typst/schule/mathe/tests/test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sympy import symbols, latex\n",
    "\n",
    "x = symbols('x')\n",
    "expr = x**2 + 2*x + 1\n",
    "\n",
    "# LaTeX-String erstellen\n",
    "latex_code = latex(expr)\n",
    "\n",
    "# Plot erstellen\n",
    "plt.text(0.5, 0.5, f\"${latex_code}$\", fontsize=12, ha='center')\n",
    "plt.axis('off')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x^{2} + 2 x + 1\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, latex\n",
    "\n",
    "x = symbols('x')\n",
    "expr = x**2 + 2*x + 1\n",
    "\n",
    "# LaTeX-String erzeugen\n",
    "latex_code = latex(expr)\n",
    "print(latex_code)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 x^{2} + 2\n",
      "\\frac{x^{4}}{4} + x^{2} + x\n"
     ]
    }
   ],
   "source": [
    "from sympy import diff, integrate, symbols, latex\n",
    "\n",
    "x = symbols('x')\n",
    "f = x**3 + 2*x + 1\n",
    "\n",
    "# Ableitung\n",
    "derivative = diff(f)\n",
    "print(latex(derivative))  # Ausgabe: 3 x^{2} + 2\n",
    "\n",
    "# Integral\n",
    "integral = integrate(f)\n",
    "print(latex(integral))  # Ausgabe: \\frac{x^{4}}{4} + x^{2} + x\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "3 x^{2} + 2\n",
    "\\frac{x^{4}}{4} + x^{2} + x\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "from sympy import solve\n",
    "\n",
    "eq = x**2 - 4\n",
    "solution = solve(eq)\n",
    "\n",
    "# Lösungen anzeigen\n",
    "for sol in solution:\n",
    "    print(latex(sol))  # Ausgabe: -2 und 2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ -2, \\  2\\right]$"
      ],
      "text/plain": [
       "[-2, 2]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import symbols, solve, init_printing\n",
    "from IPython.display import display\n",
    "\n",
    "# SymPy-Darstellung aktivieren\n",
    "init_printing()\n",
    "\n",
    "x = symbols('x')\n",
    "eq = x**2 - 4\n",
    "\n",
    "# Gleichung lösen und anzeigen\n",
    "solutions = solve(eq)\n",
    "display(solutions)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ableitung von f(x) = exp(0.5*x):\n",
      "0.5*exp(0.5*x)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0.5 e^{0.5 x}$"
      ],
      "text/plain": [
       "     0.5⋅x\n",
       "0.5⋅ℯ     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import symbols, diff, exp, init_printing\n",
    "from IPython.display import display\n",
    "init_printing()\n",
    "\n",
    "# Symbol für die Variable x definieren\n",
    "x = symbols('x')\n",
    "\n",
    "# Funktion definieren: f(x) = e^(0.5x)\n",
    "f = exp(0.5 * x)\n",
    "\n",
    "# Ableitung berechnen\n",
    "f_derivative = diff(f, x)\n",
    "\n",
    "# Ergebnis anzeigen\n",
    "print(f\"Ableitung von f(x) = {f}:\")\n",
    "print(f_derivative)\n",
    "display(f_derivative)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (Nix)",
   "language": "python",
   "name": "nix-python"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}