{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "441f116b",
   "metadata": {},
   "source": [
    "# Pyfeyn\n",
    "\n",
    "https://pyfeyn.hepforge.org/examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "804707a8",
   "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\n",
    "from pyfeyn2.auto.label import auto_label\n",
    "from pyfeyn2.auto.bend import auto_bend\n",
    "from feynml import Momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d4b571dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: d0b590b 'PDF' (237x158)>"
      ]
     },
     "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: a711385 'PDF' (472x315)>"
      ]
     },
     "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: 9f75187 '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: cb877ac 'PDF' (696x451)>"
      ]
     },
     "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: 0dfdeaf 'PDF' (664x503)>"
      ]
     },
     "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": "iVBORw0KGgoAAAANSUhEUgAAAIsAAACLCAQAAAD7EKJ0AAAAIGNIUk0AAHomAACAhAAA+gAAAIDoAAB1MAAA6mAAADqYAAAXcJy6UTwAAAACYktHRAD/h4/MvwAAAAlwSFlzAAAAZAAAAGQAD5bF3QAAAAd0SU1FB+kFChMmAfB7IWUAAAL2elRYdFJhdyBwcm9maWxlIHR5cGUgeG1wAABIibVWWZKcMAz91ylyBCPJEhwHsP2Xqnzm+HmyoZcZOtUzqUDRgK3lPW00/f75i37gmKZZSHZpPnuyycQ2y66cjC2b22JVCntt27Y1dqwvprGSXbIWSVo8qUB2toV09tWhmMVXrVkNdxgUgRK7NKlpDWdwpNbCBRefbfLExQymd1e4Z3KBJ7iAamFWyay7GvNpwmdZoQjfVgKvTZzi3XarLrEXGG2i04+sY+Mm3snczWBt67RmLTlxvDecO9AvEQ4S5ioLromLTCK8A6GB7NRNujU8b5ywX8VAduBkADBZgV+BHw7pAeTYDKCzK84kK3A17wdXhxDXbti5wekSJ54SwDQgwq0MI7iLI1dBzWcEEw6w7c9RsSXPn91RF64POakog2aFWyiEZ1BKEbFnUqojRXhfIoKEBDar8HkIwCQDPgIeWcTxnKN0Td8qvcIzVA5EcuQwHSEOt83UM6RRQ2GY8JYUmVL4ABKBlwfAkS0QAznRTjHCfEmRTpUvUuy19UiRTo4vKY52eAp61Hs3tGoJigBh5ItGsgEQAhw1gS5BQ/Zf0MqKlUlWEUGVSxTm1qXiOcneXZWO6G710ejos8NvxCyPnVdu6Wt+XxlNK136RRvkoyml5mwVrRnN4VYVEUMZ7GAgXbYnSXa69PVkqON5Uc+HmQPRX4XeLQga6dWC0XlR+O8WhRWK5aO/T4OBrQFZjokUs0CRzXADNLnP7RVXlgizRqpifhC4ZADnnr0JU5h7OvuJQSIStNBjmD2OK0fSY5p/bBX6t8hARkZI6GkWJiiw7fc5GIL4zVC8EUXcRmyOud6NrQQyoVQi7eN7cFUnt7HSO22oxh6uvVf5TrfkT/GF6g15koKxk0h/m1CU3oMeYxghAYgJ4Yce5tGo3Lt1hPWhAMPYh5K8ORzET2R0Qnuneh+lxofotjrTx+9obHH6+knfUXrb0Hcw/V9Egenyf1NMptF1Pv7y0B/lBCvYE2FyrQAAASJJREFUeNrt0LERABAAwEDsvzMDSE/xP0Eucw9u63XAn2xJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJtiRbki3JlmRLsiXZkmxJB8qHAhVPh/q7AAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDI1LTA1LTEwVDE5OjM4OjAxKzAwOjAwyOERFAAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyNS0wNS0xMFQxOTozODowMSswMDowMLm8qagAAAAodEVYdGRhdGU6dGltZXN0YW1wADIwMjUtMDUtMTBUMTk6Mzg6MDErMDA6MDDuqYh3AAAAIHRFWHRwZGY6SGlSZXNCb3VuZGluZ0JveAAxMDB4MTAwKzArMEmNHP4AAAATdEVYdHBkZjpWZXJzaW9uAFBERi0xLjQkMWpXAAAASnRFWHRzaWduYXR1cmUANDRiZDZjNjA3NDI3ZWNiZTUwYWJkNmE1ZjllNGRmYjY3YzNiMWNiNGQzM2UwMmExNjg2YTZlNzk4YmZjZjE5ZGJTh70AAAAodEVYdHhtcDpDcmVhdGVEYXRlADIwMjUtMDUtMTBUMjE6Mzg6MDErMDI6MDCNs+V8AAAAInRFWHR4bXA6Q3JlYXRvclRvb2wAVW5rbm93bkFwcGxpY2F0aW9urlCuMQAAACh0RVh0eG1wOk1vZGlmeURhdGUAMjAyNS0wNS0xMFQyMTozODowMSswMjowMDlN2UUAAAAASUVORK5CYII=",
      "text/plain": [
       "<wand.image.Image: 44bd6c6 '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: 7cce159 'PDF' (805x756)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Info in <TCanvas::SaveSource>: C++ Macro file: /tmp/tmpirofgrqd.tex has been generated\n",
      "Info in <TCanvas::Print>: TeX file /tmp/tmpphtm9s41.tex has been created\n"
     ]
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-1, 0)\n",
    "v2 = Vertex().with_xy(1, 0)\n",
    "v3 = Vertex().with_xy(2, 1)\n",
    "v4 = Vertex().with_xy(2, -1)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1, v2, v3, v4,\n",
    "    Propagator().connect(v1, v2).with_type(\"boson\").with_label(\"$\\\\gamma/Z$\"),\n",
    "    Propagator(pdgid=1).connect(v2, v3),\n",
    "    Propagator(pdgid=-1).connect(v2,v4),\n",
    "    Propagator(name=\"g\").connect(v3,v4).with_style(\"bend-direction : left\"),\n",
    "    Leg(pdgid=11).with_target(v1).with_xy(-3, 2).with_incoming().with_style(\"momentum-arrow : true; momentum-arrow-sense : 1\").with_momentum(Momentum(name=\"$\\\\vec p$\")),\n",
    "    Leg(pdgid=-11).with_target(v1).with_xy(-3, -2).with_incoming(),\n",
    "    Leg(pdgid=1).with_target(v3).with_xy(3, 2).with_outgoing(),\n",
    "    Leg(pdgid=-1).with_target(v4).with_xy(3, -2).with_outgoing(),\n",
    ")\n",
    "auto_label(fd.propagators + fd.legs)\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "43ef0922",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<wand.image.Image: be88f1a 'PDF' (316x75)>"
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     },
     "metadata": {},
     "output_type": "display_data"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: b487a95 'PDF' (630x50)>"
      ]
     },
     "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: f523bbe 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
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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: 28c3a29 'PDF' (896x60)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mermaid:\n"
     ]
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     "output_type": "stream",
     "text": [
      "asciipdf:\n"
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       "<wand.image.Image: 0f6cf76 'PDF' (664x337)>"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unicodepdf:\n"
     ]
    },
    {
     "data": {
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       "<wand.image.Image: 3be897c 'PDF' (13837x9)>"
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     "metadata": {},
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    },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "madgraph:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
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       "<wand.image.Image: 6cb23b2 'PDF' (139x139)>"
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     "output_type": "stream",
     "text": [
      "root:\n"
     ]
    },
    {
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      "text/plain": [
       "<wand.image.Image: cca4299 'PDF' (4821x1169)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Error in <TCanvas::Range>: illegal world coordinates range: x1=-4.400000, y1=0.000000, x2=4.400000, y2=0.000000\n",
      "Info in <TCanvas::SaveSource>: C++ Macro file: /tmp/tmpwnvz1tx4.tex has been generated\n",
      "Info in <TCanvas::Print>: TeX file /tmp/tmp82w82usj.tex has been created\n"
     ]
    }
   ],
   "source": [
    "v1 = Vertex(x=-2,y=0)\n",
    "v2 = Vertex(x= 2,y=0)\n",
    "l1 = Leg(x=-4,y=0,pdgid=25)\n",
    "l2 = Leg(x= 4,y=0,pdgid=25)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1, v2,\n",
    "    Propagator(pdgid=6).connect(v1, v2),\n",
    "    Propagator(pdgid=-6).connect(v1, v2),\n",
    "    l1.with_target(v1).with_incoming(),\n",
    "    l2.with_target(v2).with_outgoing(),\n",
    ")\n",
    "auto_label(fd.propagators + fd.legs)\n",
    "auto_bend(fd)\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8abc4e93",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: fdc04a0 'PDF' (158x75)>"
      ]
     },
     "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: 1000587 'PDF' (315x50)>"
      ]
     },
     "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: a11bec3 '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: 085a695 'PDF' (523x60)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mermaid:\n"
     ]
    },
    {
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     "text": [
      "asciipdf:\n"
     ]
    },
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       "<wand.image.Image: d929d4c 'PDF' (664x337)>"
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    },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unicodepdf:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: 3be897c 'PDF' (13837x9)>"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "madgraph:\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: 6cb23b2 'PDF' (139x139)>"
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     "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: 80c89eb 'PDF' (814x1169)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Error in <TCanvas::Range>: illegal world coordinates range: x1=-2.200000, y1=0.000000, x2=2.200000, y2=0.000000\n",
      "Info in <TCanvas::SaveSource>: C++ Macro file: /tmp/tmpuaegz_vt.tex has been generated\n",
      "Info in <TCanvas::Print>: TeX file /tmp/tmpmqxqycro.tex has been created\n"
     ]
    }
   ],
   "source": [
    "v1 = Vertex(x=-2,y=0)\n",
    "v2 = Vertex(x= 2,y=0)\n",
    "l1 = Leg(x=-4,y=0,pdgid=25)\n",
    "l2 = Leg(x= 4,y=0,pdgid=25)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1, v2,\n",
    "    Propagator(pdgid=6).connect(v1, v2),\n",
    "    Propagator(pdgid=-6).connect(v1, v2),\n",
    "    #l1.with_target(v1).with_incoming(),\n",
    "    #l2.with_target(v2).with_outgoing(),\n",
    ")\n",
    "auto_label(fd.propagators + fd.legs)\n",
    "auto_bend(fd)\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e06dc9c3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cffd8d56",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d90210fd",
   "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
}