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    "### **Grundlegende Operatoren und Funktionen**\n",
    "\n",
    "1. **Exponentiation** (Potenz)\n",
    "\n",
    "   - `**`: Exponentiation\n",
    "     ```python\n",
    "     x**2  # x hoch 2\n",
    "     ```\n",
    "   - `exp(x)`: Exponentielle Funktion \\( e^x \\)\n",
    "     ```python\n",
    "     from sympy import exp\n",
    "     exp(x)\n",
    "     ```\n",
    "\n",
    "2. **Logarithmen**\n",
    "\n",
    "   - `log(x)`: Natürlicher Logarithmus \\( \\ln(x) \\)\n",
    "     ```python\n",
    "     from sympy import log\n",
    "     log(x)\n",
    "     ```\n",
    "   - `log(x, base)`: Logarithmus zur Basis `base`\n",
    "     ```python\n",
    "     log(x, 10)  # Logarithmus zur Basis 10\n",
    "     ```\n",
    "\n",
    "3. **Trigonometrische Funktionen**\n",
    "\n",
    "   - `sin(x)`: Sinus\n",
    "     ```python\n",
    "     from sympy import sin\n",
    "     sin(x)\n",
    "     ```\n",
    "   - `cos(x)`: Kosinus\n",
    "     ```python\n",
    "     from sympy import cos\n",
    "     cos(x)\n",
    "     ```\n",
    "   - `tan(x)`: Tangens\n",
    "     ```python\n",
    "     from sympy import tan\n",
    "     tan(x)\n",
    "     ```\n",
    "   - `csc(x)`: Kosekans (1/sin(x))\n",
    "     ```python\n",
    "     from sympy import csc\n",
    "     csc(x)\n",
    "     ```\n",
    "   - `sec(x)`: Sekans (1/cos(x))\n",
    "     ```python\n",
    "     from sympy import sec\n",
    "     sec(x)\n",
    "     ```\n",
    "   - `cot(x)`: Kotangens (1/tan(x))\n",
    "     ```python\n",
    "     from sympy import cot\n",
    "     cot(x)\n",
    "     ```\n",
    "\n",
    "4. **Hyperbolische Funktionen**\n",
    "\n",
    "   - `sinh(x)`: Sinus hyperbolicus\n",
    "     ```python\n",
    "     from sympy import sinh\n",
    "     sinh(x)\n",
    "     ```\n",
    "   - `cosh(x)`: Kosinus hyperbolicus\n",
    "     ```python\n",
    "     from sympy import cosh\n",
    "     cosh(x)\n",
    "     ```\n",
    "   - `tanh(x)`: Tangens hyperbolicus\n",
    "     ```python\n",
    "     from sympy import tanh\n",
    "     tanh(x)\n",
    "     ```\n",
    "\n",
    "5. **Trigonometrische Inverse Funktionen**\n",
    "   - `asin(x)`: Arkussinus (Inverser Sinus)\n",
    "     ```python\n",
    "     from sympy import asin\n",
    "     asin(x)\n",
    "     ```\n",
    "   - `acos(x)`: Arkuskosinus (Inverser Kosinus)\n",
    "     ```python\n",
    "     from sympy import acos\n",
    "     acos(x)\n",
    "     ```\n",
    "   - `atan(x)`: Arkustangens (Inverser Tangens)\n",
    "     ```python\n",
    "     from sympy import atan\n",
    "     atan(x)\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Algebraische Operationen**\n",
    "\n",
    "1. **Addition, Subtraktion, Multiplikation, Division**\n",
    "\n",
    "   - `+`, `-`, `*`, `/`\n",
    "     ```python\n",
    "     x + y  # Addition\n",
    "     x - y  # Subtraktion\n",
    "     x * y  # Multiplikation\n",
    "     x / y  # Division\n",
    "     ```\n",
    "\n",
    "2. **Exponenten**\n",
    "\n",
    "   - `**`: Potenz\n",
    "     ```python\n",
    "     x**2  # x hoch 2\n",
    "     ```\n",
    "\n",
    "3. **Wurzeln**\n",
    "   - `sqrt(x)`: Quadratwurzel\n",
    "     ```python\n",
    "     from sympy import sqrt\n",
    "     sqrt(x)\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Integral- und Ableitungsoperationen**\n",
    "\n",
    "1. **Ableitungen**\n",
    "\n",
    "   - `diff(f, x)`: Erste Ableitung von `f` nach `x`\n",
    "     ```python\n",
    "     from sympy import diff\n",
    "     diff(f, x)\n",
    "     ```\n",
    "\n",
    "2. **Integrale**\n",
    "   - `integrate(f, x)`: Unbestimmtes Integral von `f` nach `x`\n",
    "     ```python\n",
    "     from sympy import integrate\n",
    "     integrate(f, x)\n",
    "     ```\n",
    "   - `integrate(f, (x, a, b))`: Bestimmtes Integral von `f` von `a` bis `b`\n",
    "     ```python\n",
    "     integrate(f, (x, 0, 1))\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Summen, Produkte und Faktorisierung**\n",
    "\n",
    "1. **Summe**\n",
    "\n",
    "   - `sum(iterable)`: Summe über eine Reihe oder Liste\n",
    "     ```python\n",
    "     from sympy import Sum, symbols\n",
    "     n = symbols('n')\n",
    "     Sum(n, (n, 1, 10))\n",
    "     ```\n",
    "\n",
    "2. **Produkt**\n",
    "\n",
    "   - `product(iterable)`: Produkt über eine Reihe oder Liste\n",
    "     ```python\n",
    "     from sympy import Product\n",
    "     Product(n, (n, 1, 10))\n",
    "     ```\n",
    "\n",
    "3. **Faktorisierung**\n",
    "\n",
    "   - `factor(x)`: Faktorisieren eines Polynoms\n",
    "     ```python\n",
    "     from sympy import factor\n",
    "     factor(x**2 - 4)\n",
    "     ```\n",
    "\n",
    "4. **Entwicklung in Reihen**\n",
    "   - `series(f, x)`: Taylor-Reihe von `f` um `x`\n",
    "     ```python\n",
    "     from sympy import series\n",
    "     series(f, x)\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Matrixoperationen**\n",
    "\n",
    "1. **Matrix**\n",
    "\n",
    "   - `Matrix([[1, 2], [3, 4]])`: Erstellen einer Matrix\n",
    "     ```python\n",
    "     from sympy import Matrix\n",
    "     A = Matrix([[1, 2], [3, 4]])\n",
    "     ```\n",
    "\n",
    "2. **Determinante**\n",
    "\n",
    "   - `det(A)`: Determinante einer Matrix\n",
    "     ```python\n",
    "     A.det()\n",
    "     ```\n",
    "\n",
    "3. **Inverses einer Matrix**\n",
    "   - `inv(A)`: Inverse der Matrix `A`\n",
    "     ```python\n",
    "     A.inv()\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Grenzwerte und Limes**\n",
    "\n",
    "1. **Grenzwert (Limit)**\n",
    "\n",
    "   - `limit(f, x, c)`: Grenzwert von `f` für `x → c`\n",
    "     ```python\n",
    "     from sympy import limit\n",
    "     limit(f, x, 0)\n",
    "     ```\n",
    "\n",
    "2. **Unendlicher Grenzwert**\n",
    "   - `limit(f, x, oo)`: Grenzwert für `x → ∞`\n",
    "     ```python\n",
    "     limit(f, x, float('inf'))\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Differentialgleichungen**\n",
    "\n",
    "1. **Lösen von Differentialgleichungen**\n",
    "   - `dsolve(eq, func)`: Lösen einer gewöhnlichen Differentialgleichung\n",
    "     ```python\n",
    "     from sympy import Function, dsolve, Derivative\n",
    "     f = Function('f')\n",
    "     dsolve(Derivative(f(x), x) - f(x), f(x))\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Sonstige nützliche Funktionen**\n",
    "\n",
    "1. **Ganze Zahlen (Modulararithmetik)**\n",
    "\n",
    "   - `mod(x, y)`: Modulo-Operation\n",
    "     ```python\n",
    "     from sympy import mod\n",
    "     mod(x, y)\n",
    "     ```\n",
    "\n",
    "2. **Boden- und Deckenfunktion**\n",
    "   - `floor(x)`: Abrunden auf die nächste ganze Zahl\n",
    "     ```python\n",
    "     from sympy import floor\n",
    "     floor(x)\n",
    "     ```\n",
    "   - `ceiling(x)`: Aufrunden auf die nächste ganze Zahl\n",
    "     ```python\n",
    "     from sympy import ceiling\n",
    "     ceiling(x)\n",
    "     ```\n",
    "\n",
    "---\n",
    "\n",
    "### **Zusammenfassung der wichtigsten Funktionen**\n",
    "\n",
    "| **Funktion**                | **SymPy-Befehl**                              | **Beschreibung**                       |\n",
    "| --------------------------- | --------------------------------------------- | -------------------------------------- |\n",
    "| Exponentiation              | `exp(x)`                                      | \\( e^x \\)                              |\n",
    "| Trigonometrische Funktionen | `sin(x)`, `cos(x)`, `tan(x)`                  | Sinus, Kosinus, Tangens                |\n",
    "| Ableitung                   | `diff(f, x)`                                  | Ableitung von `f` nach `x`             |\n",
    "| Integral                    | `integrate(f, x)`                             | Unbestimmtes Integral von `f` nach `x` |\n",
    "| Summe                       | `Sum(expression, (variable, start, end))`     | Summe über eine Reihe                  |\n",
    "| Produkt                     | `Product(expression, (variable, start, end))` | Produkt über eine Reihe                |\n",
    "| Faktorisierung              | `factor(f)`                                   | Faktorisierung von `f`                 |\n",
    "| Grenzwert                   | `limit(f, x, c)`                              | Grenzwert von `f` für `x → c`          |\n",
    "| Matrixoperationen           | `Matrix([[1, 2], [3, 4]])`                    | Erstellen von Matrizen                 |\n",
    "| Differentialgleichung lösen | `dsolve(eq, func)`                            | Lösen von Differentialgleichungen      |\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "<!--->siehe https://chatgpt.com/share/673b2049-b010-8013-a3d7-9552c03da480</--->\n"
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