342 lines
26 KiB
Plaintext
342 lines
26 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"id": "902e4b59-77b9-4db6-9ec2-3cff55766dd5",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:28:45.280232Z",
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"start_time": "2026-03-14T20:28:45.240030Z"
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}
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},
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"source": [
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"\n",
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"def abs(c):\n",
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" return (c.real**2 + c.imag**2)**0.5\n",
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"\n",
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"def add(c1, c2):\n",
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" return complex(c1.real + c2.real, c1.imag + c2.imag)\n",
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"\n",
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"def sub(c1, c2):\n",
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" # (a+bi) - (c+di) = (a-c) + (b-d)i\n",
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" return complex(c1.real - c2.real, c1.imag - c2.imag)\n",
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"\n",
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"def mul(c1, c2):\n",
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" # (a+bi)(c+di) = (ac-bd) + (ad+bc)i\n",
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" return complex(c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c1.imag * c2.real)\n",
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"\n",
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"\n",
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"\n",
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"print(mul(1+2j, 2+1j))"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5j\n"
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]
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}
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],
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"execution_count": 12
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},
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{
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"cell_type": "code",
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"id": "3fb82de2-875a-4dac-935a-e64bad48c895",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:28:45.320152Z",
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"start_time": "2026-03-14T20:28:45.281685Z"
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}
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},
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"source": [
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"def add(v1, v2):\n",
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" return (v1[0] + v2[0], v1[1] + v2[1])\n",
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"\n",
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"def sub(v1, v2):\n",
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" return (v1[0] - v2[0], v1[1] - v2[1])\n",
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"\n",
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"\n",
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"\n",
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"print(add((2, 1), (3, 4)))\n"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(5, 5)\n"
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]
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}
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],
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"execution_count": 13
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},
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{
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"cell_type": "code",
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"id": "3a562f0e-162b-4760-ac6b-22587bf0bd60",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:28:45.659050Z",
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"start_time": "2026-03-14T20:28:45.349987Z"
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}
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},
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"source": [
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"from sympy import Interval, Symbol\n",
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"\n",
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"# 1. Variable definieren\n",
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"x = Symbol('x')\n",
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"\n",
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"# 2. Intervall erstellen (z.B. [2, 5) - links abgeschlossen, rechts offen)\n",
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"# left_open=False (Standard) bedeutet inklusive 2, right_open=True bedeutet exklusive 5\n",
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"mein_intervall = Interval(2, 5, left_open=False, right_open=True)\n",
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"\n",
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"# 3. In Mengenangabe / Ungleichung umwandeln\n",
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"mengen_angabe = mein_intervall.as_relational(x)\n",
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"\n",
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"print(f\"Intervall: {mein_intervall}\")\n",
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"print(f\"Mengenangabe: {mengen_angabe}\")\n"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Intervall: Interval.Ropen(2, 5)\n",
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"Mengenangabe: (2 <= x) & (x < 5)\n"
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]
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}
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],
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"execution_count": 14
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},
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{
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"cell_type": "code",
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"id": "5f024814-9f83-4d5f-a81f-4283e47e22b9",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:28:45.760535Z",
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"start_time": "2026-03-14T20:28:45.660677Z"
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}
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},
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"source": [
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"from sympy import Symbol, And\n",
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"\n",
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"x = Symbol('x')\n",
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"\n",
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"# Eine Mengenangabe als logische Verknüpfung (2 <= x < 5)\n",
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"mengen_angabe = And(x >= 2, x < 5)\n",
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"\n",
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"# Umwandlung in ein Intervall-Objekt\n",
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"intervall = mengen_angabe.as_set()\n",
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"\n",
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"print(intervall) \n",
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"# Ausgabe: [2, 5)\n"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Interval.Ropen(2, 5)\n"
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]
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}
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],
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"execution_count": 15
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},
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{
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"cell_type": "code",
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"id": "b58b7c16-2c79-46a4-bde0-1d8fcc16cfa9",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:28:45.791872Z",
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"start_time": "2026-03-14T20:28:45.765958Z"
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}
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},
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"source": [
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"from sympy import Symbol, solve_univariate_inequality\n",
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"\n",
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"x = Symbol('x')\n",
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"\n",
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"# Eine Ungleichung definieren\n",
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"ungleichung = x**2 <= 4\n",
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"\n",
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"# Lösen und als Intervall ausgeben lassen (relational=False)\n",
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"intervall = solve_univariate_inequality(ungleichung, x, relational=False)\n",
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"\n",
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"print(intervall)\n",
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"# Ausgabe: [-2, 2]\n"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Interval(-2, 2)\n"
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]
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}
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],
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"execution_count": 16
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},
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{
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"cell_type": "code",
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"id": "dd0522d3-0612-44f1-9504-1ba48542e37e",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:28:45.850425Z",
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"start_time": "2026-03-14T20:28:45.792950Z"
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}
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},
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"source": [
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"from sympy import Symbol, solve_univariate_inequality\n",
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"\n",
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"x = Symbol('x')\n",
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"\n",
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"# Eine Ungleichung definieren\n",
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"ungleichung = abs(x)<8\n",
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"\n",
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"# Lösen und als Intervall ausgeben lassen (relational=False)\n",
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"intervall = solve_univariate_inequality(ungleichung, x, relational=False)\n",
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"\n",
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"print(intervall)"
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],
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"outputs": [
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{
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"ename": "AttributeError",
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"evalue": "'Symbol' object has no attribute 'real'",
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"output_type": "error",
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"traceback": [
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"\u001B[31m---------------------------------------------------------------------------\u001B[39m",
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"\u001B[31mAttributeError\u001B[39m Traceback (most recent call last)",
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"\u001B[36mCell\u001B[39m\u001B[36m \u001B[39m\u001B[32mIn[17]\u001B[39m\u001B[32m, line 6\u001B[39m\n\u001B[32m 3\u001B[39m x = Symbol(\u001B[33m'\u001B[39m\u001B[33mx\u001B[39m\u001B[33m'\u001B[39m)\n\u001B[32m 5\u001B[39m \u001B[38;5;66;03m# Eine Ungleichung definieren\u001B[39;00m\n\u001B[32m----> \u001B[39m\u001B[32m6\u001B[39m ungleichung = \u001B[38;5;28;43mabs\u001B[39;49m\u001B[43m(\u001B[49m\u001B[43mx\u001B[49m\u001B[43m)\u001B[49m<\u001B[32m8\u001B[39m\n\u001B[32m 8\u001B[39m \u001B[38;5;66;03m# Lösen und als Intervall ausgeben lassen (relational=False)\u001B[39;00m\n\u001B[32m 9\u001B[39m intervall = solve_univariate_inequality(ungleichung, x, relational=\u001B[38;5;28;01mFalse\u001B[39;00m)\n",
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"\u001B[36mCell\u001B[39m\u001B[36m \u001B[39m\u001B[32mIn[12]\u001B[39m\u001B[32m, line 2\u001B[39m, in \u001B[36mabs\u001B[39m\u001B[34m(c)\u001B[39m\n\u001B[32m 1\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34mabs\u001B[39m(c):\n\u001B[32m----> \u001B[39m\u001B[32m2\u001B[39m \u001B[38;5;28;01mreturn\u001B[39;00m (\u001B[43mc\u001B[49m\u001B[43m.\u001B[49m\u001B[43mreal\u001B[49m**\u001B[32m2\u001B[39m + c.imag**\u001B[32m2\u001B[39m)**\u001B[32m0.5\u001B[39m\n",
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"\u001B[31mAttributeError\u001B[39m: 'Symbol' object has no attribute 'real'"
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]
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}
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],
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"execution_count": 17
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},
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{
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"cell_type": "code",
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"id": "99ed5f78-8032-40eb-99ce-988de647549b",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-14T20:30:39.429411Z",
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"start_time": "2026-03-14T20:30:39.352620Z"
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}
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},
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"source": [
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"import matplotlib.pyplot as plt\n",
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"from sympy import Interval\n",
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"\n",
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"def plot_interval(intervall, x_range=(0, 10)):\n",
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" fig, ax = plt.subplots(figsize=(8, 2))\n",
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"\n",
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" # Zahlenstrahl-Optik\n",
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" ax.set_xlim(x_range)\n",
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" ax.set_ylim(-1, 1)\n",
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" ax.set_yticks([])\n",
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" ax.spines['top'].set_visible(False)\n",
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" ax.spines['right'].set_visible(False)\n",
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" ax.spines['left'].set_visible(False)\n",
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" ax.spines['bottom'].set_position('center')\n",
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"\n",
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" # Start- und Endpunkte extrahieren\n",
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" start, end = float(intervall.start), float(intervall.end)\n",
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"\n",
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" # Die Linie für das Intervall zeichnen\n",
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" ax.plot([start, end], [0, 0], color='blue', lw=4)\n",
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"\n",
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" # Punkte zeichnen: gefüllt = inklusive, weiß/leer = exklusive\n",
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" ax.plot(start, 0, 'o', color='blue', mfc='blue' if not intervall.left_open else 'white', markersize=10)\n",
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" ax.plot(end, 0, 'o', color='blue', mfc='blue' if not intervall.right_open else 'white', markersize=10)\n",
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"\n",
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" plt.title(f\"Intervall: {intervall}\")\n",
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" plt.show()\n",
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"\n",
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"# Beispiel: [2, 5)\n",
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"mein_intervall = Interval(2, 5, left_open=False, right_open=True)\n",
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"plot_interval(mein_intervall, x_range=(0, 7))\n"
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],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<Figure size 800x200 with 1 Axes>"
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],
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"image/png": 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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data",
|
|
"jetTransient": {
|
|
"display_id": null
|
|
}
|
|
}
|
|
],
|
|
"execution_count": 19
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2026-03-14T20:30:39.750872Z",
|
|
"start_time": "2026-03-14T20:30:39.440529Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"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"
|
|
],
|
|
"id": "cdb0080c9d06840a",
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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"
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},
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"metadata": {},
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"output_type": "display_data",
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"jetTransient": {
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"display_id": null
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}
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},
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{
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"data": {
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"text/plain": [
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"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x10eef2210>"
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]
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},
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"execution_count": 20,
|
|
"metadata": {},
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"output_type": "execute_result"
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}
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],
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"execution_count": 20
|
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.13.11"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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