Hermite interpolation using quintic polynomials

hermite_quintic.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "91906542",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "23ec6e11",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy as sym\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5007fda1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.11.1 (Python 3.11.5-64-bit) (ground types: python)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.11.1/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "sym.init_session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "167e739c",
   "metadata": {},
   "outputs": [],
   "source": [
    "a, b = symbols(\"a b\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b80be86c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L0/CGZ+H5XveU0T4P3dXtlXH/ajxjqHIIdxClxvTEB/B/I0lAisWg8Oaj86R07WSn81mF0D2VnQLRvTFVmBWQtwpfkxg/Ookf85wGecnBozgYQHBDDuvD5Sq/6OWpeIrnucEjHgXheMVn3ULdD+pNcWrCmRLuhwpM9ZZcnRb/sWE+rYk711ChMBsYC0FjjWnt165UIU+rXUsOFE4K/lnBVhjGi41RqZhOlrrGuDNAHQ/iMgAbP69oixM6/UG8xLqlgEP8V4xHz1ABFvcQHcfRj3hBBxeNrML/S7jOrrHRedM4I9h2S3lMlTOMsJNJTbjvjOtrZzHMoNgbnalwjjwI3HcbBPb/LH6ygXzXEiyeu89Q8qB1xgjRlWC5RHcojMFaKjyFgANZUvjPWjSF8d9rHTUQhZjuQUfiD/3D9xbxdDgyLsDIYbQlvRnPQ2dXPsNI0u/n/t56A9XgfhwyOnCN98Rrxqc6M3jOOZzQptvlSHxgFCCECTHAS9eKtWiTvW1wKef9UKkxVoxPxWRuNC0VvDmexScVHn4ZzKWrhQHruoG6X43EBy3uvefN+AAfS0HMC9kMHgNw7eyxghECO2WMhgOdbUJv4jOLhI0uLfXZXiTQ0NNw/p/C3vpEqtHvLjcgzdLUxiKp8ODNULDca+ONsX/B7t7wXAD0AUfBGeOfArfScG9kdX50F2fQ7psEmgSaBGqTQEnXrzbeD8GPWhO6Igy6013kTRQvNX7TuZtEqvtGTQK7lkAzVJWrVwaJcbfU25nKOW/sNQlMJ4FmqKaTZUspQwJH8RCPgjNW+Vy4m6GKJd3uZ5XAUTzEo+CMC8tcuNtgeizpdt8k0CRQnQQwVIyBMFh7NvmwOk4bQ00CTQJHkwDzuLBNJ7p+vFVi0heBNtFLl42aBKaXgLoGzPh+4VOm7EGfKnxXZU94wHavAweAayZIv1S4Tf7V7f5JePksUN/C5yEBID9s09dtjGpIVO3/qSXApFXXSpKwrimIzMrfxURWMHliGgmzv90qCZ1ZntI2IDXpFJ7vCuO36E0CYyXwXJWWltKICt02IDVpLHiWHlhEf0YKY62qebpn/5XceB2ffS2k5Pk4bpFHpcztCwqs9aMFpHWcjJmYuZx75Y+wWZO1+mdexQsKtjlPfGUAt59vg2/S3fd4zPuhywY+dM4wwa1EeqnPGd+a3uTPCR9linWYhr04Dz0b69wtgSpOaN4H2gakc8pXhYBKw3fGMQQYhNEtgNIYReIJHliR3n0sT9cYdvro4ULeUfks9bB4RsZnO7IojMrWNiAtUIJkRpfvmQ7KhusGFjw+d1TqD4RhxuFgQTzjaGPHC/Ga2wakCFJH24BUpWpGYkEoBQ7jZGSelA2GW/hNZ6VNBSH9Wwdbb8r32kPiyT51ci1a9n9Kj6VOH+loG5BmS+0y4t1lUDKE79PEriwR+QQGn8Og9T06Me7SNiDNLAUqM3igeJyrd9mNZfGE4cSbGOtRWJLurHRJjyEBus3ksUvyOuXzxpMPB+WOUVEJU26rMcT/VXxHacUSgLfB1lJ9hfzdFXkrzlo4wHO2Y4zCzLviTd3NpHQwUnQrXTfZ3590tvJ0c9ojH3wmHs66u7ekpzTQdduA1H98UPKgQXqt8802YtBQeaEP6evJUIS9/y854XWmyLWg+r/zSL1M7QN7zK/hK6lUXsYyoFFKfUhi2l/xTGNEgWOQ+azRKsGjuODE0GEQzLtg0NpeQuhyeRIvdPmuGuBcnIrH0ATjP6HhRX40Yt/qqIbEJ+UQw8qXctHNxVyvAtyU8bCckx7pjx73ulMiQ2RGCCH3EUAbRRKQgqmIKCuuhHQB2gakD/OnmEPFWNi18hVJdtpb5Y2OMC6hYUllUqI3Gq4XSvNzDl3jPVbTzfXgqLdtA1IvjCOfmDbBllLdt6N0TQuDZ2JEBaVLhVcF0TB0/ys+hckGr6lQ0GIzuZV/10rqGj7bBqROBc47uqa3Tm4P0ev7lT5d19s40z0TVOny41m6Cbi6LyqvQVp43Weet/13y5mu3zv+QTvH6byJA4J787aYV9UokIAUjLJRfNwlLN3QkVa8m8/j011lJrfyxuhiWNsGpA9vKtlNB3mcdI71TPAWCa+SF2RtA9Itaq+EZymZVmiSDUiVDt0iDINNDcDbIoyBe1rtWYj0STiRB5M1GW/hKN6AVOmt6iGK547ECx4qM7GHunwnxYll/YmefdklFl0ofjU4I9bcrfibZQPSiXH/arzjUeUQlcS6HWF886isEoX/HfJaiqI7MOUGpHhTGIelCa/tJDyTbkCqJKvxEMULZXqWDUgrwyl2LuhDhaR6S65OS++xYaYs0DhhgLu3dwrjnv/echbNot9cQ8VYSzdu4th5+GGiXuf+BuGHvJSy8EIm3YBUacb9fAwXXcqLgjSx0Cl4k29AqjTxBhf3EFOyER80sBeNrMJHb0BaE84UdoXNsgHpXLjvekCcBUtxVBb2nMNbcKRrLCnurw0CP/yx/C+vVSHz7h7uFv6VPGidMeh0JdzmjnZWGK/0qfi0SBzIEvmdtWgK4z8m0SZJ/2MI0cESM7l5UznHBqRreYhJmfYEohsOo1v0VjtOV0YNIGeVL95OQjbeVg3u7H39BALF4VW91cHg+VMdF3MuFLYIiR+MAoQw4Q0Pg7GGVTYgFT+/KO9U91jBzuvk1bTJkLgn3TNFAcPD2xe6Whiwzq3WfUcKJ20G6Fk6hA5mJ+WDbK3Qkh884No7L0Tnm/GQGKQ0KFN/1Xn1z7yIB+QLRnBD6IKGg4YaPov1pmcc1YQz4AmsNnWGhp6Gk/ltrnzpvKp+lT9jvRjUR9mGSg80WkkCUpQrUDrTSp/8PefBQeCVWM7KVvzjIdLg1Da/KIv/3EhHwRnLYyxuPd8Zqsdx4u2+LglIWRgpWvqqZnKPlZLHhZeydyOF/naPMy4PU+u3GapYwvXd0yXEBXdv4Yw9FQTnXdn9ls6+EGN43YRDf3/SedMeYqwDj2v3OJfA3QxVLOXK7lXYzxYGV8ZeMTu+8u7OQ4wFcRScS+FuhiqWdLufWwK78xB7BHYUnDH8WXA3QxWLud3PKoG9eYh9wjoKzhj/XLjv4ozafZNAk0CTQG0SwFAxgMnA7Nnkw9oYbfw0CTQJHE4CzNdzL43o+tnrbwLdRK/DiaMBbhJYQALqFvH29oXPinoHLfbJnofslv8VbrDe68AZ4jp3sjjP8OLl6zZGJSk0ahJYSAKzLNhdiPcx2TCPjPWpbt2qzizVKdqM9W5M7u3ZJoEmgSIJPFclxUswogLvcfNVw2fnl7p4ZTc6sz63aKipyKOSkBEs9JuO1TcgrY0fJ5mMH/GN+2trrOxzG0wM/Dnj8cWjBHK2vF/VyqsxOHQW/1eX7+j/OXTEeMsan+w5leBR3EnrudKLyzXrWy2PIVW5/7MNlTJjfgSLkN2iWZ3dbGmd2a9s8RnFyrMqfrKkrUjimwrAQsvuM7C6RmnVbVTqeWUtHkbUFiJzz7H6ImLxUETCQJkd3LjW455cR0p3lU/2lOBR3NnqldKmy/dMB7KNZXFVl1ldPyXK4kA+X9Kt7Nc1A+/cM9i1KNXGTyF4jJJ7k2HPCQ/eFfLEANRE8IP35IyUZ4zKvnjDNIVQKLM6cjaunV1H4mPJT/Zk4RFPs9ZzpX/zZqxZhkqFhE99xO4bZee1jnsxQOFdkmrjpwQ7YxTVb1QqneKeU5nOWj6F40F33mAJ8A3FnVVHkh9eNcZjqQXZuXhmr1fCToNMw8yLBcpXFuV2/QB6VmB96tay8n/nbWXlPC5SbfyUoME72cJGpXh9eCAUrKPRbDryRmrphcq5eCavV8KLEzN6M9bHQyXQZzQU7clQhKn+r42fUlzin1YrRa510f8pzzUVf+4wBvl5pQxfjCvYC5TwM8KOB68Tug3QUx2f6sBr4DnoteIs2ZA95Hrjr3jN1lEJdsVFJosvyM7B43EMSayr57m4FY/G7o0SNqeGPDCINIDZm7He8dQAGXPXWlas5lJUGz+jcUuRGAMKMS5xLWQ6/VD84QHwNVK8LAwV3cKQcOM3saFqyHTJtfD16agEOwPVVFLOdjBl4VrdKmEzO24CT2m9KsGN4X+hPG/ejHXQo8pEbt8tz4w+e7Ta+BkCzKD12UalQw/M+b8KlBkpuqhxl59W8BuFu40fdMaTYrzFiEqHIcOrgqgA4f8nPUP6fG+fb8kv8f13ZTWaLnRUil3xa/pkzwWeDAm5enUDbnoJo3oKOYYKt62PzArTLViKauNnFG4pna4AXay+7sao9Ec+HLrrlhSeAMaJriFjH0UbqgonngleBWQG8eGu0t8rOirCXgu8Hjwl9Wpx3INdP4GihYRShcrCUgX64amJf2vjZww8YaHCJzcqHZPu2GcDGZvuU0nSVT0pbtxS4im9Sj1g8fUMr6kXKzN9vOSEi9deHZVi9/iZ5kN3D4O/OPXhUbjp2up0yJuFOZ0pbpHOSUjPjMKd41GRDy2nK5jcBGQeFf8vSbXxU4xdiqN7lLVRaXHi0zzQJ2NL/cLQCBOeEoW6GzingPKAzm85b4nEc7aOFHcQu+Ks6k1m4OnTeW89Xwr3oEflCxb9WVz9mBhfWGMD0tr4ieVy9d4X2L6NSq+54FfTnfhPuqSpxgmd8yaHMSpaSbYns66cTWkIjRiDqFs0UhiVXh3dgl3PUFdW8SaV71U8vuwM1qu1cGcZKjHHgCp7ztHCOIJhXeDm26Dpwx8L/NbGTwlk8U7lp0BQyVlK0B0Ks41KS5KcJa74wivCGHUD4bqOdY6B4qBs8N+ZkVUY/73WUSO5gWExZt5Cx6P4ztHRZrBn4jkpXk49XwX34047wxe0pLySZJ4Mg+ecP9J93F9V8CJUGz+5oNl9mIrA2EdMa8ky5sPdS7fMQkfntkyKSh3qnK4ChZvCe1I8DC0eFvEZg8GAdd1A4qxN4odGAnI868x0CzzAcOPaHB1tCXsOHmQCDdWrVXC3DUgflNN+F5aAjAPeOUZwc4ubx4rqqNhLcSs+jTk9jkdZXb+ximnPNwk0CTQJjJFASddvTD7t2SYBJwG1jnR7GXSn68VH4xgD+01nBpkbNQkkJdAMVVIsLXAuCcggMR5U01KhuaC2dCeUQDNUEwqzJdUkcE0CR/Ump8DdDNW1ktX+axKYUAJH9SanwN0G0ycsiC2pJoEmgXkk0DyqeeTaUm0SuJCAPAsmxb7wf/BSAWr7+j3I4epvM1RXxdP+bBKYVALMG+ONpyNd28TYvc8l481u29fP672dmgRql8BzGaf7gEkqcNvXLxBI32XzqPok08KbBKaXAN7UT9MnW3eKMs7x0jC3KqGE6yJDpQxtgSpr/doGpCWSDuJKjoxP2FwivkrBYt62AWkgo7kvpQO+JsC6v+ROMHPoSGnGX0vFcNEliivy5PBL8CjuLPVc6c67rx9SUyYsMuUj/e772bqmorGQ0wYFdbsc1cZPLnIvL9YvsYDXPsVLQWUD0rBbkJvkbPHgVQd6R8/oHZ2jb1vYO1vecyQs/vliBYuQGRtiI9Jk2dX/hM+qI+WBocSzYBHwrFSCR3Fnq+dKm9UHH+lgsTtGK5vucmIqURYHouRuJbyu3yqMe5S+KNXGTyF4WqtuQJVnhQcDgDxrMwDw80r8sWLeiDdX4femLLz6s3C81bH6BqTiAUNIOUh6czMIMqvMia/Z6zk6ED7KOy8WMNZZlGWolBLf8065p68Vfq8MKbxLUm38lGDHa2obkJZIbPm4s+lIdQUjhXeKV4HhxGslbE7KxTN5vRI2HJz/6giNEsYKYtgji3INFUAZR4nJWlb+X5Jq46cEO94J4xKmrPjZpY1+nL/d4/VRkfr4tHh7PM+iI8kSg0QPhG4lO/xQefEuUnVLwZNRLp7J65UvP+AzWwEo8qFcfctNDj0eiqSMcirOk6F0pvq/Nn5KcYl/Wq0UuRZH/6c811T8ucNo7TCo8PVMh71AYYwn7AqedE8ZsQ8BPtV124A0vfkq45DO9vAAAAO1SURBVD/IinNHkt/ZUED3x0QXSn+wzHkdDuXY1fNCnZP/Cz1DGYIoI0Xd3kFDpQSNOSxgH+UYs75nS8Nr46eU/4v4UiDGwHUJLv5cL8B06jYgNTbEK248s6m78Ur9101kVDiDpAxU24sXPAjGSML4ut0WCVefjrKxK41q9vVL4CmtVyW4aXxHNcA5hiqnRL2XE2nBOLXxMwSdQetDbECqCoIBfOEFYmMzW1hGcqEjYcGLxAgb0ZjzJs/2EaDyh/9bvBrOF3gymHL1ag3cOYaK/mUfmRU2l64v3pThtfEzCpuUjsdBF6vPPR+V/siHw3EFS4puCxWUriFdwNLNKLuWWM+ePH7SrHYZyRUdlWIH8urUg6ekXi2Oe9BQCRQDqgjXugKhoC0sVaDDeJNd18bPGGDCQoWvcgNSr3M8hD5y3pDixS49OxO97HtI4SwjCce58DgIY3A5TutKMsv8JZ56dZTg9yp2xae+rOpN9uFReHY9XwP3oKHyxYGW09z0sISYR3U2uBpGmOm6Nn6KYUrZdBGOuAEpA8c/FQtshQdKdKS492IRQ9SNxSnMNeQ6m8Ff1ZvMwFNcr5bCfZepf/qzuPoxMauWTRVNEfH/c93Xxk8RTsnrAz3Qu7llUWLzRaZLmmqc0Dmt700bkOq5r6PyguFaZBlJiaiGdKT/39XBjH0MFAQO5BL2LnjTFdYNPEeLzzN4k4ssSla+OWVusF4pnVVwZxkqMZezMSGCX4Rq46cEtHin8lMgUDjzabpDYYfagFTYqTx4lhi/pckNDCtT6xV0+WfqCIPDUbL56ireZCaek+Ll1PNVcD/utDN8QWHCdWUOBIPnnMPNKHW7KNXGTy74ks0gc9OcJZ50zexpdI53BVGpQ53TVbhpA1KlicHGoyiaT6P4o0j50khAVDiI8TK8oNk3IFU+ay1KLilzQ/WqWOdT4G4bkLqy2n6WlIAKLkaKZSR4GCd/zznsNi3J0uJ5CSveJEZzUUO9ONAowxLcisuLDHocj0o8qijLdtskUC4BFTqMFB4ahorKCmGwWEpyCPIyWNybXFu4Y3A3Q7W29o6XP3OmeBvGuSMVYudddQE7vfCV1S1KBqK/57xrb9LjvBl3M1Q7rRC1wlKBrWYZydIy8pX1cN7kFLiboVq6tLb8jiyBo3qTo3E3Q3XkatOwLyqBo3qTU+AODRUfc4sVx0LZGtegxXy2+yaBJoENS0B25hexz4uWJGGoGMTrG8jc9QBfUiItsEmgSWANCfAWtJf+H8rST3HxnyjoAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & x_{1} & x_{1}^{2} & x_{1}^{3} & x_{1}^{4} & x_{1}^{5}\\\\1 & x_{2} & x_{2}^{2} & x_{2}^{3} & x_{2}^{4} & x_{2}^{5}\\\\0 & 1 & 2 x_{1} & 3 x_{1}^{2} & 4 x_{1}^{3} & 5 x_{1}^{4}\\\\0 & 1 & 2 x_{2} & 3 x_{2}^{2} & 4 x_{2}^{3} & 5 x_{2}^{4}\\\\0 & 0 & 2 & 6 x_{1} & 12 x_{1}^{2} & 20 x_{1}^{3}\\\\0 & 0 & 2 & 6 x_{2} & 12 x_{2}^{2} & 20 x_{2}^{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡         2      3      4       5  ⎤\n",
       "⎢1  x₁  x₁     x₁     x₁      x₁   ⎥\n",
       "⎢                                  ⎥\n",
       "⎢         2      3      4       5  ⎥\n",
       "⎢1  x₂  x₂     x₂     x₂      x₂   ⎥\n",
       "⎢                                  ⎥\n",
       "⎢                 2      3       4 ⎥\n",
       "⎢0  1   2⋅x₁  3⋅x₁   4⋅x₁    5⋅x₁  ⎥\n",
       "⎢                                  ⎥\n",
       "⎢                 2      3       4 ⎥\n",
       "⎢0  1   2⋅x₂  3⋅x₂   4⋅x₂    5⋅x₂  ⎥\n",
       "⎢                                  ⎥\n",
       "⎢                         2       3⎥\n",
       "⎢0  0    2    6⋅x₁   12⋅x₁   20⋅x₁ ⎥\n",
       "⎢                                  ⎥\n",
       "⎢                         2       3⎥\n",
       "⎣0  0    2    6⋅x₂   12⋅x₂   20⋅x₂ ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1, x2, x = sym.symbols(\"x1 x2 x\")\n",
    "V = sym.Matrix([\n",
    "    [1, x1, x1**2, x1**3, x1**4, x1**5],\n",
    "    [1, x2, x2**2, x2**3, x2**4, x2**5],\n",
    "    [0, 1, 2*x1, 3*x1**2, 4*x1**3, 5*x1**4],\n",
    "    [0, 1, 2*x2, 3*x2**2, 4*x2**3, 5*x2**4],\n",
    "    [0, 0, 2, 6*x1, 12*x1**2, 20*x1**3],\n",
    "    [0, 0, 2, 6*x2, 12*x2**2, 20*x2**3]])\n",
    "V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8076eecd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{b^{3} \\left(- 10 a^{2} + 5 a b - b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{a^{3} \\left(a^{2} - 5 a b + 10 b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{a b^{3} \\cdot \\left(4 a - b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{a^{3} b \\left(- a + 4 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & - \\frac{a^{2} b^{3}}{2 a^{3} - 6 a^{2} b + 6 a b^{2} - 2 b^{3}} & \\frac{a^{3} b^{2}}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)}\\\\\\frac{30 a^{2} b^{2}}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & - \\frac{30 a^{2} b^{2}}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{b^{2} \\left(- 12 a^{2} - 4 a b + b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{a^{2} \\left(a^{2} - 4 a b - 12 b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{a b^{2} \\cdot \\left(3 a + 2 b\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} & \\frac{a^{2} b \\left(- 2 a - 3 b\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)}\\\\\\frac{30 a b \\left(- a - b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{30 a b \\left(a + b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{6 a b \\left(2 a + 3 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{6 a b \\left(3 a + 2 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{b \\left(- 3 a^{2} - 6 a b - b^{2}\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} & \\frac{a \\left(a^{2} + 6 a b + 3 b^{2}\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)}\\\\\\frac{10 \\left(a^{2} + 4 a b + b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{10 \\left(- a^{2} - 4 a b - b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{2 \\left(- 2 a^{2} - 10 a b - 3 b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{2 \\left(- 3 a^{2} - 10 a b - 2 b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{a^{2} + 6 a b + 3 b^{2}}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} & \\frac{- 3 a^{2} - 6 a b - b^{2}}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)}\\\\\\frac{15 \\left(- a - b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{15 \\left(a + b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & \\frac{7 a + 8 b}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{8 a + 7 b}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{- a - \\frac{3 b}{2}}{a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}} & \\frac{\\frac{3 a}{2} + b}{a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}}\\\\\\frac{6}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & - \\frac{6}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} & - \\frac{3}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & - \\frac{3}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} & \\frac{1}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} & - \\frac{1}{2 a^{3} - 6 a^{2} b + 6 a b^{2} - 2 b^{3}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡            3 ⎛      2            2⎞                          3 ⎛ 2          \n",
       "⎢           b ⋅⎝- 10⋅a  + 5⋅a⋅b - b ⎠                         a ⋅⎝a  - 5⋅a⋅b +\n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5   5      4         3  2      \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b   a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅\n",
       "⎢                                                                             \n",
       "⎢                        2  2                                             2  2\n",
       "⎢                    30⋅a ⋅b                                         -30⋅a ⋅b \n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5   5      4         3  2      \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b   a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                30⋅a⋅b⋅(-a - b)                                   30⋅a⋅b⋅(a +\n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5   5      4         3  2      \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b   a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅\n",
       "⎢                                                                             \n",
       "⎢                 ⎛ 2            2⎞                               ⎛   2       \n",
       "⎢              10⋅⎝a  + 4⋅a⋅b + b ⎠                            10⋅⎝- a  - 4⋅a⋅\n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5   5      4         3  2      \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b   a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                  15⋅(-a - b)                                       15⋅(a + b\n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5   5      4         3  2      \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b   a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅\n",
       "⎢                                                                             \n",
       "⎢                       6                                               -6    \n",
       "⎢───────────────────────────────────────────────  ────────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5   5      4         3  2      \n",
       "⎣a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b   a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅\n",
       "\n",
       "     2⎞                            3                                 3        \n",
       " 10⋅b ⎠                         a⋅b ⋅(4⋅a - b)                      a ⋅b⋅(-a +\n",
       "───────────────────  ───────────────────────────────────  ────────────────────\n",
       " 2  3        4    5   4      3        2  2        3    4   4      3        2  \n",
       "a ⋅b  + 5⋅a⋅b  - b   a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b   a  - 4⋅a ⋅b + 6⋅a ⋅b\n",
       "                                                                              \n",
       "                           2 ⎛      2            2⎞              2 ⎛ 2        \n",
       "                          b ⋅⎝- 12⋅a  - 4⋅a⋅b + b ⎠             a ⋅⎝a  - 4⋅a⋅b\n",
       "───────────────────  ───────────────────────────────────  ────────────────────\n",
       " 2  3        4    5   4      3        2  2        3    4   4      3        2  \n",
       "a ⋅b  + 5⋅a⋅b  - b   a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b   a  - 4⋅a ⋅b + 6⋅a ⋅b\n",
       "                                                                              \n",
       "                                                                              \n",
       " b)                           6⋅a⋅b⋅(2⋅a + 3⋅b)                    6⋅a⋅b⋅(3⋅a \n",
       "───────────────────  ───────────────────────────────────  ────────────────────\n",
       " 2  3        4    5   4      3        2  2        3    4   4      3        2  \n",
       "a ⋅b  + 5⋅a⋅b  - b   a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b   a  - 4⋅a ⋅b + 6⋅a ⋅b\n",
       "                                                                              \n",
       "     2⎞                     ⎛     2               2⎞             ⎛     2      \n",
       "b - b ⎠                   2⋅⎝- 2⋅a  - 10⋅a⋅b - 3⋅b ⎠           2⋅⎝- 3⋅a  - 10⋅\n",
       "───────────────────  ───────────────────────────────────  ────────────────────\n",
       " 2  3        4    5   4      3        2  2        3    4   4      3        2  \n",
       "a ⋅b  + 5⋅a⋅b  - b   a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b   a  - 4⋅a ⋅b + 6⋅a ⋅b\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")                                 7⋅a + 8⋅b                            8⋅a + 7\n",
       "───────────────────  ───────────────────────────────────  ────────────────────\n",
       " 2  3        4    5   4      3        2  2        3    4   4      3        2  \n",
       "a ⋅b  + 5⋅a⋅b  - b   a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b   a  - 4⋅a ⋅b + 6⋅a ⋅b\n",
       "                                                                              \n",
       "                                     -3                                   -3  \n",
       "───────────────────  ───────────────────────────────────  ────────────────────\n",
       " 2  3        4    5   4      3        2  2        3    4   4      3        2  \n",
       "a ⋅b  + 5⋅a⋅b  - b   a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b   a  - 4⋅a ⋅b + 6⋅a ⋅b\n",
       "\n",
       "                              2  3                           3  2            ⎤\n",
       " 4⋅b)                       -a ⋅b                           a ⋅b             ⎥\n",
       "───────────────  ─────────────────────────────  ─────────────────────────────⎥\n",
       "2        3    4     3      2          2      3    ⎛ 3      2          2    3⎞⎥\n",
       "  - 4⋅a⋅b  + b   2⋅a  - 6⋅a ⋅b + 6⋅a⋅b  - 2⋅b   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠⎥\n",
       "                                                                             ⎥\n",
       "       2⎞                  2                           2                     ⎥\n",
       " - 12⋅b ⎠               a⋅b ⋅(3⋅a + 2⋅b)              a ⋅b⋅(-2⋅a - 3⋅b)      ⎥\n",
       "───────────────  ─────────────────────────────  ─────────────────────────────⎥\n",
       "2        3    4    ⎛ 3      2          2    3⎞    ⎛ 3      2          2    3⎞⎥\n",
       "  - 4⋅a⋅b  + b   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠  2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠⎥\n",
       "                                                                             ⎥\n",
       "                      ⎛     2            2⎞           ⎛ 2              2⎞    ⎥\n",
       "+ 2⋅b)              b⋅⎝- 3⋅a  - 6⋅a⋅b - b ⎠         a⋅⎝a  + 6⋅a⋅b + 3⋅b ⎠    ⎥\n",
       "───────────────  ─────────────────────────────  ─────────────────────────────⎥\n",
       "2        3    4    ⎛ 3      2          2    3⎞    ⎛ 3      2          2    3⎞⎥\n",
       "  - 4⋅a⋅b  + b   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠  2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠⎥\n",
       "                                                                             ⎥\n",
       "         2⎞             2              2                  2            2     ⎥\n",
       "a⋅b - 2⋅b ⎠            a  + 6⋅a⋅b + 3⋅b              - 3⋅a  - 6⋅a⋅b - b      ⎥\n",
       "───────────────  ─────────────────────────────  ─────────────────────────────⎥\n",
       "2        3    4    ⎛ 3      2          2    3⎞    ⎛ 3      2          2    3⎞⎥\n",
       "  - 4⋅a⋅b  + b   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠  2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠⎥\n",
       "                                                                             ⎥\n",
       "                                 3⋅b                       3⋅a               ⎥\n",
       "                            -a - ───                       ─── + b           ⎥\n",
       "⋅b                                2                         2                ⎥\n",
       "───────────────    ─────────────────────────      ─────────────────────────  ⎥\n",
       "2        3    4     3      2          2    3       3      2          2    3  ⎥\n",
       "  - 4⋅a⋅b  + b     a  - 3⋅a ⋅b + 3⋅a⋅b  - b       a  - 3⋅a ⋅b + 3⋅a⋅b  - b   ⎥\n",
       "                                                                             ⎥\n",
       "                               1                             -1              ⎥\n",
       "───────────────  ─────────────────────────────  ─────────────────────────────⎥\n",
       "2        3    4    ⎛ 3      2          2    3⎞     3      2          2      3⎥\n",
       "  - 4⋅a⋅b  + b   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠  2⋅a  - 6⋅a ⋅b + 6⋅a⋅b  - 2⋅b ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V_inv = sym.simplify(V.subs({x1:a, x2:b}).inv())\n",
    "sym.factor(V_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6c6c95be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{30 a^{2} b^{2} x}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{30 a b x^{2} \\left(- a - b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{b^{3} \\left(- 10 a^{2} + 5 a b - b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{6 x^{5}}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{15 x^{4} \\left(- a - b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{10 x^{3} \\left(a^{2} + 4 a b + b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}}\\\\\\frac{a^{3} \\left(a^{2} - 5 a b + 10 b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} - \\frac{30 a^{2} b^{2} x}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{30 a b x^{2} \\left(a + b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} - \\frac{6 x^{5}}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{15 x^{4} \\left(a + b\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}} + \\frac{10 x^{3} \\left(- a^{2} - 4 a b - b^{2}\\right)}{a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}}\\\\\\frac{a b^{3} \\cdot \\left(4 a - b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{6 a b x^{2} \\cdot \\left(2 a + 3 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{b^{2} x \\left(- 12 a^{2} - 4 a b + b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} - \\frac{3 x^{5}}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{x^{4} \\cdot \\left(7 a + 8 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{2 x^{3} \\left(- 2 a^{2} - 10 a b - 3 b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}}\\\\\\frac{a^{3} b \\left(- a + 4 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{a^{2} x \\left(a^{2} - 4 a b - 12 b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{6 a b x^{2} \\cdot \\left(3 a + 2 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} - \\frac{3 x^{5}}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{x^{4} \\cdot \\left(8 a + 7 b\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}} + \\frac{2 x^{3} \\left(- 3 a^{2} - 10 a b - 2 b^{2}\\right)}{a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}}\\\\- \\frac{a^{2} b^{3}}{2 a^{3} - 6 a^{2} b + 6 a b^{2} - 2 b^{3}} + \\frac{a b^{2} x \\left(3 a + 2 b\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} + \\frac{b x^{2} \\left(- 3 a^{2} - 6 a b - b^{2}\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} + \\frac{x^{5}}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} + \\frac{x^{4} \\left(- a - \\frac{3 b}{2}\\right)}{a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}} + \\frac{x^{3} \\left(a^{2} + 6 a b + 3 b^{2}\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)}\\\\\\frac{a^{3} b^{2}}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} + \\frac{a^{2} b x \\left(- 2 a - 3 b\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} + \\frac{a x^{2} \\left(a^{2} + 6 a b + 3 b^{2}\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)} - \\frac{x^{5}}{2 a^{3} - 6 a^{2} b + 6 a b^{2} - 2 b^{3}} + \\frac{x^{4} \\cdot \\left(\\frac{3 a}{2} + b\\right)}{a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}} + \\frac{x^{3} \\left(- 3 a^{2} - 6 a b - b^{2}\\right)}{2 \\left(a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                       2  2                                              2   \n",
       "⎢                   30⋅a ⋅b ⋅x                                    30⋅a⋅b⋅x ⋅(-\n",
       "⎢─────────────────────────────────────────────── + ───────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5    5      4         3  2     \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10\n",
       "⎢                                                                             \n",
       "⎢             3 ⎛ 2               2⎞                                      2  2\n",
       "⎢            a ⋅⎝a  - 5⋅a⋅b + 10⋅b ⎠                                  30⋅a ⋅b \n",
       "⎢─────────────────────────────────────────────── - ───────────────────────────\n",
       "⎢ 5      4         3  2       2  3        4    5    5      4         3  2     \n",
       "⎢a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10\n",
       "⎢                                                                             \n",
       "⎢                                                  3                          \n",
       "⎢                                               a⋅b ⋅(4⋅a - b)                \n",
       "⎢                                    ─────────────────────────────────── + ───\n",
       "⎢                                     4      3        2  2        3    4    4 \n",
       "⎢                                    a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  \n",
       "⎢                                                                             \n",
       "⎢                                               3                             \n",
       "⎢                                              a ⋅b⋅(-a + 4⋅b)                \n",
       "⎢                                    ─────────────────────────────────── + ───\n",
       "⎢                                     4      3        2  2        3    4    4 \n",
       "⎢                                    a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                      2  3   \n",
       "⎢                                                                     a ⋅b    \n",
       "⎢                                                       - ────────────────────\n",
       "⎢                                                            3      2         \n",
       "⎢                                                         2⋅a  - 6⋅a ⋅b + 6⋅a⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                     3  2    \n",
       "⎢                                                                    a ⋅b     \n",
       "⎢                                                        ─────────────────────\n",
       "⎢                                                          ⎛ 3      2         \n",
       "⎣                                                        2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅\n",
       "\n",
       "                                   3 ⎛      2            2⎞                   \n",
       "a - b)                            b ⋅⎝- 10⋅a  + 5⋅a⋅b - b ⎠                   \n",
       "──────────────────── + ─────────────────────────────────────────────── + ─────\n",
       "  2  3        4    5    5      4         3  2       2  3        4    5    5   \n",
       "⋅a ⋅b  + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b    a  - \n",
       "                                                                              \n",
       "                                              2                               \n",
       "⋅x                                    30⋅a⋅b⋅x ⋅(a + b)                       \n",
       "──────────────────── + ─────────────────────────────────────────────── - ─────\n",
       "  2  3        4    5    5      4         3  2       2  3        4    5    5   \n",
       "⋅a ⋅b  + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b    a  - \n",
       "                                                                              \n",
       "            2                           2   ⎛      2            2⎞            \n",
       "     6⋅a⋅b⋅x ⋅(2⋅a + 3⋅b)              b ⋅x⋅⎝- 12⋅a  - 4⋅a⋅b + b ⎠            \n",
       "──────────────────────────────── + ─────────────────────────────────── - ─────\n",
       "     3        2  2        3    4    4      3        2  2        3    4    4   \n",
       "- 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - \n",
       "                                                                              \n",
       "   2   ⎛ 2               2⎞                       2                           \n",
       "  a ⋅x⋅⎝a  - 4⋅a⋅b - 12⋅b ⎠                6⋅a⋅b⋅x ⋅(3⋅a + 2⋅b)               \n",
       "──────────────────────────────── + ─────────────────────────────────── - ─────\n",
       "     3        2  2        3    4    4      3        2  2        3    4    4   \n",
       "- 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     2                           2 ⎛     2            2⎞      \n",
       "                  a⋅b ⋅x⋅(3⋅a + 2⋅b)          b⋅x ⋅⎝- 3⋅a  - 6⋅a⋅b - b ⎠      \n",
       "───────── + ───────────────────────────── + ───────────────────────────── + ──\n",
       " 2      3     ⎛ 3      2          2    3⎞     ⎛ 3      2          2    3⎞     \n",
       "b  - 2⋅b    2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠   2⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                 2                               2 ⎛ 2              2⎞        \n",
       "                a ⋅b⋅x⋅(-2⋅a - 3⋅b)           a⋅x ⋅⎝a  + 6⋅a⋅b + 3⋅b ⎠        \n",
       "──────── + ───────────────────────────── + ───────────────────────────── - ───\n",
       " 2    3⎞     ⎛ 3      2          2    3⎞     ⎛ 3      2          2    3⎞      \n",
       "b  - b ⎠   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠   2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠   2⋅a\n",
       "\n",
       "                    5                                             4           \n",
       "                 6⋅x                                          15⋅x ⋅(-a - b)  \n",
       "────────────────────────────────────────── + ─────────────────────────────────\n",
       "   4         3  2       2  3        4    5    5      4         3  2       2  3\n",
       "5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b \n",
       "                                                                              \n",
       "                    5                                             4           \n",
       "                 6⋅x                                          15⋅x ⋅(a + b)   \n",
       "────────────────────────────────────────── + ─────────────────────────────────\n",
       "   4         3  2       2  3        4    5    5      4         3  2       2  3\n",
       "5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b \n",
       "                                                                              \n",
       "              5                              4                               3\n",
       "           3⋅x                              x ⋅(7⋅a + 8⋅b)                2⋅x \n",
       "────────────────────────────── + ─────────────────────────────────── + ───────\n",
       "   3        2  2        3    4    4      3        2  2        3    4    4     \n",
       "4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - 4⋅\n",
       "                                                                              \n",
       "              5                              4                               3\n",
       "           3⋅x                              x ⋅(8⋅a + 7⋅b)                2⋅x \n",
       "────────────────────────────── + ─────────────────────────────────── + ───────\n",
       "   3        2  2        3    4    4      3        2  2        3    4    4     \n",
       "4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - 4⋅a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b    a  - 4⋅\n",
       "                                                                              \n",
       "                                     4 ⎛     3⋅b⎞                             \n",
       "             5                      x ⋅⎜-a - ───⎟              3 ⎛ 2          \n",
       "            x                          ⎝      2 ⎠             x ⋅⎝a  + 6⋅a⋅b +\n",
       "─────────────────────────── + ───────────────────────── + ────────────────────\n",
       "⎛ 3      2          2    3⎞    3      2          2    3     ⎛ 3      2        \n",
       "⎝a  - 3⋅a ⋅b + 3⋅a⋅b  - b ⎠   a  - 3⋅a ⋅b + 3⋅a⋅b  - b    2⋅⎝a  - 3⋅a ⋅b + 3⋅a\n",
       "                                                                              \n",
       "                                     4 ⎛3⋅a    ⎞                              \n",
       "            5                       x ⋅⎜─── + b⎟             3 ⎛     2        \n",
       "           x                           ⎝ 2     ⎠            x ⋅⎝- 3⋅a  - 6⋅a⋅b\n",
       "────────────────────────── + ───────────────────────── + ─────────────────────\n",
       "3      2          2      3    3      2          2    3     ⎛ 3      2         \n",
       "  - 6⋅a ⋅b + 6⋅a⋅b  - 2⋅b    a  - 3⋅a ⋅b + 3⋅a⋅b  - b    2⋅⎝a  - 3⋅a ⋅b + 3⋅a⋅\n",
       "\n",
       "                                 3 ⎛ 2            2⎞            ⎤\n",
       "                             10⋅x ⋅⎝a  + 4⋅a⋅b + b ⎠            ⎥\n",
       "────────────── + ───────────────────────────────────────────────⎥\n",
       "        4    5    5      4         3  2       2  3        4    5⎥\n",
       " + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b ⎥\n",
       "                                                                ⎥\n",
       "                                3 ⎛   2            2⎞           ⎥\n",
       "                            10⋅x ⋅⎝- a  - 4⋅a⋅b - b ⎠           ⎥\n",
       "────────────── + ───────────────────────────────────────────────⎥\n",
       "        4    5    5      4         3  2       2  3        4    5⎥\n",
       " + 5⋅a⋅b  - b    a  - 5⋅a ⋅b + 10⋅a ⋅b  - 10⋅a ⋅b  + 5⋅a⋅b  - b ⎥\n",
       "                                                                ⎥\n",
       " ⎛     2               2⎞                                       ⎥\n",
       "⋅⎝- 2⋅a  - 10⋅a⋅b - 3⋅b ⎠                                       ⎥\n",
       "────────────────────────────                                    ⎥\n",
       " 3        2  2        3    4                                    ⎥\n",
       "a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b                                     ⎥\n",
       "                                                                ⎥\n",
       " ⎛     2               2⎞                                       ⎥\n",
       "⋅⎝- 3⋅a  - 10⋅a⋅b - 2⋅b ⎠                                       ⎥\n",
       "────────────────────────────                                    ⎥\n",
       " 3        2  2        3    4                                    ⎥\n",
       "a ⋅b + 6⋅a ⋅b  - 4⋅a⋅b  + b                                     ⎥\n",
       "                                                                ⎥\n",
       "                                                                ⎥\n",
       "    2⎞                                                          ⎥\n",
       " 3⋅b ⎠                                                          ⎥\n",
       "─────────                                                       ⎥\n",
       "  2    3⎞                                                       ⎥\n",
       "⋅b  - b ⎠                                                       ⎥\n",
       "                                                                ⎥\n",
       "                                                                ⎥\n",
       "    2⎞                                                          ⎥\n",
       " - b ⎠                                                          ⎥\n",
       "────────                                                        ⎥\n",
       " 2    3⎞                                                        ⎥\n",
       "b  - b ⎠                                                        ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polys = sym.factor(V_inv.T * sym.Matrix([1, x, x**2, x**3, x**4, x**5]))\n",
    "polys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "77d170d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\frac{\\left(- b + x\\right)^{3} \\cdot \\left(10 a^{2} - 5 a b - 15 a x + b^{2} + 3 b x + 6 x^{2}\\right)}{\\left(a - b\\right)^{5}}\n",
      "- \\frac{\\left(- a + x\\right)^{3} \\left(a^{2} - 5 a b + 3 a x + 10 b^{2} - 15 b x + 6 x^{2}\\right)}{\\left(a - b\\right)^{5}}\n",
      "- \\frac{\\left(- a + x\\right) \\left(- b + x\\right)^{3} \\left(- 4 a + b + 3 x\\right)}{\\left(a - b\\right)^{4}}\n",
      "- \\frac{\\left(- a + x\\right)^{3} \\left(- b + x\\right) \\left(a - 4 b + 3 x\\right)}{\\left(a - b\\right)^{4}}\n",
      "\\frac{\\left(- a + x\\right)^{2} \\left(- b + x\\right)^{3}}{2 \\left(a - b\\right)^{3}}\n",
      "- \\frac{\\left(- a + x\\right)^{3} \\left(- b + x\\right)^{2}}{2 \\left(a - b\\right)^{3}}\n"
     ]
    }
   ],
   "source": [
    "for poly in polys:\n",
    "    print(latex(sym.factor(poly)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d94f4e0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\left(- b + x\\right)^{3} \\cdot \\left(10 a^{2} - 5 a b - 15 a x + b^{2} + 3 b x + 6 x^{2}\\right)}{\\left(a - b\\right)^{5}}$"
      ],
      "text/plain": [
       "        3 ⎛    2                     2              2⎞\n",
       "(-b + x) ⋅⎝10⋅a  - 5⋅a⋅b - 15⋅a⋅x + b  + 3⋅b⋅x + 6⋅x ⎠\n",
       "──────────────────────────────────────────────────────\n",
       "                              5                       \n",
       "                       (a - b)                        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{\\left(- a + x\\right)^{3} \\left(a^{2} - 5 a b + 3 a x + 10 b^{2} - 15 b x + 6 x^{2}\\right)}{\\left(a - b\\right)^{5}}$"
      ],
      "text/plain": [
       "         3 ⎛ 2                       2               2⎞ \n",
       "-(-a + x) ⋅⎝a  - 5⋅a⋅b + 3⋅a⋅x + 10⋅b  - 15⋅b⋅x + 6⋅x ⎠ \n",
       "────────────────────────────────────────────────────────\n",
       "                               5                        \n",
       "                        (a - b)                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{\\left(- a + x\\right) \\left(- b + x\\right)^{3} \\left(- 4 a + b + 3 x\\right)}{\\left(a - b\\right)^{4}}$"
      ],
      "text/plain": [
       "                  3                  \n",
       "-(-a + x)⋅(-b + x) ⋅(-4⋅a + b + 3⋅x) \n",
       "─────────────────────────────────────\n",
       "                      4              \n",
       "               (a - b)               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATkAAAA5CAYAAABNllxFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAMTklEQVR4Ae2d67HVNhDHLwwFEOiAdMCjgkAHPCoAOoDJJ/h2BzoAKoDQQZIKIHQQUkFuTgfk//OVPH7Ib8lH9tmd0ZEty9Luf6X1ruxjX/nx48eZUR4IvH79+pY4ua90ocT2PaVzlX9TbmQIGAIzELg24xw7JR0Cb9T0dxm193Sh/IWyP5V+Yt/IEDAEpiNgRm46ZinPOG80flP7eHVGhoAhMBMBM3IzgUtxWiAsfah+8O6MDAFDYCYCZuRmApfyNBemPlEf77RdhK4p+7O2DYE9I3A1tXCapCygGwmBsVio3ltV/0XpgbZZl5tEY/uZ1OjGKsfAIEYbG4Ntk+wO6SmpkVPnTNDbm0QuDdO3HCaDraveQZVeKr3R9mgMDfMS2tFYl2dUNgzHChj5b/bq+kqqR0g0SFhPuqeciWrkEHCT56C8FoZq/7qq/KP0i7aLR0aU4wX/rfS8WV9lLVKd6JirTfj6Temu0oX2f251nGmBeOUi28J6iN0UOA71GeO4+OZiyFh57tvTdlb6Ez+Mac8fvLHPhfwPz/OcXOd36jqJJ+eA/VW5GbiGxoQJoSgDEQWXpP2DdriT+r0svHxmjvJPlbLgpmsvOubwpfRAncLXooEYZDxhofgOYt3XZSoc+/qMeIyL0Y1qeznpz2H7UrlPGLt3Sr+rjAv0bNL5nbpOYuTEKXcEYT57Ejj3lZ6tzCjYhO6aPlI5huoFSdsYlzvaxtANUWrM8RJ+H2Ji6LhkWRvvLqy7WE2NY1e/i8rdeOlrIwf9Mc+eideqQfMXzl/7mB95LKjrVEbusQSphWMjmTxGNTwq0mrksAGjWr/a/6bEVe6tS4+UVz27Ph6TYS4e7ruO/YDs42Po2Kp4i3fGYQvrHiaT4djT56JDkhEDdnCp1VZG+mMZpsaneGM/CnXpOvojJOoIKz12YkYRbqONgNFjpcUXgxUwL8LVmANyZZ2NwnoFHFOJ/US8c3H0a13NfrLQn/jjIln7947DHH7xwmJQS9fRjZy4BNAYV/xOgQXMLR0krECgf5U+Kz1UOXH5qqQ+8Ux8uMt/TZ8qwR/PuUFfVAf+mgRGYLXYyLl2UmKOJ4eXSQgNIefHDrmKCil+VsB6cOyKh2zGHhiLH3QyZCCy0F9zTIh3+GIet26s6Vi0eZUiXOUuHHcEk5AD5i817hcvMWxFLO6ASdJvT6PcGSrCS9X5ovRBiXUnbrqgKJQYIjBiwsSgZJg7TAmH4PU9sirHkP+m7Vj8q7lRlBrrXhwlL5Mym7Hn8OfGEBf7IOkYYzAX/RU8iqfbShhnPE9C2K/FgfpPNF1frbcbZQ9QuUsYnZzCuIOEgasqlm3+2H6I3mlPg+oPD65qxOifcN17Zzcax7VbEhjFMhLJMBePTGyIR1sKfF3uZb08mvh3Jaw7cVT/HMtm7Dm4Wx5QQA1Z6K/Kl7AkKsAx4EbbR6W/tM28KUjbUefVNd9wxJyJXUyGZptinoHCWzXIxxKL71h7CINyXfveiBSF+kGRoZDQHz/TOXh7XuFluTbgl+Oh9QyUgSK66KuOV43tHVXknEL+gXM5bwoOXTxQnhJzQrhSpgoT8M4LBIIk2WPjvQbWnThKyCVjD6yWjPsWxsIXQzAUpnJeLvpryUCB5PisxHwhMvjJbUfVdQojFxTGCYQwGIK5xEJ9be1JoDCA8Ih6H29QvZARO1M5VxCemJ68nqdzvPFVEwXB37nbHsr6JtTQuaOPi8elmLcuIGrTXywIz4OkOlHxzgDrJWNvqQ5qGAsLxjsX++oFtlanspOF/uBH/N52eXPeEK7CZ8Gr6jWPL5pX1+g0Ml2oPQxPVJLgtElqGjMAAMCa8aNsTVL/KAj+So/S8QxvhwAv1AWrGJQEc8cYE6ppzLx3exTME2IdxNHpMaexh074NxHhc5UwIlywKWf5hnXhnPTHeuaZ+PIeG7u9pLqL51UKI8fVBWBTUfPqVbjjdCZA8MoIrZp1ovOiPhj0DCYWSJnseC7NReC+fyDgycXiczXMndxcWFgPChlvHYpLK2I9hGNTX8cae4y31gVGOP1HuXJ/EfKKKPl2WK6qP8+EcsYL/DXHzV1Xh2PR59XVCgOxNr+poXuxGvPtOGBQbGlAVYZR4+rl787w1o5Sof7cRDlXGNKFU0zNK1MZx5oeUJWVYv2uWrBgOwnmjh88Uz8IKcKwf5J8zXVRjqWitbAO4ihZi8kp4XIZe104YyBIVcpBf54fPMtaJCZsmcPw7C+a0XV9zfceMeduCRMhBXGF+iBgXihn0Zu+uJriTVE2ZiFW1aIQBpeJjlLO1D9K4j948IBbjvErQ1fqNIjzgutWjXpjdlNi/lQMgDl/zGcwskC8poFD/rWw7sMxp7EHJiW5MecN8H3tM/94PtM/7nNs/RW8Mm6U4K86T+Eb58R7ptF1neQtJGKYZ8Cqd0ULIXP8Ea9cSWbdeJgrj/pEsRjEaG/02Arma+M9Feut4Dh37C09b239TeG3S9dXpzQyoe4b1Y3lpUzodlbVg84irUm47WAUk7aC+dp4T8V6KzjGHDtT2lpbf1N4C+o6iScHV7KqxN6EcGutkU0B42h13dXmnXLC7KhkmNfhnIu14VjHcQt7fbpO5cmBC2sY1dh7C1itwSOYpPJyDfO6BudibTjWcdzCXqeuk3lyoOKs61H+OJ+jVoQHN0d4wjuZd2uYX2p+KdaGY44zKMzTkK6TGrkwS1ZqCBgChsB6CKQMV9eTwnoyBAwBQ6ADATNyHcBYsSFgCOwDgSuvXr26LlEWvyFBcfGPfUBiUhgChsCeELA1uT1p02QxBAyBFgIWrrYgsQJDwBDYEwJm5PakTZNlMQJadileB7S4IWsgGwTMyGWjCmPk2Ai4562KFzsemxfrPx4CZuTiYWktbRgBGTjeCpPsIe0NQ7N51s3IbV6FJsBSBGTgeMIAD86/7mdpk3Z+RgiYkctIGTmyIgNwK0e+xvI0kv9nqjf5Gx9jebB6x0XAjNxx8c+6d018/mu79TUq3hWIHEHSMd4n2Pdy0+B5VrgdBMzIbUdXq3LqJv9N5dkaAPHGF6t4+eh/SryotUUqL0JQ5XzCr0Yqw0u9odzW4mrI7GvHHgbelz6jSKNJX/wLRvmSz0dG4WVMI+KTxz74VmfnK6xcnfID2bSrMrzUJ2w7Qm6MIaErrw/P1sA7fi0bgUCKbzyM6NaqZI4Ab8fd0rsAMVbnA5giT+2tvzJifLiGVJD28ewwcufaPlyW2u/WEbBwdesaTMP/Y03ytT9WM0sS8Vl8SEgn994ZdfIgF95ai1SOccMIQnwYibU6ox0gYJ7cDpQYUwQ3ube0RsVr5PmQ8hjPC7keK7UMuM6nrFWuMqONI2BGbuMKTMA+RmPIKyKsw+vBaPyrxNrVsd4AjSfHB8X9HdR72v+o/dB6GnIhnxkzgXAqZOHqqWh6vJx3VTV4p5ImZDwwKiz0v9Q2iUX6Yr1L28FQUMeTkOuP9TiMLt/09N8Z5duwlDUJuULlzXq2vyMEzMjtSJmRRMFQXYTackaFDxdj3KohLdtjQ8ZQ03PLMLhQeddUfBG2kkJrashlRk4gnBJZuHpK2h4n6w1Vw0iEiBCVZ9Oa4R7GJhQelm04A7n45axlg5cbhJ6Eqk1+r6v8ZqMuuxhjjhmdEAJm5E5I2RFEZdG+tl7njBfeEd/Z7SRniGI/d9cyruqHMujLZVb77TPgtYq2sx8ELFzdjy5jSUJI1/J2nDGjvGnMMHxnOl4zfpStQBjXpjHjm6lQiB/4D4bixRn2s0sEzMjtUq2LhCKkw3h0UXUtjjpFyMiGDB13WPvOpVpsKvlR3xgxjO5zbR8CHeHJlfUDx61ohwiYkduhUheK9E3n8xhGjZzRwDsqjZjKWNzn7uZXV/mBytY0IqwDcjfYEzdFPomH5pqhP064jHxGJ4SArcmdkLJHivpR9TAWISIU/CAjwjNpLOxTF0+OfwhQtvZfwZ6qT/j5WTleHI+OdBk4HT5jva7z/61UMNofAvYH/f3pdLFEMhQ8T/ZI+W68HsmCB8obSzCIRieEgIWrJ6TsCaLyqMjePJ6Xkgm5jE4MATNyJ6bwMeLK2yHk42WT5frbmPNyrePkQJ6+UDZX9o2vhQiYkVsI4I5PZ/1t7TW2VHAix94801RY7a5dW5PbnUrjCeQ8oGP98T6KIJKBGyKfla951zcK79ZIHAT+B0Q4GCYmpJ+jAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle - \\frac{\\left(- a + x\\right)^{3} \\left(- b + x\\right) \\left(a - 4 b + 3 x\\right)}{\\left(a - b\\right)^{4}}$"
      ],
      "text/plain": [
       "         3                          \n",
       "-(-a + x) ⋅(-b + x)⋅(a - 4⋅b + 3⋅x) \n",
       "────────────────────────────────────\n",
       "                     4              \n",
       "              (a - b)               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\left(- a + x\\right)^{2} \\left(- b + x\\right)^{3}}{2 \\left(a - b\\right)^{3}}$"
      ],
      "text/plain": [
       "        2         3\n",
       "(-a + x) ⋅(-b + x) \n",
       "───────────────────\n",
       "              3    \n",
       "     2⋅(a - b)     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{\\left(- a + x\\right)^{3} \\left(- b + x\\right)^{2}}{2 \\left(a - b\\right)^{3}}$"
      ],
      "text/plain": [
       "         3         2 \n",
       "-(-a + x) ⋅(-b + x)  \n",
       "─────────────────────\n",
       "               3     \n",
       "      2⋅(a - b)      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for poly in polys:\n",
    "    display((sym.factor(poly)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c52cd2d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} & \\frac{1}{2} & \\frac{5}{16} & - \\frac{5}{16} & \\frac{1}{16} & \\frac{1}{16}\\\\- \\frac{15}{16} & \\frac{15}{16} & - \\frac{7}{16} & - \\frac{7}{16} & - \\frac{1}{16} & \\frac{1}{16}\\\\0 & 0 & - \\frac{3}{8} & \\frac{3}{8} & - \\frac{1}{8} & - \\frac{1}{8}\\\\\\frac{5}{8} & - \\frac{5}{8} & \\frac{5}{8} & \\frac{5}{8} & \\frac{1}{8} & - \\frac{1}{8}\\\\0 & 0 & \\frac{1}{16} & - \\frac{1}{16} & \\frac{1}{16} & \\frac{1}{16}\\\\- \\frac{3}{16} & \\frac{3}{16} & - \\frac{3}{16} & - \\frac{3}{16} & - \\frac{1}{16} & \\frac{1}{16}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ 1/2   1/2   5/16   -5/16  1/16   1/16⎤\n",
       "⎢                                      ⎥\n",
       "⎢-15     15                            ⎥\n",
       "⎢────    ──   -7/16  -7/16  -1/16  1/16⎥\n",
       "⎢ 16     16                            ⎥\n",
       "⎢                                      ⎥\n",
       "⎢  0     0    -3/8    3/8   -1/8   -1/8⎥\n",
       "⎢                                      ⎥\n",
       "⎢ 5/8   -5/8   5/8    5/8    1/8   -1/8⎥\n",
       "⎢                                      ⎥\n",
       "⎢  0     0    1/16   -1/16  1/16   1/16⎥\n",
       "⎢                                      ⎥\n",
       "⎣-3/16  3/16  -3/16  -3/16  -1/16  1/16⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V_inv = sym.simplify(V.subs({x1:-1, x2:1}).inv())\n",
    "sym.factor(V_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dfb3efd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{3 x^{5}}{16} + \\frac{5 x^{3}}{8} - \\frac{15 x}{16} + \\frac{1}{2}\\\\\\frac{3 x^{5}}{16} - \\frac{5 x^{3}}{8} + \\frac{15 x}{16} + \\frac{1}{2}\\\\- \\frac{3 x^{5}}{16} + \\frac{x^{4}}{16} + \\frac{5 x^{3}}{8} - \\frac{3 x^{2}}{8} - \\frac{7 x}{16} + \\frac{5}{16}\\\\- \\frac{3 x^{5}}{16} - \\frac{x^{4}}{16} + \\frac{5 x^{3}}{8} + \\frac{3 x^{2}}{8} - \\frac{7 x}{16} - \\frac{5}{16}\\\\- \\frac{x^{5}}{16} + \\frac{x^{4}}{16} + \\frac{x^{3}}{8} - \\frac{x^{2}}{8} - \\frac{x}{16} + \\frac{1}{16}\\\\\\frac{x^{5}}{16} + \\frac{x^{4}}{16} - \\frac{x^{3}}{8} - \\frac{x^{2}}{8} + \\frac{x}{16} + \\frac{1}{16}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           5      3                 ⎤\n",
       "⎢        3⋅x    5⋅x    15⋅x   1      ⎥\n",
       "⎢      - ──── + ──── - ──── + ─      ⎥\n",
       "⎢         16     8      16    2      ⎥\n",
       "⎢                                    ⎥\n",
       "⎢          5      3                  ⎥\n",
       "⎢       3⋅x    5⋅x    15⋅x   1       ⎥\n",
       "⎢       ──── - ──── + ──── + ─       ⎥\n",
       "⎢        16     8      16    2       ⎥\n",
       "⎢                                    ⎥\n",
       "⎢     5    4      3      2           ⎥\n",
       "⎢  3⋅x    x    5⋅x    3⋅x    7⋅x   5 ⎥\n",
       "⎢- ──── + ── + ──── - ──── - ─── + ──⎥\n",
       "⎢   16    16    8      8      16   16⎥\n",
       "⎢                                    ⎥\n",
       "⎢     5    4      3      2           ⎥\n",
       "⎢  3⋅x    x    5⋅x    3⋅x    7⋅x   5 ⎥\n",
       "⎢- ──── - ── + ──── + ──── - ─── - ──⎥\n",
       "⎢   16    16    8      8      16   16⎥\n",
       "⎢                                    ⎥\n",
       "⎢      5    4    3    2              ⎥\n",
       "⎢     x    x    x    x    x    1     ⎥\n",
       "⎢   - ── + ── + ── - ── - ── + ──    ⎥\n",
       "⎢     16   16   8    8    16   16    ⎥\n",
       "⎢                                    ⎥\n",
       "⎢     5    4    3    2               ⎥\n",
       "⎢    x    x    x    x    x    1      ⎥\n",
       "⎢    ── + ── - ── - ── + ── + ──     ⎥\n",
       "⎣    16   16   8    8    16   16     ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polys = sym.factor(V_inv.T * sym.Matrix([1, x, x**2, x**3, x**4, x**5]))\n",
    "polys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41b40e68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ - \\frac{\\left(x - 1\\right)^{3} \\cdot \\left(3 x^{2} + 9 x + 8\\right)}{16}, \\  \\frac{\\left(x + 1\\right)^{3} \\cdot \\left(3 x^{2} - 9 x + 8\\right)}{16}, \\  - \\frac{\\left(x - 1\\right)^{3} \\left(x + 1\\right) \\left(3 x + 5\\right)}{16}, \\  - \\frac{\\left(x - 1\\right) \\left(x + 1\\right)^{3} \\cdot \\left(3 x - 5\\right)}{16}, \\  - \\frac{\\left(x - 1\\right)^{3} \\left(x + 1\\right)^{2}}{16}, \\  \\frac{\\left(x - 1\\right)^{2} \\left(x + 1\\right)^{3}}{16}\\right]$"
      ],
      "text/plain": [
       "⎡        3 ⎛   2          ⎞          3 ⎛   2          ⎞          3            \n",
       "⎢-(x - 1) ⋅⎝3⋅x  + 9⋅x + 8⎠   (x + 1) ⋅⎝3⋅x  - 9⋅x + 8⎠  -(x - 1) ⋅(x + 1)⋅(3⋅\n",
       "⎢───────────────────────────, ─────────────────────────, ─────────────────────\n",
       "⎣             16                          16                          16      \n",
       "\n",
       "                         3                     3        2          2        3⎤\n",
       "x + 5)   -(x - 1)⋅(x + 1) ⋅(3⋅x - 5)   -(x - 1) ⋅(x + 1)    (x - 1) ⋅(x + 1) ⎥\n",
       "───────, ────────────────────────────, ───────────────────, ─────────────────⎥\n",
       "                      16                        16                  16       ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polys = [sym.factor(poly) for poly in polys]\n",
    "polys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3c6dd9d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "- \\frac{\\left(x - 1\\right)^{3} \\cdot \\left(3 x^{2} + 9 x + 8\\right)}{16}\n",
      "\\frac{\\left(x + 1\\right)^{3} \\cdot \\left(3 x^{2} - 9 x + 8\\right)}{16}\n",
      "- \\frac{\\left(x - 1\\right)^{3} \\left(x + 1\\right) \\left(3 x + 5\\right)}{16}\n",
      "- \\frac{\\left(x - 1\\right) \\left(x + 1\\right)^{3} \\cdot \\left(3 x - 5\\right)}{16}\n",
      "- \\frac{\\left(x - 1\\right)^{3} \\left(x + 1\\right)^{2}}{16}\n",
      "\\frac{\\left(x - 1\\right)^{2} \\left(x + 1\\right)^{3}}{16}\n"
     ]
    }
   ],
   "source": [
    "for poly in polys:\n",
    "    print(latex(poly))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7ad45e00",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hermite_interp(fun, grad, hess, x0=-1, x1=1, npts=101):\n",
    "    jaco = (x1 - x0)/2\n",
    "    x = np.linspace(-1, 1, npts)\n",
    "    f1 = fun(x0)\n",
    "    f2 = fun(x1)\n",
    "    g1 = grad(x0)\n",
    "    g2 = grad(x1)\n",
    "    h1 = hess(x0)\n",
    "    h2 = hess(x1)\n",
    "    N1 = -(x - 1)**3*(3*x**2 + 9*x + 8)/16\n",
    "    N2 = (x + 1)**3*(3*x**2 - 9*x + 8)/16\n",
    "    N3 = -(x - 1)**3*(x + 1)*(3*x + 5)/16\n",
    "    N4 = -(x - 1)*(x + 1)**3*(3*x - 5)/16\n",
    "    N5 = -(x - 1)**3*(x + 1)**2/16\n",
    "    N6 = (x - 1)**2*(x + 1)**3/16\n",
    "    interp = N1*f1 + N2*f2 + jaco*(N3*g1 + N4*g2) + jaco**2*(N5*h1 + N6*h2)\n",
    "    return interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "169bb25a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fun(x):\n",
    "    return np.sin(2*np.pi*x)/(2*np.pi*x)\n",
    "\n",
    "\n",
    "def grad(x):\n",
    "    return np.cos(2*np.pi*x)/x - np.sin(2*np.pi*x)/(2*np.pi*x**2)\n",
    "\n",
    "def hess(x):\n",
    "    return -2*pi*sin(2*pi*x)/x - 2*cos(2*pi*x)/x**2 + sin(2*pi*x)/(pi*x**3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2f652b99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute('tabindex', '0');\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;' +\n",
       "            'z-index: 2;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box;' +\n",
       "            'pointer-events: none;' +\n",
       "            'position: relative;' +\n",
       "            'z-index: 0;'\n",
       "    );\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box;' +\n",
       "            'left: 0;' +\n",
       "            'pointer-events: none;' +\n",
       "            'position: absolute;' +\n",
       "            'top: 0;' +\n",
       "            'z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            /* This rescales the canvas back to display pixels, so that it\n",
       "             * appears correct on HiDPI screens. */\n",
       "            canvas.style.width = width + 'px';\n",
       "            canvas.style.height = height + 'px';\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        /* User Agent sniffing is bad, but WebKit is busted:\n",
       "         * https://bugs.webkit.org/show_bug.cgi?id=144526\n",
       "         * https://bugs.webkit.org/show_bug.cgi?id=181818\n",
       "         * The worst that happens here is that they get an extra browser\n",
       "         * selection when dragging, if this check fails to catch them.\n",
       "         */\n",
       "        var UA = navigator.userAgent;\n",
       "        var isWebKit = /AppleWebKit/.test(UA) && !/Chrome/.test(UA);\n",
       "        if(isWebKit) {\n",
       "            return function (event) {\n",
       "                /* This prevents the web browser from automatically changing to\n",
       "                 * the text insertion cursor when the button is pressed. We\n",
       "                 * want to control all of the cursor setting manually through\n",
       "                 * the 'cursor' event from matplotlib */\n",
       "                event.preventDefault()\n",
       "                return fig.mouse_event(event, name);\n",
       "            };\n",
       "        } else {\n",
       "            return function (event) {\n",
       "                return fig.mouse_event(event, name);\n",
       "            };\n",
       "        }\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    canvas_div.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    canvas_div.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.canvas_div.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "function getModifiers(event) {\n",
       "    var mods = [];\n",
       "    if (event.ctrlKey) {\n",
       "        mods.push('ctrl');\n",
       "    }\n",
       "    if (event.altKey) {\n",
       "        mods.push('alt');\n",
       "    }\n",
       "    if (event.shiftKey) {\n",
       "        mods.push('shift');\n",
       "    }\n",
       "    if (event.metaKey) {\n",
       "        mods.push('meta');\n",
       "    }\n",
       "    return mods;\n",
       "}\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    // from https://stackoverflow.com/q/1114465\n",
       "    var boundingRect = this.canvas.getBoundingClientRect();\n",
       "    var x = (event.clientX - boundingRect.left) * this.ratio;\n",
       "    var y = (event.clientY - boundingRect.top) * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        modifiers: getModifiers(event),\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.9833333333333\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 2\n",
    "b = 5\n",
    "nels = 7\n",
    "npts = 200\n",
    "x = np.linspace(a, b, npts)\n",
    "y = fun(x)\n",
    "plt.plot(x, y, color=\"black\")\n",
    "xi = np.linspace(a, b, num=nels, endpoint=False)\n",
    "dx = xi[1] - xi[0]\n",
    "\n",
    "\n",
    "for x0 in xi:\n",
    "    x1 = x0 + dx\n",
    "    x = np.linspace(x0, x1, npts)\n",
    "    y = hermite_interp(fun, grad, hess, x0=x0, x1=x1, npts=npts)\n",
    "    plt.plot([x[0], x[-1]], [y[0], y[-1]], marker=\"o\", color=\"#4daf4a\",\n",
    "         linewidth=0)\n",
    "    plt.plot(x, y, linestyle=\"dashed\", color=\"#4daf4a\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend([\"Exact function\", \"Interpolation\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d71fc52",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}

hermite_quintic.py

# -*- coding: utf-8 -*-
"""
Compute a (quintic) Hermite interpolation

@author: Nicolas Guarin-Zapata
@date: January 2024
"""
import numpy as np
import matplotlib.pyplot as plt


def hermite_interp(fun, grad, hess, x0=-1, x1=1, npts=101):
    jaco = (x1 - x0)/2
    x = np.linspace(-1, 1, npts)
    f1 = fun(x0)
    f2 = fun(x1)
    g1 = grad(x0)
    g2 = grad(x1)
    h1 = hess(x0)
    h2 = hess(x1)
    N1 = -(x - 1)**3*(3*x**2 + 9*x + 8)/16
    N2 = (x + 1)**3*(3*x**2 - 9*x + 8)/16
    N3 = -(x - 1)**3*(x + 1)*(3*x + 5)/16
    N4 = -(x - 1)*(x + 1)**3*(3*x - 5)/16
    N5 = -(x - 1)**3*(x + 1)**2/16
    N6 = (x - 1)**2*(x + 1)**3/16
    interp = N1*f1 + N2*f2 + jaco*(N3*g1 + N4*g2) + jaco**2*(N5*h1 + N6*h2)
    return interp


def fun(x):
    return np.sin(2*np.pi*x)/(2*np.pi*x)


def grad(x):
    return np.cos(2*np.pi*x)/x - np.sin(2*np.pi*x)/(2*np.pi*x**2)


def hess(x):
    return -2*np.pi*np.sin(2*np.pi*x)/x - 2*np.cos(2*np.pi*x)/x**2\
        + np.sin(2*np.pi*x)/(np.pi*x**3)

#%% Test
a = 2
b = 5
nels = 7
npts = 200
x = np.linspace(a, b, npts)
y = fun(x)
plt.plot(x, y, color="black")
xi = np.linspace(a, b, num=nels, endpoint=False)
dx = xi[1] - xi[0]


for x0 in xi:
    x1 = x0 + dx
    x = np.linspace(x0, x1, npts)
    y = hermite_interp(fun, grad, hess, x0=x0, x1=x1, npts=npts)
    plt.plot([x[0], x[-1]], [y[0], y[-1]], marker="o", color="#4daf4a",
         linewidth=0)
    plt.plot(x, y, linestyle="dashed", color="#4daf4a")
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Exact function", "Interpolation"])
plt.show()