{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Einstein Tensor calculations using Symbolic module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pytest\n",
    "import sympy\n",
    "from sympy import cos, simplify, sin, sinh, tensorcontraction\n",
    "from einsteinpy.symbolic import EinsteinTensor, MetricTensor, RicciScalar\n",
    "\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining the Anti-de Sitter spacetime Metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "syms = sympy.symbols(\"t chi theta phi\")\n",
    "t, ch, th, ph = syms\n",
    "m = sympy.diag(-1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2).tolist()\n",
    "metric = MetricTensor(m, syms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the Einstein Tensor (with both indices covariant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-3.0 & 0 & 0 & 0\\\\0 & 3.0 \\cos^{2}{\\left(t \\right)} & 0 & 0\\\\0 & 0 & \\left(\\sin^{2}{\\left(t \\right)} - 1\\right) \\sinh^{2}{\\left(\\chi \\right)} + 4.0 \\cos^{2}{\\left(t \\right)} \\sinh^{2}{\\left(\\chi \\right)} & 0\\\\0 & 0 & 0 & \\left(\\sin^{2}{\\left(t \\right)} - 1\\right) \\sin^{2}{\\left(\\theta \\right)} \\sinh^{2}{\\left(\\chi \\right)} + 4.0 \\sin^{2}{\\left(\\theta \\right)} \\cos^{2}{\\left(t \\right)} \\sinh^{2}{\\left(\\chi \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-3.0       0                             0                                   \n",
       "⎢                                                                             \n",
       "⎢             2                                                               \n",
       "⎢ 0    3.0⋅cos (t)                        0                                   \n",
       "⎢                                                                             \n",
       "⎢                   ⎛   2       ⎞     2             2        2                \n",
       "⎢ 0         0       ⎝sin (t) - 1⎠⋅sinh (χ) + 4.0⋅cos (t)⋅sinh (χ)             \n",
       "⎢                                                                             \n",
       "⎢                                                                  ⎛   2      \n",
       "⎣ 0         0                             0                        ⎝sin (t) - \n",
       "\n",
       "                   0                              ⎤\n",
       "                                                  ⎥\n",
       "                                                  ⎥\n",
       "                   0                              ⎥\n",
       "                                                  ⎥\n",
       "                                                  ⎥\n",
       "                   0                              ⎥\n",
       "                                                  ⎥\n",
       " ⎞    2        2             2       2        2   ⎥\n",
       "1⎠⋅sin (θ)⋅sinh (χ) + 4.0⋅sin (θ)⋅cos (t)⋅sinh (χ)⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "einst = EinsteinTensor.from_metric(metric)\n",
    "einst.tensor()"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}