{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 4\n", "The new python in this class is just drawing solution curves. Consider the ODE: \n", "$$\n", "\\frac{dx}{dt} \n", "= \\frac{3t^2 + 4t + 2}{2(t-1)}.\n", "$$\n", "We found that it has solution given implicitly by: \n", "$$\n", "x^2 - 2x - t^3 - 2t^2 - 2t = C. \n", "$$\n", "\n", "For a fixed value of $C$, this equation defines a curve in the $(t,x)$ plane. We would like to use python to plot some\n", "sample curves. \n", "\n", "The first step is to make a meshgrid for a range of ```t``` and ```x``` values. I got the ones I did below by \n", "experimenting. Below, ```T``` and ```X``` are both matrices and so ```Z``` is a matrix of the same dimension. The \n", "entries of ```Z``` are just $x^2 - 2x - t^3 - 2t^2 - 2t$ where $t$ and $x$ come from the corresponding entries \n", "in the ```T``` and ```X``` matrices. \n", "\n", "The ```ax.contour(T,X,Z [3])``` function looks at all of the values in the ```Z``` matrix. If these values are equal to \n", "```3```, then it draws a dot at the corresponding point from the ```T``` and ```Z``` matrix. Then it connects those dots \n", "(actually, if draws the dot if the value of ```Z``` is \"close\" to ```3```). The ```[3]``` is an array that contains only \n", "```3``` and it says to draw the level set when the \"$C$\" is $3$.\n", "\n", "(Notice if you change the ```.2``` to ```2``` you will get \n", "a much less smooth curve). " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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XPHoZfS7UKZQiUje54qybbwG3e2UzLSWDl2+fRNdzO3PTX652Oo6IiGNcetaNuyg8WsgzV71Ig8b1efzf9+Hr5+t0JBERx3jlK5OfvjCbnRvT+ducxwlt0czpOCIijvK6PfqsXdlM/cd0BlzRV1MbiIjghUX/1kP/AuC28Tc4nERExD14VdGvXbyBrz9dztWPXEpEq9p9U5aIiLvymqIvLSnl9Xsn07x1GFc9NNLpOCIibsNrin72G/PZuSGd2ybcSP2G9Z2OIyLiNryi6POy8/ngqWkkDu1K/0v7OB1HRMSteEXRz3hlLofzjzDunzdrVkoRkV/x+KIvKizmi7cXcNbFibSKi3E6joiI2/H4ov/2sxXkZeUz6s4LnY4iIuKWPL7oZ74+j+gOkSQO7ep0FBERt+TRRZ+6Zjublm/hkjuG4ePj0f8UEZEzxqPbcdbr82jQuD4X3DjI6SgiIm7LY4v+4IECFk35liHXnkuToMZOxxERcVseW/SLpyyj6FgxI8cNczqKiIhb89iiT1qUTPPYcNp0a+V0FBERt+aRRV9WVsb6pZvoMSje6SgiIm7PI4t+R/IuCg4copuKXkSkSh5Z9OsWbwSgu4peRKRKnln0SzfSom0E4TGhTkcREXF7Hlf0paWlrF+6iW4DtTcvIlIdHlf0OzekcyjvsA7biIhUk8cVfebObABaxUU7nERExDN4XNHnZeUDEBjW1OEkIiKeweOKPrei6INU9CIi1eJxRZ+ffZBGAQ2p16Ce01FERDyCS4reGDPZGJNljNngivWdTF52PkHh2psXEakuV+3Rvw8Md9G6Tio/+6COz4uInAKXFL219mvggCvWVZW8rIMEhQfWxqZERLxCrR2jN8aMNcasMsasys7OPu31lJWW4ePrcS8tiIg4ptYa01o7yVrby1rbKyws7LTXExjWlPzsgy5MJiLi3Txu1zgovOnxc+lFRKRqnlf0YYHaoxcROQWuOr1yCrAc6GiMyTDGjHHFeisTGNaUgtzDlBSXnKlNiIh4FT9XrMRaO9oV66mOn864yc8pICQyuLY2KyLisTzw0E35OfQ6Ti8iUj0eV/Sh0SEA7NmW6XASERHP4HFF3y6hNfUb1mP90o1ORxER8QgeV/T+9fyJ79+RdUtU9CIi1eFxRQ/QfVAXdiTvIj9Hp1mKiFTFQ4u+/GME1y/d5HASERH355FF37F3Wxo0qq/DNyIi1eCRRe/n70f8OZ1U9CIi1eCRRQ/QY3AXdm5MJzPt9GfCFBGpCzy26M8b3R8fH8Pnb853OoqIiFvz2KIPbxlGv1G9mfvuQoqOFTkdR0TEbXls0QOMHDec/JwCln6y3OkoIiJuy6OLPuG8LsR0imLWxHlORxERcVseXfTGGEaOG8aPP2xl88qtTscREXFLHl30AOffMJCGTRowU3v1IiKV8viib9y0EUOvH8iSqd+Rs+eA03FERNyOxxc9wJUPXgLW8s6jHzkdRUTE7XhF0Ue2ieCKBy9h4UffsGHZj07HERFxK15R9ACjH7+c0KhmvH7PZEpLS52OIyLiNrym6Bs2bsDY8TewNWkH895d5HQcERG34TVFDzDo6rPpem5nJj8xhYLcQ07HERFxC15V9MYY7nz5Fg7lHuKDJ6c5HUdExC14VdEDtO3emhG3XcDsN75k69odTscREXGc1xU9wE1/vZqg8ED+NvqfHCk46nQcERFHeWXRN20WwONT7mN36l5evmMS1lqnI4mIOMYrix6g+8B4bnj6ahb9+1u+mLTA6TgiIo7x2qIHGP3YZfQa1p2J973H1iQdrxeRusklRW+MGW6M2WyM2WqMedQV63QFHx8fHv3XPQSGBvDXq1/kcP5hpyOJiNS6Ghe9McYXeB24EIgDRhtj4mq6XlcJDG3KE1PvZ9+OLCbc+qaO14tIneOKPfo+wFZr7XZrbREwFRjlgvW6TJf+nRjzt9/zzX9WMPM1TWcsInWLK4o+Ckj/2fcZFT/7BWPMWGPMKmPMquzsbBds9tRc8eAl9L2kJ2888D5Lpi2r9e2LiDjFFUVvKvnZb46PWGsnWWt7WWt7hYWFuWCzp8bHx4fHP76Xzn3b8+zof/Len6Zo8jMRqRNcUfQZQMzPvo8G9rhgvS7XsElDnl/wFBeOGcK///Zfnhz1HIfy9AKtiHg3VxT9SqC9MSbWGFMPuAaY5YL1nhH16vtz/6TbuGfirayev567znqMtE3pVf+iiIiHqnHRW2tLgLuAL4EU4BNr7caarvdMMsZwye0X8MKipzhy8Ah3932cZTN+cDqWiMgZ4ZLz6K21c6y1Hay1ba21z7pinbWhyzmdmbjqOVrFRfPny8fz/pNTKSsrczqWiIhLefU7Y6sjNCqECUueZvjNg/n4mc946tLn9cYqEfEqdb7oAeo1qMcD79zB3a/9gZXz1nJbj4dYu3iD07FERFxCRV/BGMPIccN48eu/4FfPj4eGPM3r907m2JFCp6OJiNSIiv5X4vp24M2k8Vx694XMeHUutyc8xKblm52OJSJy2lT0lWjQqD53vnwL4xc+RUlRCfcP+D/eefQjigqLnY4mInLKVPQn0WNwFyatn8DwW85j2vMzubPXI6Su2e50LBGRU6Kir0KjgIbcP+l2/jbncQpyD3F338d5/d7JZGfsdzqaiEi1qOirqffwBN5OfpFhNw1i9hvzuaHtnbw09k32bs90OpqIyEkZJ+Zn79Wrl121alWtb9dV9u3M4pPnZzLvvcWUlpTS/7I+jBo3nG4D4zCmsjneRERqzhiz2lrb65R/T0V/+vbvzeW/L33O3MmLKDhwiNbxMVxyxzCGXn8ujQIaOh1PRLyMit5BhUcLWTz1O2ZNnEfq6u00CmjI+TcM5JJxw2jVOdrpeCLiJVT0bsBay48/bGXWxHksnfYdxUUl9DivCyPHDefskb3w9fN1OqKIeDAVvZvJy85n3ruLmP3mfLJ25RAWHcKIsedz0a1DCI4IcjqeiHggFb2bKi0t5fsv1jBr4pesnr8OP39fepzXhd7DE+hzYQJR7SP1Aq6IVIuK3gNkbNnDnLcXsOLz1aRvLv8Qrsg2EfQe3oPewxPoPjieho0bOJxSRNyVit7D7N2Rycq5a1k5L4m1izZw7Egh/vX96XpuZxLO60r3QfF06NlGx/VF5DgVvQcrOlZE8jcprJybxKr560jblAFAwyYN6DKgM90HxtN9UBztE1X8InWZit6L5Gbmsf7rFNYt3sC6pRvZlbIbKJ+OocuATrTrEUur+BhaxUUT07EF9RrUczixiNQGFb0Xy83MY/3STaxdvIHkb1JI37yHstLyjzz08TFEtm1O6/hoWnaOpnV8DC3jomnZKUoPACJeRkVfhxQVFrM7dS9pG9NJ25RB2qbyr7tT91FaUgqUPwA0bxNRXvwVDwCt4qKJ6dSC+g3rO/wvEJHTcbpF73cmwsiZVa++P7FdWhLbpeUvfl5cVMzu1H3l5b8xnbSU8q/ff7Hm+AOAMYbgiEDCYkIIjQ4hLDqE8JjQ8usxIYTHhBDSopleCxDxItqjrwNKikvKnwFsymBXym4y07LJ2b2f7PTyy5GCo79Y3sfHENw8iLCYUMJiQgiLKn8QCIsJJSy6Gc0igwmOCNQzA5Fapj16OSE/fz9axcXQKi6m0tsP5x8mO+MA2ek5ZKfvJys9h5yMA2Rn5LAzeRcr5yRV+tm5jQIaEtw8iOCIwPKv4YEERwQRFB5IYFhTgsKaHv/aJLgxPj6aFVvECSp6oXFgYxoHNqZ1fOUPBNZaDuUdLn8GkLGf3H155Gbmk5uZV3HJJ21jOmsXJlOQe7jSdfj4GJqGBBAY1pTgiECCIoJoFhF0/HpwRCDNKh40gsID8fPXXVPEVfTXJFUyxhAQ3ISA4Ca06dbqpMsWFxWTn32QvOyDHMwpIC/7IPkVl7zsg+TnHCQ3M48tq7aRl5n/m8NGPwlo1uR4+QdF/O/ZQrPIIJq3Dqd5bDih0c3w9dVrCSJVUdGLS/nX8yc0KoTQqJBqLX/sSOHxZwW/fKbwv2cMW1ZtI3dfHkcPHfvF7/r6+RLeMpTmseHHy/+nS2RsOEHhgZpHSAQVvTisQaP6RMZGEBkbUeWyx44Usn/PATJ3ZrNvRxZ7d2Sxb2cW+3ZksXz2KvKy8n+z7uPlX/FA0KJdc9r2aE1YdIgeBKTOqFHRG2OuBP4MdAb6WGt1Ko2cMQ0a1SeqXSRR7SIrvf3o4WP/exDYnsm+nz0QrF+66ReHiQJDA2iX2Ib2CbG079mG9oltaB4brvIXr1TTPfoNwOXAWy7IIlIjDRs3oHV8TKUvKltrKThwiIwte9iatJPUNdtJXbOdTyfMPv4egyZBjWmX0Jr2iW3KHwQSY4lqH6mzhcTj1ajorbUpgPaCxO0ZU37WT1y/jsT163j850WFxezcsIvU1dtJXbODrUnbmfHaPIoLi4HyieXa9igv//aJbejQqw0tO0frPi8eRcfopU6rV9+fDj3b0qFn2+M/KykuIW1TRnnxr9lOatIO5r6zkOlH5gAQHBFIwpCuJAzpRuKQLoS3DHMqvki1VPnOWGPMAqB5JTc9Ya2dWbHMEuCPJztGb4wZC4wFaNmyZc+0tLTTzSxS60pLS8nYvIeUFakkLUomaWEyuZnlL/5GtY8kcUhXEoZ0pfvgeJo2C3A4rXgrRyc1q07R/5ymQBBPZ61l58Z0khYkk7QomXVLNnL00DGMMbTv2YaE87qQOLQb8f07aqoIcRkVvYiDSopL+PGHrSQtLN/bT1mxhZLiUvzr+xPfvyOJQ7qROLQr7RJj9SYvOW2OFL0x5jLgVSAMyAPWWmuHVfV7KnrxdkcPHSX5mx9Zs2A9SYuS2b6u/FBlYGgAg0efw7CbBtMuIdbhlOJpNB+9iBvLzcpn7aINLJvxPd/NWElxUQlturdi2I2DOe/acwgKC3Q6ongAFb2Ihzh4oIAlU79j/geL2bxyG75+vvS9OJELbhxMn4sSNKGbnJCKXsQD7diwi/nvL2HBR1+Tl5VPYGgA517Rj0HX9KfLOZ30Zi35BRW9iAcrKS5h1Zfr+OpfS/n+89UUHi0iNKoZA686m8HX9KdDr7Z6k5ao6EW8xdFDR1k+ezVLpi1j5dwkSopLiWwTwaCrz2bItQNO+AEy4v1U9CJeqCD3EMtmrGTJtGUkLUymrLSMs0Ykcs0jl9LlnM5Ox5NapqIX8XK5WfnMmbSA6a98QX5OAfH9OzL60cvoc1GiDuvUESp6kTri2JFC5r27iE8nzCJrVw6xXVtyzSOXMvCqs/H105uxvJmKXqSOKSkuYfGUZUx7fgZpmzJoHhvOVX8cyQU3DdK0C15KRS9SR5WVlbFi9mqm/GM6P36fSlB4IJfedSEjbhuqN2J5GRW9SB1nrWX915uY9twMVs5bi399f84bfQ6X3nMh7XpougVvoKIXkePSUjKY+epcvvpwKceOFNL13M5cds8Izh7VS5OqeTAVvYj8RkHuIea9u4iZr88jMy2bFm0juPX56+l/aR+dqeOBVPQickKlpaV8N3MVHzw5lbRNGfQYHM/tL95E2+6tnY4mp+B0i14TaYjUAb6+vgy4/CzeWvsCd706hm3r0rgj8WFeGvsmuVn5TseTM0xFL1KH+Pr5MurO4XyQ+iqX3XMRX76/hJva380n42dSVPGB6OJ9VPQidVBAcBPueOkm3k6eQLeBcbz9yEf8If5+vvlsBU4czpUzS0UvUofFdIzir7Me5e/z/kT9hvX4y5UTuKff46xZmOx0NHEhFb2I0OuC7ryZNJ4H3x3HgX15PHL+X3j4/L+weeVWp6OJC6joRQQoP34//ObBvLf5Fe546Sa2r9vJXWc9xtNXvEBaSobT8aQGdHqliFTqSMFRPnvpc/4zYTbHDh9j6A0DufHPVxHeMszpaHWWTq8UEZdqFNCQ65+8kg+3vcZl945g8ZRljIm/n9lvztcLth5GRS8iJxUY2pTbJ9zI+5tfJr5/J14Z9zaPDn+GrPQcp6NJNanoRaRawluG8fe5T3DvG2PZ9N1mbu36APPeW6y9ew+goheRajPGcPFt5zNp3QTaJcQyYcxEHh3+DHu27XM6mpyEil5ETllkmwjGL3yKu14dw48rUrm16wNM/cd0SopLnI4mlVDRi8hp8fHxYdSdw3l300v0uSiRdx//N+N6PcKmFVucjia/oqIXkRoJjQrhqf/8kaenP0zBgUPc1/9PvHrXOxw+eMTpaFJBRS8iLnH2qN68u+mfjLprOLPfmM+YuPv4dvr3TscSalj0xpjxxpgfjTHrjTHTjTFBLsolIh6oUUBD7nz5Fl5Z/iyBYU15+ncv8NRlz5Odsd/paHVaTffovwK6WGu7AVuAx2oeSUQ8Xac+7Xn9h3/wh39cx+r56xgTdx/TX5lDaWmp09HqpBoVvbV2vrX2p5fZVwDRNY8kIt7Az9+Pqx8exdvJLxLfvyMT73uPrUk7nY5VJ7lsrhtjzGxgmrX2oxPcPhYYW/FtR2BzDTYXCrjz2/KU7/S5czZQvppSvprpaK0NONVfqrLojTELgOaV3PSEtXZmxTJPAL2Ay20tvE3OGLPqdCb2qS3Kd/rcORsoX00pX82cbj6/qhaw1g6tYsM3AhcDQ2qj5EVE5NRUWfQnY4wZDjwCDLTW6qRZERE3VNOzbl4DAoCvjDFrjTFvuiBTdUyqpe2cLuU7fe6cDZSvppSvZk4rnyMfPCIiIrVH74wVEfFyKnoRES/nEUVf3akWjDHDjTGbjTFbjTGP1mK+K40xG40xZcaYE576ZIzZaYxJrng9o9Y+NPcU8tX6+BljmhljvjLGpFZ8DT7BcrU6dlWNhSn3SsXt640xiWc60ynmG2SMya8Yr7XGmCdrMdtkY0yWMWbDCW53euyqyufk2MUYYxYbY1Iq/mbvrWSZUx8/a63bX4ALAL+K688Bz1WyjC+wDWgD1APWAXG1lK8z5W8CWwL0OslyO4FQB8avynxOjR/wPPBoxfVHK/u/re2xq85YABcBcwED9AW+r8X/z+rkGwR8Xtv3tYptnwskAhtOcLtjY1fNfE6OXSSQWHE9gPKpZWp83/OIPXpbvakW+gBbrbXbrbVFwFRgVC3lS7HW1uSdvmdUNfM5NX6jgA8qrn8AXFoL26xKdcZiFPChLbcCCDLGRLpRPsdYa78GDpxkESfHrjr5HGOt3WutXVNxvQBIAaJ+tdgpj59HFP2v3EL5o9mvRQHpP/s+g98OkNMsMN8Ys7piSgh34tT4RVhr90L5nRwIP8FytTl21RkLJ+9v1d12P2PMOmPMXGNMfO1EqxZP+Ft1fOyMMa2BBODXcz2f8vjV6A1TrnQKUy2UAB9XtopKfuayc0erk68a+ltr9xhjwil/78GPFXsX7pDvjI3fybKdwmrO2NhVojpjcUbvb1WozrbXAK2stYeMMRcBM4D2ZzpYNTk5dtXh+NgZY5oAnwH3WWsP/vrmSn7lpOPnNkVvaz7VQgYQ87Pvo4E9tZWvmuvYU/E1yxgznfKn4C4pKxfkO2Pjd7JsxphMY0yktXZvxdPPrBOs44yNXSWqMxZn9P5WhSq3/fNysNbOMcZMNMaEWmvdYcIuJ8euSk6PnTHGn/KS/9ha+99KFjnl8fOIQzfmf1MtjLQnnmphJdDeGBNrjKkHXAPMqq2MVTHGNDbGBPx0nfIXmCt91d8hTo3fLODGius3Ar959uHA2FVnLGYBN1ScAdEXyP/pEFQtqDKfMaa5McZUXO9D+d+6u3z6h5NjVyUnx65iu+8CKdbaF0+w2KmPnxOvLJ/GK9FbKT8mtbbi8mbFz1sAc371avQWys9IeKIW811G+aNsIZAJfPnrfJSfIbGu4rLR3fI5NX5ACLAQSK342swdxq6ysQBuB26vuG6A1ytuT+YkZ1s5lO+uirFaR/kJDGfXYrYpwF6guOJ+N8bNxq6qfE6O3TmUH4ZZ/7O+u6im46cpEEREvJxHHLoREZHTp6IXEfFyKnoRES+nohcR8XIqehERL6eiFxHxcip6EREv9/94Xz/NWhQHugAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "t = np.arange(-2.2,2.2,.2)\n", "x = np.arange(-2,4.2,.2)\n", "T, X = np.meshgrid(t,x)\n", "Z = X**2 - 2*X - T**3 - 2*T**2 - 2*T \n", "\n", "fig, ax = plt.subplots()\n", "CS = ax.contour(T, X, Z, [3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code below adds labels to the contour. That is, the label tells you what $C$ is. It also adds labels. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'x axis')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "CS = ax.contour(T, X, Z, [3])\n", "ax.clabel(CS, inline=1, fontsize=10)\n", "ax.set_title('Integral Curves')\n", "plt.xlabel('t axis')\n", "plt.ylabel('x axis')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code below draws several level curves, one each for the levels $-1,0,1,2,3$. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'x axis')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "CS = ax.contour(T, X, Z, [-1,0,1,2,3])\n", "ax.clabel(CS, inline=1, fontsize=10)\n", "ax.set_title('Integral Curves')\n", "plt.xlabel('t axis')\n", "plt.ylabel('x axis')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you don't tell it which levels to use, it picks them for you: " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'x axis')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "CS = ax.contour(T, X, Z)\n", "ax.clabel(CS, inline=1, fontsize=10)\n", "ax.set_title('Integral Curves')\n", "plt.xlabel('t axis')\n", "plt.ylabel('x axis')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And if instead of an array ```[]``` you just put a number (e.g. ```7``` as below) it will draw that many curves (it \n", "picks the levels by itself). " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'x axis')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "CS = ax.contour(T, X, Z, 7)\n", "ax.clabel(CS, inline=1, fontsize=10)\n", "ax.set_title('Integral Curves')\n", "plt.xlabel('t axis')\n", "plt.ylabel('x axis')" ] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }