{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be16a389",
   "metadata": {},
   "source": [
    "# Overleaf\n",
    "\n",
    "Reimplementation of diagrams from https://www.overleaf.com/learn/latex/Feynman_diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "873be78f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from feynml import FeynmanDiagram, Leg, Propagator, Vertex\n",
    "from pyfeyn2.render.all import AllRender\n",
    "from pyfeyn2.render.latex.tikzfeynman import TikzFeynmanRender\n",
    "from pyfeyn2.auto.position import feynman_adjust_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0a179236",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_484/3445839438.py:7: DeprecatedWarning: put_style is deprecated as of 0.0.0.\n",
      "  Propagator().connect(v1, v2).with_type(\"photon\").put_style('opacity',0.2).with_style_property('color','red').with_momentum(\"$k$\"),\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: 5e8eebd 'PDF' (171x83)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: fd23d14 'PDF' (315x157)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynmp:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: 19f5d6a 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<wand.image.Image: 6fedee0 'PDF' (496x251)>"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mermaid:\n"
     ]
    },
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      "asciipdf:\n"
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     "text": [
      "unicodepdf:\n"
     ]
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    {
     "data": {
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       "<wand.image.Image: 3be897c 'PDF' (13837x9)>"
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     "output_type": "stream",
     "text": [
      "madgraph:\n"
     ]
    },
    {
     "data": {
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       "<wand.image.Image: 44bd6c6 'PDF' (139x139)>"
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     "text": [
      "root:\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<wand.image.Image: 88d28cf 'PDF' (788x756)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Info in <TCanvas::SaveSource>: C++ Macro file: /tmp/tmpnaab_9_v.tex has been generated\n",
      "Info in <TCanvas::Print>: TeX file /tmp/tmp96oc6ou1.tex has been created\n"
     ]
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-1, 0)\n",
    "v2 = Vertex().with_xy(1, 0)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,\n",
    "    v2,\n",
    "    Propagator().connect(v1, v2).with_type(\"photon\").put_style('opacity',0.2).with_style_property('color','red').with_momentum(\"$k$\"),\n",
    "    Leg().with_target(v1).with_xy(-2, 1).with_type(\"fermion\").with_incoming().with_label(\"$e^{+}$\").with_style_property('opacity',0.2),\n",
    "    Leg().with_target(v1).with_xy(-2, -1).with_type(\"fermion\").with_incoming().with_label(\"$e^{-}$\").with_style_property('opacity',0.2),\n",
    "    Leg().with_target(v2).with_xy(2, 1).with_type(\"fermion\").with_outgoing().with_label(\"$\\\\mu^+$\").with_style_property('opacity',0.2),\n",
    "    Leg().with_target(v2).with_xy(2, -1).with_type(\"fermion\").with_outgoing().with_label(\"$\\\\mu^-$\").with_style_property('opacity',0.9),\n",
    ")\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6446cf50",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<wand.image.Image: 6c916dd 'PDF' (158x80)>"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: af6b809 'PDF' (329x157)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynmp:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: 9f97546 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot:\n"
     ]
    },
    {
     "data": {
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       "<wand.image.Image: 0efa385 'PDF' (496x251)>"
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     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mermaid:\n"
     ]
    },
    {
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white-space: nowrap; line-height: 1.5; max-width: 200px; text-align: center;\"><span class=\"nodeLabel \"><p>Leg21</p></span></div></foreignObject></g></g><g class=\"node default hidden \" id=\"flowchart-Leg22-4\" transform=\"translate(158, 8)\"><rect class=\"basic label-container\" style=\"display:none !important\" x=\"-30\" y=\"-15\" width=\"60\" height=\"30\"/><g class=\"label\" style=\"\" transform=\"translate(0, 0)\"><rect/><foreignObject width=\"0\" height=\"0\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: table-cell; white-space: nowrap; line-height: 1.5; max-width: 200px; text-align: center;\"><span class=\"nodeLabel \"><p>Leg22</p></span></div></foreignObject></g></g><g class=\"node default hidden \" id=\"flowchart-Leg23-5\" transform=\"translate(158, 58)\"><rect class=\"basic label-container\" style=\"display:none !important\" x=\"-30\" y=\"-15\" width=\"60\" height=\"30\"/><g class=\"label\" style=\"\" transform=\"translate(0, 0)\"><rect/><foreignObject width=\"0\" height=\"0\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: table-cell; 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      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "asciipdf:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<wand.image.Image: 1f4ff77 'PDF' (664x453)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unicodepdf:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: 3be897c 'PDF' (13837x9)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "madgraph:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: cc73e9b 'PDF' (139x139)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 0b2d674 'PDF' (788x756)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Info in <TCanvas::SaveSource>: C++ Macro file: /tmp/tmpqgl5e966.tex has been generated\n",
      "Info in <TCanvas::Print>: TeX file /tmp/tmpy2n93fur.tex has been created\n"
     ]
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-1, 0)\n",
    "v2 = Vertex().with_xy(1, 0)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,\n",
    "    v2,\n",
    "    Propagator().connect(v1, v2).with_type(\"fermion\"),\n",
    "    Leg().with_target(v1).with_xy(-2, 1).with_type(\"fermion\").with_incoming(),\n",
    "    Leg().with_target(v1).with_xy(-2, -1).with_type(\"photon\").with_incoming(),\n",
    "    Leg().with_target(v2).with_xy(2, 1).with_type(\"fermion\").with_outgoing(),\n",
    "    Leg().with_target(v2).with_xy(2, -1).with_type(\"photon\").with_outgoing(),\n",
    ")\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ede56f63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ4AAAC3CAQAAABJLy8OAAAAIGNIUk0AAHomAACAhAAA+gAAAIDoAAB1MAAA6mAAADqYAAAXcJy6UTwAAAACYktHRAD/h4/MvwAAAAlwSFlzAAAAZAAAAGQAD5bF3QAAAAd0SU1FB+kFChIJLkh0TmYAAAV8SURBVHja7d2hjxtHFMfx76UhgVvYqlK6KYtKsgH9AyaoKnRhoAMDHVq2gYU2Cr4DRZEq+VCksHNUFNDGy6qoxC6rpVbaAq999sVn73rGnrd3vw+JrbuMn9/NzszOzuyelMi+7sQOoM2UPA9KnoeTgGW55avz2F9L5Cb7LGhpXToUTGN/qWMJ2eYBjHlsNnnG2+SUi9ghHFPYoYqz+Tc9lNBt3oyEp0z5GPuLbdDjIQldq3/gMSng6McOZIOcHtBhGDuQzRYtXtdggCmT8IWGbPPS6oDIDB4YHUbhCw1/bpuQMThCOpoplslzXuWsCdlhFDjgOT9RHDEt9bynw4wUR2GvM0urf7PYgWyJLiWJHchmOWN6VoNjyJBu7CCul1NSUtI3WfeGlJRMyJdHiCmL5JWUXNA1VgeHK9Gd0glV7Al5kLryDffX3v/Ln3zwLvUe3wL/8c6znEd8vvb+Hz7wV4BvHchqzSsZB617/pMNw7XohqHq3t1gX3FhwFngQXK4dmrKgEG4gVTI5BWchQxtKcy5wYgBZzbnGjsHGwqkAc6Ue4cZA4SeST6EMS+qAe6UgaW6E3Y+7zDe4rjHOQUPecjb2OFcCt9hhDdaafUCntb7a9eKAVtD75YlLzvErNz+2pU8Y9rQ215y9ClISJgy5UnscNrrNH7nocP2VrJ3ha5FDCymbsMZxmZPeQ9kdPiCj8xihNCu3nZVRo+EEfOh87PY4bRXpPbvJvS20U7abkLyslgX2W9C8og1x9eGKaldimoWOwMKXhwvle3tbVelpEBBQZ+Cl8f62JtQ8+Zpm5ses/toY5uXb/3pEdcG2qp5adV6DSiqFJ1zjsNVr+qUcIs5yurASyiXV/bztemnbTVvsRIlPcaElbUOI2FSxZQw4UlV27oMuKyX88n4YuP604xTkuUupFs3XVpWF6i7TKrac/Vyel6zpH3XuPTo4up8isUOI2Feu0YkQHrk84ccGJCYXGe40xjHvLYNyWHDMo66NW+8x6c32nJgr+YVpDjOqnduw8XGF7VLaq7RlgNbQ5W5lPlobT5Xt/+4LaXDFEeTNS6rWw52frLF5DkeV6+6PPAo51mVuBGOvOZ06Vk1qkxtXV6v63JMN98tFoJrNF1qdstBndA/feWr1sADE9eC7enVTN58PXXt/ST2ettDaHIYpuSM6+0nsXZ6dhgpQwrgd37Z+nvrLeMfvOb1tl+32NuGV/CYjIK3POC32v/rK77jJM4VYYsSLrYuPLe8i8mA7emzvH/OhG3ps7xz04hdB69sFSh9t6O3vWrKE4ZQ814Ixm+jFIMOXi9Kn5d66evSwQWb4blBdqcv5RTIak/+3yq70pcwYah6d53d6euodbze9enLqqtpGzdjt3c1fEgzzviZxYb8Pu+Xl4tmzLhHRmLw/liGLGpfn/LK/f8yne/ulnDBm+reP0pXY6+W83nqHhrqr91WRxrort31p9RFyGZS+kyWybN401jjErqMq/Td6iW6+3O8ouTX2GG019eM1efuT/N9XpQ+L0qfF6XPi9LnRenzovR5Ufq8KH1elD4vSp8Xpc+L0uelSt/tXJ/na7G+T/aUaKJeRERERERERERERERERERERERERERERERERERERERERERERERERERW5HpEpQ+zT4K6EzuAnZzdh0G3IXmj2CFcx/INV3NGgOPH2IG0T17di9hsi2dXWj1X1lm+J6zVNq9TdROGWzy7yZtSAPO+thM7mOtYfbJywQ/McMBHZlUipYEMQE9cbCojV9L25SgpGdpt7SxzK084zu0+X/vE5LPSH/Fy7f1r3vAudlCfuktmsHW5f+X993xJyt+xw2oHt/ZocsMHrkWL5J2qy2jOMWnDYOV/UEx6+7XAWJAAAAAldEVYdGRhdGU6Y3JlYXRlADIwMjUtMDUtMTBUMTg6MDk6NDYrMDA6MDAiuvXaAAAAJXRFWHRkYXRlOm1vZGlmeQAyMDI1LTA1LTEwVDE4OjA5OjQ2KzAwOjAwU+dNZgAAACh0RVh0ZGF0ZTp0aW1lc3RhbXAAMjAyNS0wNS0xMFQxODowOTo0NiswMDowMATybLkAAAATdEVYdHBkZjpWZXJzaW9uAFBERi0xLjVTNlrBAAAASnRFWHRzaWduYXR1cmUANjdlZjViNjg0ZTI2NzlmYzc0MjI5OTgzZGEyYTU1MjNkYmQ4NGIxNWM3Njk4N2Y1NDAxOGY2NWJjMjk3MDFhM7mjJ40AAAAASUVORK5CYII=",
      "text/plain": [
       "<wand.image.Image: 67ef5b6 'PDF' (158x183)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 18f98dc 'PDF' (315x365)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynmp:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: e7cd408 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot:\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<wand.image.Image: c27dde7 'PDF' (523x451)>"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mermaid:\n"
     ]
    },
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      "asciipdf:\n"
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      "text/plain": [
       "<wand.image.Image: 3be897c 'PDF' (13837x9)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "madgraph:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<wand.image.Image: 44bd6c6 'PDF' (139x139)>"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root:\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<wand.image.Image: 4bfe64e 'PDF' (788x825)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Info in <TCanvas::SaveSource>: C++ Macro file: /tmp/tmpsaj8ngxb.tex has been generated\n",
      "Info in <TCanvas::Print>: TeX file /tmp/tmp6_je8lvq.tex has been created\n"
     ]
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-2, -2)\n",
    "v2 = Vertex().with_xy(2, -2)\n",
    "\n",
    "i1 = Vertex().with_xy(-2, 2)\n",
    "o1 = Vertex().with_xy(2,  2)\n",
    "o2 = Vertex().with_xy(2,  1)\n",
    "o3 = Vertex().with_xy(2,  0)\n",
    "\n",
    "p1 = Vertex().with_xy(0,  2)\n",
    "p2 = Vertex().with_xy(1,  1)\n",
    "\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,\n",
    "    v2,\n",
    "    Propagator().connect(v1,v2).with_type(\"fermion\").with_label(\"$d$\").with_tension(0),\n",
    "    Leg().with_target(v1).with_point(v1).with_type(\"phantom\").with_incoming(),\n",
    "    Leg().with_target(v2).with_point(v2).with_type(\"phantom\").with_outgoing(),\n",
    "    \n",
    "    i1,p1,p2,o1,o2,o3,\n",
    "    Propagator().connect(p2,p1).with_type(\"boson\").with_label(r\"$W^{+}$\"),\n",
    "    Leg(label=r\"$\\bar{b}$\").with_target(p1).with_point(i1).with_type(\"fermion\").with_incoming(),\n",
    "    Leg(label=r\"$\\bar{c}$\").with_target(p1).with_point(o1).with_type(\"fermion\").with_outgoing(),\n",
    "    Leg(label=r\"$c$\").with_target(p2).with_point(o2).with_type(\"fermion\").with_outgoing(),\n",
    "    Leg(label=r\"$\\bar{s}$\").with_target(p2).with_point(o3).with_type(\"fermion\").with_outgoing()\n",
    ")\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52d52beb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8e1fd4d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09790aa7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}