{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contravariant & Covariant indices in Tensors (Symbolic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from einsteinpy.symbolic import ChristoffelSymbols, RiemannCurvatureTensor\n",
    "from einsteinpy.symbolic.predefined import Schwarzschild\n",
    "import sympy\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysing the schwarzschild metric along with performing various operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAAB0CAYAAABZjfMMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAU6klEQVR4Ae2dW7LUthaGNxTPKU6oygDIDEgYAZsZHDgjIMyAFE/JG5XMgGQECcyAMAIuMyADSFUIlQns83/elnF7y92y22pf9KvKLVuWdfmkXl5ekuVrFxcXZ2t1P/74439V9vvaXtV1uC3/a20/6dyfdZg9EzABE1gdgRsSYndU6nc9JX+p8w/a5+r4LxT2jfY/tc/NsP+l8qQsbM9Unp+1URfqZOEsCKlO3H6q4/4t3ze4VHAH4pnrAUAjT2+Bq+rwQdVHobzidO7ajVboz9oncttVAk4RbyrwV20ftX2rLZqgwk/mVCbK8Ie2c21/6pjy4x5p//3lrn9TCIgXNzRubi+JL5/2fif/vjbf5IAywomduY7gduiSDXENClG7ylgCsAictYXz874/osLRkCsNWvtPtI9mOqsLZZVPZRDSldOxBXOAkeCL13eKdlN+JZi5RPuf6uPnOoSv3UAC4meuA5mlRN8SV9Xll26dFUZQJZyvd0+u8BjNOdicrxRflb1Dg4btSgQHcNON3dDeKPxc3NCi7YYTMNfhzFKuKIbrqoWzBAemDbS+RnOOtO5jnecO9bs2bKl2uwS4uWGu6jqelnCctxtOwFyHM0u5ohiuN1JoLDgOwrl5HO8p5wsJZx7PccG/PCr8V1xStGIGXe0GEDDXAbAGRC2N69o15z/UYJUtPNbGOscsDgYLH8v/XhuDmXafCQTBG7Tkz2c+a9MpArx9nffPzsw1Ty8oiuvaNedDXeA3RcBuymP7l/KvGOAPJeDzZ7fMIAsBc82CdTv9NbtwlkBE83qtbYgG9kDXxQapBjWn0jhk8hiU3gYjx2zNoZpBS2Hes90wAuY6jFdq7KK4nkI488j8TSr91HgSvEe92qjrr6XmtdV4YsCUOaoXu3GGMM9zHtgBzHUgsMTopXHNLpwTuQ+OpoYqXrgOhha/gJkuDKx2XdCc982E6V7j488EzPUziyn3iuG66gHBKVu84LQYNI0NlPK08x5tpWA2x1TdXI+h139tMVwtnPs7QRFnJHwZJP0ov3oriUprH5PGQ22POLYbTsBchzNLuaIkrslmDUHhjsWfNmhZrL3AoN0b+WFdixS+jrM8AmjJT9WOwbxxV8f36vZdXmnXUyJzzdNWRXC99sMPP9wRPxZo+Vp/Rg/+5OlMTtUETMAEDhKQDGZNFtY52lmV7uCFS4+gCvFozkI9Ya0NNEEvf7n0hnP5TMAErhDYms2ZGQaYX1je9LaENeYWzDA8HdiZgAmYwGoIbEY4SxCjJYdpNt31nf0yymq6pAtqAiYAgeQBwaXjknAOHwbw+s5LbyyXzwRM4CCBzWjOrZqeaz/YnFvB3jUBEzCB9RDYlHCuTRuH1ndeT+u4pCZgAsUS2IxZo25B7M62L2fozrrxhRdT+HgB80ztTMAEMhLYlHCW0GBAkM1uQgLiymwXzEU4hLSdCZhAZgKbEs6ZWRWbvIQzb4KyzkbzinexMFxxEzgRgU3ZnE/EzNmYgAmYQHYCi9GcpZX9VNeWxd39Vl/2pncGpyDgfp2HcglcF6E5CzRre7CA0vfaeKuP7/290j4DfHYmsEoC7td5mq0UrrMLZ4FmoQ+mvzWzLLT/SWEc+2vZefq3U81MwP06D+CSuM4unNWEfD2bAaeue6MAPs7q2QFdMj5eAwH36zytVAzXJQhnpmjFPtyI9owLU7guj/xrAusg4H6dp52K4XojD7+0VBO1Ylaas5uRgNrptrJ/rI0/Bqv9YW76IN8fWRCIrnO/7hKZ5rg0rrMKZzVZELxBS263YtCmbdZoU5lhX38KFpVikNYujYD7dRqnobGK4roEs8ahBrp1KILPm8AKCbhf52m0zXCdW3MO2nGsmcJdknnPq3P1I9hrFXyI5v9A18UGR1dX/8ILvNl+PXO7FsV1VuEsQfRJG+0dE2AhbJXfNaRuqtfRCwQpnQsA2fUTEKNr/WdPf4a210bGoQ+3CxHCVtmv2xU59X5pXGcVznXjhq+XdNs6aM5FL2SUQ/AoTQb1ViMc1lZe9+vuX3nS42LkBTbnL2p0wZ+UZEJifPOP7/x1HVoni+2ggdpNREA8nyipOxMld6pkuJlQ7jU59+s8rbV1rl8FbLMPCOpP94sK81F+s+KZ9nn0e6jtUSio/eMJ1IxvyW/exjw+1fwpqLzV01Nd/vwZTpCDyup+PQHHbhIlccWs8W8NIPhdHqc4Rkt+KvDMp8Xd1XZPx++rI//0EhAjbmpwY5Qa/7nCrpiCFMYND8ZH28GVTrJTfryeT56sn4KrbK4KHzRHmvja3mn7Q9tanqbcry/bfOrfLXP9K8Bags35rP6zeR5taJVh/q/i9x8ukY/g+0dbbICMVf/mWKsE2zbl+kbl4ysq3EDGmlUoP/XghZjFO9WVm4j79cQtVQrXRQjniduutOTamjCCr0+rfIhwjMFROMITM9Lkn6BS2mi6CKhKSGkfYd0MRuoYQd2MOegYc0DUcU7bP9pYvbCvntFrHWgCayNwfW0Fdnl3CUhINYJOZ9AqWRhmxynOuQLa8ZrzOodwrFYGlI+QzuG+VT59JipuCAjk37WxjvchRz24kdiZwKYJWHPeSPNKwPHIj0YZE4II7Ct2aKpex8/2CSqlj8CP5k3+ci8UJ5hbgn95Jv5LWve19WrY8cscagLrImDhvKL2khBDM+aNSR7pWQO7GlSrw6tHffa1de2cmA1SBJ+iTetUFsp6RZsnF51jWhTlRntGiKMRx24uCm7cB+3xJGBnApsmYLPGSppXwguhxNdhEMhvtT2l6DpmFsQTbdhieZuwmZKo/eAQfB/DwYL831SWc5WbMmMTT9GGqQf1sTOBTROw5ryC5pXQQuv9U34wD2B3vUfRFdYeECQo5r5UIBrsSZ3KNujVc8VvtHvtx2acUH7qzsCnnQlsmoCF8zqal8f95oUcCS4E7aHH/0lqprwYMMSccshhmtgZdNwjYA+lte/8LDeafQXyORPIQcDCOQfV6dPkMf4YYYzQHGUKkIAlXwbgluKoB6YNOxPYNAHbnNfRvAjInUd5Cc0UbTbUDmG2c304sUIfzXlHQ19hHVxkEzhIAM2Zjs7LCdZGDuKaLQKzHZjVEAQs2uOzAaVBuN+Nxa/TpP3Pta3hE1TY2F/F6uIwE9gAAcaVqpfFEM784RmIIfCTNruFEZAADTfQsSVDmDWDbe1E6rS7U+/aUSbdV37HrrXBTWTIU8Ok5XdiJpCZAP2b/+ov1zNn5OQXQEACsZrlIZ/BvbkdNxqmBbLWBlPnWCEvyUyh+NWTg/yk+ErXzgRWS8DCebVNN7jgaJvV49LgKye8QIKVGwUDjJUmj6DVlrqEKRq+teYJ28NJLZeAhfNy22bSkkkAoqViU660z0kTH57YvrU2oqnV5ab8KS+qRNNwoAmsiYCF85pa6/iyMrAYtT0fn3RaChKuDGZWZpa0K5pYlDv6GngTwzsmsCECFs4basxDVZFgZMCXl0UYlJvFUQZtg4RsXV7K7QHrWVrNmc5BgNkadgURkIBjMG1VpgGVeVXlPaY7qa6sM4Lp6VbtR79sc0wevnYdBCyc19FOLmU5BFK/bFMOkUJrarNGoQ3vai+WQHshKzRom3IW21R5C2bhnJevUzeBQQRqs1O4hmmDg+zz4UL76ydgs8b629A12CABCWlmp/R92WaDNXaVugTQnL+oA4PfjeNjEzCBExKQYEZjrgRzvX/C3J3VzAS+CvmjOf9bHwQ/nLNvAiYwIQEJWmZi8HZkWLgJmzIfteXTYtUr6fL5sg2v2T/Rvrzq1faTrX1ChnazEvgr5L4Ys4Y6Yngtl2/k7XTYUFj7+QiYfz62rZS/1D7fTWR7JuY/awvCOAjn9oBg61LvtgmU0F8XMSBYd9A38nmU4xt5aAp8Lw/Nwi4zAfPPDFjJ132ZNyPp06wnUn2cV/uPtJ+6toii24kXN7TNy4vZhbNA87YaX5JuOqj2mT7E8ayvGiv/zTvzP00TizMCGe0Ys0bz+rrCWGvbLpFASf11duGsNmGqUKyDvlE4X2a+mdhujjaOgPmP4zb2qnNdGGzOY9Mo+bpi+usShDOd9WOkt4XJ95y3y0fA/POx3UlZisZtBfCU2GjOOxF8kEKgmP46q3BO1IoZRLHLQMD8M0DdnyTCuTHf7Y/qs10CpfXXG10AJz4Ogjdoye3sgzZts0abyrT75j8tz72p1Rqztea9lPaeLKq/zqo5722GzydZnctuPgLmPx975zycwGb669yac9COY00Q7pLMe7bLQ8D8E7jWj9OvFXXIU9wDXfc+IXlHSSdQVH+dVTir87LwOk0T6/QhrJqcn95+jplKwPzTSMFJMY96OURpXKTl1h9LaVzrP7v9M6X111mFc92dwsT8bu8KmrNtdF0y0x6b/7Q8o6mlCFbF8UL7UXo7gcX01xvqEDx6zXlH5lXW8Op2uxXQVN5zt2wHen9yAuY/OdLRCXqh/cPoNt1fJe/46k/15Z/rOrij7UIb03xO7urCfJSP1lA57WPSeKjt0WWIf3MRMP9cZEel2zad8H+0YtLBuPX+qvp9p60ygS3BrAF+OuVTFSrcIO7q+J6OPaACnfzO/PMzPpiD+nt7fMUL7fcTK6K/LkI4q1OiIXhZxP7OmPWM+WfFOzhxtYcX2t9DrZT+ugjhvKcdfMoENklAAgbNmGmiKCa80l2tUleHszojM5lY59lKyyZ7wOFKreEllMO1cAwTWBEBCdwPKi5L4iKQ32p7SvF1zFKYT7T9o33sjs04jPbtCiNgzbmwBnd15yUgoYvJguVDwxRR7Mz3KJXC2gOCBNkVTMDCueDGd9VnIbAzC0kCGbOGB75naYplZ2qzxrLbx6XbHoGbqpKF8fbadfIaWThPjtQJmsBeAgjmMGW0iijtOfYS1t5EfHL7BGzW2H4bu4bLIsCXPJiNEQQ0mvSzZRXRpVkCAQvnJbSCy1AMAQllBgAfF1PhnoqKw2zriMyZdw+OaLCFcxSLA03ABDITmHMdkTnzTsZqm3MyKkc0AROYkEB72iAmHmatnMqNyhuNW1swRx0sq+IyZ320s+Y8Gp0vNAETGEtAgmuSdUSUzncqAzb8r1PLMibvOh/mp7fLfaZjhDVvcfJiEcfVm55hX8fPtY0yY1lzhqKdCZjALAQQXsoY4RpeyhlaDt6wJI3BLjVvxWPQ9n63jHV4KD9C+X91WLssLxQ2ajaOhXMbo/dNwARORqAWWghm1m0fJcDqaxttNbXwA/OmbLEbAGtLI3yDSeajjs/bZdA5bjrn8hHwg5zNGoNwObIJmEAKAQkjZmPc1/aqjs/jP6YHFnPCPMA6Ine0PdG+vDPMBdFFnnQe220QgKTxt8J+1obAQ0Ai/KoPhsgnH8I4x7RFjtnu6hzHZ/KT8ya+HOnvmCZ0TJqEU8fgCIu5SkDrxMvYyb4wC+c+Mg43ARM4hgCfmas0S/nPJMQQpkEoIpzbg3K9+SgemugtrieSfARgtSCU9lm5D6FZ2Xvr86SNECbstvYrgSj/nTYG9F5qS8q7To/8wo2BoOC4kXRNMcTdsUnXkd/IR4hbONdA7JmACcxAQMIPIRW0RYRlMDs80v7QV9cxFaBdowmjhZNu9Rkn+TjO97m28CQe5RrquCaWBzcN6hbMMVXaPfVDuA/OezGac6uSf6sizeOP9u1OQMD880AukavqXGmP8tEWGwGp4/dDKXNNnQ6aKpo4bifdy6Crv7qurfG2969G7g/hphC7FmH7INRJPjbp9k2jnWJMuLfPR/evR0NPHKiK8bjzRj6DA9xlaQjWux18tzlx0TeRnfnnaUZzrQbHgs15FGQxxC79Vj6zJbArY8YI2uqoNAdexI0GAR1zbRMGqw32lQs51o4bS+tK2OzCWcCZp8iXIBp7jPa5U3EcGyG9UgkHjCdg/uPZ7buydK6qPwKJ/3WjOe/jtecc6TRCT+mhnY7RRPsE7J6sKxs32j5l6LpG2KpMyClMNk1YJzLXN3bxzrnew+u9Z053AuN97HEHIzqjoaOgnq74q8/J/PM0YelcEUiNwnUkYgb+sDvzZWoEdTVzopYNv5K29itFrg6rhHkrDAXwW23MQ8ZWPNRhW6Y+bUcZ+Cg1efGUv6+ugwcDyWgJNmdgxWw1aM84zu+reBXJP6MJmP9odHsvLJqrhBUa87Fa81kt9KL/f51DRnATbFxPGPIlJmOa6w7shBtCM9VP+STVT/Eq5VJ+n1bdm/WsmnMoeG/pLk8wJccuAwHzzwBVSZprHq5zpar2RBBjoulqzylFeqpIOzeQlIuIM6twVv5B8AYtuV3uYFeq7jztE96fjID5T4ZyJyFz3cGx/gMJZswYjxNvvFWFFRdzCiaPmHw7CGVu4XywgIpwKyWS42QjYP550JprHq7ZUpWQbcwaiZn8rmtGm3ZuJGaSK1rQjmPpB+2Dec92eQiYv7k2BCRIeEp9rW3I02oz1zckpHQuwv4WfdUvuVqxuAqrXjU/lMiswlmFZBSWMsY6QwgbbEg/VGmfvyRg/nl6wlq5Um4RSX61uY+e0kkSPn3XO/ySwKzCuW4E1P6YoT1ozqMfC9zISQTMPwnT4EjmOhhZngt0s5jtk1jH1GgJwplXMqt5iZ2KcAfn1U3u5nb5CJh/HrbmmofrmFRX8VmqbsVmHxCU8K3e+KnvblX5tI9Jg9chH3UL7ONpCZj/tDxDauYaSCzCb5tqeEpfhcK3BM2Z1gMeb9sE88ZdHd/TcezNQeLbTUvA/KflGVIz10BiRl9ypD1uxVP6qHnHp67CIoSz4HEnGzpN5dSsNpuf+edpWnPNw3VfqmKO8GWGFzKFF0fCcqVn2ucV7+rLK/IX72Y3ayyekAtoAiawCgISviwuxEsfCOS32ng7r3IKQ2gf9UmsOqmTeRbOJ0PtjEzABHIRqLViFigKs7swZdwjP4WxJDGfuvpH+8zBrr6kIn/Rrm3W+KCCdwvLJ11WYZ/pFtzHJmACRRHYmUAguYVZoxqz0n57QHAxUFSu6lNafQVCOHOHqZbgi0RqG9Ijpx1kAiZgAosgcFOlWNsEgtgU4gbmtYuLTb9p2VTUOyZgAtslIC0U0wU25WDWONM+X/pe7USDtlljuy3nmpmACWydAOZXhHOYjosm/WzNlf4/rTA0xLXtwWAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 - \\frac{r_{s}}{r} & 0 & 0 & 0\\\\0 & - \\frac{1}{c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0\\\\0 & 0 & - \\frac{r^{2}}{c^{2}} & 0\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡    rₛ                                 ⎤\n",
       "⎢1 - ──       0        0         0      ⎥\n",
       "⎢    r                                  ⎥\n",
       "⎢                                       ⎥\n",
       "⎢            -1                         ⎥\n",
       "⎢  0     ───────────   0         0      ⎥\n",
       "⎢         2 ⎛    rₛ⎞                    ⎥\n",
       "⎢        c ⋅⎜1 - ──⎟                    ⎥\n",
       "⎢           ⎝    r ⎠                    ⎥\n",
       "⎢                                       ⎥\n",
       "⎢                       2               ⎥\n",
       "⎢                     -r                ⎥\n",
       "⎢  0          0       ────       0      ⎥\n",
       "⎢                       2               ⎥\n",
       "⎢                      c                ⎥\n",
       "⎢                                       ⎥\n",
       "⎢                             2    2    ⎥\n",
       "⎢                           -r ⋅sin (θ) ⎥\n",
       "⎢  0          0        0    ────────────⎥\n",
       "⎢                                 2     ⎥\n",
       "⎣                                c      ⎦"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch = Schwarzschild()\n",
    "sch.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{r}{r - r_{s}} & 0 & 0 & 0\\\\0 & \\frac{c^{2} \\left(- r + r_{s}\\right)}{r} & 0 & 0\\\\0 & 0 & - \\frac{c^{2}}{r^{2}} & 0\\\\0 & 0 & 0 & - \\frac{c^{2}}{r^{2} \\sin^{2}{\\left(\\theta \\right)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  r                                   ⎤\n",
       "⎢──────       0         0        0     ⎥\n",
       "⎢r - rₛ                                ⎥\n",
       "⎢                                      ⎥\n",
       "⎢         2                            ⎥\n",
       "⎢        c ⋅(-r + rₛ)                  ⎥\n",
       "⎢  0     ────────────   0        0     ⎥\n",
       "⎢             r                        ⎥\n",
       "⎢                                      ⎥\n",
       "⎢                        2             ⎥\n",
       "⎢                      -c              ⎥\n",
       "⎢  0          0        ────      0     ⎥\n",
       "⎢                        2             ⎥\n",
       "⎢                       r              ⎥\n",
       "⎢                                      ⎥\n",
       "⎢                                 2    ⎥\n",
       "⎢                               -c     ⎥\n",
       "⎢  0          0         0    ──────────⎥\n",
       "⎢                             2    2   ⎥\n",
       "⎣                            r ⋅sin (θ)⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch_inv = sch.inv()\n",
    "sch_inv.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOCAYAAAD9lDaoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVQoFW2RMRKCMBBFg3qAjEeA1orRnsIjWNupR6CEVm8gpa2tnRY0tt5AjoDeIL4fBycqf+ZPsn//bnYhcs6ZsixjY0wOhSlsYY5+kzCEMmwRllmWnWBV1/UE7cB5JW4GMsAV/IACdX3Co0SZ5vBBwkoIcOFu0WOZFDQEquyDNRq8j0VR3CEp55/7q6ZriqiF/MZ6rg8auMK8UzJSuxAk9oo5N53+1YnE+tegeNS5MSy4J2EH7prrPTiBBp1xdr9GOUGFbcSacp+hvleIMUFKYaLntImMfh7OEP4HvwBvn1+w+m4NrAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch.order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ll'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sch.config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtaining Christoffel Symbols from Metric Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{r_{s}}{2 r^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0\\\\\\frac{r_{s}}{2 r^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}\\frac{r_{s} c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)}{2 r^{2}} & 0 & 0 & 0\\\\0 & - \\frac{r_{s}}{2 r^{2} \\left(1 - \\frac{r_{s}}{r}\\right)} & 0 & 0\\\\0 & 0 & - r \\left(1 - \\frac{r_{s}}{r}\\right) & 0\\\\0 & 0 & 0 & - r \\left(1 - \\frac{r_{s}}{r}\\right) \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{r} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{r}\\\\0 & 0 & 0 & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}}\\\\0 & \\frac{1}{r} & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                      ⎡    2 ⎛    rₛ⎞                        \n",
       "⎢                                      ⎢rₛ⋅c ⋅⎜1 - ──⎟                        \n",
       "⎢                                      ⎢      ⎝    r ⎠                        \n",
       "⎢⎡                     rₛ           ⎤  ⎢──────────────        0             0 \n",
       "⎢⎢      0        ─────────────  0  0⎥  ⎢        2                             \n",
       "⎢⎢                  2 ⎛    rₛ⎞      ⎥  ⎢     2⋅r                              \n",
       "⎢⎢               2⋅r ⋅⎜1 - ──⎟      ⎥  ⎢                                      \n",
       "⎢⎢                    ⎝    r ⎠      ⎥  ⎢                     -rₛ              \n",
       "⎢⎢                                  ⎥  ⎢      0         ─────────────       0 \n",
       "⎢⎢      rₛ                          ⎥  ⎢                   2 ⎛    rₛ⎞         \n",
       "⎢⎢─────────────        0        0  0⎥  ⎢                2⋅r ⋅⎜1 - ──⎟         \n",
       "⎢⎢   2 ⎛    rₛ⎞                     ⎥  ⎢                     ⎝    r ⎠         \n",
       "⎢⎢2⋅r ⋅⎜1 - ──⎟                     ⎥  ⎢                                      \n",
       "⎢⎢     ⎝    r ⎠                     ⎥  ⎢                                  ⎛   \n",
       "⎢⎢                                  ⎥  ⎢      0               0        -r⋅⎜1 -\n",
       "⎢⎢      0              0        0  0⎥  ⎢                                  ⎝   \n",
       "⎢⎢                                  ⎥  ⎢                                      \n",
       "⎢⎣      0              0        0  0⎦  ⎢                                      \n",
       "⎢                                      ⎢      0               0             0 \n",
       "⎣                                      ⎣                                      \n",
       "\n",
       "                         ⎤                                                   ⎤\n",
       "                         ⎥                                                   ⎥\n",
       "                         ⎥                                                   ⎥\n",
       "               0         ⎥                                                   ⎥\n",
       "                         ⎥                             ⎡0  0    0       0   ⎤⎥\n",
       "                         ⎥  ⎡0  0  0        0       ⎤  ⎢                    ⎥⎥\n",
       "                         ⎥  ⎢                       ⎥  ⎢                1   ⎥⎥\n",
       "                         ⎥  ⎢      1                ⎥  ⎢0  0    0       ─   ⎥⎥\n",
       "               0         ⎥  ⎢0  0  ─        0       ⎥  ⎢                r   ⎥⎥\n",
       "                         ⎥  ⎢      r                ⎥  ⎢                    ⎥⎥\n",
       "                         ⎥  ⎢                       ⎥  ⎢              cos(θ)⎥⎥\n",
       "                         ⎥  ⎢   1                   ⎥  ⎢0  0    0     ──────⎥⎥\n",
       "                         ⎥  ⎢0  ─  0        0       ⎥  ⎢              sin(θ)⎥⎥\n",
       " rₛ⎞                     ⎥  ⎢   r                   ⎥  ⎢                    ⎥⎥\n",
       " ──⎟           0         ⎥  ⎢                       ⎥  ⎢   1  cos(θ)        ⎥⎥\n",
       " r ⎠                     ⎥  ⎣0  0  0  -sin(θ)⋅cos(θ)⎦  ⎢0  ─  ──────    0   ⎥⎥\n",
       "                         ⎥                             ⎣   r  sin(θ)        ⎦⎥\n",
       "         ⎛    rₛ⎞    2   ⎥                                                   ⎥\n",
       "      -r⋅⎜1 - ──⎟⋅sin (θ)⎥                                                   ⎥\n",
       "         ⎝    r ⎠        ⎦                                                   ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chr = ChristoffelSymbols.from_metric(sch_inv) # can be initialized from sch also\n",
    "chr.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ull'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chr.config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Changing the first index to covariant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{r_{s}}{2 r^{2}} & 0 & 0\\\\\\frac{r_{s}}{2 r^{2}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}- \\frac{r_{s}}{2 r^{2}} & 0 & 0 & 0\\\\0 & \\frac{r_{s}}{2 r^{2} c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)^{2}} & 0 & 0\\\\0 & 0 & \\frac{r}{c^{2}} & 0\\\\0 & 0 & 0 & \\frac{r \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & - \\frac{r}{c^{2}} & 0\\\\0 & - \\frac{r}{c^{2}} & 0 & 0\\\\0 & 0 & 0 & \\frac{r^{2} \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}}{c^{2}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & - \\frac{r \\sin^{2}{\\left(\\theta \\right)}}{c^{2}}\\\\0 & 0 & 0 & - \\frac{r^{2} \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}}{c^{2}}\\\\0 & - \\frac{r \\sin^{2}{\\left(\\theta \\right)}}{c^{2}} & - \\frac{r^{2} \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}}{c^{2}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                    ⎡-rₛ                                   ⎤                 \n",
       "⎢                    ⎢────          0          0       0    ⎥                 \n",
       "⎢                    ⎢   2                                  ⎥                 \n",
       "⎢                    ⎢2⋅r                                   ⎥  ⎡0   0    0    \n",
       "⎢                    ⎢                                      ⎥  ⎢              \n",
       "⎢⎡       rₛ       ⎤  ⎢              rₛ                      ⎥  ⎢        -r    \n",
       "⎢⎢ 0    ────  0  0⎥  ⎢ 0    ─────────────────  0       0    ⎥  ⎢0   0   ───   \n",
       "⎢⎢         2      ⎥  ⎢                      2               ⎥  ⎢          2   \n",
       "⎢⎢      2⋅r       ⎥  ⎢         2  2 ⎛    rₛ⎞                ⎥  ⎢         c    \n",
       "⎢⎢                ⎥  ⎢      2⋅r ⋅c ⋅⎜1 - ──⎟                ⎥  ⎢              \n",
       "⎢⎢ rₛ             ⎥  ⎢              ⎝    r ⎠                ⎥  ⎢   -r         \n",
       "⎢⎢────   0    0  0⎥  ⎢                                      ⎥  ⎢0  ───   0    \n",
       "⎢⎢   2            ⎥  ⎢                         r            ⎥  ⎢     2        \n",
       "⎢⎢2⋅r             ⎥  ⎢ 0            0          ──      0    ⎥  ⎢    c         \n",
       "⎢⎢                ⎥  ⎢                          2           ⎥  ⎢              \n",
       "⎢⎢ 0     0    0  0⎥  ⎢                         c            ⎥  ⎢              \n",
       "⎢⎢                ⎥  ⎢                                      ⎥  ⎢             r\n",
       "⎢⎣ 0     0    0  0⎦  ⎢                                  2   ⎥  ⎢0   0    0   ─\n",
       "⎢                    ⎢                             r⋅sin (θ)⎥  ⎢              \n",
       "⎢                    ⎢ 0            0          0   ─────────⎥  ⎣              \n",
       "⎢                    ⎢                                  2   ⎥                 \n",
       "⎣                    ⎣                                 c    ⎦                 \n",
       "\n",
       "                                                                          ⎤\n",
       "                                                                          ⎥\n",
       "                  ⎡0       0               0                   0         ⎤⎥\n",
       "      0        ⎤  ⎢                                                      ⎥⎥\n",
       "               ⎥  ⎢                                             2        ⎥⎥\n",
       "               ⎥  ⎢                                       -r⋅sin (θ)     ⎥⎥\n",
       "      0        ⎥  ⎢0       0               0              ───────────    ⎥⎥\n",
       "               ⎥  ⎢                                             2        ⎥⎥\n",
       "               ⎥  ⎢                                            c         ⎥⎥\n",
       "               ⎥  ⎢                                                      ⎥⎥\n",
       "               ⎥  ⎢                                      2               ⎥⎥\n",
       "      0        ⎥  ⎢                                    -r ⋅sin(θ)⋅cos(θ) ⎥⎥\n",
       "               ⎥  ⎢0       0               0           ──────────────────⎥⎥\n",
       "               ⎥  ⎢                                             2        ⎥⎥\n",
       "               ⎥  ⎢                                            c         ⎥⎥\n",
       "2              ⎥  ⎢                                                      ⎥⎥\n",
       " ⋅sin(θ)⋅cos(θ)⎥  ⎢         2        2                                   ⎥⎥\n",
       "───────────────⎥  ⎢   -r⋅sin (θ)   -r ⋅sin(θ)⋅cos(θ)                     ⎥⎥\n",
       "       2       ⎥  ⎢0  ───────────  ──────────────────          0         ⎥⎥\n",
       "      c        ⎦  ⎢         2               2                            ⎥⎥\n",
       "                  ⎣        c               c                             ⎦⎥\n",
       "                                                                          ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_chr = chr.change_config('lll') # changing the configuration to (covariant, covariant, covariant)\n",
    "new_chr.tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'lll'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_chr.config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Any arbitary index configuration would also work!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & \\frac{r_{s}}{2 r \\left(r - r_{s}\\right)} & 0 & 0\\\\\\frac{r_{s} c^{2} \\left(- r + r_{s}\\right)}{2 r^{3}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}- \\frac{r_{s}}{2 r \\left(r - r_{s}\\right)} & 0 & 0 & 0\\\\0 & \\frac{r_{s} \\left(- r + r_{s}\\right)}{2 r^{3} \\left(1 - \\frac{r_{s}}{r}\\right)^{2}} & 0 & 0\\\\0 & 0 & - \\frac{1}{r} & 0\\\\0 & 0 & 0 & - \\frac{1}{r}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & r - r_{s} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & - \\left(- r + r_{s}\\right) \\sin^{2}{\\left(\\theta \\right)}\\\\0 & 0 & 0 & \\sin{\\left(\\theta \\right)} \\cos{\\left(\\theta \\right)}\\\\0 & \\frac{1}{r} & \\frac{\\cos{\\left(\\theta \\right)}}{\\sin{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                       ⎡    -rₛ                              \n",
       "⎢                                       ⎢────────────        0          0    0\n",
       "⎢                                       ⎢2⋅r⋅(r - rₛ)                         \n",
       "⎢⎡                      rₛ           ⎤  ⎢                                     \n",
       "⎢⎢       0         ────────────  0  0⎥  ⎢               rₛ⋅(-r + rₛ)          \n",
       "⎢⎢                 2⋅r⋅(r - rₛ)      ⎥  ⎢     0        ──────────────   0    0\n",
       "⎢⎢                                   ⎥  ⎢                           2         \n",
       "⎢⎢    2                              ⎥  ⎢                 3 ⎛    rₛ⎞          \n",
       "⎢⎢rₛ⋅c ⋅(-r + rₛ)                    ⎥  ⎢              2⋅r ⋅⎜1 - ──⎟          \n",
       "⎢⎢───────────────       0        0  0⎥  ⎢                   ⎝    r ⎠          \n",
       "⎢⎢         3                         ⎥  ⎢                                     \n",
       "⎢⎢      2⋅r                          ⎥  ⎢                              -1     \n",
       "⎢⎢                                   ⎥  ⎢     0              0         ───   0\n",
       "⎢⎢       0              0        0  0⎥  ⎢                               r     \n",
       "⎢⎢                                   ⎥  ⎢                                     \n",
       "⎢⎣       0              0        0  0⎦  ⎢                                   -1\n",
       "⎢                                       ⎢     0              0          0   ──\n",
       "⎣                                       ⎣                                    r\n",
       "\n",
       " ⎤                                                              ⎤\n",
       " ⎥                                                              ⎥\n",
       " ⎥                                                              ⎥\n",
       " ⎥                                                              ⎥\n",
       " ⎥  ⎡0  0    0        0    ⎤  ⎡0  0    0             0         ⎤⎥\n",
       " ⎥  ⎢                      ⎥  ⎢                                ⎥⎥\n",
       " ⎥  ⎢0  0  r - rₛ     0    ⎥  ⎢                            2   ⎥⎥\n",
       " ⎥  ⎢                      ⎥  ⎢0  0    0     -(-r + rₛ)⋅sin (θ)⎥⎥\n",
       " ⎥  ⎢   1                  ⎥  ⎢                                ⎥⎥\n",
       " ⎥  ⎢0  ─    0        0    ⎥  ⎢0  0    0       sin(θ)⋅cos(θ)   ⎥⎥\n",
       " ⎥  ⎢   r                  ⎥  ⎢                                ⎥⎥\n",
       " ⎥  ⎢                      ⎥  ⎢   1  cos(θ)                    ⎥⎥\n",
       " ⎥  ⎢              -cos(θ) ⎥  ⎢0  ─  ──────          0         ⎥⎥\n",
       " ⎥  ⎢0  0    0     ────────⎥  ⎣   r  sin(θ)                    ⎦⎥\n",
       " ⎥  ⎣               sin(θ) ⎦                                    ⎥\n",
       " ⎥                                                              ⎥\n",
       "─⎥                                                              ⎥\n",
       " ⎦                                                              ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_chr2 = new_chr.change_config('lul')\n",
    "new_chr2.tensor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtaining Riemann Tensor from Christoffel Symbols and manipulating it's indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & - \\frac{r_{s}}{r^{2} \\left(r - r_{s}\\right)} & 0 & 0\\\\0 & 0 & \\frac{r_{s}}{2 r} & 0\\\\0 & 0 & 0 & \\frac{r_{s} \\sin^{2}{\\left(\\theta \\right)}}{2 r}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0       0        0       0     ⎤\n",
       "⎢                               ⎥\n",
       "⎢       -rₛ                     ⎥\n",
       "⎢0  ───────────   0       0     ⎥\n",
       "⎢    2                          ⎥\n",
       "⎢   r ⋅(r - rₛ)                 ⎥\n",
       "⎢                               ⎥\n",
       "⎢                 rₛ            ⎥\n",
       "⎢0       0       ───      0     ⎥\n",
       "⎢                2⋅r            ⎥\n",
       "⎢                               ⎥\n",
       "⎢                           2   ⎥\n",
       "⎢                     rₛ⋅sin (θ)⎥\n",
       "⎢0       0        0   ──────────⎥\n",
       "⎣                        2⋅r    ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm = RiemannCurvatureTensor.from_christoffels(new_chr2)\n",
    "rm[0,0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ulll'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm.config"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & - \\frac{r_{s} c^{4} \\left(- r + r_{s}\\right)^{2}}{r^{3} \\left(r - r_{s}\\right)^{2}} & 0 & 0\\\\0 & 0 & \\frac{r_{s} c^{4}}{2 r^{4} \\left(r - r_{s}\\right)} & 0\\\\0 & 0 & 0 & \\frac{r_{s} c^{4}}{2 r^{4} \\left(r - r_{s}\\right) \\sin^{2}{\\left(\\theta \\right)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0          0                 0                  0          ⎤\n",
       "⎢                                                           ⎥\n",
       "⎢        4          2                                       ⎥\n",
       "⎢   -rₛ⋅c ⋅(-r + rₛ)                                        ⎥\n",
       "⎢0  ──────────────────        0                  0          ⎥\n",
       "⎢       3         2                                         ⎥\n",
       "⎢      r ⋅(r - rₛ)                                          ⎥\n",
       "⎢                                                           ⎥\n",
       "⎢                               4                           ⎥\n",
       "⎢                           rₛ⋅c                            ⎥\n",
       "⎢0          0           ─────────────            0          ⎥\n",
       "⎢                          4                                ⎥\n",
       "⎢                       2⋅r ⋅(r - rₛ)                       ⎥\n",
       "⎢                                                           ⎥\n",
       "⎢                                                  4        ⎥\n",
       "⎢                                              rₛ⋅c         ⎥\n",
       "⎢0          0                 0        ─────────────────────⎥\n",
       "⎢                                         4             2   ⎥\n",
       "⎣                                      2⋅r ⋅(r - rₛ)⋅sin (θ)⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm2 = rm.change_config(\"uuuu\")\n",
    "rm2[0,0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & \\frac{r_{s} c^{2} \\left(- r + r_{s}\\right)^{2}}{r^{3} \\left(r - r_{s}\\right)^{2}} & 0 & 0\\\\0 & 0 & - \\frac{r_{s} c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)}{2 r^{2} \\left(r - r_{s}\\right)} & 0\\\\0 & 0 & 0 & - \\frac{r_{s} c^{2} \\left(1 - \\frac{r_{s}}{r}\\right)}{2 r^{2} \\left(r - r_{s}\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0         0                 0                 0        ⎤\n",
       "⎢                                                       ⎥\n",
       "⎢       2          2                                    ⎥\n",
       "⎢   rₛ⋅c ⋅(-r + rₛ)                                     ⎥\n",
       "⎢0  ────────────────         0                 0        ⎥\n",
       "⎢      3         2                                      ⎥\n",
       "⎢     r ⋅(r - rₛ)                                       ⎥\n",
       "⎢                                                       ⎥\n",
       "⎢                          2 ⎛    rₛ⎞                   ⎥\n",
       "⎢                     -rₛ⋅c ⋅⎜1 - ──⎟                   ⎥\n",
       "⎢                            ⎝    r ⎠                   ⎥\n",
       "⎢0         0          ────────────────         0        ⎥\n",
       "⎢                         2                             ⎥\n",
       "⎢                      2⋅r ⋅(r - rₛ)                    ⎥\n",
       "⎢                                                       ⎥\n",
       "⎢                                            2 ⎛    rₛ⎞ ⎥\n",
       "⎢                                       -rₛ⋅c ⋅⎜1 - ──⎟ ⎥\n",
       "⎢                                              ⎝    r ⎠ ⎥\n",
       "⎢0         0                 0          ────────────────⎥\n",
       "⎢                                           2           ⎥\n",
       "⎣                                        2⋅r ⋅(r - rₛ)  ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm3 = rm2.change_config(\"lulu\")\n",
    "rm3[0,0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & - \\frac{r_{s}}{r^{2} \\left(r - r_{s}\\right)} & 0 & 0\\\\0 & 0 & \\frac{r_{s}}{2 r} & 0\\\\0 & 0 & 0 & \\frac{r_{s} \\sin^{2}{\\left(\\theta \\right)}}{2 r}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0       0        0       0     ⎤\n",
       "⎢                               ⎥\n",
       "⎢       -rₛ                     ⎥\n",
       "⎢0  ───────────   0       0     ⎥\n",
       "⎢    2                          ⎥\n",
       "⎢   r ⋅(r - rₛ)                 ⎥\n",
       "⎢                               ⎥\n",
       "⎢                 rₛ            ⎥\n",
       "⎢0       0       ───      0     ⎥\n",
       "⎢                2⋅r            ⎥\n",
       "⎢                               ⎥\n",
       "⎢                           2   ⎥\n",
       "⎢                     rₛ⋅sin (θ)⎥\n",
       "⎢0       0        0   ──────────⎥\n",
       "⎣                        2⋅r    ⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rm4 = rm3.change_config(\"ulll\")\n",
    "rm4.simplify()\n",
    "rm4[0,0,:,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### It is seen that `rm` and `rm4` are same as they have the same configuration"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}