{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Kurzeinführung\n",
    "\n",
    "[Python](http://www.python.org) ([Wikipedia](http://en.wikipedia.org/wiki/Python_%28programming_language%29))\n",
    "ist eine\n",
    "[multiparadigmatische](http://en.wikipedia.org/wiki/Programming_paradigm#Multi-paradigm)\n",
    "([imperativ](http://en.wikipedia.org/wiki/Imperative_programming),\n",
    "[prozedural](http://en.wikipedia.org/wiki/Procedural_programming),\n",
    "[funktional](http://en.wikipedia.org/wiki/Functional_programming),\n",
    "und\n",
    "[objektorientierte](http://en.wikipedia.org/wiki/Object-oriented_programming)) Programmiersprache.\n",
    "Sie wurde 1991 von [Guido van Rossum](http://en.wikipedia.org/wiki/Guido_van_Rossum) veröffentlicht\n",
    "und wurde von [ABC](http://en.wikipedia.org/wiki/ABC_%28programming_language%29),\n",
    "Java, Haskell und anderen Sprachen maßgeblich beeinflusst.\n",
    "Seit bald 10 Jahren gehört sie zu den am weitesten verbreiteten und flexiblesten Programmiersprachen weltweit.\n",
    "Aus der Sicht der Mathematik ist die große Sammlung an mathematischen, statistischen und wissenschaftlichen\n",
    "[Programmbibliotheken](http://en.wikipedia.org/wiki/Library_%28computing%29) hervorzuheben,\n",
    "und darauf aufbauende Tools wie <a href=\"http://en.wikipedia.org/wiki/Sage_(mathematics_software)\">SageMath</a> erwähnenswert.\n",
    "Außerdem ist Python eine exzellente Sprache zum funktionellen Kombinieren diverser Programme, Utilities und Systeme."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der beste Weg Python kennen zu lernen ist ein Sprung ins kalte Wasser.\n",
    "Ein Programm zu programmieren folgt keinen kochrezeptartigen Regeln,\n",
    "sondern bedarf des kreativen Kombinierens von Konzepten, Regeln und Ideen.\n",
    "Daher ist kreatives Denken und ein Schatz an Erfahrungen wichtig --\n",
    "ganz ähnlich wie das Führen von Beweisen in der Mathematik.\n",
    "\n",
    "Die Funktionsweise der hier vorliegenden Worksheets ist die folgende:\n",
    "Die mit `In[]` gekennzeichneten Boxen sind die Eingabezellen.\n",
    "In ihnen stehen in oder mehrere Zeilen Code.\n",
    "Durch betätigen des <button class=\"btn\"><i class=\"fa fa-play\"></i></button> Buttons oder der <button class=\"btn\">Strg (Ctrl)</button>+<button class=\"btn\">Return</button> Tasten wird die aktive Zelle ausgeführt.\n",
    "Die Ausgabe steht darunter und ist mit `Out[n]` gekennzeichnet.\n",
    "\n",
    "Die folgenden Beispiele zeigen anschauliche Beispiele,\n",
    "die einen ersten groben Umriss um die Funktionalität Python's liefert.\n",
    "Davon neugierig gemacht, werden in der Folge die darin vorkommenden Grundprinzipien erklärt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Keine Scheu, kopiere einzelne Zellen in ein neues IPython Notebook und fange an zu experimentieren!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Einfache Rechenbeispiele"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "format": "row"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "14 + 3 * (8 - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Achtung, potenziert wird mit `**`!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "banane = 3**2 + 1\n",
    "print(banane)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierbei ist `banane` eine Variable, die auf den Wert `10` gesetzt wurde.\n",
    "Das ist das Ergebnis der Auswertung des Ausdrucks `3**2 + 1`.\n",
    "Abgerufen kann der Wert von `banane`, wenn es an letzter Stelle einer Code-Zelle steht,\n",
    "oder durch den `print` Befehl."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "print(banane)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "banane"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für \"mathematisches\" Dividieren muss mindestens ein Argument eine Flißekommazahl sein;\n",
    "Ganzzahldivisionen werden abgerundet!\n",
    "(Ausnahme: entweder es ist Python in Version 3 **oder** mittels `from __future__ import division` wurde das modernere Verhalten importiert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.791000000000002"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2.2 * 9.81) / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Beide Zahlen sind Ganzzahlen, daher striktes Abrunden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "51 / 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ist mindestens eine der beiden Zahlen eine Fließkommazahl (sichtbar an dem kleinen `.` nach der `51`),\n",
    "so wird eine Fließkommadivision durchgeführt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "51. / 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aktivieren des alternativen Verhaltens für Divisionen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "51 / 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das IPython Notebook merkt sich derweilen weiter oben definierte Variable `banane`,\n",
    "solange die \"Session\" aktiv ist.\n",
    "Kernel &gt; Restart bzw. <button class=\"btn\"><i class=\"fa fa-repeat\" ></i></button> starten die Session neu."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`print` kann in Python 2 als Statement verwendet werden,\n",
    "es geht aber auch die in Python 3 gebräuchliche Variante als Funktion.\n",
    "Damit können jederzeit Zwischenergebnisse, die während des Ablaufs des Programmes passieren, ausgegeben werden.\n",
    "Ansonsten wird immer nur der Wert des letzten Ausdrucks ausgegeben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "47.519999999999996\n",
      "29.810000000000002\n"
     ]
    }
   ],
   "source": [
    "apfel = 8.76\n",
    "print(3 * banane + 2 * apfel)\n",
    "apfel = 9.81\n",
    "print(2 * banane + apfel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Brüche können mit `Fraction` angegeben werden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(2673, 38275585202254501783218213917955539030103719395100)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from fractions import Fraction\n",
    "a = Fraction(\"33/31003100\")\n",
    "b = Fraction(\"-9/100000100001\")\n",
    "a * b ** 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liste von Zahlen von 0 bis 9. Es ist außerdem und ganz generell so, dass bei `0` zu zählen begonnen wird und Intervalle auf der linken Seite geschlossen und auf der rechten Seite offen sind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 10)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jede dritte Zahl in $-10 \\leq x < 10,\\; x \\in \\mathbb{Z}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(-10, 10, 3)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(-10, 10, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eine `for`-Schleife iteriert -- das heißt, sie wiederholt den darin vorhandenen Codeblock -- für alle angegebenen Werte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x ist -10 und y ist -29\n",
      "x ist  -6 und y ist -17\n",
      "x ist  -2 und y ist  -5\n",
      "x ist   2 und y ist   7\n",
      "x ist   6 und y ist  19\n"
     ]
    }
   ],
   "source": [
    "for x in range(-10, 10, 4):\n",
    "    y = 3 * x + 1\n",
    "    print(\"x ist %3d und y ist %3d\" % (x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`if`-Verzweigungen erlauben, Codeblöcke nur unter bestimmten Bedingungen auszuführen.\n",
    "Das Wort `else` kann optional dazu verwendet werden, einen Codeblock bei nichterfüllung der Bedingung auszuführen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k ist negativ\n"
     ]
    }
   ],
   "source": [
    "k = -4\n",
    "if k >= 0:\n",
    "    print(\"k ist positiv\")\n",
    "else:\n",
    "    print(\"k ist negativ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eine `for`-Schleife mit einer darin enthaltenen `if`-Bedingung.\n",
    "Sie summiert alle Zahlen bis 100, die durch 3 und 7 teilbar sind, auf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "210\n"
     ]
    }
   ],
   "source": [
    "summe = 0\n",
    "for i in range(100):\n",
    "    if i % 3 == 0 and i % 7 == 0:\n",
    "        summe += i\n",
    "print(summe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das `import` Statement dient dazu, Funktionalitäten aus diversen Programmbibliotheken zu importieren.\n",
    "\n",
    "Beispiel: Die Sinusfunktion `sin` aus der `math`-Bibliothek importieren und mit Standardgenauigkeit berechnen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.979318433952318e-11"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import sin\n",
    "sin(3.1415926535)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier wird die `sin`-Funktion mit 100 Stellen Genauigkeit durch dessen Version in der `mpmath`-Bibliothek in Sympy berechnet.\n",
    "Beachte, dass `mpm` vorangestellt wird, um Vermischungen mit der schon importieren `sin` zu vermeiden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpf('0.00000000008979323846264338327938221965910388125990692946182694867743526330407406677351504727435623041438215811254')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import mpmath as mpm\n",
    "mpm.mp.dps = 100\n",
    "\n",
    "mpm.sin(mpm.mpf(\"3.1415926535\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolische Ausdrücke, Funktionen, Differenzieren\n",
    "\n",
    "Symbolische Ausdrücke können mit der Programmbibliothek `SymPy` erzeugt werden.\n",
    "Hierfür importieren wir z.B. in einem ersten Schritt die Variable $x$ und den Operator $\\sin$,\n",
    "mit der die Ausdrücke aufgebaut werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import sin, pi\n",
    "from sympy.abc import x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$f(x) := \\frac{2 x}{x - \\sin(x)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2*x/(x - sin(x))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = 2 * x / (x - sin(x))\n",
    "f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Differenzieren nach $x$ mit `.diff(x)` und anschließendes Vereinfachen des Ausdrucks durch `.simplify()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2*(x*cos(x) - sin(x))/(x - sin(x))**2"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_prime = f.diff(x).simplify()\n",
    "f_prime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auswertung von symbolischen Ausdrücken"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier wird das `x` in dem zuvor definierten symbolischen Ausdruck `f` mittels der Methode `.subs(<variable>, <expression>)` ersetzt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$f(x)\\Big\\rvert_{x=1}=\\dots$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2/(-sin(1) + 1)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(x, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pi wurde weiter oben via `from sympy import pi` definiert.\n",
    "\n",
    "$f(x)\\Big\\rvert_{x=\\pi}=\\dots$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(x, pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numerische Auswertung nach der Substitution durch `.evalf()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.6159870328875"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(x, 1).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.61598703288748005502704347964832025794268409451527860450480203069959865248247113838572429676781402"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(x, 1).evalf(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\LaTeX{}$-Formatierung mittels SymPy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.display import Math\n",
    "from sympy import latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{2 x}{x - \\sin{\\left (x \\right )}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Math(latex(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{2 x \\cos{\\left (x \\right )} - 2 \\sin{\\left (x \\right )}}{\\left(x - \\sin{\\left (x \\right )}\\right)^{2}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Math(latex(f_prime))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Listen und Listenverarbeitung"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eine \"Liste\" ist eine geordnete Sammlung von Objekten.\n",
    "Sie ist so ziemlich die zentralste *Datenstruktur* überhaupt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Haus', 99]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1 = [\"Haus\", 99]\n",
    "l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a', 0, 'x']"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l2 = [\"a\", 0, \"x\"]\n",
    "l2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Haus', 99, 'a', 0, 'x']"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1 + l2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verarbeiten von Listen mittels\n",
    "\n",
    "`[ <ausdruck> for <variable> in <liste> ]`\n",
    "\n",
    "(genannt \"list-comprehension\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0, 3.0, 4.0, 8.0, 14.2, 18.0, 42.0]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ll = [2., 2.5, 3., 5., 8.1, 10., 22.]\n",
    "k1 = [2*i-2 for i in ll]\n",
    "k1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[k**2 + 2*k + 1 for k in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zugriff auf Elemente in einer Liste -- achtung, wie schon erwähnt wird ab `0` indiziert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'h'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = [\"P\", \"y\", \"t\", \"h\", \"o\", \"n\"]\n",
    "p[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das zweit-letzte Element mittels `-2`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'o'"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p[-2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grafische Darstellungen\n",
    "\n",
    "Dies geschieht mittels der `matplotlib`-Bibliothek. Sie muss zur Ausgabe von Grafiken aktiviert werden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (10,6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotten paarweiser Punkte\n",
    "\n",
    "`xx` und `yy` beinhalten jeweils die x- und y-Koordinaten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3.3)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wlpEB7dvDpk2+E8W3oiLbF7BhA8ybZ60wIpIYNCEuMaj4kbDIy7M3Dzk5vpOI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\nWCD8AAAAAIgFwg8AAACAWPj/o/g25Rkfb64AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9d02cabeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = [20, 15,  11, 7.57, 9.6, 13,  21,  24, 28, 23, 20]\n",
    "yy = [3, 2.5, 2.3, 2.66,  3, 3.1, 2.3, 2.5, 2.8, 3,  3]\n",
    "\n",
    "plt.plot(xx, yy, \"o-\")\n",
    "plt.xlim(5, 30)\n",
    "plt.ylim(2, 3.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Funktionen und deren Graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definieren einer Funktionen mit `SymPy` und zeichnen ihres Graphen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import sin\n",
    "from sympy.abc import x\n",
    "sin_square = sin(x) * x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.63718970730273"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin_square.subs(x, -2).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "146.314764035351"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin_square.subs(x, 15).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vveX7axNGAAAAAC9asMAMFPeHWbROp2ZN6dprzRoovkYYAQAAALxo9mypUyepRQvblZxZ\nYqK0fLl04IBvr0sYAQAAALxk507p44/9t1WkRP/+UlGRqdWXCCMAAACAl/zrX1LFitLNN9uu5Owa\nN5Yuv1z6z398e13CCAAAAOAFJWuLDBwo1aplu5pfl5hoZtUqKvLdNQkjAAAAgBdkZEjffON/a4uc\nSWKitG+ftHKl765JGAEAAAC8YPZsqVEjM1NVILjySikqyrddtQgjAAAAgIcdOWLW7Rg+XAoPt11N\n2YSHS/36+XaKX8IIAAAA4GEffCAdPGjCSCDp319av17ats031yOMAAAAAB726qtS167SpZfaruTc\n9OljVon3VesIYQQAAADwoO+/l5KT/X9tkdOpWVO6+mrfjRshjAAAAAAe9K9/SVWqSEOG2K6kfBIT\npcWLpbw871+LMAIAAAB4iOuaWbQGDZJq1LBdTfkkJkrHjkkpKd6/FmEEAAAA8JAVK6SsrMBZW+R0\nLr1UatbMN121CCMAAACAh8yeLV1wgdS9u+1Kzk9iohnE7rrevQ5hBAAAAPCAvDzpnXfMdL5hAX6X\nnZgo7dwpffGFd68T4F8mAAAAwD+8957000+Bt7bI6XTtKkVGer+rFmEEAAAA8IBXXzXdsy66yHYl\n569CBSkhgTACAAAA+L3vvjPT4QbywPVTJSZKGRlSTo73rkEYAQAAAM7TnDlStWpmSt9gcd11kuNI\nixZ57xqEEQAAAOA8FBebLlpDhkjVq9uuxnOioqROnbzbVYswAgAAAJyH5culrVulO+6wXYnnJSZK\nn3xiFkH0BsIIAAAAcB5efdUMWu/WzXYlnpeYKB06ZAKXNxBGAAAAgHI6dEj6979Nq4jj2K7G89q0\nkRo39l5XLcIIAAAAUE7vvisdPhwca4ucjuNI/ftLCxZ4ZzV2wggAAABQTrNnS9deKzVpYrsS70lM\nlLZskTZt8vy5CSMAAABAOezYYVoLgmltkdO59lqpShXvdNUijASg5cuX6/rrr1fDhg0VFhamDz/8\nsNTzd955p8LCwkpt/fr1K3XMsWPHNGrUKNWrV081atTQ4MGDtXv3bl++DAAAgID23/9KaWmmG1Mw\nq1JF6tmTMIKf5eXlqV27dpo+fbqcM4yUuu6665STk6Ps7GxlZ2frzTffLPX8mDFjtHDhQs2bN0/L\nli3Tzp07NSiYVukBAADwsk8+keLjpVq1bFfifYmJUmqqtH+/Z88b4dnTwRf69u2rvn37SpLcM4wk\nqlSpkqKiok77XG5urmbNmqW33npL3bt3lyTNnj1bLVu2VEZGhuLj471TOAAAQJAoKpJSUqRRo2xX\n4hv9+0v33msC2M03e+68tIwEqSVLlig6OlotWrTQyJEjtW/fvuPPZWZmqrCwUD179jy+r3nz5mrS\npInS09NtlAsAABBQPv9c2rdP6t3bdiW+0aiR1K6d57tqEUaC0HXXXac5c+Zo8eLFmjp1qpYuXap+\n/fodb0XJzs5WxYoVFRkZWerzoqOjlZ2dbaNkAACAgJKcLFWvLnXqZLsS30lMlBYtMq1CnkI3rSA0\nZMiQ4x9fdtllatOmjS6++GItWbJE11xzjcXKAAAAgkNystSjh1Shgu1KfCcxUZo8WVq5UurSxTPn\nJIyEgKZNm6pevXrKysrSNddco5iYGOXn5ys3N7dU60hOTo5iYmLOeq6xY8eqZs2apfYlJSUpKSnJ\nK7UDAAD4m7w8M4vWX/5iuxLfuvJKKSrKdNUijKDMduzYob1796pBgwaSpLi4OEVERCglJUUDBw6U\nJG3atEnbt29X586dz3quadOmqUOHDl6vGQAAwF8tWybl54fOeJESYWFSv34mjDzzjGfOSRgJQHl5\necrKyjo+BmTLli1at26d6tSpozp16mjSpEkaNGiQYmJilJWVpUceeUTNmjVTQkKCJCkyMlJ33XWX\nHnzwQdWuXVs1atTQAw88oC5dujCTFgAAwK9ITjYDups3t12J7yUmSq+95rnzEUYC0Jo1a3TNNdfI\ncRw5jqOHHnpIkjR8+HBNnz5dX375pebMmaMDBw4oNjZWCQkJeuqpp1ThpE6N06ZNU3h4uAYPHqxj\nx46pb9++eumll2y9JAAAgICRnGxaRc6w3FtQ69NHivBggnDOtE7FaZT5QASftWvXKi4uTpmZmXTT\nAgAAIWvXLik2VnrjDSlUh8w+8YQ0aZI8EsWY2hcAAAAoo08/NY+9etmtw6ZJkzx3LsIIAAAAUEaf\nfCK1b29mlcL5I4wAAAAAZeC6pmUk1GbR8ibCCAAAAFAGGzZI2dmEEU8ijAAAAABlkJwsVa4sde1q\nu5LgQRgBAAAAyiA5Wbr6ahNI4BmEEQAAAOBXHD0qLV1KFy1PI4wAAAAAv2LFCunIEcKIpxFGAAAA\ngF+RnCzVry+1aWO7kuBCGAEAAAB+RXKyWegwjLtnj+LLCQAAAJzFnj3S2rVSnz62Kwk+hBEAAADg\nLFJSzIKHvXrZriT4EEYAAACAs0hOllq1kho2tF1J8CGMAAAAAGfguiaMMIuWdxBGAAAAgDPYvFna\nvp0w4i2EEQAAAOAMkpOlChWk7t1tVxKcCCMAAADAGSQnS1ddJVWvbruS4EQYAQAAAE6joEBavJgu\nWt5EGAEAAABOIyND+uknwog3EUYAAACA00hOlmrXluLibFcSvAgjAAAAwGkkJ0vXXiuFh9uuJHgR\nRgAAAIBTHDworVol9elju5LgRhgBAAAATvHZZ1JREeNFvI0wAgAAAJwiOVm6+GKpaVPblQQ3wggA\nAABwiuRkWkV8gTACAAAAnGTbNmnzZsKILxBGAAAAgJMkJ0thYWYmLXgXYQQAAAA4ySefSPHxUq1a\ntisJfoQRAAAA4GdFRVJKCl20fIUwAgAAAPzs88+lffsII75CGAEAAAB+lpwsVa8udepku5LQQBgB\nAAAAfpacLF1zjVShgu1KQgNhBAAAAJCUlyelpdFFy5cIIwAAAICkZcuk/HzCiC8RRgAAAABJGRlS\n//5S8+a2KwkdhBEAAABA0scfSzVqSI5ju5LQQRgBAABAyDtyRFqzRura1XYloYUwAgAAgJCXkSEV\nFBBGfI0wAgAAgJCXmipFRkqtW9uuJLQQRgAAABDyUlOlLl2k8HDblYQWwggAAABCWlGRtGIFXbRs\nIIwAAAAgpG3YIOXmEkZsIIwAAAAgpKWmShUqSFdeabuS0EMYAQAAQEhbvly64gqpShXblYQewggA\nAABCluuaMEIXLTsIIwAAAAhZ27ZJO3cSRmwhjAAAACBkpaaax6uusltHqCKMBKDly5fr+uuvV8OG\nDRUWFqYPP/zwF8dMnDhRsbGxqlq1qnr37q2srKxSzx87dkyjRo1SvXr1VKNGDQ0ePFi7d+/21UsA\nAADwC6mpUsuWUr16tisJTYSRAJSXl6d27dpp+vTpchznF89PmTJFL774ombOnKmMjAxVq1ZNCQkJ\nys/PP37MmDFjtHDhQs2bN0/Lli3Tzp07NWjQIF++DAAAAOtSU6Vu3WxXEboibBeAc9e3b1/17dtX\nkuS67i+ef+655zRhwgQlJiZKkubMmaPo6Gh98MEHGjJkiHJzczVr1iy99dZb6t69uyRp9uzZatmy\npTIyMhQfH++7FwMAAGDJvn3SV19Jjzxiu5LQRctIkNm6dauys7PVs2fP4/siIyPVsWNHpaenS5LW\nrFmjwsLCUsc0b95cTZo0OX4MAABAsFuxwjwyeN0ewkiQyc7OluM4io6OLrU/Ojpa2dnZkqScnBxV\nrFhRkZGRZzwGAAAg2C1fLsXGShdeaLuS0EUYAQAAQEhKTTWtIqcZggsfYcxIkImJiZHrusrJySnV\nOpKTk6P27dsfPyY/P1+5ubmlWkdycnIUExNz1vOPHTtWNWvWLLUvKSlJSUlJHnwVAAAA3nXkiLR6\ntTR0qO1KQhthJMg0bdpUMTExSklJUdu2bSVJubm5WrVqlUaNGiVJiouLU0REhFJSUjRw4EBJ0qZN\nm7R9+3Z17tz5rOefNm2aOnTo4N0XAQAA4GVr1kgFBYwXsY0wEoDy8vKUlZV1fCatLVu2aN26dapT\np44aN26sMWPGaPLkybrkkkt04YUXasKECWrUqJEGDBggyQxov+uuu/Tggw+qdu3aqlGjhh544AF1\n6dKFmbQAAEBISE2VatSQfn7vFpYQRgLQmjVrdM0118hxHDmOo4ceekiSNHz4cM2aNUvjx4/X4cOH\ndc899+jAgQPq1q2bPvroI1WsWPH4OaZNm6bw8HANHjxYx44dU9++ffXSSy/ZekkAAAA+lZpqVl0P\nD7ddSWhzTrdOxRmU+UAEn7Vr1youLk6ZmZl00wIAAAGtuFiqU0d6+GHp8cdtVxOwPDLsn9m0AAAA\nEFI2bJAOHmS8iD8gjAAAACCkpKZKERESQ2XtI4wAAAAgpKSmSnFxUtWqtisBYQQAAAAhpWSxQ9hH\nGAEAAEDI2L5d+v57woi/IIwAAAAgZKSmmscuXezWAYMwAgAAgJCRmio1by5FRdmuBBJhBAAAACEk\nNVXq1s12FShBGAEAAEBI2L/frDHCeBH/QRgBAABASFixQnJdwog/IYwAAAAgJKSmSjEx0kUX2a4E\nJQgjAAAACAkl64s4ju1KUIIwAgAAgKB39KiUkUEXLX9DGAEAAEDQy8yU8vMJI/6GMAIAAICgl5oq\nVasmXX657UpwMsIIAAAAgt7y5VLnzlJEhO1KcDLCCAAAAIJacbGUlsZih/6IMAIAAICgtnGjdOAA\n40X8EWEEAAAAQS01VQoPlzp2tF0JTkUYAQAAQFBLTZU6dDAD2OFfCCMAAAAIaiWLHcL/EEYAAAAQ\ntHbskLZvJ4z4K8IIAAAAglZamlS9unTVVbYrwekQRgAAABC00tOlqCgpJsZ2JTgdwggAAACCVnq6\nWewQ/okwAgAAgKB05Ii0di1dtPwZYQQAAABBKTNTKiykZcSfEUYAAAAQlFasMGuLtGljuxKcCWEE\nAAAAQSk9XYqPlyIibFeCMyGMAAAAIOi4LoPXAwFhBAAAAEFn61YpJ4fB6/6OMAIAAICgk55uHjt1\nslsHzo4wAgAAgKCzYoXUvLlUt67tSnA2hBEAAAAEHcaLBAbCCAAAAILKoUPSl18SRgIBYQQAAABB\nZfVqqaiIweuBgFmXAQDwI/n50uHDZl2EqlWlMN42BM5ZeroUGSm1amW7EvwawggAAJYUFkqffSYt\nWCClpZmbp1q1pEqVzBoJhw9LBQUmoHTpYrqcdOsm1ahhu3LAv61YYWbRIsz7P8IIAAA+VBJA/v1v\n6b33pL17pYsvlvr1ky69VKpTR6pQwRyblyft3Cl99ZU0a5Y0ebJUs6Z0yy3S449LsbF2Xwvgj1xX\nWrlSuu8+25WgLAgjAAB42ckB5P33pT17TAAZMUK66SapfXvJcc5+DteVNm+WFi6UnnlGev116Y9/\nlEaOlMLDffM6gECwebMJ+QxeDww0XgEA4CVFRdILL5h+6336SCkp0u9+J2VmmhumZ56ROnT49SAi\nmWOaNZPGjpU2bTKtI6NHSx07SmvWeP+1AIFixQrz89Kxo+1KUBaEEQAAvOB//5O6dzeBYcAAExiy\nss4tgJxJ7drSjBnmpquwUIqPN11SDhzwXP1AoEpPN28A1KpluxKUBWEEAAAPcl1p5kzp8svNeI9l\ny6Rnn5Xi4s4vgJxOp04m5Pztb9Jrr0ktWkhvvGFqAELVihVM6RtICCMAAHhIdrb0m99I99wjJSVJ\n69ZJXbt695oREdKYMdI335iZtm69VerdW/r2W+9eF/BHBw+aCR8YLxI4CCMAAHjAvHlS69ZmsbUP\nP5Reftm3U/A2bGgGyC9aJG3ZIrVpIz3xhHT0qO9qAGxbtcq0DBJGAgdhBACA83DggDRsmDR4sBkj\nsmGDaR2x5brrzDvD48eb8SmtW0tLltirB/Cl9HQzPXazZrYrQVkRRgAAKKeUFKltW2n+fDNm4913\npago21VJVapITz8tffmlaTF55BGzsCIQ7NLTWeww0PBfBQDAOTpyxIzT6NVLuuQSaf160zri6QHq\n56tFC2nxYhNIhg41UwoDwaq42Cx2yOD1wEIYCUKTJk1SWFhYqa1Vq1aljpk4caJiY2NVtWpV9e7d\nW1lZWZYsfCqAAAAgAElEQVSqBYDAkpNjFiucMUOaNk369FOpSRPbVZ1ZeLhZILF1a9N97PvvbVcE\neMfXX5sB7IwXCSyEkSDVunVr5eTkKDs7W9nZ2UpNTT3+3JQpU/Tiiy9q5syZysjIULVq1ZSQkKD8\n/HyLFQOA/9u5U+rRw3TPSkszrSOB0B2kalUzqL5SJal/fyk313ZFgOetWGF+HuPjbVeCcxEAv0JR\nHhEREYqKilL9+vVVv3591alT5/hzzz33nCZMmKDExES1bt1ac+bM0c6dO/XBBx9YrBgA/NuOHSaI\nHDokLV9u1g0JJNHR0sKF0vbt0k03SQUFtisCPCs93Yzhql7ddiU4F4SRILV582Y1bNhQF198sW67\n7TZ9/3O7/NatW5Wdna2ePXsePzYyMlIdO3ZUenq6rXIBwK9t22Zmyjp2TFq61IwTCUStWpkpiBcv\nlkaNYnFEBJf0dLpoBSLCSBDq1KmTXn31VX388ceaMWOGtm7dqquvvlp5eXnKzs6W4ziKjo4u9TnR\n0dHKzs62VDEA+K+tW00QcV2zmvpFF9mu6Pz07GnWQHn5ZWnqVNvVAJ6xb59Z+JPB64EnwnYB8LyE\nhITjH7du3Vrx8fG64IIL9M4776hFixYWKwOAwJKVJV17rRlr8dlnUqNGtivyjDvukP73P+nRR6Wm\nTaUhQ2xXBJyflSvNIy0jgYcwEgJq1qypZs2aKSsrSz169JDrusrJySnVOpKTk6P27dv/6rnGjh2r\nmjVrltqXlJSkpKQkj9cNADZt2mSCSI0apltTbKztijzrqafMSu3DhpmQxTvKCGQrVkj16wd+y2Uo\nIoyEgEOHDikrK0vDhw9X06ZNFRMTo5SUFLVt21aSlJubq1WrVmnUqFG/eq5p06apQ4cO3i4ZAKza\nuNF0Z6pTx8ycFRNjuyLPcxxp1iwzoH3AAPPO8sUX264KKJ+S8SL+ttYPfh1jRoLQuHHjtGzZMm3b\ntk0rVqzQwIEDVaFCBQ0dOlSSNGbMGE2ePFkLFizQ+vXrNWzYMDVq1EgDBgywXDkA2Ld+vZk1KypK\nWrIkOINIiUqVpA8+kGrXlvr1k/butV0RcO4KC6WMDLpoBSpaRoLQjh07dMstt2jv3r2KiopS165d\ntXLlStWtW1eSNH78eB0+fFj33HOPDhw4oG7duumjjz5SxYoVLVcOAHZ98YVZVb1JEyk5Wfr512ZQ\nq1tXWrRI6tRJuvFG6ZNPTEgBAsWGDWbKbboaBibHLfu8fkwAGMLWrl2ruLg4ZWZm0k0LQFD67jtz\nMx4VJb31lmktCCVpadJDD5kWkokTbVcDlN0//iE98IBZzLNKFdvVhBSPdIqjmxYAIOQdPCglJprH\nuXNDL4hIUpcu0m9+Iz39tHmnGQgUK1ZI7dsTRAIVYQQAENIKC83Utj/8YFYor1fPdkX2PPywWdDx\n//5PKi62XQ1QNix2GNgIIwCAkOW60v33m6l7582TQn0ppkqVpOnTpdRU6dVXbVcD/Lrdu82aOYSR\nwEUYAQCErOeek2bMMH3Or73WdjX+4ZprpNtuk8aPZ3Yt+L/0dPPI4PXARRgBAISkBQukBx80N92/\n+53tavzLX/4iFRVJjzxiuxLg7NLTzYKkjRvbrgTlRRgBAIScL76QkpKkgQOlZ56xXY3/iY42X5dX\nXjGzbAH+asUK0yrCYoeBizACAAgpO3eambNatpT+9S8pjL+Ep3X33VJ8vHTvvVJBge1qgF8qKJBW\nr2a8SKDjVzAAIGTk5Znpax1H+vBDqWpV2xX5r7AwM55m40YztgbwN198IR09ShgJdIQRAEBIKCqS\nbr1V+vZb6T//kRo0sF2R/2vf3sw29sQT0vbttqsBSktPlypWlFiLObARRgAAIeHRR82g9bfeki6/\n3HY1geOpp6RataTRo21XApSWni7FxZkpqRG4CCMAgKA3c6aZIWraNKl/f9vVBJbISOnvf5c++MCE\nOcBflAxeR2AjjAAAgtqnn0ojR5rt/vttVxOYBg+WEhLM1y8vz3Y1gPTDD2ZcE+NFAh9hBAAQtDZu\nNDfSvXubQdhM/1k+jiO9+KKUnS1Nnmy7GsC0inz3HWEkGBBGAABBafduM4Vv48bS229LERG2Kwps\nl1wi/eEPprvbV1/ZrgahLi1NatrULHiIwEYYAQAEnYICs6p648Zm5qzISNsVBYfx46WLLjJd3lzX\ndjUIZWlpUpcutquAJxBGAABBZ9w46aOPpD/+UbrgAtvVBI9KlaTp06Vly6T33rNdDUJVXp70+eeE\nkWBBGAEABJXXXzfjQ/7+d6lrV9vVBJ+ePaURI6SHH2ZldtiRkWHWDSKMBAfCCAAgaHzxhXT33dLw\n4aYrEbzj/vvN4OHXX7ddCUJRWppUs6Z02WW2K4EnEEYAAEFh715p4ECpZUvpH/9g5ixvatPGfK3/\n9CepsNB2NQg1aWlmFq0w7mKDAv+NAICAV1Qk3XKLdOiQGctQpYrtioLf449LWVlmRXvAV4qLzcrr\ndNEKHoQRAEDAe/xxs7jh228zYN1XOnQwUyf/8Y8mDAK+8NVX0sGDhJFgQhgBAAS0efOkP/9ZmjJF\nuvZa29WElgkTpG++kd5913YlCBVpaVJ4uBQfb7sSeAphBAAQsDZulO64Q7r5Zumhh2xXE3ri46WE\nBLMqe3Gx7WoQCtLSpPbtpWrVbFcCTyGMAAAC0sGD0g03SBdeKL3yCgPWbZkwQdqwQZo/33YlCAUs\ndhh8CCMAgIBTXCzdfrv044/S++/zLqlNXbqY7nFPP82q7PCuXbukrVsJI8GGMAIACDiTJ0v/+Y80\nd650ySW2q8GECWZF7IULbVeCYJaWZh4JI8GFMAIACCgLF0pPPilNmiT162e7GkhS9+5St27SU0/R\nOgLvSUsz3TJjY21XAk8ijAAAAsbmzdKtt0q/+Y30hz/YrgYlHMe0jqxeLX3yie1qEKwYLxKcCCMA\ngICQmyuNGSNddpk0Zw6rL/ubXr2kjh1pHYF3HD5sugISRoIPv8oBAH6vqMi0iKSmmpmzata0XRFO\n5TjSxInSihXSZ5/ZrgbBJiNDKiwkjAQjwggAwO899pi0aJFZYb1FC9vV4Eyuu06KizOtI4AnpaVJ\nkZGmZRTBhTACAPBrc+ZIU6dKf/2r1Lev7WpwNiVjR5YulZYvt10NgklamtS5s1l9HcGFMAIA8Fvp\n6dKIEdJdd0mjR9uuBmVx/fVS27Zm3RHAE4qLze8CumgFJ8IIAMAvbd9uVljv2FGaPp0V1gNFSetI\ncrK0cqXtahAMNm6UDhwgjAQrwggAwO/k5UkDBkhVqkjz5kkVK9quCOfixhulVq1oHYFnpKWZ7lkd\nO9quBN5AGAEA+JXiYmn4cCkrS1qwQIqKsl0RzlVYmPT442bSgTVrbFeDQJeWJrVrJ1WrZrsSeANh\nBADgVyZNkt57T5o7V2rTxnY1KK8hQ6RmzaTJk21XgkDHYofBjTACAPAbb79tpoX905/MQGgErvBw\nMyXzli3SV1/ZrgaBKjvbfA8RRoIXYQQA4BfWrJHuuMMsbvjII7argSckJUn79kl//7vtShCo0tLM\nI2EkeBFGAADW7dxpBqy3bSv985/MnBUsKlaU/u//TJe7vXttV4NAlJYmXXCB1LCh7UrgLYQRAIBV\nR46YKXwdR/rgA6lyZdsVwZNGjJCKiqRXXrFdCQIR40WCH2EEAGCN65oFDTdskObPlxo0sF0RPK1+\nfWnoULNWTFGR7WoQSA4fltauJYwEO8IIAMCaZ56R3nxTeu01KS7OdjXwlgcekLZtM1M1A2W1erVU\nWEgYCXaEEQCAFe+/L/3hD9ITT0g33WS7GnhTXJzUubP0/PO2K0EgSUuTIiOl1q1tVwJvIowAAHxu\n3Trp9tulwYOliRNtVwNfeOAB6bPPTJc8oCzS0qROncw00QhehBEAgE/t3m3WEGnWTHr1VbNaN4Lf\noEFmTNCLL9quBIGguFhasYIuWqGAPwEAAJ85dky68UbzOH++VK2a7YrgKxUqSPfeK/3rX9L+/bar\ngb/7+mvpwAHCSCiIsF0A7HrppZf0l7/8RdnZ2br88sv1wgsv6Morr7RdVtAqLDS/XA8ePLHl5kpH\nj5qFwYqLpYIC8+8DB8wc/fn5Zn/FimbmocJCMwVqhQrmnAUF5rmKFU1TdrVq5vhatUxf2zp1pKgo\nM6NN3bq8C+2P3nzzTSUlJdkuw+tc16w5sWaNtGSJ1Lix7Yrga/fcI02eLM2aJT30kG+uGSo/X8Em\nLc38TevY0XYlOBPHcZJc133zfM9DGAlhb7/9th566CHNnDlT8fHxmjZtmhISEvTtt9+qXr16tsvz\ne8XFJjD8+KPpdvLjjye2kn//9JOUnW2Cxr59Jny0aiVt3Ci1aSOtX2/O1aGD6UPfrZtUvfqJc194\n4YkgEhlpgkRRkbmpi4gwHx88aP5dXCwdOmTCypIl5p3n6tVN2GnXTvriC/M50dGmhurVzfmbNjXb\npZdKF19sjoFvhcLNkutKjz8ubdokvfyy6QeO0BMdLd18s+mqNWaMb8YChMLPVzBKS5Muv9z8rYLf\nSpJEGEH5TZs2Tffcc4+GDRsmSZoxY4YWLlyoWbNmafz48Zar872CAhMY9uwx24ED0q5dZw4ae/b8\ncs78sDDT+lDSEtG4sVk1tm5d00JR0kpRvbpUs6bZIiOlGjWkSpU8u+p0SSvMvn2mS8SuXWbLzjah\nZcMG6T//MdNt5udLV14pffml1LKlCUonb7GxrIiN8/Pkk9Kf/iQ9+6wZuI7Q9cAD0uuvSwsXmrFD\nwOmkpUn9+tmuAr5AGAlRBQUFyszM1GOPPXZ8n+M46tWrl9LT0y1Wdv4KC090gdq/v/RWUCB9992J\nwHHyduBA6fM0bSpt3y7Vq3ciXERFmVaFqKgTW8n+qCipdm3/mfUjIsLU/muNXMXFJqRs3mxaakq2\n996T8vLMMbVrS337mnepevaU2rf3n9cJ/zdpkvTUU9LUqdLDD9uuBrZdeaXpevPCC4QRnF5OjvS/\n/zFeJFQQRkJEUZG56SwuNh/v2rVHRUVFqlYt+ng3H9eVataM1ldfbfrF4MKDB0887tt3Yn/J5538\n8clbyfVKHks+Liw0W0GB2VcyTuLYsRPdjSQTEI4cMe/K79ljbo7z8syqrFWrSlu2mK5QF1xg3kXJ\nzTXPSdLVV0vLlp2o1XGka66Rvv/+xE16y5YnPi7ZoqLMY926ZtxFsI+xCAszrTcNG0o9epzYX1xs\ngtv69aYL2cqV0tNPS48+asLJNdeYYNKzp5kViZYTnM5TT5lWkT//WRo3znY18Bf33y/ddpvpstqq\nle1q4G/S0swjYSQ0lCmMOI5TNTMz09u1hBTXNTfZP/1kbqAPHTI30Xl5psvMwYPm+SNHzM16ySDn\nqlXNu9jHjpnzHDpkugIVFpqZJyIipCZNzI3k/v0nuuS0aydlZZmPW7aUwsN/lOtKffp8o+JiMxK6\nYUPphx9yJOWpTp21p1T8tSTp2mu/LrX38svNjapkuvMcPGhaE9q3Nx9v2WKeO/n6zZub1/H556be\nSy81XZS++EKqUkVq0cI816aNeU2VKpmb3ZwcqXJlM0C7YkUpJsYM4m7c2PRDHjDAPFejhukGFRkp\n3X23eYyMNM+VNVj89JPZYL6+jRtLiYkmNG7YIGVkmG3+fPP9Wb++FB9/YouKsl11YDl48KDWrj31\nZy7wvfyyNGOGNGqU1Lu3FIQvEeV0ySXmDZ8nnpB+/3vvXitYf76C2Xvvmb/xu3ebDX6rpuM4VV3X\nPXw+J3Hckre1z3aQ43SQRBoBAAAAUCLOdd3zSvtlDSNV69TJzCvpnlO9unl3u3lzqXVrM7i1USPT\npSXQu2qUtFiUjDE4eFDau9d8fOCAeSwZEFyyHT164vNbtjTv5leseGKAcq1a5jE21rwzX6NG6a16\ndfNYteqJzRf98YcPH67WrVtr3M99J1zXVf/+/TV06NDjg9pLfP3117rtttv0+uuvq2XLlt4vDgFp\n3z4zbWtGhrRqlelaV6mS6R9+3XWmyb1kSmIEr1mzpJdeMmtKjBhhuxr4qx9/lPr3l0aPlm691XY1\n8BdHj0rdu5upn4cMsV0NziYuLi5O0jc+aRn5mbtrl+k+c/IWHS2VjHeuWdM0vV5yibkpj401XX9i\nY82qq3Xr+nbaUNc1XW1ODg/79pnuUDt2mBulk2dJKtlODheVK5t/R0aefsDyyR+XjDWoV88ECn/3\nzjvv6I477tCMGTOOT+377rvv6ptvvlHUKf1s1q5dq7i4OGVmZqpDhw6WKkagycqS3n9fmjvXdOer\nXVu66SbTV7xLl+AfjxOKpkwx44qefNJ0wQHO5tZbzXi0b79lUgwYy5aZMPL556aLN/yaR5ogzimM\nnG7nTz+ZcQFZWWY2nqwssxUXS6mpJhA0b27mlnccqU8fM0PCZZeZ8REtWpgb/ipVzFahgvmFFB5u\nblRiY80YiZLBzwUF5tx795pzHz5sxkXUqmWuERNj+iUfPGjGImRk/LLm1q3NOU8OESVB4tR9UVEm\nRFWuXP4vsj+bPn26pk6dqpycHLVr104vvPCCrrjiil8cRxjB+dqwwYSSN94w44qaNJFuucXcjLRu\nbbs6eMLUqdIjj0gTJ5oZtIBfs3Kl1LmztGCBGZcGPPOM2fbvJ6AGAP8II2dTWGiCQsn6Brt3m1aG\n7dtNMNm61bxTeuyYCRnh4ebRdU3wKBmM/f33J2ZZchzTBWrPHtO1yXXNc02bmmBy4YXmHJGRJphU\nrmyuUaeOeaxd27Tg8A1+bggj8JTiYjNTyty50jvvmD84bduaUJKUxKrcgeovfzGzZT3+uJlBK9C7\n7MI3XNe0ltaubSY8ABITzUQ+n3xiuxKUgf+HEQQPwgi8IT9f+u9/TTD58EMpLs60ct5/v5l9iW5c\ngeFvfzP9ux97TJo8mSCCc/PKK2Zs0ZYt5g1FhK7iYtNLZfRounkGCI/8tudPPcrknXfekSRdddVV\n6tSpk1avXm25IgSDihXNomdvv22mbh4xQvrhB7PAYsuW0vPPm2mtg9GkSZMUFhZWamsVgAsu/P3v\nJoj8/vcEEZTPzTebiVxmzSrf5y9fvlzXX3+9GjZsqLCwMH344Ye/OGbixImKjY1V1apV1bt3b2Vl\nZZ1n1fCGb74xreWsL+I/fu3ny3Gc2Y7jFJ+yLTqXaxBG8KvefvttTZs2TZI0d+5cXX755UpISNCe\nPXssV4ZgEhkpDR9uxnwtX27WqnnoITMJxqhRZpa6YNO6dWvl5OQoOztb2dnZSk1NtV3SOXnuOWns\nWDNO5I9/JIigfKpXN+PHXnnFdO8+V3l5eWrXrp2mT58u5zTfhFOmTNGLL76omTNnKiMjQ9WqVVNC\nQoLy8/M9UD08KS3NtIh37Gi7EpT4tZ+vn30kKVpSzM9b0jldxHXdsm4IUR07dnSHDh3qSnIzMzPd\n4uJit2HDhu6UKVNsl4Ygt2OH606c6LrR0a4ruW7Pnq77wQeuW1hou7Lz9+STT7rt27e3XUa5Pf+8\n+T8ZN851i4ttV4NAl5lpvp8+/PD8zuM4jjt//vxS+xo0aOD+7W9/O/7vgwcPupUrV3bffvvt87sY\nPG74cNcN4F+LQe80P1+SNFvSe27Z88QvNlpGcFYFBQXKzMxUfHz88X2O46hXr15KL5nTGfCShg3N\nrEzbtkmvv25m4LvhBunii83MTXv32q7w/GzevFkNGzbUxRdfrNtuu03ff/+97ZJ+VVGRNGHCiXEi\nU6bQIoLz16GD2WbO9Ox5t27dquzsbPXs2fP4vsjISHXs2JG/YX4oLY0uWgGqh+M4OY7jfOM4znTH\nceqcyycTRnBWe/bsUVFRkerUKf19FR0drezsbEtVIdRUqmRm20pPl1avNnPQT5hgFlu96y7piy9s\nV3juOnXqpFdffVUff/yxZsyYoa1bt+rqq69WXl6e7dLOaNcuM7HAn/5kumc9+yxBBJ5z993SokVm\nHTBPyc7OluM4io6OLrWfv2H+JyfHLA1BGAk4H0kaJulaSeMldZe0yDlLn65TEUYABJQrrpBee83c\nsEyYYKZ/bN9e6trVTBVcUGC7wrJJSEjQoEGD1Lp1a/Xu3VuLFi3S/v37j08W4W9SUszX+euvzccP\nPEAQgWclJZnp+Ms7kB2BbdUqqVMnwkigcV33Hdd1/+O67leu634oKVFSvKQeZT0HYQRnVa9ePYWH\nh2vfvn2l9ufk5CgmJsZSVYBZkPSxx8x6Re++a9YlevFFs+bQn/8snfIt6/dq1qypZs2a+d0sP0VF\nZjX13r2lNm1MK1SPHrarQjCKjDSB5JVXzPedJ8TExMh1XeXk5JTaz98w/5OcLP34I2tNBTrXdbdK\n2iPpkrJ+DmEEZ1WhQgXFxcUp46Sl7F3XVUpKiq666iqLlQFGRIQ0aJC0ZIkJIwkJ5ua5USPp//7P\nTBUZCA4dOqSsrCw1aNDAdinHZWebEPL002bszn//K53S2wXwqBEjzMLInlrwrmnTpoqJiVFKSsrx\nfbm5uVq1ahV/w/zM4sXStdfargLny3GcRpLqStpV1s8hjOBXPfjgg3r//fclmcGA9957rw4fPqw7\n7rjDbmHAKdq2Ne+qbt9u1r14/32zXkm/fubmpuxrvHrfuHHjtGzZMm3btk0rVqzQwIEDVaFCBSUl\nnduMiN6yeLHUrp3plvXpp6ZLXHi47aoQ7OLjzc/xuazGnpeXp3Xr1umLnwePbdmyRevWrTs+IcSY\nMWM0efJkLViwQOvXr9ewYcPUqFEjDRgwwBsvAeWwa5e0cSNhxB+d7efLcZxqjuNMdRyno+M4FziO\n01PSB5K+lfRxmS9yDlNvIYQ98sgjriS3UqVKbqdOndzVq1fbLgn4VUePuu5rr7luu3Zm2tBWrVx3\n5kzXPXzYdmWuO3ToULdhw4Zu5cqV3caNG7tJSUnuli1bbJflFha67pNPuq7jmKmUs7NtV4RQ8+KL\nrhsR4bo7d5bt+CVLlriO47hhYWGltjvvvPP4MU888YTboEEDt0qVKm6fPn3czZs3e6l6lMfcueZ3\nNL9v/M/Zfr4kVZb0X0nZko5K2iLpH5Ki3HOY2tdxy/5WoR+9pwhfW7t2reLi4pSZmakOHTrYLgc4\nJ65rFlKcNk2aP1+qU0e65x6zmGJsrO3q/EdOjpm1bPFi09XtD3+gNQS+d+CA+bmcMMG0cCL4/e53\nZgD7+vW2K8E58sg0JnTTAhD0HEe6+mrTbSsrS7r9dumFF6QLLpBuu01as8Z2hfZ99pnplrVhg+mW\nNXEiQQR21KolDRki/fOfUnGx7WrgC4wXCW2EEQAh5aKLTAvJjh3SX/4irVhhgsrVV0szZph3ZUPJ\nzp3SuHFSr17SZZeZ2bK4KYBtI0ZIW7aYm1QEt61bzcbvndBFGAEQkiIjpdGjpc2bpXnzzL9HjZIa\nNDBdlT79NLjfld20yXSNaNrUrHr9//6f9PHHErOdwh9cdZXUqtW5DWRHYFq8WAoLM4vZIjQRRgCE\ntPBw6brrpP/8R/r+ezNWIjPTTGnbtKn0xBPmXbtgsXq1NHiwmWVs4UIzbe/27SaY0C0L/sJxTOvI\n+++btScQvBYvluLiTPc8hCbCCAD8LDZWeuQRM51tWprUp4/p0nXRRdI110hz5kh5ebarPHeua1p6\nevUyU6euW2daQrZulcaPl2rWtF0h8Eu3327eMX/tNduVwFtcl/EiIIwAwC84jukm8vLLZv77OXPM\nvuHDTTeuESPM7FyeWiXaW4qKpH//W7riCtPSs3+/9M47ZiHIESOkypVtVwicWd26ZkHTl1/2rzWC\n4Dlff20WVyWMhDbCCACcRbVq5h3axYvNgNqxY80Cio8/LtWrZ26Wpk+Xvv3Wf26Yjh4140BatDCz\nEtWuLSUnm1nDbrqJ7lgIHHffbX62li2zXQm8YfFiqUIFqUsX25XAJtYZQZmwzghwQnGxlJFhBnx/\n+qm0cqVUWCg1biz17Gm6Q/Xs6dvB4EVFZiaslBTTtSwnR7rxRtPt7MorfVcH4Emua0L1FVdIc+fa\nrgaeduON0t690tKltitBObHOCADYEBYmdepkBrcvXy7t22cGgw8eLK1da9YuadBAat1aGjNG+vBD\n0xXBky0nRUVmoP1f/yr95jdmIccrrjAzgyUmmq5Y775LEEFgKxnIPm+euWlF8CgqkpYsoYsWaBlB\nGdEyApRdTo7pfpCSYrpH1a0rff656S512WVSmzam1aRRI6lhQ/N8jRpSlSqmy0JYmPlDfeSIdOiQ\nGeuxa5f0v/+ZqYi//dYct3y5+ZyrrpJ69DDblVdKlSrZ/goAnvPjj+bnZOpUE+4RHDIzzRsoy5ZJ\n3brZrgbl5JGWkQhPnAQAcEJ0tJSUZDbXlbZtM12ovvrKtFhkZpqAsXmz1LatCRwXX2wCSXi4GVie\nl2e6g+XnS3v2mM+LiJCaNzdb587Sn/5E+EDwi4oya/+kp5u1gRyP3P7AtsWLzZspHTvargS2EUYA\nwIscR7rwQrPdcEPp544dM60oe/eaQHL0qAkfEREmiFSpIlWvblpUoqPNx0AoSkqSEhKkBx/k5jVY\nLF5sWkQqVrRdCWwjjACAJZUqSU2amA3AmfXsaX5OXnmFMBIM8vNNN9OJE21XgnOxZ88etWnTRqNH\nj9ajjz4qSXIc5ypJn0nq67ruZ+U5LwPYAQCAXwsPl+64Q3rrrcBceBSlZWSY/0cGrweWevXqadas\nWXriiSe0du1aOY5TXdIcSc+XN4hIhBEAABAA7rxT+uknM0scAtvixVLNmlL79rYrwbm67rrrdPfd\nd+uWW26RpBmSDkl67HzOSRgBAAB+78ILTXetWbNsV4LztXixmf2PBVgD07PPPqvCwkJJGizpFtd1\nC87nfIQRAAAQEH77WzMV7ObNtitBeR0+bGZG69nTdiUor6ysLO3cuVMyOaLp+Z6PMAIAAALCwIFS\nrQ3x/pQAABX4SURBVFrS7Nm2K0F5paWZAeyMFwlMBQUFuv322zV06FBJmiDpFcdx6p3POQkjAAAg\nIFSpIt1yi/Tqq5LpJYJAs3ixVL++1KqV7UpQHo899phyc3P1wgsvSNJUSZskndfbA4QRAAAQMO66\nS9q1S/r4Y9uVoDwWLzatIixeGXiWLl2q559/Xq+//rqqVasm13VdScMkdXUc557ynpd1RgAAQMBo\n3166/HKz5kj//rarwbk4eFBas0YaMcJ2JSiP7t2769ixY6X2ua67TVLt8zkvLSMAACBgOI5pHVmw\nQNq923Y1OBdLl0rFxYwXQWmEEQAAEFBuuUUKC5Nef912JTgXixdLF1wgNT3v+ZcQTAgjAAAgoNSt\na2bWeuX/t3fnwVHWhx/H35sEBVMm3ERa5fBAKWkrKIiOUWiHWKznUFp0oqBouQQpKIOCx0CDGAes\nHWxpQQ7hV4TWoz86NbQNYNVfCgWHqAhqPYrVoFhLKYrm2N8fD0RAjgCbfLO779fMDmSfZ3c/O8Rx\nP/t8j3kQj4dOo7pyvogOxjIiSZKSzo03wqZNsHZt6CSqiw8+gJdecn8RfZllRJIkJZ1vfxtOPTW6\nOqLGb9Wq6M++fcPmUONjGZEkSUknMxOGDIGlS2HXrtBpdCSlpXDWWdChQ+gkamwsI5IkKSkNGQI7\nd8JvfhM6iY5k73wR6UCWEUmSlJQ6d46Gaz36aOgkOpx//APeeMP5Ijo4y4gkSUpaN94Izz4Lr78e\nOokOpbQ0WkHr4otDJ1FjZBmRJElJ6+qroUULmD8/dBIdSmkpfOtb0ZLM0oEsI5IkKWk1axZtgrhg\nAVRVhU6jA8XjzhfR4VlGJElSUrvpJnj/fXjmmdBJdKDXXoN//tMyokOzjEiSpKR2zjkwaBAsWhQ6\niQ5UWgpZWXDRRaGTqLGyjEiSpKQWi0Ufdp98ErZtC51G+yothV69oHnz0EnUWFlGUlCnTp3IyMio\nvWVmZvLAAw/sd87WrVu57LLLyM7OJjc3lzvuuIOamppAiSVJOj7XXRdthOjVkcajpibaed0hWjqc\nrNABlHixWIxp06Zx8803E4/HAWi+z1cSNTU1DBgwgA4dOlBWVsZ7771HYWEhJ5xwAtOmTQsVW5Kk\nY9ayJQwcCHPnwoQJ0dUShVVeDh99ZBnR4XllJEV95StfoW3btrRr14527drRrFmz2mMlJSVs3ryZ\nJUuWkJeXR0FBAVOnTmX27NlUuRSJJClJDRsWTZh+7rnQSQTREK2mTaFPn9BJ1JhZRlLU/fffT5s2\nbejRowcPPvgg1dXVtcfKysrIy8ujTZs2tfcVFBSwY8cOXnnllRBxJUk6bhdfDKefHl0dUXilpXDh\nhVEhkQ7FMpKCxo4dy9KlS1m9ejXDhw+nqKiIiRMn1h6vqKigffv2+z1m788VFRUNmlWSpESJxaJl\nfpcvh3//O3Sa9FZZCWvWOERLR2YZSRKTJk3ab1L6gbfMzExee+01AG677Tby8/Pp3r07t9xyCzNn\nzuRnP/sZlZWVgd+FJEn164Yb4PPP4de/Dp0kvf3tb/Df/1pGdGROYE8SEyZMYOjQoYc9p0uXLge9\nv1evXlRVVfH2229zxhlnkJuby7p16/Y7Z9uetRBzc3MP+xrjxo0jJydnv/sGDx7M4MGDj/QWJEmq\ndyefDJddFg3VGjEidJr0VVoaLed77rmhk6ixs4wkidatW9O6detjeuyLL75IRkYG7dq1A6BPnz4U\nFRWxffv22nkjK1euJCcnh27duh32uWbNmkWPHj2OKYckSQ1h2DC44grYsAH8X1YYpaXRHJ4sP2nq\nCBymlWLKysr46U9/Snl5OW+99RZLlizhxz/+MYWFhbVXNPr370+3bt0oLCykvLyckpISpkyZwujR\no2nSpEngdyBJ0vH57nejKyTz5oVOkp5274bnn3eIlurGMpJiTjzxRJYuXcoll1xC9+7dmT59OuPH\nj2fOnDm152RkZLBixQoyMzO54IILuP766xkyZAj33XdfwOSSJCVGVhYMHQpLlsAnn4ROk35eeAGa\nNbOMqG5iezfFq4M6n6jUs2HDBnr27Mn69esdpiVJavT+/vdomd9Fi6CwMHSa9HLrrbBiRfRvkOHX\n3qksIVuL+isiSZJSzmmnRd/Mu+dIw6quht/+Fq66yiKiuvHXRJIkpaRhw+DZZ6Nd2dUwnn8e3n8f\nBg0KnUTJwjIiSZJS0tVXQ8uWTmRvSMuXw9e+Br17h06iZGEZkSRJKalp02i+yIIF0Y7gql/V1fCb\n38D3v+8QLdWdvyqSJCll3XQTfPAB/P73oZOkvueeg4qKqIxIdWUZkSRJKesb34BevZzI3hCWL4dT\nTnGIlo6OZUSSJKW0YcPgD3+Ad98NnSR17R2iNXCgQ7R0dPx1kSRJKe2HP4w24VuwIHSS1PXcc7Bt\nm6to6ehZRiRJUkpr3jz6kLx0KdTUhE6TmpYtc4iWjo1lRJIkpbzhw+HNN6GkJHSS1LN3o8Pvfx9i\nCdmTW+nEMiJJklLeeedB167w85+HTpJ6/vKXaIiWq2jpWFhGJElSyovFYORIWLEC3n47dJrUsnw5\nnHqqQ7R0bCwjkiQpLVx7bTR/5Je/DJ0kdewdojVwoEO0dGwsI5IkKS1kZ8OQIdGeI599FjpNatg7\nRMtVtHSsLCOSJCltDB8OH34YfZuv47dsWTREq1ev0EmUrCwjkiQpbZx9NvTtC488EjpJ8nMVLSWC\nZUSSJKWVkSPh+eehvDx0kuT27LPwwQcO0dLxsYxIkqS0cuWVcPLJLvN7vJYvh44do2WTpWNlGZEk\nSWmlSRO45RZ47DH4z39Cp0lODtFSolhGJElS2rn5Zti9OyokOnp7h2i50aGOl2VEkiSlna9+Fa66\nKprIHo+HTpN8li1ziJYSwzIiSZLS0ogRsGlT9C2/6q6qCp54wiFaSgzLiCRJSkv9+kHXri7ze7Rc\nRUuJZBmRJElpKRaLro488QRUVIROkzyWL4dOneDcc0MnUSqwjEiSpLR1ww3R6lpz54ZOkhyqqlxF\nS4llGZEkSWmrRQu47jqYMyf6oK3DW7MGPvzQVbSUOJYRSZKU1kaMgHffhRUrQidp/ByipUSzjEiS\npLTWo0c0XGv+/NBJGjeHaKk+WEYkSVLau/xy+N3v4K9/DZ2k8VqzBrZvdxUtJZZlRJIkpb2rroIz\nzoAZM0InabyWLYuGaPXsGTqJUollRJIkpb3MTLj9dnjqKdiyJXSaxmfvRoeDBjlES4llGZEkSQIK\nC6F9e3jwwdBJGp/Vq6MhWq6ipUSzjEiSJAFNm8Jtt8GiRfD++6HTNC7Ll0Pnzg7RUuJZRiRJkvYY\nPhxOPBEeeih0ksbDIVqqT5YRSZKkPXJyokLyi1/Ajh2h0zQODtFSfbKMSJIk7eO222D37qiQKFpF\nq0uXaD8WKdEsI5IkSfvo0CGazP7QQ1EpSWd7h2i50aHqi2VEkiTpALffDtu2wWOPhU4S1qpV8NFH\nbnSo+mMZkSRJOkDXrtFGiMXFUF0dOk04y5dHQ7TOOSd0EqUqy4gkSdJBTJwIr78OTz8dOkkYlZWu\noqX6ZxmRJEk6iN694eKLYcYMiMdDp2l4q1dHQ7RcRUv1yTIiSZJ0CBMnwtq1sGZN6CQNb9kyOO00\nh2ipfllGJEmSDuHSSyEvL7o6kk4qK+HJJ11FS/XPMiJJknQIsRjccQc88wxs3Bg6TcMpKXEVLTUM\ny4gkSdJh/OAHcOqp8MADoZM0nJkz4cor4VvfCp1Eqc4yIkmSdBhNmsD48fD44/D226HT1L8//Sna\nX2ToUIdoqf5ZRiRJko7gppugRQt48MHQSepXPA533gnnnw9XXBE6jdKBZSTJFBUVceGFF5KdnU2r\nVq0Oes7WrVu57LLLyM7OJjc3lzvuuIOampr9zikvLyc/P59mzZrRsWNHiouLGyK+JElJKTsbpk2D\npUvh1VdDp6k/Tz0F69ZBUZFXRdQwLCNJprKykkGDBjFixIiDHq+pqWHAgAFUVVVRVlbGwoULWbBg\nAXfffXftOTt37qSgoIDOnTuzYcMGiouLuffee5k7d25DvQ1JkpLOkCHQsiWMHJma+45UV8PkyfCd\n70DfvqHTKF1YRpLMPffcw9ixY8nLyzvo8ZKSEjZv3sySJUvIy8ujoKCAqVOnMnv2bKqqqgBYvHgx\nlZWVzJs3j7PPPptBgwYxZswYZs6c2ZBvRZKkpNK0KcyeHW0GuGRJ6DSJt3gxbNoUXRWRGoplJMWU\nlZWRl5dHmzZtau8rKChgx44dvPLKK7Xn5Ofnk5WVtd85W7ZsYceOHQ2eWZKkZNG/f7Tc7fjx8PHH\nodMkzmefwT33wDXXwHnnhU6jdGIZSTEVFRW0b99+v/v2/lxRUVHncyRJ0sHNmgWffgp33RU6SeL8\n6lewdStMnRo6idKNZaQRmDRpEhkZGYe8ZWZm8tprr4WOKUmSgA4dosnsv/gFrF0bOs3x27Urej+F\nhdCtW+g0SjdZRz5F9W3ChAkMHTr0sOd06dKlTs+Vm5vLunXr9rtv27Zttcf2/rn3vkOdcyjjxo0j\nJydnv/sGDx7M4MGD65RPkqRUMHIkLFgAw4dHhSQriT9RPfww/OtfcO+9oZMoHSXxfzqpo3Xr1rRu\n3Tohz9WnTx+KiorYvn177byRlStXkpOTQ7c9X3f06dOHyZMnU11dTWZmZu05Xbt2/VLRONCsWbPo\n0aNHQrJKkpSssrKiKyPnnw+PPAJjxoROdGw+/jjaWf5HP4JOnUKnUTpymFaS2bp1Kxs3buSdd96h\nurqajRs3snHjRnbt2gVA//796datG4WFhZSXl1NSUsKUKVMYPXo0TZo0AeDaa6/lhBNO4MYbb2TT\npk08/vjjPPzww4wfPz7kW5MkKan06hV9iJ88Gd57L3SaY1NcDJ9/nlrzX5RcYvG6L5SdgitqJ5+h\nQ4eyaNGiL92/atUq8vPzgaiwjBgxgtWrV5Odnc2QIUOYPn06GRlfdM+XX36ZUaNGsW7dOtq0acOY\nMWOYMGHCIV93w4YN9OzZk/Xr13tlRJKkPT7+GM46K9qXY+nS0GmOTkUFnHYajB3rcr46JgnZFtMy\nojqxjEiSdHCLF0eTv0tKoqV/k8Xo0dF+KW++GW3mKB2lhJQRh2lJkiQdh+uui66MjBoFu3eHTlM3\nb70Fv/wlTJxoEVFYlhFJkqTjEItFk9jfeQfuvz90mrq5915o1QpuvTV0EqU7y4gkSdJxOussuP12\nmD4dXn89dJrDe+UVeOwxmDIFsrNDp1G6s4xIkiQlwF13RRsijhoFdZ+S2/CmTIGOHeHmm0MnkSwj\nkiRJCXHSSTB7Nvzxj/D446HTHNzatfDkk3DffXDCCaHTSJYRSZKkhBkwAK65BsaNgx07Qqf5sjvv\nhK9/PZp0LzUGlhFJkqQEeugh2LkzGg7VmPz5z9Ft2jTIzAydRopYRiRJkhLolFOiYVCzZ8P69aHT\nROLx6KpIr15w5ZWh00hfsIxIkiQl2Jgx0L07DB8O1dWh08DTT0fzRYqKoqWIpcbCMiJJkpRgTZrA\nz38Of/tbtAdJSNXVMHky9OsH3/522CzSgSwjkiRJ9eCCC6LNBWfOhHnzwmSoro6WGm7TJroqIjU2\nWaEDSJIkpao774T334dhw+Dll6G4GLIa6NPXp59Gq2Y9/TTMmQO9ezfM60pHwzIiSZJUT/YO18rL\ng7Fj4dVXYelSaNGifl/3o4/g8sth48aojHzve/X7etKxcpiWJElSPYrFoqFSzzwDf/0rnH8+vP56\n/b3eW29FQ8TeeANWrbKIqHGzjEiSJDWA73wnKiMQDZn6058S/xrr10dlp6YGXnghWspXaswsI5Ik\nSQ3kzDOhrAzOOw8uvTTaiyRR/vAHuPhi6NQpKiKnn56455bqi2VEkiSpAbVoAb//Pdx6K4weDSNH\nQmXl8T3no49Gc0T69YPSUmjbNjFZpfpmGZEkSWpgWVkwaxb86lcwdy4UFESTzo9WPB7t9n7TTdGK\nXU88AdnZic8r1RfLiCRJUiDDhkVzR156KZpHsmlT3R9bVQW33BLtZfKTn0SrdjXUssFSolhGJEmS\nAsrPh7VroVmzaPL5U09FVzwOZ+tWuOIKWLAAFi6M9jOJxRokrpRQ9mdJkqTAOneOJp1fdx088ACM\nGxcN3broIsjNhYwM2LUr2jdk1aro1rdvNPekf//Q6aVjZxmRJElqBJo3j66KrFkTzf14/nnYvBna\ntYvKyCefwOrVcPXV0SpcAwdCmzahU0vHxzIiSZLUSGRkRFc8+vaNft65E957Dz7/HFq3/uIqiZQq\nLCOSJEmNVPPm0LVr6BRS/bFbS5IkSQrCMiJJkiQpCMuIJEmSpCAsI5IkSZKCsIxIkiRJCsIyIkmS\nJCkIy4gkSZKkICwjkiRJkoKwjEiSJEkKwjIiSZIkKQjLiCRJkqQgLCOSJEmSgrCMSJIkSQrCMiJJ\nkiQpCMuIJEmSpCAsI5IkSZKCsIxIkiRJCsIyIkmSJCkIy4gkSZKkICwjkiRJkoKwjEiSJEkKwjIi\nSZIkKQjLiCRJkqQgLCNJpqioiAsvvJDs7GxatWp10HMyMjL2u2VmZrJs2bL9zikvLyc/P59mzZrR\nsWNHiouLGyK+JEmSVCsrdAAdncrKSgYNGkSfPn149NFHD3newoULufTSS4nH4wC0aNGi9tjOnTsp\nKCigf//+zJkzh5deeomhQ4fSsmVLhg0bVu/vQZIkSQLLSNK55557gKhsHE5OTg5t27Y96LHFixdT\nWVnJvHnzyMrK4uyzz+bFF19k5syZlhFJkiQ1GIdppahRo0bRtm1bevfuzfz58/c7VlZWRn5+PllZ\nX3TRgoICtmzZwo4dOxo6qiRJktKUV0ZS0NSpU+nXrx8nnXQSK1euZOTIkezatYvRo0cDUFFRQZcu\nXfZ7TPv27WuP5eTkNHhmSZIkpR/LSCMwadIkZsyYccjjsViMV199lTPPPLNOz3fXXXfV/v2b3/wm\nu3btori4uLaMSJIkSY1BbO8EZ4UTi8VaA62PcNqb8Xi8ap/H3ADMisfjB19Sa//nHwD8L9A0Ho9X\nxmKxhUDzeDx+zT7nXAL8GWgVj8e/NFYrFov1ANYDzwIHHv91PB7/9ZFySJIkSfvyykgjEI/HPwI+\nqseXOAf4OB6PV+75+f+AabFYLDMej1fvua8/sOVgRWSPzUBPYHM8Hv+kHrNKkiQpTVhGkkwsFjsF\naAV0BDJjsdg39xx6Ix6P74rFYt8D2gNlwG6ikjEJeGCfp/kf4G7g0VgsNgPIA8YAYw/1unsKyIYE\nvx1JkiSlMYdpJZlYLDYfuP4gh/rG4/FnY7FYATAdOA2IAW8Aj8Tj8bkHPE93YDZwHrAdeDgejz9Y\nr+ElSZKkfVhGJEmSJAXhPiOSJEmSgrCMSJIkSQrCMiJJkiQpCMuIJEmSpCAsI5IkSZKCsIxIkiRJ\nCsIyIkmSJCkIy4gkSZKkICwjkiRJkoKwjEiSJEkKwjIiSZIkKQjLiCRJkqQg/h9SwhFGrxfXIgAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9d00bd14e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f9d00be0a58>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.plotting import plot\n",
    "plot(sin_square, (x, -3, 15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interaktive Funktionen\n",
    "\n",
    "`@interact` führt eine Funktion mit interaktiven Argumenten (`a` und `b`) aus.\n",
    "`a = (0, 20, .1)` definiert, dass der Slider von `0` bis `20` mit Schrittweite `0.1` gehen soll.\n",
    "Das `a = 10` in der Funktion `damped_oscillation` selbst ist der initiale default Wert,\n",
    "den der Slider am Anfang bekommen soll."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fBgYOBGrUAFq1AmbNCnpURERERERmxFwAAzAcwDit9bta69UAbgNwEMAtZdwuU2u90/rn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\n6sljyI8A40UAsxpI+DUNcc8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07LOFRYKWLeU517GjBO7UVPngLtrXWasRy5Yt8jOsXSuh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\nAACO/H/84PSOMHxKEgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9d0094c9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.html.widgets import interact\n",
    "from sympy.abc import x\n",
    "from sympy import exp, cos\n",
    "from sympy.plotting import plot\n",
    "\n",
    "@interact(a = (0, 20, .1), b = (0, 3, .1))\n",
    "def damped_oscillation(a = 10, b = .5):\n",
    "    f2 = a * exp(-b * x) * cos(a * x) / a\n",
    "    plot(f2, (x, 0, 10), ylim=(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parametrischer Plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Matrix $\\bigl(\\begin{smallmatrix}a&b\\\\ c&d\\end{smallmatrix} \\bigr)$ beinhaltet die Parameter,\n",
    "und wird mit dem von $\\phi$ abhängigen Vektor multipliziert."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(\\phi) := \n",
    "\\begin{pmatrix}\n",
    "a & b \\\\ c & d\n",
    "\\end{pmatrix}\n",
    "\\cdot \\log(1+\\phi)\n",
    "\\begin{pmatrix}\n",
    "\\sin(\\phi) \\\\ \\cos(\\phi)\n",
    "\\end{pmatrix}\n",
    "\\qquad \\phi \\in [0,\\,8 \\pi]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6OjrD16Oios7axdmrVy+9jyC8j+HDo9GsGe+SLV0KlC0bhYED3fE+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\nMtapg3rhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9d00ae62e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.html.widgets import interact\n",
    "import numpy as np\n",
    "\n",
    "@interact(a=(-2, 2, .1), b =(-2, 2, .1), c=(-2, 2, .1), d=(-2, 2, .1))\n",
    "def elliptic_plot(a = 1., b = 0, c = 0, d = -1):\n",
    "    phi = np.linspace(0, 8 * np.pi, 1000)\n",
    "    m = np.array([[a, b],\n",
    "                  [c, d]])\n",
    "    v = np.c_[np.sin(phi), \n",
    "              np.cos(phi)].T\n",
    "    r = np.log1p(phi)\n",
    "    \n",
    "    xx, yy = m.dot(r * v)\n",
    "    \n",
    "    plt.plot(xx, yy)\n",
    "    plt.grid()\n",
    "    plt.ylim(-4, 4)\n",
    "    plt.xlim(-4, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Gauss](https://docs.python.org/2/library/random.html#random.gauss)-Glocke für $\\mu = 2$ und $\\sigma = .5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from random import gauss\n",
    "data = [gauss(2, .5) for i in range(10000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAIAOwhMAAEAH4QkAAKCD8AQAANBBeAIAAOggPAEAAHQQngAAADoITwAAAB2EJwAAgA7C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\nAAA6CE8AAAAdhCcAAIAO/z+ahGlWvAyU/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9d02dbbb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(data, 20, color=\"grey\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Anaconda (Python 3)",
   "language": "python",
   "name": "anaconda3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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