symbolicalgebra.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symbolic algebra with Sympy\n",
    "\n",
    "This is known as symbolic algebra.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cos(x)\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "\n",
    "x = symbols('x')\n",
    "\n",
    "f = sin(x)\n",
    "\n",
    "print(diff(f, x))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-cos(x)\n"
     ]
    }
   ],
   "source": [
    "print(integrate(f, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partial fractions decomposition\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Converting symbolic expressions to numeric functions\n",
    "\n",
    "While symbolic expressions are convenient for performing manipulations, often we require numeric values.  Sympy allows us to convert expressions into functions that can be evaluated numerically with the =lambdify= method.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi40LCBodHRwOi8vbWF0cGxvdGxpYi5vcmcv7US4rQAAIABJREFUeJzt3Xl4lNXd//H3N3uAQCCELQsBWRQQBMKitlafuiCt4lpRUVEotdbax9a22vaxLdrN2traUhUVERURrW2RYnFXXICEHYJgiEDCloU1hKxzfn8k+ktjIBMyyT0z+byuK9c1kznMfE9m8snNuc99jjnnEBGR8BLhdQEiIhJ4CncRkTCkcBcRCUMKdxGRMKRwFxEJQwp3EZEwpHAXEQlDCncRkTCkcBcRCUNRXr1w9+7dXUZGhlcvLyISklatWlXsnEtuqp1n4Z6RkUF2drZXLy8iEpLMbIc/7TQsIyIShpoMdzObY2aFZrbxOI+bmT1sZrlmtt7MRgW+TBERaQ5/jtznAhNO8PjFwMC6rxnAIy0vS0REWqLJcHfOvQfsP0GTScA8V2s5kGhmvQNVoIiINF8gxtxTgPx69wvqvvcFZjbDzLLNLLuoqCgALy0iIo0JRLhbI99rdAcQ59xs51ymcy4zObnJmTwiInKSAhHuBUBavfupwO4APK+IiJykQIT7IuDGulkz44FDzrk9AXheEZGw4vM5fvXvHPL3l7X6azV5EZOZPQ+cC3Q3swLg50A0gHPuUWAJMBHIBcqAm1urWBGRUPaXt3J5fNmn9E/uxLVj01v1tZoMd+fctU087oDvBKwiEZEw9O7WIv705lauGJXC5DFpTf+DFtIVqiIirWzXwWN8b8EaBvdM4FeXnY5ZY/NQAkvhLiLSiiqqa7jtudXU1DgemTKa+JjINnldzxYOExFpD2a+ksO6/IM8OmU0/bp3bLPX1ZG7iEgreTE7n+dW7OTWr5zChGG92vS1Fe4iIq1g465D/PSfGzl7QBJ3XTiozV9f4S4iEmAHyyq59dlVJHWM4eHJI4mKbPuo1Zi7iEgA1fgcdyxYS+HhCl741niSOsV6UofCXUQkgB56fSvvbS3iN1eczsj0rp7VoWEZEZEAWbppL399O5fJY9Ja/QrUpijcRUQCILewlB8sXMeI1C784tKhXpejcBcRaakj5VXMeCab2KgIHpkymrjotrlQ6UQ05i4i0gI+n+P7C9exo6SM56aPo09ivNclATpyFxFpkb++ncvrOfv42ddOY3z/JK/L+ZzCXUTkJL25eR8PvbGVK0amMPWsDK/L+S8KdxGRk5BbWMr/LljL0D6d+fUVbbPSY3Mo3EVEmulw3QnUmKgIHrshMyhOoDakE6oiIs3g8zn+d8FadtadQE0JkhOoDenIXUSkGf74+lbe+riQn18yhHFBdAK1IYW7iIifFq/f/fkVqFPG9/W6nBNSuIuI+GHjrkPc9eI6Mvt2ZeakYUF3ArUhhbuISBOKSyuYMS+brh1ieGTKaGKigj86dUJVROQEKqt9fPvZVZQcreSlW88iOcGbJXybS+EuInIczjn+758bydp+gL9cO5LTU7t4XZLfgv//FiIiHpn74XZeyM7n9vMGcMmIPl6X0ywKdxGRRiz7pIj7Fudw4ZCefP+Ctt8DtaUU7iIiDWwrKuW251YzqGcCD11zBhERwT0zpjEKdxGReg6WVTL96WxiIiN4/MZMOsaG5qnJ0KxaRKQVVNX4+M781ew6cIznvjmOtG4dvC7ppCncRUSonRnzy1c28UFuCQ9ePYIxGd28LqlFNCwjIgI8/eF2nl2+k2+d05+rRqd6XU6LKdxFpN17e0shMxfncMGQnvx4wqlelxMQfoW7mU0wsy1mlmtmdzfyeLqZvW1ma8xsvZlNDHypIiKBt2XvEb47fw2n9urMn0J0Zkxjmgx3M4sEZgEXA0OAa81sSINmPwMWOudGApOBvwW6UBGRQCs6UsG0p7PoEBPJk1NDd2ZMY/w5ch8L5Drn8pxzlcACYFKDNg7oXHe7C7A7cCWKiAReeVUNM57Jpri0giduyqR3l+DcdONk+fNnKgXIr3e/ABjXoM0vgNfM7LtAR+D8gFQnItIKfD7HXS+uY83Ogzw6ZRTDUxO9Ling/Dlyb2wAyjW4fy0w1zmXCkwEnjGzLzy3mc0ws2wzyy4qKmp+tSIiAfDQG1tZvH4Pd198KhOG9fa6nFbhT7gXAGn17qfyxWGXacBCAOfcR0Ac0L3hEznnZjvnMp1zmcnJySdXsYhIC7yYnc9f3srlmsw0vnVOf6/LaTX+hHsWMNDM+plZDLUnTBc1aLMT+CqAmZ1Gbbjr0FxEgsqHucXc8/IGzh6QxP2XB/9uSi3RZLg756qB24GlwGZqZ8VsMrOZZnZpXbMfAN80s3XA88BU51zDoRsREc/kFh7hW8+uol/3jvzt+tFER4b3ZT5+zftxzi0BljT43r31bucAZwe2NBGRwCg6UsHUp7KIjYpkztQxdImP9rqkVhfef7pEpN0rq6xm+tNZlJRW8uRNmSG9GFhzKNxFJGzV+Bx3PL+GDbsO8fC1IxmRFn5THo9H4S4iYck5x8xXNvHG5kJ+fslQLhjS0+uS2pTCXUTC0hPLPuXpj3Yw/Uv9uOmsDK/LaXMKdxEJO4vW7eZXSzbzteG9+cnE07wuxxMKdxEJK8vzSrhr4TrGZnTjD1ePCJtVHptL4S4iYeOTfUeYMS+btG7xzL5xNHHRkV6X5BmFu4iEhb2HyrlpzkpioyOZe/NYEjvEeF2SpxTuIhLyDpdXMfWplRwur2buzWPazVz2E1G4i0hIq6iu4VvzVpFbWMqjU0YztE8Xr0sKCuGz7YiItDs+n+P7C9fxUV4JD10zgi8N/MJitO2WjtxFJCQ55/jlK5v49/o9/GTiqVw+MtXrkoKKwl1EQtLf3tn2+UVKM845xetygo7CXURCzsKsfH6/dAuXndGn3V6k1BSFu4iElKWb9nL3y+s5Z1AyD1zVfi9SaorCXURCxoq8Er77/BpOT03kketHEROlCDse/WREJCTk7D7M9HnZpHWN56mpY+gYq8l+J6JwF5Ggt734KDfOWUmn2CjmTRtHt47t++pTfyjcRSSo7TtczpQnV1Dj8/HMtLGkJMZ7XVJIULiLSNA6VFbFjU+u5MDRSubePJYBPRK8LilkaNBKRILS0Ypqps5dyafFR3nq5jHtaou8QFC4i0jQqaiuYcYz2awvOMSs60Zx9gAtK9BcGpYRkaBSXePjjufX8EFuCQ9cOZwJw3p5XVJIUriLSNDw+Rw/+vt6lm7ax88vGcKVo7VezMlSuItIUHDO8YtXNvHy6l3cef4gbj67n9clhTSFu4gEhQeWbmHeRzuYcU5/7vjqAK/LCXkKdxHx3Ky3c3nknW1cPy6dey4+FTOtF9NSCncR8dST73/K75du4fKRKdw3aZiCPUAU7iLimfkrdnLf4hwuHtaL3181XCs8BpDCXUQ88fLqAn76zw2cNziZP08eSVSk4iiQ9NMUkTa3eP1u7npxHWf2T+KRKaO1dG8r8OsnamYTzGyLmeWa2d3HafMNM8sxs01mNj+wZYpIuFi6aS/fW7CWzL7deOKmTOKiI70uKSw1ufyAmUUCs4ALgAIgy8wWOedy6rUZCNwDnO2cO2BmPVqrYBEJXW9/XMjt81czPLULc24eQ4cYrYDSWvw5ch8L5Drn8pxzlcACYFKDNt8EZjnnDgA45woDW6aIhLp3txbxrWdXMbhXAnNvHksnbbbRqvwJ9xQgv979grrv1TcIGGRmH5jZcjObEKgCRST0vf9JMTPmZTMguRPPThtHl/hor0sKe/786WxsbpJr5HkGAucCqcAyMxvmnDv4X09kNgOYAZCent7sYkUk9Hy4rZjp87Lo170jz04fR2IH7aLUFvw5ci8A0urdTwV2N9LmX865Kufcp8AWasP+vzjnZjvnMp1zmcnJySdbs4iEiOV5JUybm016tw48N13b47Ulf8I9CxhoZv3MLAaYDCxq0OafwHkAZtad2mGavEAWKiKhZXleCTc/lUVq13iemz6epE6xXpfUrjQZ7s65auB2YCmwGVjonNtkZjPN7NK6ZkuBEjPLAd4GfuicK2mtokUkuK2oC/aUrvHM/+Z4khMU7G3NnGs4fN42MjMzXXZ2tievLSKt57Mj9j6JcTw/Yzw9EuK8LimsmNkq51xmU+00F0lEAubDbcVMm5tNqo7YPadrfkUkID7ILeaWuVmkdVOwBwOFu4i02Ltbi7hlbhZ9u3VUsAcJDcuISIu8uXkf3352Naf06MSz08ZqVkyQULiLyElbumkvt89fzam9OvPMtLG6QCmIKNxF5KS8sm43d76wlmEpXXj6lrFaUiDIaMxdRJrtpVUFfG/BGkamJ/LMNAV7MNKRu4g0y/wVO/nJPzZw9oAkHr8xU8v2Bim9KyLityeW5XH/vzdz3uBkHpkyWhttBDGFu4g0yTnHX97K5Y+vb+XiYb348+SR2hovyCncReSEnHP89j8f89i7eVwxKoUHrhyuzaxDgMJdRI6rxuf4v39tZP6KnUwZn87MS4cREdHYFg8SbBTuItKoqhofd724jn+t3c23zz2FH100GDMFe6hQuIvIF5RX1XD7/NW8sbmQH00YzG3nDvC6JGkmhbuI/JfD5VVMfzqbrO37ue+yYdwwvq/XJclJULiLyOeKSyu4ac5Ktuw9wp+uOYNJZ6R4XZKcJIW7iABQcKCMG59cye5Dx3jipkzOHdzD65KkBRTuIsLHew9z05yVHKus4bnp4xjdt5vXJUkLKdxF2rms7fuZNjeL+JhIXrz1LAb3SvC6JAkAhbtIO/ZGzj6+M381KYnxzJs2ltSuHbwuSQJE4S7STi1YWbsA2LCULjw1dYw22QgzCneRdqb+OjFfGZTM364fRcdYRUG40Tsq0o5U1/i4d9Em5q/YyRWjUvjdlcOJ1joxYUnhLtJOlFVWc8fza3hjc6GWE2gHFO4i7UBJaQW3PJ3NhoKD3DdpKDecmeF1SdLKFO4iYS6vqJSb52ax91A5j04ZzYVDe3ldkrQBhbtIGMvevp/p87KJMOP5GeMZld7V65KkjSjcRcLUv9fv4c6Fa0lJjGfuzWPom9TR65KkDSncRcKMc45H3t3GA//ZQmbfrjx+YyZdO8Z4XZa0MYW7SBipqvHxs39s5IXsfC4d0YcHrhquTazbKYW7SJg4VFbFbfNX8UFuCXf8zwDuvGCQpjq2Ywp3kTCwo+QoN8/NIn9/GQ9ePYKrRqd6XZJ4zK9L08xsgpltMbNcM7v7BO2uMjNnZpmBK1FETmRFXgmXzfqA/UcreXbaOAW7AH6Eu5lFArOAi4EhwLVmNqSRdgnAHcCKQBcpIo1bmJXPlCdX0LVjDP+87WzG9U/yuiQJEv4cuY8Fcp1zec65SmABMKmRdvcBDwDlAaxPRBpR43PcvziHH/19PeP7J/GP284mo7umOsr/50+4pwD59e4X1H3vc2Y2Ekhzzi0+0ROZ2Qwzyzaz7KKiomYXKyKfbWCdxRPvf8pNZ/blqalj6BIf7XVZEmT8OaHa2Ol29/mDZhHAQ8DUpp7IOTcbmA2QmZnpmmguIg18WnyU6U9nsaOkjPsuG8YN4/t6XZIEKX/CvQBIq3c/Fdhd734CMAx4p27aVS9gkZld6pzLDlShIu3dsk+K+M5zq4mMMJ6ZNo4zT9H4uhyfP+GeBQw0s37ALmAycN1nDzrnDgHdP7tvZu8AdynYRQLDOccTyz7lN69uZmCPBJ64KZO0btoOT06syXB3zlWb2e3AUiASmOOc22RmM4Fs59yi1i5SpL0qr6rhnpc38I81u5gwtBd/+MYI7ZokfvHrU+KcWwIsafC9e4/T9tyWlyUiuw4e49ZnVrFx9yHuunAQ3zlvgK44Fb/pEEAkCH2YW8ztz6+hqtrH4zdkcv6Qnl6XJCFG4S4SROqPr5+S3InHbhhN/+ROXpclIUjhLhIkSiuq+fFL6/n3hj1cPKwXv796BJ00vi4nSZ8ckSCQW1jKrc+uIq+olHsuPpUZ5/TX+Lq0iMJdxGOL1+/mxy+tJy46kmenj+OsU7o3/Y9EmqBwF/FIZbWPXy/ZzNwPtzMqPZFZ14+id5d4r8uSMKFwF/HA7oPH+M781azZeZBbzu7HPRNPJTrSrxW4RfyicBdpY29/XMidC9dSXeOYdd0ovja8t9clSRhSuIu0keoaHw++tpVH393GkN6dmXX9KPppmV5pJQp3kTaw6+Ax7nh+Dat2HOC6cenc+/Uh2rhaWpXCXaSVvZ6zj7teXEd1jY+Hrx3JpSP6eF2StAMKd5FWUlFdw2+WfMzcD7cztE9n/nqdhmGk7SjcRVpBbmEpdzy/hpw9h5l6Vgb3TDyV2CgNw0jbUbiLBJBzjhey8vnlKznERUfw5E2ZfPU0LfolbU/hLhIgB8squeflDby6cS9n9k/ioWvOoFeXOK/LknZK4S4SAB9uK+b7L6yj5GgF91x8Kt/8cn8iIrQ2jHhH4S7SAhXVNfzhta08viyPfkkdefzGszk9tYvXZYko3EVO1pa9R/jegjV8vPcIU8an85OJp9EhRr9SEhz0SRRpphqf48n383hw6VY6x0cxZ2om/3OqTppKcFG4izRD/v4yfrBwHSu37+eioT359eWnk9Qp1uuyRL5A4S7iB+ccz63Yya+XbCbSjD9cPYIrRqVoQw0JWgp3kSbsPniMH/99Pcs+KebLA7vz2yuHk5KoddcluCncRY7DOceCrHx+9e/N+Jzj/suGcf24dB2tS0hQuIs0ouBAGfe8vIFlnxRzZv8kfnflcNKTOnhdlojfFO4i9fh8jmeW7+B3//kYA+6/bBjXjU3XBUkSchTuInVyC0u5++/ryd5xgHMGJfPry4eR2lVH6xKaFO7S7lVW+3j03W389a1c4mMiNRNGwoLCXdq1VTsOcM/L69m6r5SvD+/Nzy8ZSnKC5q1L6FO4S7t06FgVD/znY+av3EnvznG6ylTCjsJd2hXnHK+s38PMV3LYf7SCW87ux50XDKJTrH4VJLzoEy3tRl5RKff+axPv5xZzekoX5t48hmEpWsFRwpNf4W5mE4A/A5HAE8653zZ4/PvAdKAaKAJucc7tCHCtIiflWGUNf3snl8fezSM2OoKZk4Zy/bi+RGp6o4SxJsPdzCKBWcAFQAGQZWaLnHM59ZqtATKdc2Vm9m3gAeCa1ihYxF/OOZZu2sd9i3PYdfAYl53Rh5987TR6JGh3JAl//hy5jwVynXN5AGa2AJgEfB7uzrm367VfDkwJZJEizZVbWMrMxTm8t7WIwT0TWDBjPOP7J3ldlkib8SfcU4D8evcLgHEnaD8NeLUlRYmcrMPlVTz8xifM/XA78dGR/N/Xh3DjmX2JjozwujSRNuVPuDc2MOkabWg2BcgEvnKcx2cAMwDS09P9LFGkaTU+x4vZ+Tz42hZKjlbyjdFp3HXRYM1Zl3bLn3AvANLq3U8FdjdsZGbnAz8FvuKcq2jsiZxzs4HZAJmZmY3+gRBpro+2lXDf4hxy9hxmdN+uzJk6huGpiV6XJeIpf8I9CxhoZv2AXcBk4Lr6DcxsJPAYMME5VxjwKkUakVdUym9f/ZjXcvaRkhjPX64dydeH99ayASL4Ee7OuWozux1YSu1UyDnOuU1mNhPIds4tAn4PdAJerPvF2umcu7QV65Z2bP/RSh5+8xOeXb6D2KgIfnjRYKZ9qR9x0ZFelyYSNPya5+6cWwIsafC9e+vdPj/AdYl8wbHKGuZ88CmPvrONo5XVTB6bzp3nD9K4ukgjdIWqBL3qGh8vrSrgoTe2su9wBeef1pMfTxjMwJ4JXpcmErQU7hK0nHO8unEvDy7dQl7xUUamJ/LX60YxJqOb16WJBD2FuwQd5xzvbC3iD69tYeOuwwzs0YnZN4zmgiE9dbJUxE8KdwkqH24r5o+vbSV7xwFSu8bz4NUjuHxkitaBEWkmhbsEheV5JTz0+lZWfLqfnp1juf+yYXwjM42YKF1ZKnIyFO7iGeccy/P28/Cbn/BRXgnJCbH8/JIhXDs2XdMaRVpI4S5tzjnH+7nF/OXNXFZu309yQiw/+9ppTBnfV6EuEiAKd2kzPp/jjc37mPV2LusKDtGrcxy/vHQo14xJU6iLBJjCXVpdVY2PRWt389h729i6r5T0bh34zRWnc8WoFGKjFOoirUHhLq2mtKKaF7LyeXJZHrsPlTO4ZwJ/uuYMvj68N1FaglekVSncJeD2HS7nqQ+289yKHRwpr2ZsRjd+dfnpnDs4WfPURdqIwl0CZkPBIZ58P4/F6/fgc46Lh/Vm+pf7MTK9q9elibQ7CndpkaoaH0s37eXpD7eTtf0AnWKjuPHMDKaelUF6UgevyxNptxTuclKKjlSwYOVOnluxk72Hy0nrFs/PvnYa14xJIyEu2uvyRNo9hbv4zTlH1vYDPLN8B//ZuIeqGseXB3bn/suGcd6pPbREgEgQUbhLkw6WVfL31bt4fuVOcgtLSYiL4obxGVw/Pp1Tkjt5XZ6INELhLo3y+Rwf5ZXwQlY+/9m0l8pqH2ekJfLAlcP5+ojedIjRR0ckmOk3VP5L/v4yXl69i5dW55O//xid46KYPCaNyWPSGdKns9fliYifFO7CkfIqXt2wl5fXFLA8bz9mcGb/JO66cDAXDe2lpQFEQpDCvZ2qqK7hva3F/GvtLl7P2UdFtY+MpA784IJBXD4qhdSumsYoEsoU7u1IdY2P5Xn7eWXdbl7duIfD5dV07RDNNWPSuHxkCmekJeoKUpEwoXAPc1U1PpbnlbBkwx6WbtrH/qOVdIyJ5KKhvbjkjD58aUB3orXOi0jYUbiHobLKapZ9UszSTXt5I2cfh8ur6RATyfmn9WTi6b05d3CyxtFFwpzCPUzsO1zO2x8X8sbmfSz7pJiKah+d46I4f0hPJgztxTmDFOgi7YnCPUTV+Bxr8w/y7pZC3tpSyMZdhwFISYzn2rHpXDCkJ2P7ddOQi0g7pXAPIfn7y/ggt5hlucW8/0kxh45VEWEwMr0rP7xoMF89rQeDeybopKiIKNyDWeGRcj7aVsLyvBI+2lbC9pIyAHp2juWCIT05d3AyXxrQncQOMR5XKiLBRuEeJJxz5O8/RvaO/az8tPYrr/goAAmxUYzr340bz8zgywO7M6BHJx2di8gJKdw9cqyyhg27DrE2/wBrdh4ke8cBio5UAJAQF8XYjG5cMyaNM09JYmifLlpxUUSaReHeBo5V1rB572E27T7MhoKDrC84xCeFpdT4HABp3eI5+5QkRmd0Y3R6Vwb3SlCYi0iLKNwDyOdz7Dp4jC17j7Bl3xE+3nuEzXsOk1dUSl2O07VDNKenJnL+aT05Iy2RM9IT6d4p1tvCRSTs+BXuZjYB+DMQCTzhnPttg8djgXnAaKAEuMY5tz2wpQaPQ8eq2FlSxqclR8krKiWv6CjbikrZVlRKeZXv83apXeM5tVcCE0/vzdA+nRnapzMpifEaLxeRVtdkuJtZJDALuAAoALLMbJFzLqdes2nAAefcADObDPwOuKY1Cm5tNT5HydEK9h2qYPehY+w9VM7ug8coOHCM/ANl7NxfxsGyqs/bm0GfLvH0T+7I+P59GdijEwN7dmJQzwRtNycinvHnyH0skOucywMwswXAJKB+uE8CflF3+yXgr2ZmzjkXwFqbparGR1lFDWVV1RytqOFIeRVHyqs5Ul7NwWOVHCyr4sDRSvaXVVJSWknJ0QoKD1dQcrTy87Hwz8RERZCaGE9K13gmnt6bvt060DepIxndO5CR1FFXfopI0PEn3FOA/Hr3C4Bxx2vjnKs2s0NAElAciCLrW5iVz+xleficw7naI+3qGh/VPkdVjY+K6tqvhgHdmLjoCJI6xpLUKYbunWIZ0rszPRLi6NE5ll6d4+jdJZ7eiXF06xBDhE5wikgI8SfcG0u1hsnpTxvMbAYwAyA9Pd2Pl/6ixA7RdVdhQoQZEQZRkRFERRhRkUZcVCSx0RHERUUSHxNJx9goOsREkhAXRee4aBLioknsEE2X+GgdcYtI2PIn3AuAtHr3U4Hdx2lTYGZRQBdgf8Mncs7NBmYDZGZmntSQzYVDe3Hh0F4n809FRNoNf1aVygIGmlk/M4sBJgOLGrRZBNxUd/sq4C0vx9tFRNq7Jo/c68bQbweWUjsVco5zbpOZzQSynXOLgCeBZ8wsl9oj9smtWbSIiJyYX/PcnXNLgCUNvndvvdvlwNWBLU1ERE6WFvsWEQlDCncRkTCkcBcRCUMKdxGRMKRwFxEJQ+bVdHQzKwJ2nOQ/704rLG0QAtpjv9tjn6F99rs99hma3+++zrnkphp5Fu4tYWbZzrlMr+toa+2x3+2xz9A++90e+wyt128Ny4iIhCGFu4hIGArVcJ/tdQEeaY/9bo99hvbZ7/bYZ2ilfofkmLuIiJxYqB65i4jICQR1uJvZBDPbYma5ZnZ3I4/HmtkLdY+vMLOMtq8ysPzo8/fNLMfM1pvZm2bW14s6A62pftdrd5WZOTML+VkV/vTZzL5R935vMrP5bV1ja/DjM55uZm+b2Zq6z/lEL+oMJDObY2aFZrbxOI+bmT1c9zNZb2ajWvyizrmg/KJ2eeFtQH8gBlgHDGnQ5jbg0brbk4EXvK67Dfp8HtCh7va3Q73P/va7rl0C8B6wHMj0uu42eK8HAmuArnX3e3hddxv1ezbw7brbQ4DtXtcdgH6fA4wCNh7n8YnAq9TuajceWNHS1wzmI/fPN+Z2zlUCn23MXd8k4Om62y8BXzWzUN7stMk+O+feds6V1d1dTu3OWKHOn/ca4D7gAaC8LYtrJf70+ZvALOfcAQDnXGEb19ga/Om3AzrX3e7CF3d+CznOufdoZHe6eiYB81yt5UCimfVuyWsGc7g3tjF3yvHaOOeqgc825g5V/vS5vmnU/rUPdU3228xGAmnOucVtWVgr8ue9HgQMMrMPzGy5mU1os+pajz/9/gUwxcwKqN1H4rttU5qnmvu73yS/NuvwSMA25g4hfvfHzKYAmcBXWrWitnHCfptZBPAQMLWtCmoD/rzXUdQOzZxL7f/QlpnZMOeeKOc8AAABhUlEQVTcwVaurTX50+9rgbnOuT+Y2ZnU7vI2zDnna/3yPBPwLAvmI/fmbMzNiTbmDiH+9BkzOx/4KXCpc66ijWprTU31OwEYBrxjZtupHZNcFOInVf39fP/LOVflnPsU2EJt2Icyf/o9DVgI4Jz7CIijdv2VcObX735zBHO4t8eNuZvsc93wxGPUBns4jMFCE/12zh1yznV3zmU45zKoPddwqXMu25tyA8Kfz/c/qT2Bjpl1p3aYJq9Nqww8f/q9E/gqgJmdRm24F7VplW1vEXBj3ayZ8cAh59yeFj2j12eRmzjDPBHYSu3Z9Z/WfW8mtb/YUPumvwjkAiuB/l7X3AZ9fgPYB6yt+1rkdc1t0e8Gbd8hxGfL+PleG/BHIAfYAEz2uuY26vcQ4ANqZ9KsBS70uuYA9Pl5YA9QRe1R+jTgVuDWeu/1rLqfyYZAfL51haqISBgK5mEZERE5SQp3EZEwpHAXEQlDCncRkTCkcBcRCUMKdxGRMKRwFxEJQwp3EZEw9P8AruEXz8raa2AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "func = lambdify(x, x**2)\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "x_data = np.arange(0.0, 1.0, 0.01)\n",
    "y_data = [func(x) for x in x_data]\n",
    "\n",
    "import pylab as plt\n",
    "\n",
    "plt.plot(x_data, y_data)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional resources\n",
    "\n",
    "- "
   ]
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}