{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "902e4b59-77b9-4db6-9ec2-3cff55766dd5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:28:45.280232Z",
     "start_time": "2026-03-14T20:28:45.240030Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5j\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def abs(c):\n",
    "    return (c.real**2 + c.imag**2)**0.5\n",
    "\n",
    "def add(c1, c2):\n",
    "    return complex(c1.real + c2.real, c1.imag + c2.imag)\n",
    "\n",
    "def sub(c1, c2):\n",
    "    # (a+bi) - (c+di) = (a-c) + (b-d)i\n",
    "    return complex(c1.real - c2.real, c1.imag - c2.imag)\n",
    "\n",
    "def mul(c1, c2):\n",
    "    # (a+bi)(c+di) = (ac-bd) + (ad+bc)i\n",
    "    return complex(c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c1.imag * c2.real)\n",
    "\n",
    "\n",
    "\n",
    "print(mul(1+2j, 2+1j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3fb82de2-875a-4dac-935a-e64bad48c895",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:28:45.320152Z",
     "start_time": "2026-03-14T20:28:45.281685Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5, 5)\n"
     ]
    }
   ],
   "source": [
    "def add(v1, v2):\n",
    "    return (v1[0] + v2[0], v1[1] + v2[1])\n",
    "\n",
    "def sub(v1, v2):\n",
    "    return (v1[0] - v2[0], v1[1] - v2[1])\n",
    "\n",
    "\n",
    "\n",
    "print(add((2, 1), (3, 4)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3a562f0e-162b-4760-ac6b-22587bf0bd60",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:28:45.659050Z",
     "start_time": "2026-03-14T20:28:45.349987Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intervall: Interval.Ropen(2, 5)\n",
      "Mengenangabe: (2 <= x) & (x < 5)\n"
     ]
    }
   ],
   "source": [
    "from sympy import Interval, Symbol\n",
    "\n",
    "# 1. Variable definieren\n",
    "x = Symbol('x')\n",
    "\n",
    "# 2. Intervall erstellen (z.B. [2, 5) - links abgeschlossen, rechts offen)\n",
    "# left_open=False (Standard) bedeutet inklusive 2, right_open=True bedeutet exklusive 5\n",
    "mein_intervall = Interval(2, 5, left_open=False, right_open=True)\n",
    "\n",
    "# 3. In Mengenangabe / Ungleichung umwandeln\n",
    "mengen_angabe = mein_intervall.as_relational(x)\n",
    "\n",
    "print(f\"Intervall: {mein_intervall}\")\n",
    "print(f\"Mengenangabe: {mengen_angabe}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5f024814-9f83-4d5f-a81f-4283e47e22b9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:28:45.760535Z",
     "start_time": "2026-03-14T20:28:45.660677Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interval.Ropen(2, 5)\n"
     ]
    }
   ],
   "source": [
    "from sympy import Symbol, And\n",
    "\n",
    "x = Symbol('x')\n",
    "\n",
    "# Eine Mengenangabe als logische Verknüpfung (2 <= x < 5)\n",
    "mengen_angabe = And(x >= 2, x < 5)\n",
    "\n",
    "# Umwandlung in ein Intervall-Objekt\n",
    "intervall = mengen_angabe.as_set()\n",
    "\n",
    "print(intervall) \n",
    "# Ausgabe: [2, 5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b58b7c16-2c79-46a4-bde0-1d8fcc16cfa9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:28:45.791872Z",
     "start_time": "2026-03-14T20:28:45.765958Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interval(-2, 2)\n"
     ]
    }
   ],
   "source": [
    "from sympy import Symbol, solve_univariate_inequality\n",
    "\n",
    "x = Symbol('x')\n",
    "\n",
    "# Eine Ungleichung definieren\n",
    "ungleichung = x**2 <= 4\n",
    "\n",
    "# Lösen und als Intervall ausgeben lassen (relational=False)\n",
    "intervall = solve_univariate_inequality(ungleichung, x, relational=False)\n",
    "\n",
    "print(intervall)\n",
    "# Ausgabe: [-2, 2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dd0522d3-0612-44f1-9504-1ba48542e37e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:28:45.850425Z",
     "start_time": "2026-03-14T20:28:45.792950Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interval.open(-8, 8)\n"
     ]
    }
   ],
   "source": [
    "from sympy import Symbol, solve_univariate_inequality, Abs\n",
    "\n",
    "# 1. Symbol als reell definieren\n",
    "x = Symbol('x', real=True)\n",
    "\n",
    "# 2. Die SymPy-eigene Funktion Abs() verwenden\n",
    "# Das verhindert, dass Python-Interne Funktionen dazwischenfunken\n",
    "ungleichung = Abs(x) < 8\n",
    "\n",
    "# 3. Lösen\n",
    "intervall = solve_univariate_inequality(ungleichung, x, relational=False)\n",
    "\n",
    "print(intervall)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99ed5f78-8032-40eb-99ce-988de647549b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:30:39.429411Z",
     "start_time": "2026-03-14T20:30:39.352620Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sympy import Interval\n",
    "\n",
    "def plot_interval(intervall, x_range=(0, 10)):\n",
    "    fig, ax = plt.subplots(figsize=(8, 2))\n",
    "\n",
    "    # Zahlenstrahl-Optik\n",
    "    ax.set_xlim(x_range)\n",
    "    ax.set_ylim(-1, 1)\n",
    "    ax.set_yticks([])\n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.spines['bottom'].set_position('center')\n",
    "\n",
    "    # Start- und Endpunkte extrahieren\n",
    "    start, end = float(intervall.start), float(intervall.end)\n",
    "\n",
    "    # Die Linie für das Intervall zeichnen\n",
    "    ax.plot([start, end], [0, 0], color='blue', lw=4)\n",
    "\n",
    "    # Punkte zeichnen: gefüllt = inklusive, weiß/leer = exklusive\n",
    "    ax.plot(start, 0, 'o', color='blue', mfc='blue' if not intervall.left_open else 'white', markersize=10)\n",
    "    ax.plot(end, 0, 'o', color='blue', mfc='blue' if not intervall.right_open else 'white', markersize=10)\n",
    "\n",
    "    plt.title(f\"Intervall: {intervall}\")\n",
    "    plt.show()\n",
    "\n",
    "# Beispiel: [2, 5)\n",
    "mein_intervall = Interval(2, 5, left_open=False, right_open=True)\n",
    "plot_interval(mein_intervall, x_range=(0, 7))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cdb0080c9d06840a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-14T20:30:39.750872Z",
     "start_time": "2026-03-14T20:30:39.440529Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import symbols, plot_implicit, And\n",
    "\n",
    "x = symbols('x')\n",
    "# Zeichnet den Bereich auf der x-Achse\n",
    "plot_implicit(And(x >= 2, x < 5), (x, 0, 7))\n"
   ]
  }
 ],
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