 .72296 .34697 .71951 Metetra .57 .863 .996 r .34697 .71951 .35606 .72296 .37595 .71714 .36691 .71419 Metetra .548 .869 .994 r .36691 .71419 .37595 .71714 .39595 .71132 .38697 .70894 Metetra .518 .872 .987 r .38697 .70894 .39595 .71132 .41607 .70551 .40716 .70376 Metetra .478 .869 .971 r .40716 .70376 .41607 .70551 .43632 .69971 .42748 .69867 Metetra .425 .855 .941 r .42748 .69867 .43632 .69971 .4567 .69393 .44793 .69368 Metetra .357 .827 .891 r .44793 .69368 .4567 .69393 .4772 .68817 .46852 .68881 Metetra .273 .778 .817 r .46852 .68881 .4772 .68817 .49784 .68244 .48924 .68407 Metetra .173 .705 .716 r .48924 .68407 .49784 .68244 .5186 .67674 .51011 .67949 Metetra .51011 .67949 .5186 .67674 .5395 .67109 .53113 .67508 Metetra .042 0 0 r .53113 .67508 .5395 .67109 .56054 .6655 .5523 .67087 Metetra .141 0 0 r .5523 .67087 .56054 .6655 .58172 .65996 .57363 .66689 Metetra .226 0 0 r .57363 .66689 .58172 .65996 .60305 .6545 .59513 .66317 Metetra .295 0 0 r .59513 .66317 .60305 .6545 .62452 .64913 .61679 .65973 Metetra .351 0 .021 r .61679 .65973 .62452 .64913 .64614 .64386 .63864 .65663 Metetra .394 0 .101 r .63864 .65663 .64614 .64386 .66792 .63871 .66067 .65389 Metetra .429 .024 .167 r .66067 .65389 .66792 .63871 .68985 .63369 .6829 .65157 Metetra .456 .072 .221 r .6829 .65157 .68985 .63369 .71195 .62883 .70534 .64973 Metetra .478 .113 .266 r .70534 .64973 .71195 .62883 .73423 .62414 .72801 .64841 Metetra .496 .147 .304 r .72801 .64841 .73423 .62414 .75668 .61966 .75091 .64769 Metetra .51 .175 .335 r .75091 .64769 .75668 .61966 .77931 .6154 .77408 .64765 Metetra .522 .199 .362 r .77408 .64765 .77931 .6154 .80214 .6114 .79751 .64836 Metetra .531 .22 .384 r .79751 .64836 .80214 .6114 .82517 .6077 .82125 .64993 Metetra .539 .237 .404 r .82125 .64993 .82517 .6077 .84842 .60433 .84531 .65246 Metetra .582 .84 .994 r .31795 .72047 .32716 .72488 .34697 .71951 .33781 .71549 Metetra .566 .847 .997 r .33781 .71549 .34697 .71951 .36691 .71419 .3578 .71062 Metetra .545 .853 .998 r .3578 .71062 .36691 .71419 .38697 .70894 .37792 .70587 Metetra .517 .856 .995 r .37792 .70587 .38697 .70894 .40716 .70376 .39817 .70126 Metetra .481 .855 .985 r .39817 .70126 .40716 .70376 .42748 .69867 .41855 .6968 Metetra .434 .847 .965 r .41855 .6968 .42748 .69867 .44793 .69368 .43907 .69252 Metetra .372 .826 .929 r .43907 .69252 .44793 .69368 .46852 .68881 .45974 .68845 Metetra .294 .788 .872 r .45974 .68845 .46852 .68881 .48924 .68407 .48055 .6846 Metetra .2 .729 .789 r .48055 .6846 .48924 .68407 .51011 .67949 .50152 .68102 Metetra .50152 .68102 .51011 .67949 .53113 .67508 .52264 .67773 Metetra .018 0 0 r .52264 .67773 .53113 .67508 .5523 .67087 .54393 .67478 Metetra .124 0 0 r .54393 .67478 .5523 .67087 .57363 .66689 .5654 .6722 Metetra .218 0 0 r .5654 .6722 .57363 .66689 .59513 .66317 .58705 .67005 Metetra .297 0 0 r .58705 .67005 .59513 .66317 .61679 .65973 .60889 .66837 Metetra .359 0 0 r .60889 .66837 .61679 .65973 .63864 .65663 .63094 .66723 Metetra .409 0 .047 r .63094 .66723 .63864 .65663 .66067 .65389 .6532 .6667 Metetra .448 .015 .122 r .6532 .6667 .66067 .65389 .6829 .65157 .6757 .66686 Metetra .478 .069 .184 r .6757 .66686 .6829 .65157 .70534 .64973 .69845 .66778 Metetra .502 .113 .236 r .69845 .66778 .70534 .64973 .72801 .64841 .72147 .66957 Metetra .521 .15 .278 r .72147 .66957 .72801 .64841 .75091 .64769 .74478 .67234 Metetra .536 .181 .313 r .74478 .67234 .75091 .64769 .77408 .64765 .76842 .6762 Metetra .548 .208 .343 r .76842 .6762 .77408 .64765 .79751 .64836 .79242 .68131 Metetra .558 .23 .368 r .79242 .68131 .79751 .64836 .82125 .64993 .8168 .68782 Metetra .567 .249 .389 r .8168 .68782 .82125 .64993 .84531 .65246 .84161 .69591 Metetra .585 .82 .988 r .30869 .71527 .31795 .72047 .33781 .71549 .3286 .71061 Metetra .571 .826 .993 r .3286 .71061 .33781 .71549 .3578 .71062 .34864 .70609 Metetra .554 .831 .997 r .34864 .70609 .3578 .71062 .37792 .70587 .36881 .70174 Metetra .532 .835 .999 r .36881 .70174 .37792 .70587 .39817 .70126 .38911 .69758 Metetra .504 .838 .998 r .38911 .69758 .39817 .70126 .41855 .6968 .40956 .69364 Metetra .468 .836 .992 r .40956 .69364 .41855 .6968 .43907 .69252 .43014 .68993 Metetra .421 .827 .977 r .43014 .68993 .43907 .69252 .45974 .68845 .45088 .6865 Metetra .36 .809 .948 r .45088 .6865 .45974 .68845 .48055 .6846 .47177 .68338 Metetra .284 .775 .901 r .47177 .68338 .48055 .6846 .50152 .68102 .49282 .68062 Metetra .191 .721 .829 r .49282 .68062 .50152 .68102 .52264 .67773 .51404 .67824 Metetra .085 .644 .73 r .51404 .67824 .52264 .67773 .54393 .67478 .53544 .67632 Metetra .029 0 0 r .53544 .67632 .54393 .67478 .5654 .6722 .55702 .67489 Metetra .139 0 0 r .55702 .67489 .5654 .6722 .58705 .67005 .5788 .67403 Metetra .239 0 0 r .5788 .67403 .58705 .67005 .60889 .66837 .60079 .6738 Metetra .322 0 0 r .60079 .6738 .60889 .66837 .63094 .66723 .62301 .6743 Metetra .39 0 0 r .62301 .6743 .63094 .66723 .6532 .6667 .64547 .67559 Metetra .442 0 .008 r .64547 .67559 .6532 .6667 .6757 .66686 .66819 .6778 Metetra .483 .026 .089 r .66819 .6778 .6757 .66686 .69845 .66778 .6912 .68103 Metetra .515 .082 .156 r .6912 .68103 .69845 .66778 .72147 .66957 .71452 .68542 Metetra .539 .129 .212 r .71452 .68542 .72147 .66957 .74478 .67234 .73818 .6911 Metetra .558 .168 .257 r .73818 .6911 .74478 .67234 .76842 .6762 .76222 .69826 Metetra .574 .2 .296 r .76222 .69826 .76842 .6762 .79242 .68131 .78668 .70708 Metetra .586 .227 .327 r .78668 .70708 .79242 .68131 .8168 .68782 .8116 .71779 Metetra .595 .25 .354 r .8116 .71779 .8168 .68782 .84161 .69591 .83705 .73062 Metetra .592 .795 .977 r .29939 .70905 .30869 .71527 .3286 .71061 .31935 .7046 Metetra .582 .799 .982 r .31935 .7046 .3286 .71061 .34864 .70609 .33944 .70032 Metetra .569 .803 .987 r .33944 .70032 .34864 .70609 .36881 .70174 .35966 .69625 Metetra .554 .806 .992 r .35966 .69625 .36881 .70174 .38911 .69758 .38002 .6924 Metetra .534 .809 .996 r .38002 .6924 .38911 .69758 .40956 .69364 .40052 .6888 Metetra .511 .811 .999 r .40052 .6888 .40956 .69364 .43014 .68993 .42117 .68549 Metetra .481 .81 1 r .42117 .68549 .43014 .68993 .45088 .6865 .44197 .68251 Metetra .442 .806 .996 r .44197 .68251 .45088 .6865 .47177 .68338 .46293 .67989 Metetra .394 .796 .984 r .46293 .67989 .47177 .68338 .49282 .68062 .48405 .67769 Metetra .333 .776 .962 r .48405 .67769 .49282 .68062 .51404 .67824 .50535 .67595 Metetra .256 .743 .923 r .50535 .67595 .51404 .67824 .53544 .67632 .52683 .67475 Metetra .163 .692 .862 r .52683 .67475 .53544 .67632 .55702 .67489 .54851 .67413 Metetra .056 .62 .775 r .54851 .67413 .55702 .67489 .5788 .67403 .5704 .67418 Metetra .06 0 0 r .5704 .67418 .5788 .67403 .60079 .6738 .59251 .67498 Metetra .174 0 0 r .59251 .67498 .60079 .6738 .62301 .6743 .61486 .67663 Metetra .279 0 0 r .61486 .67663 .62301 .6743 .64547 .67559 .63747 .67923 Metetra .368 0 0 r .63747 .67923 .64547 .67559 .66819 .6778 .66037 .6829 Metetra .44 0 0 r .66037 .6829 .66819 .6778 .6912 .68103 .68357 .68779 Metetra .496 0 0 r .68357 .68779 .6912 .68103 .71452 .68542 .70711 .69404 Metetra .539 .051 .046 r .70711 .69404 .71452 .68542 .73818 .6911 .73103 .70183 Metetra .572 .11 .119 r .73103 .70183 .73818 .6911 .76222 .69826 .75536 .71137 Metetra .597 .158 .179 r .75536 .71137 .76222 .69826 .78668 .70708 .78016 .72289 Metetra .616 .199 .229 r .78016 .72289 .78668 .70708 .8116 .71779 .80549 .73665 Metetra .631 .232 .27 r .80549 .73665 .8116 .71779 .83705 .73062 .8314 .75296 Metetra .601 .767 .959 r .29007 .70166 .29939 .70905 .31935 .7046 .31007 .6973 Metetra .593 .768 .963 r .31007 .6973 .31935 .7046 .33944 .70032 .33021 .69312 Metetra .584 .769 .967 r .33021 .69312 .33944 .70032 .35966 .69625 .35049 .68916 Metetra .574 .77 .972 r .35049 .68916 .35966 .69625 .38002 .6924 .3709 .68545 Metetra .562 .771 .976 r .3709 .68545 .38002 .6924 .40052 .6888 .39145 .68201 Metetra .547 .771 .981 r .39145 .68201 .40052 .6888 .42117 .68549 .41216 .67888 Metetra .53 .771 .986 r .41216 .67888 .42117 .68549 .44197 .68251 .43301 .67611 Metetra .509 .77 .99 r .43301 .67611 .44197 .68251 .46293 .67989 .45403 .67373 Metetra .484 .767 .994 r .45403 .67373 .46293 .67989 .48405 .67769 .47522 .6718 Metetra .453 .762 .995 r .47522 .6718 .48405 .67769 .50535 .67595 .49659 .67038 Metetra .415 .753 .995 r .49659 .67038 .50535 .67595 .52683 .67475 .51814 .66952 Metetra .368 .74 .989 r .51814 .66952 .52683 .67475 .54851 .67413 .53989 .66931 Metetra .31 .72 .977 r .53989 .66931 .54851 .67413 .5704 .67418 .56186 .66981 Metetra .238 .69 .954 r .56186 .66981 .5704 .67418 .59251 .67498 .58406 .67113 Metetra .152 .646 .915 r .58406 .67113 .59251 .67498 .61486 .67663 .6065 .67336 Metetra .052 .586 .858 r .6065 .67336 .61486 .67663 .63747 .67923 .62921 .67662 Metetra 0 .509 .777 r .62921 .67662 .63747 .67923 .66037 .6829 .65222 .68105 Metetra .179 0 0 r .65222 .68105 .66037 .6829 .68357 .68779 .67555 .68678 Metetra .294 0 0 r .67555 .68678 .68357 .68779 .70711 .69404 .69923 .694 Metetra .398 0 0 r .69923 .694 .70711 .69404 .73103 .70183 .7233 .70289 Metetra .487 0 0 r .7233 .70289 .73103 .70183 .75536 .71137 .74781 .71367 Metetra .557 0 0 r .74781 .71367 .75536 .71137 .78016 .72289 .77281 .72661 Metetra .612 .07 0 r .77281 .72661 .78016 .72289 .80549 .73665 .79836 .74198 Metetra .654 .137 0 r .79836 .74198 .80549 .73665 .8314 .75296 .82453 .76013 Metetra .609 .739 .938 r .28074 .69302 .29007 .70166 .31007 .6973 .30079 .6886 Metetra .604 .738 .939 r .30079 .6886 .31007 .6973 .33021 .69312 .32098 .68438 Metetra .598 .736 .941 r .32098 .68438 .33021 .69312 .35049 .68916 .34131 .68037 Metetra .591 .733 .943 r .34131 .68037 .35049 .68916 .3709 .68545 .36177 .67661 Metetra .583 .73 .945 r .36177 .67661 .3709 .68545 .39145 .68201 .38238 .67312 Metetra .574 .727 .946 r .38238 .67312 .39145 .68201 .41216 .67888 .40313 .66994 Metetra .563 .723 .949 r .40313 .66994 .41216 .67888 .43301 .67611 .42404 .66712 Metetra .552 .718 .951 r .42404 .66712 .43301 .67611 .45403 .67373 .44511 .6647 Metetra .538 .713 .953 r .44511 .6647 .45403 .67373 .47522 .6718 .46635 .66272 Metetra .523 .707 .955 r .46635 .66272 .47522 .6718 .49659 .67038 .48777 .66125 Metetra .505 .699 .956 r .48777 .66125 .49659 .67038 .51814 .66952 .50938 .66035 Metetra .485 .69 .958 r .50938 .66035 .51814 .66952 .53989 .66931 .53118 .66009 Metetra .461 .678 .959 r .53118 .66009 .53989 .66931 .56186 .66981 .5532 .66055 Metetra .434 .665 .959 r .5532 .66055 .56186 .66981 .58406 .67113 .57545 .66182 Metetra .403 .649 .958 r .57545 .66182 .58406 .67113 .6065 .67336 .59795 .66401 Metetra .366 .629 .955 r .59795 .66401 .6065 .67336 .62921 .67662 .62071 .66724 Metetra .324 .606 .949 r .62071 .66724 .62921 .67662 .65222 .68105 .64377 .67162 Metetra .275 .577 .941 r .64377 .67162 .65222 .68105 .67555 .68678 .66715 .67732 Metetra .219 .543 .928 r .66715 .67732 .67555 .68678 .69923 .694 .69088 .68451 Metetra .156 .502 .909 r .69088 .68451 .69923 .694 .7233 .70289 .715 .69337 Metetra .084 .454 .884 r .715 .69337 .7233 .70289 .74781 .71367 .73956 .70413 Metetra .005 .398 .85 r .73956 .70413 .74781 .71367 .77281 .72661 .76461 .71705 Metetra 0 .334 .808 r .76461 .71705 .77281 .72661 .79836 .74198 .79021 .73241 Metetra 0 .264 .756 r .79021 .73241 .79836 .74198 .82453 .76013 .81643 .75056 Metetra .617 .714 .915 r .2714 .6831 .28074 .69302 .30079 .6886 .29151 .6785 Metetra .613 .71 .914 r .29151 .6785 .30079 .6886 .32098 .68438 .31176 .67408 Metetra .608 .705 .913 r .31176 .67408 .32098 .68438 .34131 .68037 .33213 .66985 Metetra .603 .7 .912 r .33213 .66985 .34131 .68037 .36177 .67661 .35265 .66585 Metetra .597 .694 .91 r .35265 .66585 .36177 .67661 .38238 .67312 .3733 .66211 Metetra .591 .687 .908 r .3733 .66211 .38238 .67312 .40313 .66994 .39411 .65865 Metetra .584 .68 .906 r .39411 .65865 .40313 .66994 .42404 .66712 .41507 .65553 Metetra .577 .671 .904 r .41507 .65553 .42404 .66712 .44511 .6647 .43618 .65276 Metetra .568 .662 .901 r .43618 .65276 .44511 .6647 .46635 .66272 .45747 .65042 Metetra .559 .652 .897 r .45747 .65042 .46635 .66272 .48777 .66125 .47893 .64854 Metetra .549 .641 .894 r .47893 .64854 .48777 .66125 .50938 .66035 .50057 .64719 Metetra .538 .629 .889 r .50057 .64719 .50938 .66035 .53118 .66009 .52241 .64644 Metetra .526 .615 .884 r .52241 .64644 .53118 .66009 .5532 .66055 .54446 .64636 Metetra .513 .6 .878 r .54446 .64636 .5532 .66055 .57545 .66182 .56673 .64703 Metetra .499 .584 .871 r .56673 .64703 .57545 .66182 .59795 .66401 .58924 .64855 Metetra .484 .566 .864 r .58924 .64855 .59795 .66401 .62071 .66724 .61201 .65102 Metetra .467 .547 .855 r .61201 .65102 .62071 .66724 .64377 .67162 .63506 .65458 Metetra .45 .527 .845 r .63506 .65458 .64377 .67162 .66715 .67732 .65842 .65935 Metetra .431 .505 .834 r .65842 .65935 .66715 .67732 .69088 .68451 .68212 .6655 Metetra .412 .482 .822 r .68212 .6655 .69088 .68451 .715 .69337 .70619 .6732 Metetra .392 .458 .809 r .70619 .6732 .715 .69337 .73956 .70413 .73068 .68266 Metetra .371 .433 .795 r .73068 .68266 .73956 .70413 .76461 .71705 .75563 .69412 Metetra .35 .407 .78 r .75563 .69412 .76461 .71705 .79021 .73241 .7811 .70783 Metetra .328 .381 .764 r .7811 .70783 .79021 .73241 .81643 .75056 .80716 .72411 Metetra .624 .693 .894 r .26207 .67199 .2714 .6831 .29151 .6785 .28224 .66708 Metetra .621 .687 .891 r .28224 .66708 .29151 .6785 .31176 .67408 .30253 .66232 Metetra .617 .68 .887 r .30253 .66232 .31176 .67408 .33213 .66985 .32296 .65772 Metetra .613 .673 .883 r .32296 .65772 .33213 .66985 .35265 .66585 .34353 .65331 Metetra .609 .665 .879 r .34353 .65331 .35265 .66585 .3733 .66211 .36424 .64911 Metetra .604 .656 .874 r .36424 .64911 .3733 .66211 .39411 .65865 .38509 .64516 Metetra .599 .646 .868 r .38509 .64516 .39411 .65865 .41507 .65553 .4061 .64148 Metetra .593 .636 .863 r .4061 .64148 .41507 .65553 .43618 .65276 .42726 .63811 Metetra .587 .624 .856 r .42726 .63811 .43618 .65276 .45747 .65042 .44858 .6351 Metetra .581 .612 .849 r .44858 .6351 .45747 .65042 .47893 .64854 .47008 .63248 Metetra .573 .6 .841 r .47008 .63248 .47893 .64854 .50057 .64719 .49175 .63031 Metetra .566 .586 .833 r .49175 .63031 .50057 .64719 .52241 .64644 .5136 .62865 Metetra .558 .571 .823 r .5136 .62865 .52241 .64644 .54446 .64636 .53566 .62755 Metetra .549 .556 .814 r .53566 .62755 .54446 .64636 .56673 .64703 .55793 .6271 Metetra .541 .54 .803 r .55793 .6271 .56673 .64703 .58924 .64855 .58042 .62736 Metetra .531 .524 .792 r .58042 .62736 .58924 .64855 .61201 .65102 .60316 .62844 Metetra .522 .507 .781 r .60316 .62844 .61201 .65102 .63506 .65458 .62616 .63044 Metetra .512 .489 .769 r .62616 .63044 .63506 .65458 .65842 .65935 .64944 .63346 Metetra .502 .472 .756 r .64944 .63346 .65842 .65935 .68212 .6655 .67303 .63766 Metetra .492 .454 .743 r .67303 .63766 .68212 .6655 .70619 .6732 .69697 .64316 Metetra .482 .437 .73 r .69697 .64316 .70619 .6732 .73068 .68266 .72128 .65016 Metetra .472 .419 .717 r .72128 .65016 .73068 .68266 .75563 .69412 .746 .65883 Metetra .462 .402 .704 r .746 .65883 .75563 .69412 .7811 .70783 .77119 .66941 Metetra .452 .385 .692 r .77119 .66941 .7811 .70783 .80716 .72411 .7969 .68215 Metetra .631 .677 .876 r .25274 .65983 .26207 .67199 .28224 .66708 .27296 .6545 Metetra .628 .67 .871 r .27296 .6545 .28224 .66708 .30253 .66232 .29332 .64927 Metetra .625 .662 .866 r .29332 .64927 .30253 .66232 .32296 .65772 .31381 .64416 Metetra .622 .653 .86 r .31381 .64416 .32296 .65772 .34353 .65331 .33443 .63919 Metetra .618 .644 .853 r .33443 .63919 .34353 .65331 .36424 .64911 .35519 .63438 Metetra .614 .634 .846 r .35519 .63438 .36424 .64911 .38509 .64516 .3761 .62974 Metetra .61 .623 .839 r .3761 .62974 .38509 .64516 .4061 .64148 .39715 .62531 Metetra .606 .612 .831 r .39715 .62531 .4061 .64148 .42726 .63811 .41835 .62111 Metetra .601 .6 .822 r .41835 .62111 .42726 .63811 .44858 .6351 .43971 .61717 Metetra .596 .587 .813 r .43971 .61717 .44858 .6351 .47008 .63248 .46123 .61352 Metetra .59 .574 .803 r .46123 .61352 .47008 .63248 .49175 .63031 .48292 .61021 Metetra .584 .56 .793 r .48292 .61021 .49175 .63031 .5136 .62865 .50478 .60728 Metetra .578 .546 .782 r .50478 .60728 .5136 .62865 .53566 .62755 .52683 .60478 Metetra .572 .531 .771 r .52683 .60478 .53566 .62755 .55793 .6271 .54908 .60276 Metetra .565 .517 .76 r .54908 .60276 .55793 .6271 .58042 .62736 .57153 .60128 Metetra .559 .502 .748 r .57153 .60128 .58042 .62736 .60316 .62844 .59421 .60041 Metetra .552 .487 .736 r .59421 .60041 .60316 .62844 .62616 .63044 .61711 .60024 Metetra .545 .472 .724 r .61711 .60024 .62616 .63044 .64944 .63346 .64027 .60084 Metetra .538 .457 .712 r .64027 .60084 .64944 .63346 .67303 .63766 .66371 .60232 Metetra .531 .443 .7 r .66371 .60232 .67303 .63766 .69697 .64316 .68743 .60478 Metetra .524 .428 .688 r .68743 .60478 .69697 .64316 .72128 .65016 .71148 .60836 Metetra .518 .415 .677 r .71148 .60836 .72128 .65016 .746 .65883 .73589 .6132 Metetra .511 .402 .666 r .73589 .6132 .746 .65883 .77119 .66941 .76068 .61946 Metetra .505 .389 .655 r .76068 .61946 .77119 .66941 .7969 .68215 .78591 .62732 Metetra .637 .667 .862 r .2434 .64683 .25274 .65983 .27296 .6545 .26368 .641 Metetra .635 .659 .856 r .26368 .641 .27296 .6545 .29332 .64927 .2841 .63521 Metetra .633 .65 .849 r .2841 .63521 .29332 .64927 .31381 .64416 .30465 .62949 Metetra .63 .641 .842 r .30465 .62949 .31381 .64416 .33443 .63919 .32533 .62384 Metetra .627 .631 .834 r .32533 .62384 .33443 .63919 .35519 .63438 .34615 .61828 Metetra .624 .62 .826 r .34615 .61828 .35519 .63438 .3761 .62974 .3671 .61282 Metetra .621 .609 .818 r .3671 .61282 .3761 .62974 .39715 .62531 .3882 .60747 Metetra .617 .598 .809 r .3882 .60747 .39715 .62531 .41835 .62111 .40945 .60225 Metetra .613 .586 .799 r .40945 .60225 .41835 .62111 .43971 .61717 .43084 .59719 Metetra .609 .573 .789 r .43084 .59719 .43971 .61717 .46123 .61352 .45239 .5923 Metetra .604 .56 .778 r .45239 .5923 .46123 .61352 .48292 .61021 .47409 .58761 Metetra .599 .547 .767 r .47409 .58761 .48292 .61021 .50478 .60728 .49596 .58315 Metetra .594 .534 .756 r .49596 .58315 .50478 .60728 .52683 .60478 .518 .57894 Metetra .589 .52 .745 r .518 .57894 .52683 .60478 .54908 .60276 .54021 .57503 Metetra .584 .506 .733 r .54021 .57503 .54908 .60276 .57153 .60128 .56261 .57144 Metetra .579 .493 .721 r .56261 .57144 .57153 .60128 .59421 .60041 .5852 .56823 Metetra .573 .479 .71 r .5852 .56823 .59421 .60041 .61711 .60024 .60799 .56544 Metetra .568 .466 .698 r .60799 .56544 .61711 .60024 .64027 .60084 .631 .56313 Metetra .563 .453 .687 r .631 .56313 .64027 .60084 .66371 .60232 .65424 .56135 Metetra .557 .441 .676 r .65424 .56135 .66371 .60232 .68743 .60478 .67772 .56017 Metetra .552 .429 .665 r .67772 .56017 .68743 .60478 .71148 .60836 .70146 .55968 Metetra .547 .417 .655 r .70146 .55968 .71148 .60836 .73589 .6132 .72548 .55995 Metetra .543 .406 .645 r .72548 .55995 .73589 .6132 .76068 .61946 .7498 .56109 Metetra .538 .396 .635 r .7498 .56109 .76068 .61946 .78591 .62732 .77446 .56321 Metetra .644 .661 .852 r .23403 .63326 .2434 .64683 .26368 .641 .25438 .62687 Metetra .643 .653 .845 r .25438 .62687 .26368 .641 .2841 .63521 .27487 .62046 Metetra .641 .644 .838 r .27487 .62046 .2841 .63521 .30465 .62949 .29548 .61406 Metetra .639 .635 .83 r .29548 .61406 .30465 .62949 .32533 .62384 .31622 .60766 Metetra .636 .625 .822 r .31622 .60766 .32533 .62384 .34615 .61828 .3371 .60127 Metetra .634 .614 .813 r .3371 .60127 .34615 .61828 .3671 .61282 .35811 .59488 Metetra .631 .604 .804 r .35811 .59488 .3671 .61282 .3882 .60747 .37926 .58852 Metetra .628 .592 .794 r .37926 .58852 .3882 .60747 .40945 .60225 .40055 .58218 Metetra .625 .58 .784 r .40055 .58218 .40945 .60225 .43084 .59719 .42198 .57588 Metetra .621 .568 .774 r .42198 .57588 .43084 .59719 .45239 .5923 .44355 .56961 Metetra .617 .556 .763 r .44355 .56961 .45239 .5923 .47409 .58761 .46527 .56339 Metetra .614 .543 .752 r .46527 .56339 .47409 .58761 .49596 .58315 .48714 .55724 Metetra .609 .531 .74 r .48714 .55724 .49596 .58315 .518 .57894 .50917 .55115 Metetra .605 .518 .729 r .50917 .55115 .518 .57894 .54021 .57503 .53134 .54515 Metetra .601 .505 .718 r .53134 .54515 .54021 .57503 .56261 .57144 .55368 .53924 Metetra .597 .493 .706 r .55368 .53924 .56261 .57144 .5852 .56823 .57619 .53345 Metetra .592 .48 .695 r .57619 .53345 .5852 .56823 .60799 .56544 .59886 .52779 Metetra .588 .468 .684 r .59886 .52779 .60799 .56544 .631 .56313 .62171 .52229 Metetra .583 .457 .673 r .62171 .52229 .631 .56313 .65424 .56135 .64473 .51696 Metetra .579 .445 .663 r .64473 .51696 .65424 .56135 .67772 .56017 .66795 .51183 Metetra .575 .435 .653 r .66795 .51183 .67772 .56017 .70146 .55968 .69136 .50692 Metetra .571 .424 .643 r .69136 .50692 .70146 .55968 .72548 .55995 .71497 .50228 Metetra .567 .414 .634 r .71497 .50228 .72548 .55995 .7498 .56109 .73879 .49792 Metetra .563 .405 .625 r .73879 .49792 .7498 .56109 .77446 .56321 .76284 .4939 Metetra .652 .661 .846 r .22462 .61941 .23403 .63326 .25438 .62687 .24504 .61244 Metetra .65 .653 .839 r .24504 .61244 .25438 .62687 .27487 .62046 .26559 .60539 Metetra .649 .644 .832 r .26559 .60539 .27487 .62046 .29548 .61406 .28627 .59828 Metetra .648 .635 .824 r .28627 .59828 .29548 .61406 .31622 .60766 .30708 .5911 Metetra .646 .626 .815 r .30708 .5911 .31622 .60766 .3371 .60127 .32802 .58384 Metetra .644 .615 .806 r .32802 .58384 .3371 .60127 .35811 .59488 .34909 .57651 Metetra .642 .605 .797 r .34909 .57651 .35811 .59488 .37926 .58852 .3703 .5691 Metetra .639 .594 .787 r .3703 .5691 .37926 .58852 .40055 .58218 .39163 .5616 Metetra .637 .583 .777 r .39163 .5616 .40055 .58218 .42198 .57588 .4131 .554 Metetra .634 .571 .766 r .4131 .554 .42198 .57588 .44355 .56961 .43471 .54631 Metetra .631 .559 .755 r .43471 .54631 .44355 .56961 .46527 .56339 .45645 .53852 Metetra .628 .547 .744 r .45645 .53852 .46527 .56339 .48714 .55724 .47833 .53062 Metetra .625 .535 .733 r .47833 .53062 .48714 .55724 .50917 .55115 .50034 .5226 Metetra .621 .523 .722 r .50034 .5226 .50917 .55115 .53134 .54515 .52249 .51445 Metetra .618 .511 .711 r .52249 .51445 .53134 .54515 .55368 .53924 .54477 .50617 Metetra .614 .5 .7 r .54477 .50617 .55368 .53924 .57619 .53345 .5672 .49775 Metetra .61 .488 .689 r .5672 .49775 .57619 .53345 .59886 .52779 .58975 .48917 Metetra .607 .477 .678 r .58975 .48917 .59886 .52779 .62171 .52229 .61244 .48043 Metetra .603 .466 .667 r .61244 .48043 .62171 .52229 .64473 .51696 .63527 .4715 Metetra .599 .455 .657 r .63527 .4715 .64473 .51696 .66795 .51183 .65822 .46238 Metetra .596 .445 .648 r .65822 .46238 .66795 .51183 .69136 .50692 .68131 .45304 Metetra .592 .436 .638 r .68131 .45304 .69136 .50692 .71497 .50228 .70452 .44347 Metetra .589 .427 .63 r .70452 .44347 .71497 .50228 .73879 .49792 .72786 .43366 Metetra .586 .418 .621 r .72786 .43366 .73879 .49792 .76284 .4939 .75132 .42357 Metetra .659 .666 .845 r .21514 .6056 .22462 .61941 .24504 .61244 .23563 .59805 Metetra .659 .658 .838 r .23563 .59805 .24504 .61244 .26559 .60539 .25626 .59038 Metetra .658 .65 .831 r .25626 .59038 .26559 .60539 .28627 .59828 .27701 .58258 Metetra .657 .641 .823 r .27701 .58258 .28627 .59828 .30708 .5911 .29788 .57463 Metetra .656 .632 .814 r .29788 .57463 .30708 .5911 .32802 .58384 .31889 .56654 Metetra .655 .623 .805 r .31889 .56654 .32802 .58384 .34909 .57651 .34003 .55828 Metetra .653 .613 .796 r .34003 .55828 .34909 .57651 .3703 .5691 .36129 .54984 Metetra .652 .602 .786 r .36129 .54984 .3703 .5691 .39163 .5616 .38268 .54121 Metetra .65 .592 .776 r .38268 .54121 .39163 .5616 .4131 .554 .4042 .53237 Metetra .648 .581 .765 r .4042 .53237 .4131 .554 .43471 .54631 .42584 .5233 Metetra .646 .569 .755 r .42584 .5233 .43471 .54631 .45645 .53852 .44761 .51398 Metetra .643 .558 .744 r .44761 .51398 .45645 .53852 .47833 .53062 .4695 .5044 Metetra .641 .547 .733 r .4695 .5044 .47833 .53062 .50034 .5226 .49152 .49451 Metetra .638 .535 .722 r .49152 .49451 .50034 .5226 .52249 .51445 .51365 .48431 Metetra .635 .524 .711 r .51365 .48431 .52249 .51445 .54477 .50617 .53589 .47375 Metetra .632 .513 .7 r .53589 .47375 .54477 .50617 .5672 .49775 .55824 .46281 Metetra .629 .502 .689 r .55824 .46281 .5672 .49775 .58975 .48917 .5807 .45144 Metetra .626 .491 .678 r .5807 .45144 .58975 .48917 .61244 .48043 .60325 .43961 Metetra .623 .481 .668 r .60325 .43961 .61244 .48043 .63527 .4715 .6259 .42728 Metetra .62 .471 .658 r .6259 .42728 .63527 .4715 .65822 .46238 .64863 .41439 Metetra .617 .461 .648 r .64863 .41439 .65822 .46238 .68131 .45304 .67142 .40088 Metetra .614 .452 .639 r .67142 .40088 .68131 .45304 .70452 .44347 .69428 .38672 Metetra .611 .443 .63 r .69428 .38672 .70452 .44347 .72786 .43366 .71718 .37182 Metetra .608 .435 .622 r .71718 .37182 .72786 .43366 .75132 .42357 .74012 .35611 Metetra .667 .675 .848 r .20557 .59211 .21514 .6056 .23563 .59805 .22613 .58404 Metetra .667 .668 .841 r .22613 .58404 .23563 .59805 .25626 .59038 .24683 .57579 Metetra .667 .661 .834 r .24683 .57579 .25626 .59038 .27701 .58258 .26765 .56736 Metetra .667 .653 .827 r .26765 .56736 .27701 .58258 .29788 .57463 .2886 .55871 Metetra .667 .645 .818 r .2886 .55871 .29788 .57463 .31889 .56654 .30968 .54985 Metetra .666 .636 .81 r .30968 .54985 .31889 .56654 .34003 .55828 .33088 .54075 Metetra .666 .627 .801 r .33088 .54075 .34003 .55828 .36129 .54984 .35221 .53138 Metetra .665 .617 .791 r .35221 .53138 .36129 .54984 .38268 .54121 .37366 .52172 Metetra .664 .607 .781 r .37366 .52172 .38268 .54121 .4042 .53237 .39523 .51174 Metetra .663 .597 .771 r .39523 .51174 .4042 .53237 .42584 .5233 .41692 .50142 Metetra .662 .587 .761 r .41692 .50142 .42584 .5233 .44761 .51398 .43873 .49073 Metetra .66 .576 .75 r .43873 .49073 .44761 .51398 .4695 .5044 .46065 .47962 Metetra .658 .566 .739 r .46065 .47962 .4695 .5044 .49152 .49451 .48267 .46806 Metetra .657 .555 .728 r .48267 .46806 .49152 .49451 .51365 .48431 .5048 .456 Metetra .654 .544 .717 r .5048 .456 .51365 .48431 .53589 .47375 .52702 .44339 Metetra .652 .534 .706 r .52702 .44339 .53589 .47375 .55824 .46281 .54933 .43019 Metetra .65 .523 .695 r .54933 .43019 .55824 .46281 .5807 .45144 .57172 .41634 Metetra .648 .513 .685 r .57172 .41634 .5807 .45144 .60325 .43961 .59417 .40177 Metetra .645 .503 .674 r .59417 .40177 .60325 .43961 .6259 .42728 .61667 .38641 Metetra .643 .493 .664 r .61667 .38641 .6259 .42728 .64863 .41439 .63922 .37019 Metetra .64 .484 .654 r .63922 .37019 .64863 .41439 .67142 .40088 .66178 .35302 Metetra .638 .474 .645 r .66178 .35302 .67142 .40088 .69428 .38672 .68435 .33482 Metetra .636 .466 .636 r .68435 .33482 .69428 .38672 .71718 .37182 .70689 .31549 Metetra .633 .458 .627 r .70689 .31549 .71718 .37182 .74012 .35611 .72939 .29493 Metetra .675 .689 .855 r .19587 .57923 .20557 .59211 .22613 .58404 .21652 .57071 Metetra .676 .683 .849 r .21652 .57071 .22613 .58404 .24683 .57579 .23728 .56197 Metetra .677 .677 .843 r .23728 .56197 .24683 .57579 .26765 .56736 .25818 .55299 Metetra .677 .67 .835 r .25818 .55299 .26765 .56736 .2886 .55871 .2792 .54376 Metetra .678 .663 .828 r .2792 .54376 .2886 .55871 .30968 .54985 .30035 .53425 Metetra .679 .655 .82 r .30035 .53425 .30968 .54985 .33088 .54075 .32162 .52442 Metetra .679 .647 .811 r .32162 .52442 .33088 .54075 .35221 .53138 .34302 .51427 Metetra .679 .639 .803 r .34302 .51427 .35221 .53138 .37366 .52172 .36453 .50374 Metetra .68 .63 .793 r .36453 .50374 .37366 .52172 .39523 .51174 .38617 .49281 Metetra .68 .621 .784 r .38617 .49281 .39523 .51174 .41692 .50142 .40791 .48145 Metetra .679 .612 .774 r .40791 .48145 .41692 .50142 .43873 .49073 .42977 .46959 Metetra .679 .603 .763 r .42977 .46959 .43873 .49073 .46065 .47962 .45173 .45721 Metetra .678 .593 .753 r .45173 .45721 .46065 .47962 .48267 .46806 .47378 .44425 Metetra .678 .583 .742 r .47378 .44425 .48267 .46806 .5048 .456 .49593 .43065 Metetra .677 .573 .731 r .49593 .43065 .5048 .456 .52702 .44339 .51815 .41635 Metetra .676 .563 .72 r .51815 .41635 .52702 .44339 .54933 .43019 .54044 .40128 Metetra .675 .553 .709 r .54044 .40128 .54933 .43019 .57172 .41634 .56279 .38537 Metetra .673 .543 .699 r .56279 .38537 .57172 .41634 .59417 .40177 .58519 .36855 Metetra .672 .534 .688 r .58519 .36855 .59417 .40177 .61667 .38641 .6076 .35071 Metetra .67 .524 .678 r .6076 .35071 .61667 .38641 .63922 .37019 .63002 .33177 Metetra .668 .515 .667 r .63002 .33177 .63922 .37019 .66178 .35302 .65242 .31162 Metetra .667 .506 .658 r .65242 .31162 .66178 .35302 .68435 .33482 .67478 .29016 Metetra .665 .497 .648 r .67478 .29016 .68435 .33482 .70689 .31549 .69706 .26726 Metetra .663 .489 .639 r .69706 .26726 .70689 .31549 .72939 .29493 .71924 .24279 Metetra .682 .706 .866 r .18604 .56717 .19587 .57923 .21652 .57071 .20675 .55831 Metetra .684 .702 .861 r .20675 .55831 .21652 .57071 .23728 .56197 .22759 .54919 Metetra .686 .698 .855 r .22759 .54919 .23728 .56197 .25818 .55299 .24856 .5398 Metetra .688 .692 .849 r .24856 .5398 .25818 .55299 .2792 .54376 .26965 .53011 Metetra .689 .687 .843 r .26965 .53011 .2792 .54376 .30035 .53425 .29087 .5201 Metetra .691 .681 .836 r .29087 .5201 .30035 .53425 .32162 .52442 .31222 .50973 Metetra .693 .675 .828 r .31222 .50973 .32162 .52442 .34302 .51427 .33368 .49898 Metetra .695 .669 .82 r .33368 .49898 .34302 .51427 .36453 .50374 .35527 .4878 Metetra .696 .662 .812 r .35527 .4878 .36453 .50374 .38617 .49281 .37697 .47615 Metetra .698 .655 .803 r .37697 .47615 .38617 .49281 .40791 .48145 .39878 .46399 Metetra .699 .647 .794 r .39878 .46399 .40791 .48145 .42977 .46959 .42069 .45127 Metetra .7 .639 .785 r .42069 .45127 .42977 .46959 .45173 .45721 .44271 .43794 Metetra .701 .631 .775 r .44271 .43794 .45173 .45721 .47378 .44425 .46481 .42393 Metetra .702 .623 .765 r .46481 .42393 .47378 .44425 .49593 .43065 .48699 .40918 Metetra .703 .614 .754 r .48699 .40918 .49593 .43065 .51815 .41635 .50925 .39362 Metetra .704 .605 .744 r .50925 .39362 .51815 .41635 .54044 .40128 .53156 .37718 Metetra .704 .596 .733 r .53156 .37718 .54044 .40128 .56279 .38537 .55391 .35976 Metetra .704 .587 .722 r .55391 .35976 .56279 .38537 .58519 .36855 .57629 .34127 Metetra .704 .578 .711 r .57629 .34127 .58519 .36855 .6076 .35071 .59867 .32162 Metetra .704 .57 .7 r .59867 .32162 .6076 .35071 .63002 .33177 .62104 .30069 Metetra .704 .561 .69 r .62104 .30069 .63002 .33177 .65242 .31162 .64336 .27837 Metetra .703 .552 .679 r .64336 .27837 .65242 .31162 .67478 .29016 .6656 .25454 Metetra .703 .544 .669 r .6656 .25454 .67478 .29016 .69706 .26726 .68773 .22906 Metetra .702 .535 .659 r .68773 .22906 .69706 .26726 .71924 .24279 .70972 .20179 Metetra .688 .728 .88 r .17603 .55612 .18604 .56717 .20675 .55831 .19681 .54702 Metetra .691 .726 .877 r .19681 .54702 .20675 .55831 .22759 .54919 .21772 .53766 Metetra .694 .723 .872 r .21772 .53766 .22759 .54919 .24856 .5398 .23876 .528 Metetra .697 .72 .868 r .23876 .528 .24856 .5398 .26965 .53011 .25992 .51802 Metetra .7 .717 .863 r .25992 .51802 .26965 .53011 .29087 .5201 .28122 .50769 Metetra .703 .714 .857 r .28122 .50769 .29087 .5201 .31222 .50973 .30263 .49698 Metetra .706 .71 .851 r .30263 .49698 .31222 .50973 .33368 .49898 .32417 .48585 Metetra .71 .707 .845 r .32417 .48585 .33368 .49898 .35527 .4878 .34583 .47426 Metetra .713 .702 .838 r .34583 .47426 .35527 .4878 .37697 .47615 .3676 .46217 Metetra .717 .698 .831 r .3676 .46217 .37697 .47615 .39878 .46399 .38948 .44952 Metetra .72 .693 .824 r .38948 .44952 .39878 .46399 .42069 .45127 .41147 .43627 Metetra .724 .688 .816 r .41147 .43627 .42069 .45127 .44271 .43794 .43355 .42236 Metetra .727 .683 .807 r .43355 .42236 .44271 .43794 .46481 .42393 .45572 .40772 Metetra .731 .677 .798 r .45572 .40772 .46481 .42393 .48699 .40918 .47796 .39227 Metetra .734 .671 .789 r .47796 .39227 .48699 .40918 .50925 .39362 .50027 .37596 Metetra .737 .665 .779 r .50027 .37596 .50925 .39362 .53156 .37718 .52264 .35868 Metetra .741 .659 .769 r .52264 .35868 .53156 .37718 .55391 .35976 .54504 .34036 Metetra .744 .652 .759 r .54504 .34036 .55391 .35976 .57629 .34127 .56745 .32088 Metetra .746 .645 .748 r .56745 .32088 .57629 .34127 .59867 .32162 .58986 .30016 Metetra .749 .638 .738 r .58986 .30016 .59867 .32162 .62104 .30069 .61224 .27806 Metetra .752 .631 .727 r .61224 .27806 .62104 .30069 .64336 .27837 .63456 .25447 Metetra .754 .624 .716 r .63456 .25447 .64336 .27837 .6656 .25454 .65679 .22925 Metetra .756 .617 .705 r .65679 .22925 .6656 .25454 .68773 .22906 .67889 .20227 Metetra .758 .61 .694 r .67889 .20227 .68773 .22906 .70972 .20179 .70083 .17337 Metetra .693 .752 .898 r .16583 .54617 .17603 .55612 .19681 .54702 .18668 .53698 Metetra .696 .753 .895 r .18668 .53698 .19681 .54702 .21772 .53766 .20765 .52751 Metetra .7 .753 .893 r .20765 .52751 .21772 .53766 .23876 .528 .22876 .51774 Metetra .704 .753 .89 r .22876 .51774 .23876 .528 .25992 .51802 .24999 .50765 Metetra .708 .753 .887 r .24999 .50765 .25992 .51802 .28122 .50769 .27135 .4972 Metetra .713 .753 .884 r .27135 .4972 .28122 .50769 .30263 .49698 .29284 .48636 Metetra .718 .753 .88 r .29284 .48636 .30263 .49698 .32417 .48585 .31445 .4751 Metetra .723 .753 .876 r .31445 .4751 .32417 .48585 .34583 .47426 .33619 .46336 Metetra .728 .753 .872 r .33619 .46336 .34583 .47426 .3676 .46217 .35803 .45112 Metetra .734 .753 .868 r .35803 .45112 .3676 .46217 .38948 .44952 .37999 .43831 Metetra .74 .753 .863 r .37999 .43831 .38948 .44952 .41147 .43627 .40205 .42489 Metetra .747 .753 .857 r .40205 .42489 .41147 .43627 .43355 .42236 .42422 .4108 Metetra .754 .753 .851 r .42422 .4108 .43355 .42236 .45572 .40772 .44647 .39596 Metetra .761 .752 .845 r .44647 .39596 .45572 .40772 .47796 .39227 .46879 .38031 Metetra .769 .752 .838 r .46879 .38031 .47796 .39227 .50027 .37596 .49119 .36377 Metetra .776 .751 .831 r .49119 .36377 .50027 .37596 .52264 .35868 .51364 .34626 Metetra .784 .751 .823 r .51364 .34626 .52264 .35868 .54504 .34036 .53612 .32768 Metetra .792 .75 .814 r .53612 .32768 .54504 .34036 .56745 .32088 .55862 .30794 Metetra .8 .749 .805 r .55862 .30794 .56745 .32088 .58986 .30016 .58112 .28692 Metetra .809 .748 .796 r .58112 .28692 .58986 .30016 .61224 .27806 .60359 .26451 Metetra .817 .746 .785 r .60359 .26451 .61224 .27806 .63456 .25447 .62599 .24058 Metetra .826 .745 .775 r .62599 .24058 .63456 .25447 .65679 .22925 .64831 .21501 Metetra .834 .743 .763 r .64831 .21501 .65679 .22925 .67889 .20227 .6705 .18764 Metetra .842 .741 .752 r .6705 .18764 .67889 .20227 .70083 .17337 .69251 .15834 Metetra .694 .778 .916 r .15544 .53735 .16583 .54617 .18668 .53698 .17634 .52818 Metetra .698 .781 .916 r .17634 .52818 .18668 .53698 .20765 .52751 .19737 .51876 Metetra .702 .785 .916 r .19737 .51876 .20765 .52751 .22876 .51774 .21854 .50905 Metetra .706 .788 .915 r .21854 .50905 .22876 .51774 .24999 .50765 .23984 .49902 Metetra .712 .792 .914 r .23984 .49902 .24999 .50765 .27135 .4972 .26127 .48865 Metetra .717 .797 .914 r .26127 .48865 .27135 .4972 .29284 .48636 .28282 .47791 Metetra .723 .801 .913 r .28282 .47791 .29284 .48636 .31445 .4751 .30451 .46676 Metetra .73 .807 .912 r .30451 .46676 .31445 .4751 .33619 .46336 .32631 .45516 Metetra .737 .812 .911 r .32631 .45516 .33619 .46336 .35803 .45112 .34824 .44306 Metetra .745 .819 .91 r .34824 .44306 .35803 .45112 .37999 .43831 .37027 .43043 Metetra .753 .826 .908 r .37027 .43043 .37999 .43831 .40205 .42489 .39242 .41721 Metetra .763 .833 .906 r .39242 .41721 .40205 .42489 .42422 .4108 .41467 .40334 Metetra .773 .841 .904 r .41467 .40334 .42422 .4108 .44647 .39596 .43702 .38876 Metetra .783 .85 .901 r .43702 .38876 .44647 .39596 .46879 .38031 .45945 .3734 Metetra .795 .859 .898 r .45945 .3734 .46879 .38031 .49119 .36377 .48195 .35718 Metetra .807 .869 .893 r .48195 .35718 .49119 .36377 .51364 .34626 .50451 .34003 Metetra .82 .88 .888 r .50451 .34003 .51364 .34626 .53612 .32768 .52712 .32186 Metetra .834 .89 .882 r .52712 .32186 .53612 .32768 .55862 .30794 .54975 .30257 Metetra .848 .902 .874 r .54975 .30257 .55862 .30794 .58112 .28692 .57239 .28205 Metetra .863 .913 .864 r .57239 .28205 .58112 .28692 .60359 .26451 .59501 .2602 Metetra .877 .925 .852 r .59501 .2602 .60359 .26451 .62599 .24058 .61759 .23689 Metetra .892 .936 .838 r .61759 .23689 .62599 .24058 .64831 .21501 .64009 .212 Metetra .905 .946 .8