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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7402c3b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pseudowalls import *\n",
    "%display latex\n",
    "\n",
    "alpha = stability.Tilt().alpha\n",
    "beta = stability.Tilt().beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "30570b37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(C, D, r, c, d\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(C, D, r, c, d\\right)$"
      ],
      "text/plain": [
       "(C, D, r, c, d)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var(\"C D r c d\", domain=\"real\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1eb8a0c7",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 0 \\\\ \\mathrm{ch}_{1} = 1 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 0 \\ell^{2} \\end{array}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 0 \\\\ \\mathrm{ch}_{1} = 1 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 0 \\ell^{2} \\end{array}$"
      ],
      "text/plain": [
       "<pseudowalls.chern_character.Chern_Char object at 0x7f2735ae0ee0>"
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Chern_Char(0,1,0)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c0e0ff38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7dqzy8vL017/+tc7WWRvvv/++9u7dqxtuuCGgPTIyUqNHj9bGjRu1atUqh6qDkxrauN+0aZNGjRqlIUOGKD8/v8q+jPvKEb4IGwsWLNCll16qU045pc7WGR0drTvvvFNPP/10SP179eqlKVOm6MCBA3VWgyR9+OGHkqTU1NQK81JSUiTJ8T8Q4IxwGPehWL9+va655hqNGDFCAwYM0Lfffqvrr7++ymUY95UjfBE2lixZovT09Dpf7yWXXKLPPvtM+/btq7bvp59+qiNHjqhXr16aOHGi9u/fXyc1bNq0SZLUpUuXCvM6d+4sSdq4cWOdbAsNSziM+6qsXbtWI0aM0HXXXafLLrtM3377rSZMmKDWrVtXuyzjvnJ1Er5ut1sHDx6sdH5JSUldbAa1cPjwYS1btkyLFi3SnDlztHbt2qD9li5dqs2bN1uu7j+2bdumf//73+rfv3+lfR5//HGlpaXp3HPPDfguq7y8XMOGDVOPHj2CjrX+/fsrKipKy5Ytq7aOhIQEzZkzR19//bWioqJ07rnn6v7779eePXtq98EkHT16VHl5eZKktm3bVph/6qmnSpIKCgpqvQ0EYtzXbNwHk5OTo8svv1w33nijRo4cqW+++Ub33XefWrZsGdLyjPuq1Un4lpaW6uGHH9ZvfvObCv+ijx49qjFjxmjNmjV1sSnU0J49e7R69WrNmDFDDz74YNAjua+//lrXX3+9o7cnbNiwQZJ0/vnnB52fmZmp0tJSrVu3TklJSZowYYJ/3k8//aTPP/9c27dvD/pXdKtWrXT++edr3bp1IdcTHx+vZ555Rlu3blVsbKxSUlI0btw4fffddzX5WJJ8F52UlZUpMjJSUVFRFeZHR0dL8gUG6gbjvnbjXvKd/bn44ot1++2366abbtKOHTt09913q0WLFjVaD+O+GnV5uXVZWZlZsGCBGTFihNm0aVPAvFtuuaVW61y5cqW58sorTWJiopFkli5dWu0y2dnZpk+fPiY6Otp069bNzJs3r0bbbIy3Gl199dUmIiLCHDp0qMK86dOnG0lm1apV9bZ9j8djnn/+efP444+bxx57zBw5ciRg/owZM0xERIQpKysLuvzw4cP9y5x77rlmwIABAfPfffddI8m43e6gy1999dXmggsuqHX9hw4dMg8//LBp166due2228w333wT8rL5+flGkomOjg46/9tvvzWSTJs2bWpdX31rqLcaMe5DH/d/+9vfTHp6uunZs6d54403zNGjR0NarjKNYdyHqjaZUWff+e7YsUPPPvusNmzYoNatW2vAgAG68cYbNXr0aKWkpKhVq1a1Wm9xcbHOO+88vfTSSyH137Vrl0aMGKFBgwbJ7XZr2rRpGj9+vDIzM2u1/cbAGKPVq1frvPPO85/qOaakpESvv/66+vbtqwsvvLBetr979249+eSTuuWWWzR9+nQlJCRo8uTJAX0OHDig2NjYoLccbNq0SRdccIGioqK0bds2bd68WVdffXVAn9GjRys+Pl7du3cPWkPbtm1P6tTxqaeeqpkzZ2rHjh3q3Lmz0tPTdcstt2j79u3VLlvdbRQ//fRTSP1QM4z70Mf9oEGDNGbMGP33f/+3vvrqK/32t79VZGRkDT5tRYz7atRF6k+fPt1ERkaaiIiIgKlZs2amZcuWZvz48aawsPCkt6MQjnwnT55sevToEdB29913m/79+4e8ncZ25Ot2u40kM2HChArz/ud//sdERESY1atX18u2jx49aqZPnx7wV/SyZctMz549A/rddttt5vTTT692fQ899JBp1qyZ2bt3b0B7eXm5ueyyyypdbsKECSYmJqaG1VfO4/GYxx9/3MTHx5sbbrihyiNhr9db5RHA2rVrjaSQPr9TGuKRL+M+9HG/ZMkS07t3bzNgwADzt7/9rdr+oWgM4z5Ujhz5vvfee8rKylJmZqb27t2r0tJSlZeXq7y8XGVlZXrhhRc0YMAAxR67Q7+e5ebmaujQoQFtw4YN0/r163XkyJGgy5SUlMjr9QZMjUl2drYk6eKLLw5oz8/P16OPPqp77rlHAwcOrJdtL1y4ULfeemvAX9FbtmypcPVj8+bNVV5eXu363n77baWnp6tjx44B7Zs2bVK/fv0qXS4mJka//PJLDauvXFxcnH7/+9/rt7/9rTIzM7VixYpK+7Zp00Yul6vS8XfsCCAxMbHO6gPjXgp93F977bXavHmzHnzwQU2bNk39+vU76VuAGPdVO+nw/fTTT/Xpp59q5MiRSkxMrPDF+p133qkVK1aouLj4ZDcVkoKCAnXo0CGgrUOHDjp69GilV2TPmjVLLpfLP3Xq1MlGqdZkZWWpWbNmGjx4sL/tyJEjuvnmm9WnTx89//zzAf1Xr16tRx55RJMnT9af//znk9r2/v37ddZZZwW0vfPOO7rzzjsD2lwul/8/xsps3bpVeXl5Ff64OrbOqu45/OWXX0K6NSIUhw4d0vTp05WUlKSff/5Z33zzjcaNG1flMsnJySovL9cPP/xQYd6xqz0rO3WI2mHc12zcR0RE6LrrrtMXX3yhhx9+WDNmzFCfPn20dOnSWj/sgXFfuZMOX5fLVe2l5/fcc4/eeuutk91UyCIiIgLeHxs4J7YfM3XqVHk8Hv9U3a+2NCTl5eXKyclRSkqK/yb+0tJS/frXv1ZsbKyWLFmi5s2b+/s//PDDeu211/SHP/xBTz31lF544QW98847kqTXX39dP//8c8jb3rlzp/8PmRdffFGPPPKIrr32Wg0aNEjXXXddQN/OnTvL4/FU+Vf61q1bJUlJSUkB7UVFRfryyy/9N+0H4/F4KvxRVlMHDhzQlClT1LNnTxUWFsrtdmvu3Ln++xWrcux7xa+//rrCvGM/MH98SODkMO59ajvur7rqKv3zn//Uk08+qdmzZ+u8887Te++9F9JR+vEY95U76fBt0aJF0B17vNTUVGs3UickJFS4b+zAgQOKiorSaaedFnSZ6OhoxcXFBUyNhdvt1uHDh3XJJZdI8l0EMnToUJ199tn661//GvBZ33jjDb399tvKyMhQZGSkmjVrpptuuklPPvmkJN89iTW5cG716tX+03per1fGGJWVlQW9ACQ5OdlfX2WO/ZHXpk2bgPZHH320woUsJ9qzZ4/OPPPMkGs/XkFBgSZOnKhevXrpyJEj2rx5s1544QWdfvrpIa/j2NHJ8uXLK8xbtmyZmjdvrmuuuaZW9aEixr3PyYx7Sbriiiv02Wef6bnnntPcuXPVu3dvvf322yorKwtpecZ9FU72i+b8/HzTo0ePSi91P+auu+462U2FfMHViRc1jBs3rslecDV79mwjySxatMjMnDnTXHXVVebzzz+v0O/o0aPmjDPOMM8880xA+7Jly0xERITZvn27WbBgQY22PXXqVFNeXh7Q9sMPPxhJFS5QKioqMlFRUWbx4sWVru/QoUOmffv25o477vC3ZWRkBL2g5kTdunUzU6dOrVH9e/bsMffff79p3769mTx5sjlw4ECNlj/RkCFDTNu2bc3Bgwf9batXrzaSzPTp009q3fWtoV1wxbj3qc24r0pOTo657LLLzNlnn20WLVpU4dapYBryuA9VbTKjTq52njt3rmnRooX5/e9/X+H+XmOM2bRpk7nttttqte7CwkLjdrv9Vy7OmTPHuN1us3v3bmOM7yrAMWPG+Pvv3LnTtG7d2kyYMMFs2bLFLFy40DRv3ty8//77IW+zMYXvqFGjTOfOnc2ECRNMTk5Opf0+++wzI8l8/fXXAe1ZWVlGkrn33nvNzz//XKNtT5kypULbwYMHjSTzySefVJh36aWXmvvuu6/KdW7YsMFcfvnlpn///ubCCy80TzzxRKX3SB5z7H98oV7FuXv3bjNu3DjTvn17M23atID/aZyMvXv3mvPPP9+cf/755t133zWvvvqqSUxMNCNHjjS//PJLnWyjvjS08GXc13zc10Rubq4ZPny4efjhh6vt25DHfagcC19jjHnxxRdNq1atTLNmzUzHjh3NlVdeaW677TZz9dVXG5fLZTZs2FCr9R77j+DEaezYscYYY8aOHWsuuuiigGWys7NNSkqKadGihenatSs/shGCd955x0RFRVX4i/3Y/s/MzKzR+g4fPmxmzJhRoT03Nzfo/+yMMWbBggWma9euFWo4We+++65xuVympKSk2r733HOPiY+PN4888oj54Ycf6rQOY3w/RPP3v//d/PGPfzSzZ8+ut1td6lpDC99QMe7taKjjPlSOhq8xvgdC33HHHaZt27b+e31TUlJMdnZ2XW6m3jXF8M3Ozg56P+AHH3xgJJnDhw/XaH0ff/yxefnllyu0T5kyxXTv3j3oMj///LOJj483//jHP2q0reqMGjWq2iOLYxYvXtyk/r2HqrGGL+MedcHRX7iSfFfjLViwQD/88IMOHjwoj8ejL774QhdddFFdbgb1YODAgfrVr36lnJwcSb5bMhYtWqQdO3aodevWKigo0CuvvOLvv3DhQnXq1KnS27fWrl1b4arxn376SW+88Yb/QpYTtWzZUo8++qieeuqpOvpU0r59+7R8+XJNnDgxpP6/+c1vGtUFd6ga4x5Oqbff9Tr11FMrXJ2H8BUVFaUVK1bo448/1syZMzV79mz1799fkyZN0ltvvaW5c+eqR48e/v7l5eX65ZdfKn1ajMfjUUxMjP9H3UtLS3XnnXfqjjvu0K9//etK67j77rtVXFxcZ8/4nDFjhsaPH69u3brVyfrQuDDu4Zh6PBJvsJriaefaOHz4cNDvxI4ePeq/4nP+/Plm+vTpZtKkSSGfVtu/f7/p27dvhZ/Sq6lVq1aZfv361fiCGVTUWE871wbjHidy/DvfxoLwDc2HH35ovvvuuwrtbrfbvPfeeye17p07d5pRo0bVevn8/HxzySWXmPz8/JOqAz6E738w7nEix7/zRdNx5MgRbdy4scJv1UrSmjVrTvpXa7p166b33nuv1stv3rxZ77zzjs4444yTqgM4HuMedaXiE46BEOTl5emuu+4KOq9t27Yn/VOOJ2vEiBGObh+NE+MedSXCmFr+YnYj5vV65XK55PF4uPIVkFRcLB17MFlRkRQT42w9QDipTWZw2hkAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsI3+NkZGQoOTlZaWlpTpcCAGjEuNUoCG41AgJxqxFQOW41AgCgASB8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8j5ORkaHk5GSlpaU5XQoAoBGLMMYYp4sIN16vVy6XSx6PR3FxcU6XAziuuFiKjfW9LiqSYmKcrQcIJ7XJDI58AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPA9TkZGhpKTk5WWluZ0KQCARizCGGOcLiLceL1euVwueTwexcXFOV0O4LjiYik21ve6qEiKiXG2HiCc1CYzOPIFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywvc4GRkZSk5OVlpamtOlAAAasQhjjHG6iHDj9Xrlcrnk8XgUFxfndDmA44qLpdhY3+uiIikmxtl6gHBSm8zgyBcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsaRPjOnTtX3bp1U8uWLZWamqpVq1ZV2jc7O1sREREVpm3btlmsGACAyoV9+C5evFgPPPCApk+fLrfbrUGDBmn48OHKy8urcrnt27dr//79/ql79+6WKgYAoGphH75z5szR7bffrjvuuEM9e/bU888/r06dOmnevHlVLhcfH6+EhAT/FBkZaaliAACqFtbhW1paqg0bNmjo0KEB7UOHDtWaNWuqXDYlJUWJiYkaMmSIsrKyquxbUlIir9cbMAEAUF/COnwPHjyosrIydejQIaC9Q4cOKigoCLpMYmKi5s+fr8zMTC1ZskRJSUkaMmSIcnJyKt3OrFmz5HK5/FOnTp3q9HMAAHC8KKcLCEVERETAe2NMhbZjkpKSlJSU5H+fnp6u/Px8zZ49W4MHDw66zNSpUzVx4kT/e6/XSwADAOpNWB/5tmvXTpGRkRWOcg8cOFDhaLgq/fv3144dOyqdHx0drbi4uIAJAID6Etbh26JFC6WmpmrFihUB7StWrNCAAQNCXo/b7VZiYmJdlwcAQK2E/WnniRMnasyYMerbt6/S09M1f/585eXlady4cZJ8p4z37t2r119/XZL0/PPPq2vXrurVq5dKS0v15ptvKjMzU5mZmU5+DAAA/MI+fEePHq1Dhw5pxowZ2r9/v3r37q3ly5erS5cukqT9+/cH3PNbWlqqSZMmae/evWrVqpV69eqljz76SCNGjHDqIwAAECDCGGOcLiLceL1euVwueTwevv8FJBUXS7GxvtdFRVJMjLP1AOGkNpkR1t/5AgDQGBG+AABYRvgCAGAZ4QsAgGWELwAAlhG+AABYRvgCAGAZ4QsAgGWELwAAlhG+AABYRvgCAGAZ4QsAgGWE73EyMjKUnJystLQ0p0sBADRiPNUoCJ5qBATiqUZA5XiqEQAADQDhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhe5yMjAwlJycrLS3N6VIAAI1YhDHGOF1EuPF6vXK5XPJ4PIqLi3O6HMBxxcVSbKzvdVGRFBPjbD1AOKlNZnDkCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYTvcTIyMpScnKy0tDSnSwEANGIRxhjjdBHhxuv1yuVyyePxKC4uzulyAMcVF0uxsb7XRUVSTIyz9QDhpDaZwZEvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb7HycjIUHJystLS0pwuBQDQiEUYY4zTRYQbr9crl8slj8ejuLg4p8sBHFdcLMXG+l4XFUkxMc7WA4ST2mQGR74AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFhG+AIAYBnhCwCAZYQvAACWEb4AAFjWIMJ37ty56tatm1q2bKnU1FStWrWqyv4rV65UamqqWrZsqTPPPFMvv/yypUoBAKhe2Ifv4sWL9cADD2j69Olyu90aNGiQhg8frry8vKD9d+3apREjRmjQoEFyu92aNm2axo8fr8zMTMuVAwAQXNg/z7dfv37q06eP5s2b52/r2bOnrrnmGs2aNatC/ylTpujDDz/U1q1b/W3jxo3Tpk2blJubG9I2eZ4vEIjn+QKVa3TP8y0tLdWGDRs0dOjQgPahQ4dqzZo1QZfJzc2t0H/YsGFav369jhw5EnSZkpISeb3egAkAgPoS1uF78OBBlZWVqUOHDgHtHTp0UEFBQdBlCgoKgvY/evSoDh48GHSZWbNmyeVy+adOnTrVzQcAGomYGMkY38RRL3Dywjp8j4mIiAh4b4yp0FZd/2Dtx0ydOlUej8c/5efnn2TFAABULsrpAqrSrl07RUZGVjjKPXDgQIWj22MSEhKC9o+KitJpp50WdJno6GhFR0fXTdEAAFQjrI98W7RoodTUVK1YsSKgfcWKFRowYEDQZdLT0yv0/+STT9S3b181b9683moFACBUYR2+kjRx4kS98sorevXVV7V161ZNmDBBeXl5GjdunCTfKeNbbrnF33/cuHHavXu3Jk6cqK1bt+rVV1/VwoULNWnSJKc+AgAAAcL6tLMkjR49WocOHdKMGTO0f/9+9e7dW8uXL1eXLl0kSfv37w+457dbt25avny5JkyYoIyMDHXs2FEvvPCCrr/+eqc+AgAAAcL+Pl8ncJ8vACBUtcmMsD/ydcKxv0e43xcAUJ1jWVGTY1nCN4jCwkJJ4n5fAEDICgsL5XK5QurLaecgysvLtW/fPrVp0ybovcFer1edOnVSfn5+nZyWTktL07p16056PU1hXex759YVzvu+rtcXjusK5/3f2NdV3b43xqiwsFAdO3ZUs2ahXcfMkW8QzZo10xlnnFFtv7i4uDr5jyAyMrLOvltuCuuS2PdOrUsKz31f1+sL13VJ4bn/m8K6pKr3fahHvMeE/a1GTcG9997LuhwSrp8xXNdVl+q6rnDdZ01h/zeFddU1TjvXAldDO4d97xz2vbPY/86pj33PkW8tREdH65FHHuEnKR3AvncO+95Z7H/n1Me+58gXAADLOPIFAMAywhcAAMsIXwAALCN8AQCwjPAN0RNPPKEBAwaodevWOuWUU0JaxhijRx99VB07dlSrVq108cUX6+uvv67fQhuhH3/8UWPGjJHL5ZLL5dKYMWN0+PDhKpf53e9+p4iIiICpf//+dgpuwObOnatu3bqpZcuWSk1N1apVq6rsv3LlSqWmpqply5Y688wz9fLLL1uqtPGpyb7Pzs6uML4jIiK0bds2ixU3Djk5ObrqqqvUsWNHRURE6IMPPqh2mboY94RviEpLSzVq1Cjdc889IS/zzDPPaM6cOXrppZe0bt06JSQk6PLLL/f/djRCc9NNN2njxo36+OOP9fHHH2vjxo0aM2ZMtctdccUV2r9/v39avny5hWobrsWLF+uBBx7Q9OnT5Xa7NWjQIA0fPjzgkZ3H27Vrl0aMGKFBgwbJ7XZr2rRpGj9+vDIzMy1X3vDVdN8fs3379oAx3r17d0sVNx7FxcU677zz9NJLL4XUv87GvUGNvPbaa8blclXbr7y83CQkJJinnnrK3/bLL78Yl8tlXn755XqssHHZsmWLkWTWrl3rb8vNzTWSzLZt2ypdbuzYsWbkyJEWKmw8LrjgAjNu3LiAth49epiHHnooaP/JkyebHj16BLTdfffdpn///vVWY2NV032flZVlJJkff/zRQnVNhySzdOnSKvvU1bjnyLee7Nq1SwUFBRo6dKi/LTo6WhdddJHWrFnjYGUNS25urlwul/r16+dv69+/v1wuV7X7MTs7W/Hx8Tr77LN155136sCBA/VdboNVWlqqDRs2BIxXSRo6dGil+zk3N7dC/2HDhmn9+vU6cuRIvdXa2NRm3x+TkpKixMREDRkyRFlZWfVZJv6/uhr3hG89KSgokCR16NAhoL1Dhw7+eaheQUGB4uPjK7THx8dXuR+HDx+ut956S//4xz/0xz/+UevWrdOll16qkpKS+iy3wTp48KDKyspqNF4LCgqC9j969KgOHjxYb7U2NrXZ94mJiZo/f74yMzO1ZMkSJSUlaciQIcrJybFRcpNWV+O+ST/V6NFHH9Vjjz1WZZ9169apb9++td7GiY8kNMYEfUxhUxPqvpcq7kOp+v04evRo/+vevXurb9++6tKliz766CNdd911tay68avpeA3WP1g7qleTfZ+UlKSkpCT/+/T0dOXn52v27NkaPHhwvdaJuhn3TTp877vvPt1www1V9unatWut1p2QkCDJ91dSYmKiv/3AgQMV/mpqikLd95s3b9a///3vCvO+//77Gu3HxMREdenSRTt27KhxrU1Bu3btFBkZWeFIq6rxmpCQELR/VFSUTjvttHqrtbGpzb4Ppn///nrzzTfrujycoK7GfZMO33bt2qldu3b1su5u3bopISFBK1asUEpKiiTfdzsrV67U008/XS/bbEhC3ffp6enyeDz65z//qQsuuECS9Pnnn8vj8WjAgAEhb+/QoUPKz88P+EMI/9GiRQulpqZqxYoVuvbaa/3tK1as0MiRI4Muk56ermXLlgW0ffLJJ+rbt6+aN29er/U2JrXZ98G43W7GtwV1Nu5rdHlWE7Z7927jdrvNY489ZmJjY43b7TZut9sUFhb6+yQlJZklS5b43z/11FPG5XKZJUuWmC+//NLceOONJjEx0Xi9Xic+QoN1xRVXmHPPPdfk5uaa3Nxcc84555grr7wyoM/x+76wsNA8+OCDZs2aNWbXrl0mKyvLpKenm9NPP519X4V3333XNG/e3CxcuNBs2bLFPPDAAyYmJsZ89913xhhjHnroITNmzBh//507d5rWrVubCRMmmC1btpiFCxea5s2bm/fff9+pj9Bg1XTfP/fcc2bp0qXmX//6l/nqq6/MQw89ZCSZzMxMpz5Cg1VYWOj//7kkM2fOHON2u83u3buNMfU37gnfEI0dO9ZIqjBlZWX5+0gyr732mv99eXm5eeSRR0xCQoKJjo42gwcPNl9++aX94hu4Q4cOmZtvvtm0adPGtGnTxtx8880VbrE4ft//9NNPZujQoaZ9+/amefPmpnPnzmbs2LEmLy/PfvENTEZGhunSpYtp0aKF6dOnj1m5cqV/3tixY81FF10U0D87O9ukpKSYFi1amK5du5p58+ZZrrjxqMm+f/rpp81ZZ51lWrZsadq2bWsuvPBC89FHHzlQdcN37LatE6exY8caY+pv3PNIQQAALONWIwAALCN8AQCwjPAFAMAywhcAAMsIXwAALCN8AQCwjPAFAMAywhcAAMsIXwAALGvSD1YAUHOFhYVasGCBtmzZotLSUiUnJ+vBBx/kYQpADfDzkgBCtn79er344ouaNGmSzjnnHBljNGrUKMXExOhPf/qT0+UBDQannQGE5Msvv9Qrr7yihQsX6pxzzpHke3j4kCFD9Oabb6qwsNDhCoGGg9POAKpVUlKimTNn6vXXX1dUVOD/Nvbs2aPy8nKVlpY6VB3Q8HDaGUC1nnvuOaWmpmrw4MEV5p177rmKiorSF1984UBlQMPEaWcA1Vq3bl3Q4F2+fLm2bNmiefPmOVAV0HBx2hlAlTZt2qQ+ffpIkvLy8vTEE0+ovLxcJSUlysrK0l/+8hf169fP4SqBhoUjXwBVys7O1qWXXipJKi4u1rFvqqKiovT999/zXS9QC3znC6BKt956q1555RVFRkZWmHfDDTdo7dq1+u677+wXBjRgHPkCqFJ5eXnQ4JWkM888U7t379bOnTstVwU0bIQvgEpt2bJFPXr0qHT+oUOHJElFRUW2SgIaBcIXQKVycnJ04YUXVjp/48aNioqKUteuXe0VBTQChC+ASuXk5Oiss84KOu/gwYPasGGDLr30UsXFxVmuDGjYCF8AlVq1apV+/PHHoPNeeeUVlZWVafr06ZarAho+whdAUDt37lSPHj20ZMmSCvP27Nmjp556Sg8++GDQH98AUDXCF0BQOTk5mjx5sn744Qe99tpr/vt7t2zZoiuuuEJ33XWXnn32WYerBBom7vMFENTdd9+tOXPmqHXr1nr77bf10UcfKTIyUrGxsbrjjjuUmprqdIlAg0X4AghqzJgxeuONN5wuA2iUOO0MoIJ9+/bp9NNPd7oMoNEifAFUsHLlSl100UVOlwE0WoQvgAq+//57DRw40OkygEaL73wBALCMI18AACwjfAEAsIzwBQDAMsIXAADLCF8AACwjfAEAsIzwBQDAMsIXAADLCF8AACwjfAEAsIzwBQDAsv8HCcNZxYdrLEkAAAAASUVORK5CYII=",
       "Graphics object consisting of 4 graphics primitives"
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_range = alpha, 0, 2\n",
    "beta_range = beta, -1, 1\n",
    "black_text_args = {\"fontsize\":\"xx-large\", \"clip\":True, \"rgbcolor\":\"black\"}\n",
    "\n",
    "Theta_v_plot = implicit_plot(stability.Tilt().degree(v), beta_range, alpha_range)\n",
    "Theta_v_plot += text(r\"$\\nu_{\\alpha,\\beta}(v) < 0$\", (0.5, 1), **black_text_args)\n",
    "Theta_v_plot += text(r\"$\\nu_{\\alpha,\\beta}(v) > 0$\", (-0.5, 1), **black_text_args)\n",
    "Theta_v_plot += text(r\"$\\Theta_v$\", (-0.1, 1.5), rotation=90, fontsize=\"xx-large\")\n",
    "Theta_v_plot.axes_labels([r\"$\\beta$\", r\"$\\alpha$\"])\n",
    "Theta_v_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5bf18ed0",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 1 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 1.80000000000000 \\ell^{2} \\end{array}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 1 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 1.80000000000000 \\ell^{2} \\end{array}$"
      ],
      "text/plain": [
       "<pseudowalls.chern_character.Chern_Char object at 0x7f9ed152cc10>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_range = alpha, 0, 2\n",
    "beta_range = beta, -2, 2\n",
    "\n",
    "u_1 = Chern_Char(1,2,1.8)\n",
    "u_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "26d52f14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 1 \\\\ \\mathrm{ch}_{1} = -2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 1.80000000000000 \\ell^{2} \\end{array}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 1 \\\\ \\mathrm{ch}_{1} = -2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 1.80000000000000 \\ell^{2} \\end{array}$"
      ],
      "text/plain": [
       "<pseudowalls.chern_character.Chern_Char object at 0x7f9ed1547dd0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_2 = Chern_Char(1,-2,1.8)\n",
    "u_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "be444fa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implicit_plot(stability.Tilt().wall_eqn(u_1, v)/alpha, beta_range, alpha_range) \\\n",
    "+ implicit_plot(stability.Tilt().degree(u_1), beta_range, alpha_range) \\\n",
    "+ Theta_v_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2452201f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implicit_plot(stability.Tilt().wall_eqn(u_2, v)/alpha, beta_range, alpha_range) \\\n",
    "+ implicit_plot(stability.Tilt().degree(u_2), beta_range, alpha_range) \\\n",
    "+ Theta_v_plot"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.0",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}