Mathematik-L-sungen/Mathematik_fuer_Ingenieure_1.ipynb

{
 "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": [
    "from sympy.codegen.ast import none\n",
    "\n",
    "\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",
   "id": "99ed5f78-8032-40eb-99ce-988de647549b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-04-11T08:47:20.948655Z",
     "start_time": "2026-04-11T08:47:20.602288Z"
    }
   },
   "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"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 1
  },
  {
   "cell_type": "code",
   "id": "cdb0080c9d06840a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-04-11T09:11:05.583539Z",
     "start_time": "2026-04-11T09:11:05.524895Z"
    }
   },
   "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))"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 5
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-04-11T09:11:50.029289Z",
     "start_time": "2026-04-11T09:11:49.836426Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sympy import solveset, S, Abs, Ge, Gt, solve_univariate_inequality, oo, Symbol, latex, pprint\n",
    "from sympy.abc import x\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_interval(intervall, x_range=(-10, 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",
    "    # 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",
    "\n",
    "x = Symbol('x', real=True)\n",
    "#solveset(abs(x)<=8, x) # domain=S.Complexes is default\n",
    "a = solveset(Abs(x)<8, x, domain=S.Reals)\n",
    "b = solveset(Ge(x,2), x, domain=S.Reals)\n",
    "print( 2 in b )\n",
    "#b = solve_univariate_inequality(x >= 2, x, relational=False)\n",
    "print(Ge(x,2)) # x>=2\n",
    "print(Ge(2,x)) # x>=2\n",
    "print(Gt(x,2)) # x>2\n",
    "print(\"A= \",latex(a))\n",
    "print(\"B= \",latex(b))\n",
    "pprint(a)\n",
    "pprint(b)\n",
    "pprint(a.union(b)) # # Vereinigung\n",
    "pprint(a.intersect(b)) # Durchschnitt\n",
    "print(a-b)\n",
    "print(b-a)\n",
    "plot_interval(a)\n",
    "plot_interval(b)"
   ],
   "id": "d9cdef9bf7d1bf2e",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "x >= 2\n",
      "2 >= x\n",
      "x > 2\n",
      "A=  \\left(-8, 8\\right)\n",
      "B=  \\left[2, \\infty\\right)\n",
      "(-8, 8)\n",
      "[2, ∞)\n",
      "(-8, ∞)\n",
      "[2, 8)\n",
      "Interval.open(-8, 2)\n",
      "Interval(8, oo)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ],
      "image/png": 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isjf5ckfyer0dAKITJyImym0BABCRtiIyV0QKhmjb+Dn58qKIdBaRJZQYgFQRSAEAaQyji5I/PnJH2C4pub3jIUIpgFQRSAEAUdLT8PtFpEAqYdQbSi+JSAUROUMpAwiLPqQAgCh1Tz5NH00YleTtdPvHKWEAEdFCCgCIkg5YqpbGtgztU7pbRGpQygCyZiAtUqSIq6cGAKRJyeSR9OlVRUROUuZANnXu3LmcGUgTEhLk+HGdIgQAAABZWWJiopw4cSLnTYx/9epVe1m+fPkMT905ibYqHzhwgHKjzKhrWVDOfn9mXAtpzi63jEGZUW6ZXdd8uS3H/lKTHnw4AFFu1LWsi/coZZZcE0Rk5w30Id1HXeP9mWVwXMt6GGUPAIjShHSW1HhKGEBEBFIAQJRmJv8Ck84vGo2k5O1nUcIAsmYgvXLligwZMsRegnKjrmU9vEcps2Bnkn8O1EQRSn2/1NQp1UnxqWvUtcxCXcu6ZcY8pACADPotew2jSyldAKnilD0AII2WJP8caO/kAUteu5PXlyeMAogaLaQAgJswJVSR5JH4TH4PIO0IpAAAAHCKU/YAAADImYH05ZdfllWrVsmFCxfk1KlTIbepWLGiLFy40G5z5MgRGTVqlOTOnTvi45YoUULef/99OXPmjH3cd999VwoVKiQ5UcuWLcUYE3L51a9+FfZ+y5cvD9p+8uTJEkv27NkTVAb9+/ePeJ98+fLJxIkT7U/a6qTJ//znP6VUqVISCypXrmzfS7t375aLFy/Kzp077ajKPHnyRLxfLNa1Xr162fp16dIlWbt2rTRs2DDi9l26dJEtW7bY7Tds2CDt2rWTWDJgwAD55ptv5OzZs/Y4P2/ePKlZs2bE+3Tv3j2oXmn5xYrBgwcH7b/WoUhivZ6FO+7rosf1UGKxnt17772yYMEC+8tLur8dOnQI2mbo0KFy8OBB+1mwdOlSqV69+k0/LoZjMmIZMmSI6d27t/n73/9uTp06FXR7rly5zIYNG8ySJUtM/fr1za9//Wtz9OhRM2zYsIiP++mnn5r169ebRo0amXvuucds377dzJ49O0P2wfWSJ08eU7p0ab9l6tSpZteuXRHvt3z5cjNlyhS/+xUpUsT5/mTmsmfPHjNw4EC/MihYsGDE+7z11ltm37595r777jN33323Wb16tVm5cqXzfcmM5cEHHzTTpk0zDzzwgKlatap55JFHzOHDh83o0aMj3i/W6lrXrl3N5cuXTY8ePcztt99u9/3kyZPmlltuCbl906ZNzbVr10y/fv3MbbfdZl577TVz5coVU6dOHef7klnLZ599Zrp3725q165t6tWrZxYuXGj27t0b8f2o258+fdqvXpUqVcr5vmTWMnjwYLNx40a//U9ISAi7PfXsl3JITEz0K7M2bdoY1bJlS+qZ/FJGmrVef/1107FjR1s2HTp08Cubl156yWa29u3bmzvuuMPMnz/fZo58+fLdtONihCVj31h6YAkVSLVQrl+/7neQ6dmzpz0IaRAL9Vh6QFcNGjTw+yBNSkoyZcuWdX4QyeglPj7eHDlyxAat1ELC2LFjnb9e14H0xRdfjHr7okWL2qDQuXPnlHW1atWy9a1x48bO98fFoiEqmi8/sVTX1q5dayZMmJByPS4uzuzfv9/0798/5PYffvih+eSTT/zWrVmzxkyePNn5vrgMDeree+9N8+dGLAVSbXiJdnvqWehy0WPTjh07qGcSunxCBdKDBw+avn37+n02Xrp0yXTr1u2mHRfDLc76kDZt2lQ2btwoR48eTVn3+eefS7FixaROnTph76On6detW5eybtmyZfLzzz9L48aNJadr3769JCQkyPTp01Pd9rHHHpNjx47ZMh4+fLgUKFBAYo2eKtTT7//73/+kX79+EbuDNGjQQPLmzWvrk8+2bdtk3759tt7FIn0vnjyZ+ojpWKlr2n1B64m3jugpL70ero7oeu/2vuNcrNYpX71SqdWtwoULy969e+XHH3+U+fPnS+3atSWW1KhRw55W3bVrl+2mpl3cwqGehX6//uEPf5Bp06ZFLOdYr2deVatWlbJly/ods7Srzddffx32mJWe42I48eJImTJlbH8iL991vS3cfbwBViUlJdkDW7j75CRPPfWU/TDTg1QkH3zwgQ1S2gekXr16MnLkSKlVq5Z07qy/sBIbxo8fb4Oo1o1mzZrJiBEj7Butb9++IbfX+qO/QqF9kwPrZCzUrUC33nqrPP/88zbIRxJLdS0xMVHi4+NDHrduu+22NB3nYrFOqbi4OBk3bpysXLlSNm/eHHY7/TL45JNP2r6QGmC1Hq5evdo2VqR2/MsJNAD06NHDloMet7RP6YoVK6Ru3bpy/vz5oO2pZ8E6duwoxYsXlxkzZoQt51ivZ4F8x6W0HLPSc1y8KYFUP9S11SkSfQH6T8bNLcfy5cvLgw8+KF27dk21aN95552Uvzdt2iSHDh2SL774QqpVq2YHrcRCuY0dOzZlnbbcXb16VaZMmSJ//etf7d+xIj11rVy5crJ48WL5+OOP7UCnWKxryBiTJk2yoap58+YRt9NBEbr4aEjQATs9e/aUV199Ncf/e/T95z1+aUDVL356/E+txQ//34Dz2Wef2WNSOLFez7KaNAXSMWPGRPy2oaL9EDp8+LA0atTIb13p0qVTbgt3n8BRz3oatmTJkmHvkxWlpxyfeOIJOXHihB0dl1Z6MFM6Ui47h4QbqX9aBnpqoUqVKrJ9+/ag27X+6Ch7/ZbsbSXVOpmd6taNlpm2xujIeT0wP/PMMzFb10LR7h/Xr19POU5FU0d0fVq2z8kmTJggDz/8sLRo0SLNrU9a7uvXr49qtG9OpMckPW6F23/qmb9KlSrJ/fffL5066U/XRi/W69nh5ONS4DFKr3/33Xc37bgYidNBTd5RWE8//bQd1JQ3b96Ig5p0BLRvnY4KjoVBTTq4JLURz+GWZs2a2XLTEXOu98PV8uijj9r6Vrx48YiDmjp16pSyrmbNmjE1qKlcuXJm27Zt5oMPPrCzYKTnMXJ6XdPO++PHj/frvP/TTz9FHNS0YMECv3WrVq2KuUFNOuBBBzlUr149XffX+rhlyxYzZswY5/viYilUqJA5ceKEef7550PeTj0LHhSmg3Ny585NPZO0D2rq06dPynWdNSWaQU1pOS5GWDLmDVSxYkU7ndOgQYPM2bNn7d+66BvLO+3T4sWL7VQgbdu2tSPIvdM+NWzY0B6E9IPSO+3TunXr7G364acfoDl12iff0rp1a1txdNR34G1aNlpGWh56vVq1anYUvob2ypUr2+l7du7cab788kvn+5FZS5MmTewIe61XOoWRhlGtWzNmzAhbbr5pn3Q6mlatWtny0+Cgi+v9yYxFy0OnUFu6dKn92zt1CnXNf3oTPTg//vjj9gvy22+/bac38c0WMnPmTDN8+HC/6XiuXr1qD/D6/tUPylib9mnSpEm2UaJFixZ+9Sp//vwp2wSWm35u+KYgu+uuu+yXpIsXL9opZVzvT2Ys2vig5aXHcK1DOj2iTouoMxRQzyKXnYYhPY6PGDEi6DbqmdgM5stjSqfn1L81s/mmfdJjmmaHunXrmnnz5gVN+7Rs2TLz3HPPRX1cTMOSMW+o6dOnm1C884FVqlTJLFq0yFy4cMG+2fRN6P1Go9sqfVP61pUoUcIGUA252pr63nvvpYTcnLro/oabD1PLxluuFSpUsOHz+PHjtoJoyBg5cmSOnhsycNEPMJ1aRz8E9UNs8+bNZsCAAX4t74Hlpou+4SZOnGhbIs6fP2/mzp3rF8hy8qJnMsKhrvmXlR6I9QNP593TlgGdE9k7DZYe+7zbd+nSxWzdutVur3NLtmvXzvn/OzOXcLTOhSu3N998M6WMDx06ZOcuvfPOO53vS2Ytc+bMMQcOHLD7ry1Nel0bG6hnqZedfpFRNWrUCLqNeiYpuSqQ9/03dOhQ+77TDKGNFIFlqdMq6pfraI+L0S78lj0AAACc4rfsAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAADgFIEUAAAAThFIAQAA4BSBFAAAAE4RSAEAAOAUgRQAAABOEUgBAAAgLv0fbmsvLEgyRPYAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-04-11T09:12:20.315906Z",
     "start_time": "2026-04-11T09:12:20.229463Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sympy import Symbol, solveset, S, Abs, Interval\n",
    "\n",
    "def plot_intervals(intervals, titles, colors):\n",
    "    fig, ax = plt.subplots(figsize=(10, 3))\n",
    "\n",
    "    for i, (inter, title, color) in enumerate(zip(intervals, titles, colors)):\n",
    "        # Y-Position für jedes Intervall versetzt\n",
    "        y = i + 1\n",
    "\n",
    "        # Grenzen extrahieren\n",
    "        start = float(inter.start) if inter.start != -S.Infinity else -10\n",
    "        end = float(inter.end) if inter.end != S.Infinity else 10\n",
    "\n",
    "        # Linie zeichnen\n",
    "        ax.plot([start, end], [y, y], color=color, lw=4, label=title)\n",
    "\n",
    "        # Endpunkte (Kreise) zeichnen\n",
    "        # Links\n",
    "        if inter.start != -S.Infinity:\n",
    "            m_style = 'o' if not inter.left_open else 'o'\n",
    "            m_color = color if not inter.left_open else 'white'\n",
    "            ax.plot(start, y, marker=m_style, markeredgecolor=color,\n",
    "                    markerfacecolor=m_color, markersize=10)\n",
    "\n",
    "        # Rechts\n",
    "        if inter.end != S.Infinity:\n",
    "            m_style = 'o' if not inter.right_open else 'o'\n",
    "            m_color = color if not inter.right_open else 'white'\n",
    "            ax.plot(end, y, marker=m_style, markeredgecolor=color,\n",
    "                    markerfacecolor=m_color, markersize=10)\n",
    "\n",
    "    ax.set_ylim(0, len(intervals) + 1)\n",
    "    ax.set_xlim(-11, 11)\n",
    "    ax.set_yticks(range(1, len(intervals) + 1))\n",
    "    ax.set_yticklabels(titles)\n",
    "    ax.grid(True, axis='x', linestyle='--', alpha=0.7)\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "# --- Beispiel-Rechnung ---\n",
    "x = Symbol('x', real=True)\n",
    "i1 = Interval(2, 8)               # [2, 8] - beide zu\n",
    "i2 = Interval.open(-5, 3)         # (-5, 3) - beide offen\n",
    "ergebnis = i1.intersect(i2)        # Schnittmenge [2, 3)\n",
    "\n",
    "plot_intervals([i1, i2, ergebnis],\n",
    "               [\"Intervall A [2, 8]\", \"Intervall B (-5, 3)\", \"Ergebnis [2, 3)\"],\n",
    "               [\"blue\", \"green\", \"red\"])\n",
    "\n"
   ],
   "id": "a8b386f6c4590666",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-04-11T09:12:42.283263Z",
     "start_time": "2026-04-11T09:12:42.156960Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sympy import solveset, S, Abs, Ge, Gt, solve_univariate_inequality, oo, Symbol, latex, pretty\n",
    "from sympy.abc import x\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_intervals_with_arrows(intervals, titles, colors):\n",
    "    fig, ax = plt.subplots(figsize=(10, 4))\n",
    "\n",
    "    for i, (inter, title, color) in enumerate(zip(intervals, titles, colors)):\n",
    "        y = i + 1\n",
    "        # Sichtbarer Bereich für Unendlichkeit\n",
    "        view_min, view_max = -10, 10\n",
    "\n",
    "        start = float(inter.start) if inter.start != -oo else view_min\n",
    "        end = float(inter.end) if inter.end != oo else view_max\n",
    "\n",
    "        # 1. Die Linie zeichnen\n",
    "        ax.plot([start, end], [y, y], color=color, lw=2, label=title)\n",
    "\n",
    "        # 2. Linke Seite: Punkt oder Pfeil?\n",
    "        if inter.start == -oo:\n",
    "            ax.annotate('', xy=(view_min - 0.5, y), xytext=(start, y),\n",
    "                        arrowprops=dict(arrowstyle='->', color=color, lw=2))\n",
    "        else:\n",
    "            m_fill = color if not inter.left_open else 'white'\n",
    "            ax.plot(start, y, 'o', markeredgecolor=color, markerfacecolor=m_fill, markersize=10)\n",
    "\n",
    "        # 3. Rechte Seite: Punkt oder Pfeil?\n",
    "        if inter.end == oo:\n",
    "            ax.annotate('', xy=(view_max + 0.5, y), xytext=(end, y),\n",
    "                        arrowprops=dict(arrowstyle='->', color=color, lw=2))\n",
    "        else:\n",
    "            m_fill = color if not inter.right_open else 'white'\n",
    "            ax.plot(end, y, 'o', markeredgecolor=color, markerfacecolor=m_fill, markersize=10)\n",
    "\n",
    "    # Styling\n",
    "    ax.set_xlim(-12, 12)\n",
    "    ax.set_ylim(0, len(intervals) + 1)\n",
    "    ax.set_yticks(range(1, len(intervals) + 1))\n",
    "    ax.set_yticklabels(titles)\n",
    "    ax.axvline(0, color='black', lw=1, alpha=0.3) # Nullpunkt-Linie\n",
    "    ax.grid(True, axis='x', linestyle='--', alpha=0.5)\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "# --- Beispiel mit Unendlichkeit ---\n",
    "x = Symbol('x', real=True)\n",
    "\n",
    "#i1 = Interval(2, oo)              # [2, oo) -> Geschlossen bei 2, Pfeil rechts\n",
    "#i2 = Interval(-oo, 5, True, True) # (-oo, 5) -> Pfeil links, Offen bei 5\n",
    "#ergebnis = i1.intersect(i2)        # [2, 5)   -> Schnittmenge\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import Symbol, solveset, S, Interval, oo\n",
    "\n",
    "def plot_intervals_with_arrows(intervals, titles, colors):\n",
    "    fig, ax = plt.subplots(figsize=(10, 4))\n",
    "\n",
    "    for i, (inter, title, color) in enumerate(zip(intervals, titles, colors)):\n",
    "        y = i + 1\n",
    "        # Sichtbarer Bereich für Unendlichkeit\n",
    "        view_min, view_max = -10, 10\n",
    "\n",
    "        start = float(inter.start) if inter.start != -oo else view_min\n",
    "        end = float(inter.end) if inter.end != oo else view_max\n",
    "\n",
    "        # 1. Die Linie zeichnen\n",
    "        ax.plot([start, end], [y, y], color=color, lw=2, label=title)\n",
    "\n",
    "        # 2. Linke Seite: Punkt oder Pfeil?\n",
    "        if inter.start == -oo:\n",
    "            ax.annotate('', xy=(view_min - 0.5, y), xytext=(start, y),\n",
    "                        arrowprops=dict(arrowstyle='->', color=color, lw=2))\n",
    "        else:\n",
    "            m_fill = color if not inter.left_open else 'white'\n",
    "            ax.plot(start, y, 'o', markeredgecolor=color, markerfacecolor=m_fill, markersize=5)\n",
    "\n",
    "        # 3. Rechte Seite: Punkt oder Pfeil?\n",
    "        if inter.end == oo:\n",
    "            ax.annotate('', xy=(view_max + 0.5, y), xytext=(end, y),\n",
    "                        arrowprops=dict(arrowstyle='->', color=color, lw=2))\n",
    "        else:\n",
    "            m_fill = color if not inter.right_open else 'white'\n",
    "            ax.plot(end, y, 'o', markeredgecolor=color, markerfacecolor=m_fill, markersize=5)\n",
    "\n",
    "    # Styling\n",
    "    ax.set_xlim(-12, 12)\n",
    "    ax.set_ylim(0, len(intervals) + 1)\n",
    "    ax.set_yticks(range(1, len(intervals) + 1))\n",
    "    ax.set_yticklabels(titles)\n",
    "    ax.axvline(0, color='black', lw=1, alpha=0.3) # Nullpunkt-Linie\n",
    "    ax.grid(True, axis='x', linestyle='--', alpha=0.5)\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "# --- Beispiel mit Unendlichkeit ---\n",
    "x = Symbol('x', real=True)\n",
    "#i1 = Interval(2, oo)              # [2, oo) -> Geschlossen bei 2, Pfeil rechts\n",
    "#i2 = Interval(-oo, 5, True, True) # (-oo, 5) -> Pfeil links, Offen bei 5\n",
    "i1 = solveset(Abs(x)<8, x, domain=S.Reals)\n",
    "i2 = solveset(Ge(x,2), x, domain=S.Reals)\n",
    "\n",
    "str_i1 = pretty(i1, use_unicode=True)\n",
    "str_i2 = pretty(i2, use_unicode=True)\n",
    "\n",
    "\n",
    "ergebnis = i1.intersect(i2)        # [2, 5)   -> Schnittmenge\n",
    "str_erg =  pretty(ergebnis, use_unicode=True)\n",
    "\n",
    "plot_intervals_with_arrows([i1, i2, ergebnis],\n",
    "                           [str_i1, str_i2,\n",
    "                            str_erg],\n",
    "                           [\"blue\", \"green\", \"red\"])\n"
   ],
   "id": "310dd48010b953a0",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-04-11T13:55:04.221370Z",
     "start_time": "2026-04-11T13:55:04.187430Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# Soll: Eingabe zweier Intervalle, Ausgabe alle Lösungen, Grafik und Mengenschreibweise\n",
    "from sympy import solveset, S, Abs, Ge, Gt, solve_univariate_inequality, oo, Symbol, latex, pprint\n",
    "from sympy.abc import x\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def set_op(a,b, op):\n",
    "    convert(b)\n",
    "    pass\n",
    "\n",
    "\n",
    "def convert(desc: str):\n",
    "    # Normalisierung\n",
    "    desc = desc.replace(\" \", \"\")\n",
    "\n",
    "    if desc.startswith(( \"[\", \"]\", \"(\" )):\n",
    "        print('Intervall')\n",
    "    else:\n",
    "        print('Beschreibende Form')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def plot_interval(intervall, x_range=(-10, 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",
    "    # 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",
    "#\n",
    "set_op(\"a>2\", \"]1,6[\", \"Durchschnitt\" )\n",
    "\n",
    "\n",
    "\n"
   ],
   "id": "f0a7ff043bf0c1b2",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intervall\n"
     ]
    }
   ],
   "execution_count": 13
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
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