{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In Lecture 26 of MCS 320, we consider two dimensional plots." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1. The Graph of a Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``plot`` function takes functions ``y = f(x)``." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "e^(-x^2)*sin(pi*x^3)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = exp(-x^2)*sin(pi*x^3)\n", "f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By assigning the output of ``plot`` to a variable, we separate the computation of the plot from the display." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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32EsEMFEio2GiRE65ckVm4Nx7b9nbjB0LbNnCcQZEnlqyBBg+XJYu8ReNGkmZgMOH9Y6EqCQmSuSUlSuBnBzgj38se5vhw4Fq1eTXMBG5Z/9+YM8e/5ntZmexSPcbW5TIaJgokVMWLgQ6d5aZKWWpUUNKBCxf7r24yPckJCQgMjIS0dHReoeiiyVLpGUlNlbvSLwvNJQtSmQ8TJSoQooCrF4NDB1a8bZDhgAbNkgJASJ3xMfHIz09HSkpKXqHoovFi4EBA+SHh78JC2OLEhkPEyWqUHo6cOYM0LdvxdsOHChrU/38s+ZhEfmc06eB5GT/mu1WnL1FSVH0joToBiZKVKGffgKqVAFuu63ibcPDgSZNgI0btY+LyNcsXixjdYYN0zsSfYSFAdnZwMWLekdCdAMTJarQTz8BPXo41xVgsQC3384WJSJ3zJ8v6yc2bKh3JPqw11LiOCUyEiZKVC5FAdavd67bza53b2DbNqnkTUTOOXtWfpTcd5/ekeiHtZTIiJgoUbkOHQLOn3et8N3tt0uV7u3btYuLyNcsXCj399yjbxx6qlcPqFWLLUpkLEyUqFzbtsm9KzO1O3UCatfmOCUiV/h7txvAWkpkTEyUqFwpKdIc3qCB8/tUrgzExHCcEpGz2O12Q1gYW5TIWJgoUbm2bQO6d3d9v9tuk2nOnOZLVLFFi+T+D3/QNw4jYIsSGQ0TJSpTQQHwyy+udbvZRUXJFN/ff1c/LiJfM3++TJho1EjvSPRnLzrJH1lkFEyUqEy7dwNXr7rXotS1q9ynpqobE+ln+vTpCAsLQ7Vq1RAVFYWN5QxCW7hwIQYMGICGDRsiKCgIMTExWLVqlRejNY9z59jtVlxoqKwrefas3pEQCSZKVKZt24BKlYBu3VzfNzgYaNxYWqTI/ObNm4dJkybhpZdeQmpqKnr37o3Bgwfj6NGjDrffsGEDBgwYgOXLl2PHjh3o168fhg8fjlRmzqUsWiStJ/482604e4kAjlMio7AonrdvsoHUR02cKGu87dnj3v6DBwMBAcCyZerGRd7Xo0cPdOvWDTNmzLj+WLt27TBy5EhMnTrVqWO0b98eo0ePxt///nents/KyoLVaoXNZkNQUJBbcZtBbCxQWAisWaN3JMZw6RJQty4wdy4werTe0ZCPszizEVuUqEy7dgEdO7q/f7du7HrzBXl5edixYwdib1rOPjY2Fps3b3bqGEVFRcjOzka9evW0CNG0zp0D1q5lt1txderIjS1KZBRMlMghRfE8UeraFTh5Uhb6JPM6d+4cCgsL0bhx4xKPN27cGJmZmU4d45133sGVK1cwatSoMrfJzc1FVlZWiZuvY7ebY5z5RkbCRIkcyswELlwAOnRw/xj2sU1sVfINFkvJVmpFUUo95si3336L1157DfPmzUOjcqZ1TZ06FVar9fqtefPmHsdsdHPnAnfcwdluN2MtJTISJkrk0K5dcu9Ji1JYGGC1ckC32TVo0AABAQGlWo/OnDlTqpXpZvPmzcOjjz6K7777DnfddVe5277wwguw2WzXb8eOHfM4diM7flxmuz34oN6RGA9blMhImCiRQ7t2ATVqAC1bun8Mi0WWM9m5U724yPuqVq2KqKgoJCUllXg8KSkJvcpZBPDbb7/Fww8/jG+++QZDhw6t8DyBgYEICgoqcfNlc+YAgYHAvffqHYnxhIZKDbaiIr0jIQIq6x0AGdOuXUD79lIewBPt2wObNqkTE+ln8uTJiIuLw6233oqYmBh88sknOHr0KJ544gkA0hp04sQJfPXVVwAkSXrooYfwwQcfoGfPntdbo6pXrw6r1arb6zAKRQFmzwZGjgR8PB90S0gIkJsLnDkDNGmidzTk79iiRA799ptn3W527dsD+/ZJlW8yr9GjR+P999/H66+/ji5dumDDhg1Yvnw5QkJCAACnTp0qUVNp5syZKCgoQHx8PIKDg6/f/vrXv+r1EgwlLU0KusbF6R2JMbVoIfdllOki8irWUaJSCguBWrWAqVOBSZM8O9batcCddwJ79wIREaqER37Cl+soPf008M03wIkTsog0lXThAlC/PvDddyydQJpiHSVyT0YGcO2aZzPe7Nq3l/vduz0/FpEvKCgAvv0WGDOGSVJZ6taVH2tsUSIjYKJEpfz2m9yr0fXWqBFQrx4TJSK7pCSpLcZut7JZLNL9xkW1yQiYKFEpu3dLs3cFM7+dYrFIq1J6uufHIvIFs2cDkZE3Fo4mx0JCmCiRMTBRolL27QPatVPveJGRbFEiAoCsLKnG/dBD8iOCyhYSwq43MgYmSlSK2gOvOfONSCxYINPex47VOxLjY9cbGQUTJSpBUSSpadtWvWNGRgJ5eTJInMifzZ4N9OsH3HKL3pEYX0gIcPEikJ2tdyTqOXcO+PFHwGbTOxJyBRMlKuHkSeDyZXVblOzdeHv3qndMIrM5cgRYt46DuJ3la7WUtm0DWrUCBg6Ue66BaR5MlKgEezKjZotScLBM9d2/X71jEpnNp58CtWuzLpCz/lfL1Ce63y5eBP74R/nRmJYmr+2ee4CrV/WOjJzBRIlK2LcPqFJFFrRVi8UCtGnDRIn8V34+8Nln0ppUs6be0ZhD06ZAQIBvtCh99JF0u82fD3TuLMVGjx8HPvhA78jIGUyUqIS9e6VZWO1CeEyUyJ8tWSK1kx5/XO9IzCMgQMZymb1F6coV4MMPgcceuzE2rU0b+fcHH8j4TTI2JkpUwr592iw1wkSJnJWQkIDIyEhER0frHYpqZs4EYmLUKeLqT3yhltJ338mSLM8+W/LxiROBzEwpF0HGxkSJSti/X5IatbVpI18KWVnqH5t8S3x8PNLT05GSkqJ3KKo4eBBYvZqtSe7whVpKc+cCffveGHNlFxkJ9Owp3XBkbEyU6Lq8PPlSCg9X/9j25OvAAfWPTWRkn34K1KkDjBqldyTmY/ZaSmfPAmvWAKNHO35+9Ghg5Urg0iWvhkUuYqJE1/3+O1BUpG2ixO438id5ecCsWVKJu3p1vaMxn5AQKVmSn693JO5JSgIKC4G773b8/D33yDWyZo134yLXMFGi6+wFIbVIlKxWWTuOiRL5k0WLpFWB3W7uCQmRH28nTugdiXtWr5ZxaU2aOH6+RQsZE5qU5N24yDVMlOi6jAwpDdC8uTbH54Bu8jcffQT07i3jUch19qKTZux+UxRJlO66q/zt7rqLiZLRMVGi6zIygNBQmZarhTZtZFYdkT/YuhXYtAl4+mm9IzEvMydKBw8Cx44Bd95Z/nYDBgCHDsmNjImJEl2XkaFNt5tdq1by5aEo2p2DyCjefVc+TyNG6B2JedWoATRoYM6Zb6tXSz26Pn3K365vX/lxylYl42KiRNdpnSiFh8tikBcuaHcOIiM4cgT4/ntpTdKqhdZfmLWW0s8/A1FRsmxNeaxWoHt3YO1a78RFrmOiRACklefQIe0TJeDGoHEiX/XBB/IH8OGH9Y7E/MxaS2nbNqBHD+e27dVLumrJmJgoEQDg1ClZoJGJEpFnLl0C/vtf4Mknua6bGsxYS+nCBRlm0L27c9t37y6v8fRpbeMi9zBRIgDalgaws1qB+vWZKJFv+/RTqY0zYYLekfgGe4uSmcY22ovKO5so2Vue2KpkTEyUCMCN5KVlS23PEx7ORIl8V36+LIA6ZgwQHKx3NL4hJERau8+d0zsS523bJtXYW7VybvsWLaTOHBMlY2KiRAAkeWnaVPvqweHhnAZLvuvbb4Hjx4HJk/WOxHeYsUTAtm3SmmSxOLe9xSKtStu2aRsXuYeJkpfl5BizCVnrGW92bFEiX1VYCLzxBjB8uFRjJnXYF5M1U6K0fTsQHe3aPvZEqahIm5jIfUyUvOTCBSA2VgZ33nqr8VpVvJkonTghTelEvmTePKk8//e/6x2Jb6lfX+opmWXm29mzQGYm0Lmza/t17w5kZbEorxExUfICRQHuvx/45ReZNnzpEjBypLGSBW8mSgBw+LD25yJzSkhIQGRkJKJd/Umuo8JC4F//AoYMkR9CpB6LxVwz3377Te5dbVW0X+7sfjMeJkpesHChVF398kvgqaeAJUuA9HRg+nS9IxM2G3D+vPMDDz3BEgFUkfj4eKSnpyPFPnXIBObOBfbsYWuSVsxUdHLXLiAw0PXvU6tVvh9//VWbuMh9TJQ0pijy5Tl4MDB0qDzWoQPwpz8Bb74J5ObqGx/gndIAdsHBMmCciRL5irw8+YyPGOF8gUFyTYsW5ul627ULaNdOli9xVefOTJSMiImSxjZtktajZ54p+fjTT0tf9pIl+sRVnDcTJYtFShAwUSJf8dln0pX8xht6R+K7zNai5O5g/k6dJFEy4oQff8ZESWMzZ0oTbL9+JR9v1w647Tbg88/1iau4jAyp+VGvnnfOx5lv5CsuXwb++U9g7FhpKSZthITI8IArV/SOpHxFRTJGyd1EqXNneZ2nTqkbF3mGiZKGrl6V8UmPPAJUcvBOP/AAsGaNDO7W08GD3mlNsgsLk0VDiczuX/8CLl6UZIm0Y6+lZPTutyNHJJnzpEUJAHbuVC0kUgETJQ2tXi11k+65x/HzI0cCBQVAYqJXwyrFWzPe7EJD5QuFzctkZvv3A+++C0yZItc0accstZR27ZJ7dxOl0FCgdm2OUzIaJkoaWrwYiIgA2rZ1/HyzZkBUFLBihVfDKsXbiVJYmLS2nTnjvXMSqe3pp+Uz/Pzzekfi+5o1k1Z5oydKv/0mwxiaNnVv/0qVJMlii5KxMFHSSFGRtBTdfXf52w0YIC1PelVjzc2VJRe83aIEsPuNzGvZMmD5cmlR0nrZH5IZZM2aGb/rzT6Q29mlSxzhzDfjYaKkkV9/lVltgweXv92AAbKdXr8gDh+WLjA9EiUWnSQzunYNmDRJPrsjR+odjf8ww8y33bs9H9TfqROwd68xSseQYKKkkTVr5JdmTEz52912G1C1KrB+vXfiupk3SwPYWa1A3bpsUSJzeucd+YP94YeetRyQa4yeKBUWAgcOlD3UwlmdO8ux9uxRJy5nZWcDTzwhP2QffBA4d8675zcyJkoaWbMG6N1bKrSWJzBQxilt2eKduG6WkSExNGvm3fPaB3QTmcnu3cDrrwOTJ3v+B5FcExJi7K63o0elFSgiwrPj2FukvNn9VlQkJS7mzJHCqStXAoMGSTFVYqKkibw8YMMG4M47nds+JgZITtY2prJkZMjgakflC7QUGsquNzKX/HzgoYekLto//qF3NP6nRQtZULugQO9IHLMvZtumjWfHqV3b+0uZfP+9jKn99ltpKV21CkhNBT76yHsxGBkTJQ3s2CFlAW4uMlmWmBhpUtajyJi3Z7zZsZYSmc3UqfLH68svgWrV9I7G/4SESJfUiRN6R+LY/v3SOm+v+eSJDh2k9dIbioqklXTgQGDYMHksKgp48kn5QXD+vHfiMDImShrYskXGJ3Xp4tz29nFMerQq6ZUohYZKcqjXbD8iV2zdKkUlX3gBuPVWvaPxT/ZaSkbtftu3D2jdGggI8PxYHTpIqQFvWLpUkrJXXy35+KuvSu/IZ595Jw4jY6KkgeRk+TKtUsW57Zs1A5o3936iVFQk3V96JUq5uUBmpvfPTeSK8+eB++6Tz/Qrr+gdjf+yt9QYdUD3vn2ed7vZtW8PnDwpVd+19uWXcm3fPPGoYUPg/vuB6dOlJc+f+VWi5K1K0Fu2AD17uraPHuOUTpyQZEWvRAlg9xuVlpCQgMjISERHR+sdCoqKZAZQTg7w3XcyQ5X0UbMmUL++cROl/fs9H8htZx/QrXX328WLUg9s7FjHz8fHy/v944/axmF0Pp8oKYpM57VagaAgWeFby4TpxAng2LGKywLcLCYG2L5dBox6ix6lAeyYKFFZ4uPjkZ6ejpSUFL1Dwb/+JQNbv/lGWn1JX0ad+Xblinzvq5UoRURIkU2tu98WLJDB8aNHO37+1ltlAfc5c7SNw+h8PlF6+23g2WeBuDhg/Hjg5ZclWdKKvVXI1RalqChp3dm7V/2YypKRIXVgwsK8d0672rXl1yFnvpFRzZ0r4zT+8Q8gNlbvaAiQ7jcjtigdOCD3aiVKVatKN57WidKiRUCfPkBwsOPnLRbpfktM9O8CmD6dKO3cKYMvp0wBpk2T5QZeflm++OyLF6ptyxb51VPWhVeWzp3lPi1N9ZDKlJEB3HJLxbWetMJaSmRUGzcCDz8sP7BeflnvaMjOqEUn1SoNUFz79tp2veXmAuvWSb2k8vzhD0BWFrB2rXaxGJ1PJ0pTpsgshOI1T155Rf5A3zzCXy3Jya53uwHSLRgeLrUrvEWvGW92LBFARrR9OzB0KNCrF/Dpp6y+bST2RMlb402dtX8/0KABUK+eesfs0EF+0Gv1WjdtkrF3AwdWHEerVsDChdrEYQY+myj98guwYgXw97+XHIBZtSrw0kvS5Jieru458/KkhpKr3W52Xbp4v0VJz0SJRSfJaNLS5A9H+/bAkiX6tbaSYy1aAFevGq+2z7596nW72XXoIK/zzBl1j2u3ahXQuLGsLVcei0ValZYu1aacy4oVwJ//LOMBvTHLzx0+myhNnSpJwH33lX5uzBigUSPg44/VPWdamjRnutOiBNxIlLz1a8kIidLRo5x6SsawcSPQt6+0dK5YIePoyFjstZSM1v124ID0XqjJPvNNq3FKq1bJws7OrMowbJgkbDt2qBvDq68CQ4YAP/8M/Oc/QLduxuxl8MlE6eRJaSZ89lmZOXCzqlWBP/0JmD1b3bVstmyRX6DOFpq8WZcuklEfO6ZeTGW5cAG4dEmaVPUSFiaz/E6e1C8GIgCYP18GbHfrJmMx6tTROyJyxKiJ0qFD6v/oDA+XvydajFM6c0aqzDs7SaFXL/lM/PCDejF8/71UBP/3v+U17t4trVf33mu8NeZ0TZTWrQMeeUQGTa5bp95xv/5akqEHHih7mzFjJFFISlLvvMnJMnvN3VorXbvKvTfGKelZGsDOXiKA3W+kl/x84OmngVGjgJEjpaZMUJDeUVFZGjSQVQ+MVCIgKws4d07979KAAJmar0WLkn12dp8+zm1fubJ0SS9bps75c3KAiROlS2/KFEmQQkLkB8vOndINZyS6JUr//KeshbZtmwye7NcPeO89z4+rKMAXXwD33CO1k8rSoYOs/v3dd56f027LFve73QCgaVP5IvDGOCUjJEpG/XVI/uH4cfnemTZNFgL95huu4WZ0FovxSgTYv0tbtlT/2FotZZKcLDOzXVmXbuhQ6XpTY03SadMkuXznnZKTJaKigOefB/7v/7zTs+IsXRKlGTNkkPXrr8tFsHOnvDmTJ8sga0+kpAB79kgrVXksFvkVuXixOvUhMjOlb9Xdgdz2mLw1oDsjQ+oYlZdMaq1mTUkMjfSlR74vP19KhbRrJ5/ZDRvk1y1nt5mD0UoEaPmj014iQO1xq/bZ2a5c84MGyfYrVnh27itXgDffBB57zHENv7/9TVp1jbRckNcTpZ07gUmTpDT6K6/IG1+pkgy+HjkSePxxGT/jri++kNpA/ftXvO2oUdJsqkZ5dntTpictSoD3FkPUeyC3ndG+9Mh3KQqwerX8an3uOWDcOPmsefqZJe8yWnXuQ4fkD3v9+uofu0MH+Rt1/Lh6x8zPlwYFV6/7hg2BHj08H6e0YIH8jX/uOcfP164NvPiiDKE5dMizc6nFq4lSUZFMA2zVSprcSgRSSRbfy82V6fvuuHYN+PZb4KGHnFvBuX17mamgRr/rli2SoDVr5tlxOnSQJObqVc9jKg8TJfIXeXky9qFXL5nlU7Om/KGYNo2Dts3IiF1v4eHatEhqMfNt5075++LOD4ShQ2VcryeDrWfNki7v8roqx4+XmlRvveX+edTk1UTp00+BrVtlWr6j+iTBwdLK9N//ujfAd+lSGaD90EPO7zNkiAzg9LRp091Ckzdr315i0XopEyZK5MtycmTZhSeekDXaRo0CqlSRboPNm2V2G5lTSIiMb7lyRe9IREaGNuOTAEkKa9VSN1FKTpbPQlSU6/sOHQpkZ0spDXccOnRjEld5atSQSRazZsn6qXrzWqJ0+rSMbv/Tn4Devcve7sknJZN0Zz22WbNkjJArhb8GD5ZmTU+mYObny4B0T8Yn2UVGyr2W3W9Xr8rFZ4REKTRUEiUtCpmR71MUKamRkiKf/8mTgbvukm6QESOkq23sWPk8bdhwY5wFmZd9EohRut+0KA1gV6mS/E1QO1Hq2tW9iQtdusikI3e73774QrrW/vjHirf9y19khuPNvU96cFBlyHkWi8Vis9mc2vapp+QL6uWXpc+1PH/9qwz2njjR+QVbT5yQAlrvv1/x8YuzXzCLFrk2A6C41FRJPjp1cu3cZbnlFqksfvfdnh/LkT175L5JE3Xi9UTDhtLdmpEhVWLJt126JH9YTp6U25kz0vqTmwvk5BTi6tVCXLtmQX4+kJeXDQAYNiwLFosk04WFcrPZpGrxxYslC5aGhckg7VdekenMrVrdSIz0vtZJHXXryv2ePZ4PdfBUfr780GvaVLvrq00b6S5T6/ibNkkDgbvHu+su6b157TXX9issBD7/XGakFxRUfH6LRcYsf/SR5ALOjAFbulR6iD780LkyPVarNQhAtqKU36dkqeD5clksliAAzmVKRERERMZiVRSl3LTN00TJYrPZnOo0ycrKQvPmzXHs2DEEOVHRLSFBWp9CQkYiLW1xudsqiow5iI4GPvlEHouOjkZKSoozoeGTT6RbMDS0L375ZZ1T+xR3yy0r0abNIKdXV67ovXj5ZVlnateu0vu68rrK2ichQUozZGaW3w2hxrkqcvRoFjp2DML06TkYO7aGpudydx9vnsvVz4kn53J3v4r2OXgQmDsXmDdPukeqVpXZMr/9NhtvvhmHNm2kJaBBg5LLJ+Tm5iK3WK2OU6dOoXv37khPT0czF5oOjPReqLWfu9eFO+dydx9vnqtduyKcPPkOjh17XNfPyerV0o306683Cuh6ci5H+6xdK4UZf/nFcRefK9fGsmU3uqLvuce99yIq6g78/vt6/POfMlTGGdHR0ejUKQW//ird5M52f0dHRyM2NgVffSUxl1fO5rXXgOnTFeTmdsKxY5ucui6sVqsVTrQoedT1VtHBHQkKCnLqBfz1r8AHHwAXLkyocPuff5bm/P/+90ZV3YCAAKc/QPfcI1MVr127zeUvIQC4evV29O0b5HJF37Lei6goaW6sVEkG8hXnyusqax/7+KSKaiipca6KNG8u9+fO1UFQkGud5t6IT49zAc5/Tjw9l1qvS1FkgOd//iMDpq1WYPRo+Wz16SNjDSIjEzB+fLzLMdauXdtU74WW+7l6Xbh7LqO/hy1aFODkyTa6f05On5aq1ZGRpZfLUuu96N5d7n///cbqDY44817s3CndhJGR7r8XVarkol+/IKxZIzWPnFMXiYlBeP1112r3BQQE4MUXg/DppzIZ7PXXHW+3Z4/MYn3++Wt4442jTl8XFbUk2Rl2rbcaNaSVJzt75PWCXmX5/HMZm3DHHTcei493/gu5ZUsZAB4S8oTLcR49ChQUNMXtt7u8a5nat5d7+1ii4lx5XWXt4+yMNzXOVRH5ZfE7jh1z/VL0Rnx6nMsder6u9HQZt3DHHTIxYvZsaa2cOVPGCVWv7lmMnsan5X7ePJe7jP663NmneXMFQIhXzlXefhkZ0pLkaE1Rtd6L4GAZl6XGmm/FC0168l4MHQqsXw9cvuzcPl27/gcFBUBcnOvnCg4GnnlGqnU7miFdWCiTxMLCgKee0miROEVRPL05xWazKQAUm83m7C5KTo6iNGmiKA8/XPY2J08qStWqijJ1qtOHdWjSJEVp1kxRiopc2++bbxQFUJQzZ5zfp6L34vJlOebnn7sWi7NatVKUZ57R5tiukvdiqTJwYJ7eoRiCO58TvWRnK8rzzytK5cpyTS1Z4vrnpzzHjh1TACjHjh1T76AmZabrwhsmT76mAEd0fz9GjlSU2Fjtz9O7t6Lcf7/j55y9NvLyFKV6dUV5+23P4zl4UP5GLVrk3PbR0YoybJj758vOlr/PAwYoSmFhyedeeklRKlVSlE2b3PqcOJXneK1FKTAwEK+++ioCHRVQKkP16tKqNHu2jHtw5IMPZNaas32lZRk8WLqkXJ2G+fPPMiuhYUPn96novahZU7JjLVaNzs+XGlWtWql/bHcEBgYiOroxjh93okKoH3Dnc6KHrVtllueHHwKvvirj6UaMUHfqvf09MPp74Q1muS68JSysEiyW5ggI0Pf90LI0QHHlrdjg7LXhSaHJm4WHSy+MM2UCfvtNxiVVVDupPLVqSfmP1atlWE5hoXT3f/SRlBL697+loKxmnxNnM6pybprKyVGU4GDHrUpnzihKUJCi/O1vnp/n6lVFqVFDUd5807X9OndWlD/9yfPz32z4cEUZNEj94x44IL8EVq9W/9jueustRaldW93WCNLOhx9KK1KPHvLLUitsRaGyLF8u32O//65fDEVFilKzpjotNBWZNk1RqlSRViF3ffSRHOPqVXVimjxZUZo2rfh7e/JkRWnQQFFycz0/58cfS+tRRISidOki18DkyR797TBWi5K7qlcHXngB+Oorqf9Q3HPPyVIlzzzj+XmqVZP14ZYvd34fm02y9Ntu8/z8N2vfXpuikwcOyL1RWpQAKSCXnS01dsi4CgulHtpTT0ldk40bjVG0lPyPveiknlX9z5yR6uBaVeUurkMH6Q2wf3+7IzlZZoe7U2jSkWHDpBbali1lb5OfL2u2Pfigc3WNKvL449KL06uX/I1cvlwKUmpdRNbwiRIg3Wo9ewL33itLeyiKdLl9+aW8Sa50e5VnyBBJxpysoYn16yWWPn3UOX9x7dvLwFhnY3HWwYOyfIx9tpkRGOFLj8qXkyNTlKdPB2bMAN59V5ZBINKDvTiwnt8Z9klG3up6AxyXjHGWWsts2fXpI9/d//1v2dssWCAJ5aOPqnfemBiZwPX11zJkxhtMkShVrgwsXCgj/7t2lb7RSZNkuQJP+j1vNniwVAxdvdq57Vetkl8TWnxQ7B+M9HR1j3vggMRcyUD/5+2J0pEjuoZBZbh2DRg5Uuq5LFsm66cR6alWLVnqSs9lTOwr23ujRal+fak9lpbm3v6nT8vYVDUTpYAASYDmznVcZdveoNG//42/Z2ZloD+X5WvcGNi2TYpKDRwoX9hqrwETGirLH6xY4dz2q1ZJLFo0+7VtK8mM2t1vBw8CrVure0xPNW4szcFsUTKe/HxZUHbjRvnMDRqkd0REQu8Fte3LLt1c604rUVHAjh3u7ZucLPdqJkqATMvPzQU++6z0c2vWSLecGkNj9KZZonTkyBE8+uijCAsLQ/Xq1REeHo5XX30VeXnl1zlQFAWvvfYamjZtiurVq6Nv377Y/b/pX7VqSYGrjz6SVYy1MGSIjOQvvn6UIxkZchs40LnjvvHGG+jVqxdq1KiBOnXqVLh9tWpArVqZ+POf34fFYrl+6+nhyrsHDug/Punm98Jikab08r70yrsuzOzixYuIi4uD1WqF1WpFXFwcLlUwWOvhhx8ucU2ocV04UlAgVXxXrpS1EPv2Vf0UVMz06dMRFhaGatWqISoqChvLWaJ93bp1pa4Bi8WCvXv3ejFibWzYsAHDhw9H06ZNYbFYsHjxYofbFU+U1q9fj6ioKFSrVg0tW7bExx9/rHmcGRnatyYVfy+WLn0VW7bkorwyz2VdF8uWnUfTprKOqJqaNZNenX//u2SrUkGBjC3u3l297rGpU6ciOjoatWvXRqNGjTBy5Ejs27evwv3UuDY0S5T27t2LoqIizJw5E7t378Z7772Hjz/+GC+++GK5+7311lt49913MW3aNKSkpKBJkyYYMGAAsrOztQq1hHvvlWJ5GzaUv92PP0qXYL9+zh03Ly8P9913H550oY5BnTrHUb9+H5w6der6bbkro81vkp8v3Vt6tyg5ei8q+nWo93WhlTFjxiAtLQ0rV67EypUrkZaWhjgnqrINGjRIteuiLJMnS5f3d9+xJUlr8+bNw6RJk/DSSy8hNTUVvXv3xuDBg3G0gr6lffv2lbgOWuv94VbBlStX0LlzZ0ybNq3c7UJC5Pvs8OHDGDJkCHr37o3U1FS8+OKLeOqpp7BgwQJN4/RGaYCS78UvyM4OxLFjFe9383Wxf3+964Um1fbaa1J48u9/v/HYm2/KkisffqjeOdevX4/4+Hhs2bIFSUlJKCgoQGxsLK5cuVLmPqpdG85Ojyvn5rS33npLCQsLK/P5oqIipUmTJsp//vOf649du3ZNsVqtyscff+zKqdxWVKQooaGK8uc/l7/d3XcrSp8+rh9/1qxZitVqdWrbTp2WKIGB510/SRnspQGSklQ7pEeKvxePPaYoUVGOtzPCdaGF9PR0BYCyZcuW648lJycrAJS9e/eWud+4ceOUu+++W9PYvvhCrpWEBE1PUy5/Kg/QvXt35YknnijxWNu2bZUpU6Y43P6nn35SACgXL170QnT6AaAsKqOq4fvvK0pgoKI899zflLZt25Z47vHHH1d69uypaWxNmijKq69qeooSgKYVFnl0dF2oWWiyLB98IN8XEycqygsvKIrFIoUgtXTmzBkFgLJ+/foyt3n++ecrujaMVx7AZrOhXr16ZT5/+PBhZGZmIjY29vpjgYGBuOOOO7B582ZvhAiLBbj/fuD776UFxpHLl6VFSavuP7s6dU4gN7ceGjRogzZt2mD8+PE4c+aM28fbv1/ujfijs7wWJSNcF1pITk6G1WpFjx49rj/Ws2dPWK3WCl/XunXr0KhRI1Wui5vt2CHTcB95xPNCrlSxvLw87Nixo8T1DQCxsbEVXgddu3ZFcHAw7rzzTvz0009ahmk4YWEyPmb9+n2l3ruBAwdi+/btyC/rS9xDV65Iz4N3y2OchNV6Db/8UvGWxa+Lzz9PUa3QZFkmTpQlRmbNAt5/H3jxxbLXZVOL7X9TwsvLKZKTk1W5NryWKGVkZOCjjz7CE+VMmcnMzAQANG7cuMTjjRs3vv6cNzzwAHDhApCU5Pj5pUulwumoUdrGMXx4GADg7bdX4p133kFKSgr69+9fYoV1V+zdK2voGak0gF1oKHDunHwB3cwo14XaMjMz0ahRo1KPN2rUqNzXNXjwYMyZMwdr165V5boo7uxZWci2Y0cpBaB1fRICzp07h8LCQpeu7+DgYHzyySdYsGABFi5ciIiICNx5553YUNGYAR9iHx908mSgw/euoKAA586d0+Tc3pzxVlx4+KVyEyVH18UTT3yLqlULERWlXVwWC/Dss1ILz2YD/vUvbWdWK4qCyZMn4/bbb0eHcqbUZWZmqnJtuPxSLBbLaxaLRSl2KzVwbPv27SX2OXnyJAYNGoT77rsPjz32mDPnKPFvRVFKPaaljh1ldeVZsxw//+WXkp1/8cVrDgfOlfdeuOKppwahcmUgJ6clhg8fjhUrVmD//v34wZm68Q7s3SulFbS4gF97zbP3wplaSnpfF85y5b1wFH9Fr2v06NEYOnQoOnTooMp1YVdUJD8Srl6VsUlqFaZzVUJCAiIjIxEdHa1PADpx5fqOiIjA+PHj0a1bN8TExGD69OkYOnQo3n77bW+EagihoXKfn3+Lw/cOcPz5UoM9UfJ2wdXwcBtSUlDmgG5H10XjxqNQu/ZueGP1m4AA79RXmzBhAnbu3Ilvv/22wm3VuDYcrHlcoWkA5tr/sWdP6TXuQ+1XMCRJ6tevH2JiYvDJJ5+Ue+AmTZoAkCwwODj4+uNnzpwplRVqyWIBJkyQ26FDJX817Nkj3W5ffQUMHjwB999/f7nHKv5euKpqVSkTYC8yFhwcjJCQEBxwszzrnj1yPC1MmODZe1E8UYqMLPmcUa4LZzn7XuzcuROnT58u9dzZs2ddel2eXhd2770nU3pXr9a31TE+Ph7x8fHIysqC1WrVLxAvadCgAQICAkq1Hrl6fffs2RNff/212uEZVq1aUmy4WrW2yMwsWYnxzJkzqFy5MurXr6/JuTMypHXe218/EREXMH++nN+Z2ctFRUBWVifUqPE5gE6ax+cNEydOxNKlS7FhwwbcUsE0viZNmjj8XLl6bbicKCmKcg6AU21WJ06cQL9+/RAVFYVZs2ahUgVNGWFhYWjSpAmSkpLQtWtXANJ/v379erz55puuhuqRceOAV14B/vnPki1Lb70FNGki3W6BgQ3QoEEDTeMovhji+fPncezYsRLJgiv27gUGDFAxuGIaNPDsvWjaVH6NOGpRMtJ14Qxn34uYmBjYbDZs27YN3bt3BwBs3boVNpsNvXr1cvp8nl4XgFxjL74oM93uvNPtw5AbqlatiqioKCQlJeEPf/jD9ceTkpJw9913O32c1NRUj64BMwoLA3JyuiAp6d0Sj//444+49dZbUUWj5g17aQBvN2hHRFwAICtIOJMo/fYbcPVqDUREHNI4Mu0pioKJEydi0aJFWLduHcLCwircJyYmBomJiSUec+vacHbUdzk3h06cOKG0atVK6d+/v3L8+HHl1KlT12/FRUREKAsXLrz+7//85z+K1WpVFi5cqOzatUt54IEHlODgYCUrK6vMke1a+fjjkgvIrlsn/54+3fVj/f7770pqaqryj3/8Q6lVq5aSmpqqpKamKtnZ2de3Kf5eZGdnK88884zy+OO/K7VrFypr1/6kxMTEKM2aNXPrvTh7VmL/7jvXY1dbWe9FixaFin2Sj5GvCzUNGjRI6dSpk5KcnKwkJycrHTt2VIYNG1ZiG0fXxebNm5XDhw8rP/3k2XWhKIqSn68oXbsqSvv26i2YqQZ/mvU2d+5cpUqVKspnn32mpKenK5MmTVJq1qypHDlyRFEURZkyZYoSFxd3ffv33ntPWbRokbJ//37lt99+U6ZMmaIAUBYsWKDXS1BNdnb29e8EAMq7776rpKamKr//bwXc4u/F6NGK0qNHjlKjRg3l6aefVtLT05XPPvtMqVKlivL9999rFuPAgTLzWWuO3otWrXKUBx6QvxsVXRd33bVEAa4p33yzSPtgNfbkk08qVqtVWbduXYl8Iicn5/o2N78fhw4dqujacCrP0SxRmjVrlgLA4a04AMqsWbOu/7uoqEh59dVXlSZNmiiBgYFKnz59lF27drnyfqqmsFBR+vVTlDp1FOWZZxSlfn1F6d1bHnfVuHHjHL4XP/300/Vtir8XOTk5SmxsrBIU9KACKErTpt2VcePGKUePHnXrtfz8s/zf3rnTrd1VVdZ70anTReWBB2QbI18Xajp//rwyduxYpXbt2krt2rWVsWPHlpry7ei6aNiwoVKlShWlRYsWHl0XiqIo774r03lTUjx4IRrwp0RJURQlISFBCQkJUapWrap069atxLTncePGKXfcccf1f7/55ptKeHi4Uq1aNaVu3brK7bffrvzwww86RK0++xT3m2/jxo1TFKXkezFliqK0aKEo69atU7p27apUrVpVCQ0NVWbMmKFpjK1by6r1WnP8XsxQrNbjiqJUfF3Ur/+T0r69eiVm9FRWPlH878TN74eiVHhtOJXnWJTyynw62Sjl6QGMzGaTsUqrVwN33CEzgcqZjai6w4eliXf5cs8qnH72GTB+vCxuqtcg3YqMGyeVw0084990jh+XZXseflgq3huJfYySzWZDUFCQ3uGQAX3yiZSwuHbNe4s0FxYC1avLNPi//MU75yxu9mzgoYeA8+fL/1ukKECjRlLq41//8l58JuNU56lp1nrTi9UqF+apU7L4nzeTJEAGOdes6fmab3v2SH++UZMkQP+1m/zRpEkyKJZfpGRGYWEyYNmbi+MeOyY19rxdGsCud2+5r6gSxM6dUnKFSw95jomSwVWqJAO6d+2qeNvy7N2r3Yw3tYSESEJawXKApJLly4EFC2S2mx9MLiMfZB/Pe/iw986pV2kAu9BQKRq8alX52/3wg/zItidW5D4mSiZQfOabu8ySKCkKnFrLiDxz9ap0KQ8YAIwerXc0RO5p0UJmnnkzUcrIkB+w9pImehg0CFixoux6SoD8EBowAF6pn+TrmCiZQMeOQHq6rMjsjmvX5IukXTt141KbM0UnSR0ffigJ6bRprL5N5lW1KnDLLd5PlJo3l3PrZdAg+Z7cu9fx86dPA8nJwLBh3o3LVzFRMoFOnWRNo3373Nt/717px7+5kKPR2IscMlHS1rlzwL//LYNg27TROxoiz7RseaM7zBsyMvTrdrPr21e61RYscPz8d99Jq1exslzkASZKJvC/GotITXVv/19/lfuOHdWJRyvVqgHBwcCRI3pH4tvsi1X+/e/6xkGkhrAw749R0jtRqlFD1mScPdtx99s33wADB3p/8pGvYqJkAnXqyK8mZ1aNdmTnTtm/dm1Vw9IEZ75p69AhYMYMqcKtcVF5Iq/wZqKkKMZoUQKAuDhg/35g27aSj6ekAFu2AI88ok9cvoiJkkl06+Z+ovTrr0DnzurGoxUmStr6xz8kQZo4Ue9IiNQRFgacPQtcvqz9uS5ckNp6epUGKK5/f4nj5lWc3nlHErmRI3UJyycxUTKJbt2k662oyLX9FEUSpU4mWQ+RiZJ29uwBvv4aePllabon8gX2EgHe6LI/eFDuW7fW/lwVCQgAXn0VWLQI2LpVHktJAebPB555Rp4ndTBRMolu3YCsLNcHLWZmyuBdM7UoHTsm1W9JXf/8p8wQeuwxvSMhUo83aynZEyUjdL0BwNixwK23AvfdB8ycKeOWunWTVRhIPUyUTMI+oNvV7redO+XeLC1KoaFSBuHUKb0j8S2HDgHz5gHPP2/8uioJCQmIjIxEdHS03qGQCQQHyzXtrUSpcWPjjPcMCAAWLwaaNAGeeAJo1gxYsgSoXFnvyHwLEyWTaNRIWgNcTZR+/VWWqLD/6jI6ey0lznxT19tvA/Xrm2OAZ3x8PNLT05GSkqJ3KGQC9uKP3kiUDhwAWrXS/jyuaNZMut4uXZJB3E2b6h2R72GiZCJRUa4nSmlpUhagkkn+T7PopPpOnwZmzQKeeopjk8g3tWwps9G0dvCgMcYn3cxi4TJEWjLJn08CpO95x47yy9bfLCUFMFMPRq1aUvuDiZJ6PvxQmuLj4/WOhEgbrVrdGD+kpYMHjdeiRNpjomQivXrJ9NSyytbf7MIF+WB3765tXGrjzDf1ZGUB06cDf/4zULeu3tEQaaN1a2lR0nISyMWLwPnzTJT8ERMlE+nZUwbvbdjg3Pbbt8s9EyX/9cknwJUrwNNP6x0JkXZatwby8oDjx7U7h73FiomS/2GiZCK1ask4pY0bndt+61ap6m22D3ZoKBMlNeTmAu+9Bzz4oEwEIPJV9u+4Awe0OwcTJf/FRMlkevcG1q93bpzSzz8DMTHmWx3e3qLkylgsKu3rr6XMwnPP6R0JkbZCQ6W1XctxSgcPAg0bctC0P2KiZDJ9+kjzckUtLgUFwKZNwB13eCcuNYWEAFevyrIE5B5FAd59FxgxAmjXTu9oiLRVpYokS1q3KLE1yT8xUTKZ226T+4q631JTZWxKnz7ax6Q2lgjw3IYNQHq6lAQg8getW2vbomTEGkrkHUyUTKZ+faBDh4oHdK9bB1SvLmOazIaJkudmzAAiIoB+/fSOhMg7WrdmixJpg4mSCfXrB6xaVf4YnhUrZLuqVb0Xl1rq1QNq1mSi5K7MTGDBAlnSwGzj04jc1aqVdiUCbDYZCmDEYpOkPSZKJjRihCwca1/H7WY2m3TNDR3q3bjUYrFw5psnPvtMxmyMG6d3JETeo2WJAM54829MlEyoTx8gKEgWP3Tkxx9lMLdZEyVAut+43pvrCgtlFfEHHmCBSfIv9tYeLbrfmCj5NyZKJlS1KjB8ODBnjuPut2++keVO7GN9zIhFJ93zww/S2viXv+gdCZF3hYRoVyLg4EEZEsAfH/6JiZJJPfIIsH8/kJxc8vGzZ4Fly4CHH9YlLNUwUXLPjBmytp8ZB/ETeaJKFSAsTLsWJY5P8l9MlEyqXz/5Upg2reTjM2cClSpJ14uZhYTIWCubTe9IzCMjA1i5EnjySb0j8UxCQgIiIyMRbabVnMkQWreWH5Bq27uXiZI/Y6JkUpUqAc8+C8ybB6SlyWMXLgBvvy2znRo00DU8j4WGyj1blZz3ySfSNTB6tN6ReCY+Ph7p6elISUnROxQymXbtgD171D2mokiixMKt/ouJkok99hgQGSmtR9u3A3Fx8viLL+oblxpYS8k1BQXAl1/KNVCjht7REOmjXTvg0CGp7K+W06eBS5eYKPkzJkomVrWq1Mu5fFnGpaxbB8ydCzRurHdknmvcWF4fZ74558cf5QudJQHIn0VGSguQmt1v9hYqJkr+q7LeAZBn2rSRD3JyMtCpk28kSYB0LbZowRYlZ335pVRs79pV70iI9GNPZvbsATp3VueYe/cClSsD4eHqHI/Mhy1KPqBWLWDAAN9Jkuw48805Fy9KTa1x41iJm/xb3bpAkyayzqFa9uyR+klVqqh3TDIXJkpkWEyUnDN/PpCfD4wdq3ckRPpTe0D3nj3sdvN3TJTIsLiMiXO+/BKIjQWCg/WOhEh/7dqp26LEGW/ERIkMKyQEOHNG3RksvubAAWDzZg7iJrKLjJTPRX6+58fKzpa145go+TcmSmRYLBFQsa++AqxW4O679Y6EyBjatZMkKSPD82Pt3Sv3bdt6fiwyLyZKZFhMlMpXVCSJ0qhRQPXqekdDZAyRkXKvxjglJkoEMFEiA2vWTMoEMFFybP164OhRdrsRFde4MVCnjjqJ0p49QPPmMrOY/BcTJTKsKlUkWWKi5NhXX0ltl169tD3PxYsXERcXB6vVCqvViri4OFy6dKnM7fPz8/G3v/0NHTt2RM2aNdG0aVM89NBDOHnypLaBEkFKZLRrB+ze7fmxdu/m+CRiokQGx5lvjl27JlXZH3xQ+9pJY8aMQVpaGlauXImVK1ciLS0Ncfb1chzIycnBL7/8gldeeQW//PILFi5ciP3792PEiBHaBkr0P506ATt3en6cnTvVK1xJ5sXK3GRoISFcxsSRFStkRs7992t7nj179mDlypXYsmULevToAQD49NNPERMTg3379iEiIqLUPlarFUlJSSUe++ijj9C9e3ccPXoULVq00DZo8ntdugD//a/8oKhWzb1j2Gzy3dOpk5qRkRmxRYkMjYmSY/PmyRe41oNMk5OTYbVarydJANCzZ09YrVZs3rzZ6ePYbDZYLBbUqVOnzG1yc3ORlZVV4kbkji5dgMJCz7rfdu2Se7YoERMlMrSQEODkSXVqoviKK1eAxERg9Gjtz5WZmYlGjRqVerxRo0bIzMx06hjXrl3DlClTMGbMGAQFBZW53dSpU6+Pg7JarWjevLnbcZN/69RJJoKkpbl/jJ07ZZykg0ZT8jNMlMjQQkJkGvzx43pHYhw//ADk5HiWKL322muwWCzl3rZv3w4AsDgYBKUoisPHb5afn4/7778fRUVFmD59ernbvvDCC7DZbNdvx44dc+/Fkd+rUUMWDPckUfr1VxnIXbWqamGRSXGMEhla8VpKYWH6xmIU8+YBUVGerWY+YcIE3F/BAKfQ0FDs3LkTp0+fLvXc2bNn0biCVZjz8/MxatQoHD58GGvXri23NQkAAgMDERgYWHHwRE7o0sXzFiV2uxHARIkMzj7ulzPfRHY2sHw58Prrnh2nQYMGaNCgQYXbxcTEwGazYdu2bejevTsAYOvWrbDZbOhVTl0Ce5J04MAB/PTTT6hfv75nARO5qEsXaX0tKpJuOFcUFsoYpT/+UZPQyGTY9UaGVr26FJBjoiSWLpWZPKNGeed87dq1w6BBgzB+/Hhs2bIFW7Zswfjx4zFs2LASM97atm2LRYsWAQAKCgpw7733Yvv27ZgzZw4KCwuRmZmJzMxM5OXleSdw8ntdusgPi0OHXN93zx4ZC3jrraqHRSbERIkMjzPfbpg3D+jZ80aXpDfMmTMHHTt2RGxsLGJjY9GpUyfMnj27xDb79u2DzWYDABw/fhxLly7F8ePH0aVLFwQHB1+/uTJTjsgT3brJfUqK6/umpEh9sqgodWMic2LXGxleSAhblADg0iVg5Urg//7Pu+etV68evv7663K3URTl+n+HhoaW+DeRHho2lHF8W7YADzzg2r4pKTKQu3ZtbWIjc2GLEhkeEyWxeDFQUADcd5/ekRCZQ8+eQHKy6/tt2wZER6sfD5kTEyUyvNBQ4NgxGZTpz+bPB26/HWjaVO9IiMwhJgZITQWuXnV+n9xcmfH2v7kLREyUyPhCQoC8PMDJ+oY+yWYDVq/mLBwiV8TESCvsL784v09amhS4ZYsS2TFRIsMrXkvJXy1fLsniPffoHQmReXTsKDNnXel+27hR9mENJbJjokSGZ0+U/Hnm24IF8guXq3oQOa9KFaBHD2DDBuf3Wb8e6NWLFbnpBiZKZHhBQUCdOv7bopSTA6xYwdYkInfcdRewbp1z60UWFkqL0h13aB4WmQgTJTIFf5759uOPkiwxUSJy3YABUnhy27aKt925U8YD9u2reVhkIkyUyBRCQ/03UVq4EGjfXhb5JCLXREUBdesCSUkVb7t6tYxP4ow3Ko6JEpmCv7Yo5eXJsiWc7UbknoAAoH9/5xKlH34A7rwT4NrMVBwTJTIFe6LkbwWff/pJugL8qdstISEBkZGRiOb8bFLJoEFSofvs2bK3uXQJ+PlnYOhQr4VFJsFEiUwhJEQWqTx/Xu9IvGvJEul27NRJ70i8Jz4+Hunp6UhxZ5EuIgdGjJD7xYvL3uaHH2Qw95AhXgmJTISJEpmCP9ZSUhRg2TJg+HBZoJOI3NOokcxkmzu37G3mzAFuuw1o0cJ7cZE5MFEiU/DHRGnnTlm6ZfhwvSMhMr9x44C1a4FDh0o/l5kps0sffND7cZHxMVEiU2jQAKhRw78SpWXLgFq1gD599I6EyPzuuw+wWoHp00s/l5AAVKsGjB7t/bjI+JgokSlYLP438y0xERg4kDNwiNRQowYwcSIwYwZw+vSNxy9elERp/HgpI0B0MyZKZBr+lCidPi0F8oYN0zsSIt/x9NNSJyk+/sYM2qefBoqKgOee0zc2Mq7KegdA5KyQEGDrVr2j8I7ly+WeM3CI1FOvHjBzJnDvvcD990sr05dfArNmAU2b6h0dGRVblMg0QkOBw4f9o5bSsmWymGejRnpHQuRb/vhHYPZsqauUlCRjlh5+WO+oyMjYokSm0aqVFF+8cAGoX1/vaLSTmyszcF54Qe9IiHzTgw9yhhs5jy1KZBrh4XKfkaFvHFpbvx64fJnjk4iIjICJEpmGPVE6eFDfOLSWmChF7zp21DsSIiJiokSmERQkY3Z8OVGyV+MeNozVuImIjICJEplKeLhvd73t3g0cOcJq3ERERsFEiUylVSvfblFatgyoWRPo21fvSIiICGCiRCbj64lSYiIwYIAsp0BERPpjokSmEh4OnDkDZGfrHYn6zp0DkpPZ7UZEZCRMlMhUWrWSe18cp7R8uQzm9vdq3AkJCYiMjER0dLTeoRARwaJ4XubYD+okk1GcPw80aADMny/LEPiSUaNkLTt/WaalIllZWbBarbDZbAgKCtI7HCLyPU7NLWaLEplKvXqA1ep745Ty8oCVK1lkkojIaJgokalYLNL95mtdbxs3yrgrjk8iIjIWJkpkOr448y0xEbjlFqBzZ70jISKi4pgokemEh/tWoqQokiixGjcRkfEwUSLTadUKOH4cuHpV70jUsXcvcOgQxycRERkREyUyHXuJgMOH9Y1DLcuWAdWrA/376x0JERHdjIkSmU54uNz7SvdbYiJw112SLBERkbEwUSLTCQ4GatQADhzQOxLPXbgAbNrE2W5EREbFRIlMx2IB2rQB9u/XOxLPrVgBFBUBQ4fqHQkRETnCRIlMKSJCBkGb3bJlQFQU0LSp3pEQEZEjTJTIlNq2Bfbt0zsKz+TnS4sSZ7sRERkXEyUypYgI4PRp4NIlvSNx36ZNgM3G8UlEREbGRIlMqW1buTdzq1JiogxM79pV70iIiKgsTJTIlNq0kXszj1Natky63SrxU0hEZFj8iiZTqlkTaN7cvC1K+/fLjeOTSktISEBkZCSio6P1DoWICBZFUTw9hscHIHJHbCxQqxawcKHekbju3XeBl14Czp+XmlBUWlZWFqxWK2w2G4KCgvQOh4h8j1Ora7JFiUzLzCUCEhNlyRImSURExsZEiUyrbVtZxqSgQO9IXHPpErBxI2e7ERGZARMlMq2ICKlFZLbFcVeuBAoLOT6JiMgMmCiRaZm1RMCyZUCXLsAtt+gdCRERVYSJEplWs2Yy+81M45QKCoDly9ntRkRkFkyUyLQsFul+M1OLUnIycPEiu92IiMyCiRKZmtlmviUmAo0bA7feqnckRETkDCZKZGrt2gF79gCelwPzjmXLgKFDWY2biMgs+HVNptahgxRtPH1a70gqlpEhSR3HJxERmQcTJTK1Dh3kftcufeNwxrJlQNWqwF136R2Jay5evIi4uDhYrVZYrVbExcXh0qVLTu//+OOPw2Kx4P3339csRiIirTBRIlNr2RKoXh347Te9I6mYvRp3rVp6R+KaMWPGIC0tDStXrsTKlSuRlpaGuLg4p/ZdvHgxtm7diqZNm2ocJRGRNirrHQCRJwICgMhI4ydKNhuwfj1gtkaVPXv2YOXKldiyZQt69OgBAPj0008RExODffv2ISIiosx9T5w4gQkTJmDVqlUYOnSot0ImIlIVW5TI9Dp0MH7X28qVUkPJbOOTkpOTYbVarydJANCzZ09YrVZs3ry5zP2KiooQFxeH5557Du3bt/dGqEREmmCLEplex47A/PlAUZFxZ5MtWQJ07Qq0aKF3JK7JzMxEo0aNSj3eqFEjZGZmlrnfm2++icqVK+Opp55y+ly5ubnIzc29/u+srCzXgiUi0oBB/6wQOa9DByAnx7hrvuXnSzXuESP0juSG1157DRaLpdzb9u3bAQAWi6XU/oqiOHwcAHbs2IEPPvgAX3zxRZnbODJ16tTrA8atViuaN2/u3osjIlIRW5TI9Dp2lPvffgPCw/WNxZENG2SMkpESpQkTJuD+++8vd5vQ0FDs3LkTpx3UXjh79iwaN27scL+NGzfizJkzaFGs+aywsBDPPPMM3n//fRw5csThfi+88AImT558/d9ZWVlMlohId0yUyPSCg4G6dWWc0t136x1NaUuXygK4XbvqHckNDRo0QIMGDSrcLiYmBjabDdu2bUP37t0BAFu3boXNZkOvXr0c7hMXF4e7bqqBMHDgQMTFxeGRRx4p81yBgYEIDAx04VUQEWmPiRKZnsUirUpGnPmmKJIojRghcZpNu3btMGjQIIwfPx4zZ84EAPz5z3/GsGHDSsx4a9u2LaZOnYo//OEPqF+/PurXr1/iOFWqVEGTJk3KnSVHRGREHKNEPsGoM9927QKOHDFmS5ez5syZg44dOyI2NhaxsbHo1KkTZs+eXWKbffv2wWaz6RQhEZF22KJEPqFjR2DmTCA3FzBS783SpUDt2sAdd+gdifvq1auHr7/+utxtlAoW2ytrXBIRkdGxRYl8QpcuQGGh8brfliwBBg82VvJGRETOY6JEPqFzZ6nSvWOH3pHccOIEsH27sWa7ERGRa5gokU+oXl2WMvlf6R9DSEyU5G3wYL0jISIidzFRIp8RFWWsFqWlS4E+fYB69fSOhIiI3MVEiXxGVJTMMiu2CoZusrOBNWvY7UZEZHZMlMhnREXJciFGGNC9ahWQl8dEiYjI7Jgokc/o3FkWxTVC99v338tMvJYt9Y6EiIg8wUSJfEaNGjKgW+9E6epVYNky4N579Y2DiIg8x0SJfIoRBnSvWgVcuQLcd5++cRARkeeYKJFPsQ/ozsvTL4b586VSeJs2+sVARETqYKJEPiUqSpIkvQZ0X7sm9ZPYmuS+hIQEREZGIjo6Wu9QiIhgqWiNJid4fAAiteTkAFYr8OGHwJNPev/8S5fKArjp6UC7dt4/vy/JysqC1WqFzWZDUFCQ3uEQke+xOLMRW5TIp9SoAXTtCmzapM/5v/9eBpQzSSIi8g1MlMjn3HabPolSbq60KLHbjYjIdzBRIp9z223AkSPAyZPePe/q1YDNxrIARES+hIkS+ZzbbpN7b7cqffcdEBEBtG/v3fMSEZF2mCiRzwkOBsLCvJso5eQACxcCDzwAWJwaHkhERGbARIl80u23ezdRWrYMuHwZGDvWe+ckIiLtMVEin3T77UBqKpCd7Z3zzZkDdO8OtGrlnfMREZF3MFEin9S/P1BYCKxfr/25LlwAVqxgaxIRkS9iokQ+KTwcCAkBkpK0P9fcuUBRETB6tPbnIiIi72KiRD7JYgHuukum7Gtt1ixgyBCgcWPtz0VERN7FRIl81oABspSIlvWUdu0Ctm8HHnlEu3MQEZF+mCiRz+rfX+61bFWaNQto2BAYOlS7cxARkX6YKJHPatgQ6NJFu3FKubnA118DDz4IVK2qzTmIiEhfTJTIpw0ZAixfDhQUqH/s778Hzp4Fxo9X/9hERGQMTJTIp40cKdP3f/5Z/WN/9JEMGG/XTv1j+7OEhARERkYiOjpa71CIiGBRFMXTY3h8ACKtFBUBzZsDo0YB772n3nFTUqTA5JIlwIgR6h2XbsjKyoLVaoXNZkNQUJDe4RCR73FqwSm2KJFPq1QJuPtuYPFiwPPfBDdMmwaEhnIQNxGRr2OiRD7vD38AjhyRafxqOHNGikz+5S9AQIA6xyQiImNiokQ+r39/IDgYmD1bnePNnCktVX/6kzrHIyIi42KiRD4vIAAYMwb49lsgL8+zY2VnA++/Dzz6KFC/virhERGRgTFRIr/w0EPAuXOyeK0npk0DLl8GpkxRJy4iIjI2JkrkFzp1Arp1Az7+2P1jXL4MvPOOdLndcot6sRERkXExUSK/8dRTwMqVwL597u3/3ntAVhbwwgvqxkVERMbFRIn8xv33A40auVdP6fffgalTgUmTgBYtVA+NiIgMiokS+Y3AQGDyZODzz4GjR13b99lngTp1gFde0SQ0IiIyKCZK5Ffi4yXhefll5/dZvlzWdfu//wNq19YsNCIiMiAmSuRXatUC3nhDaipt3Fjx9idOAOPGAYMHS4kBIiLyL1zrjfxOYSFwxx2SBKWmSguTIzk5QGwscPgwkJYGNGzozSiJa70Rkca41huRIwEB0qJkswH33CMJ0c2uXpU14tLSgPnzmSQREfkrJkrkl8LCZKHcrVuBvn2lZUlR5LZpE9Cjh9z/8APQq5fe0RIRkV6YKJHf6tMH2LBBWpa6dQOaNweaNAFuvx2wWIAtW6SLjrwrISEBkZGRiI6O1jsUIiKOUSLKywNWrZIWpBo1pDVpwABZ+Jb0wzFKRKQxp8YoMVEiIkNiokREGuNgbiIiIiJPMFEiIiIiKgMTJSIiIqIyMFEiIiIiKgMTJSIiIqIyqDHrjYhIdRaLJQiADYBVUZQsveMhIv/ERImIDMlisVgA1AaQrfCLioh0wkSJiIiIqAwco0RERERUBiZKRERERGVgokRERERUBiZKRERERGVgokRERERUBiZKRERERGVgokRERERUhv8HNclhyPJy0FsAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pf = plot(f, (x, -2, 2))\n", "show(pf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The amplitude is defined by $\\pm \\exp(-x^2)$, let us add these two functions." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fplus = plot(exp(-x^2), (x, -2, 2), color='red')\n", "show(pf+fplus)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fminus = plot(-exp(-x^2), (x, -2, 2), color='green')\n", "show(pf+fplus+fminus)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider another example." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "g = 1/(x^3 - x)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(g, (x, -2, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is not an enteresting plot. One improvement is to provide bounds on the $y$-values." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(g, (x, -2, 2), ymin=-10, ymax= 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The best plot for this example is when we ask to show the poles, which then displays the asymptotes." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(g, (x, -2, 2), ymin=-10, ymax= 10, detect_poles='show')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Implicit Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Many intesting curves are defined by equations $f(x,y) = 0$. Consider a curve invented by James Watt." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-5.15000000000000*x^4 + 5.15000000000000*y^4 + (x^2 + y^2)^3 + 5.12000000000000*(x^2 + y^2)^2 - 14.7456000000000*y^2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x, y = var('x, y')\n", "watt = (x^2+y^2)^3 + 5.12*(x^2+y^2)^2 - 5.15*(x^4-y^4) - 14.7456*y^2\n", "watt" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "implicit_plot(watt, (x, -1.5, 1.5), (y, -1.5, 1.5), plot_points = 2000, color='red').show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe the difference between the two plots. When we use more points in the plot, the plot approaches the origin more. But does the origin belong to the curve?" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "watt(x=0, y=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yes it does!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. Parametric Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the curve is defined by two functions $x(t)$ and $y(t)$ for the two coordinates $(x = x(t), y = y(t))$, then the plotting can be done efficiently and accurately. Consider a Lissajous curve." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = var('t')\n", "parametric_plot((sin(2*t), sin(3*t)), (t, 0, 2*pi))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4. Polar Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In polar coordinates, a curve is represented by $r = f(t)$, with \n", "\n", "$$\n", " x = r \\cos(t) \\quad \\mbox{and} \\quad y = r \\sin(t),\n", "$$\n", "\n", "where \n", "\n", "1. $r$ is the radius of the point $(x, y)$, its distance from the origin; and\n", "\n", "2. $t$ is its argument, the angle of the vector ending in $(x,y)$ with the $x$-axis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us compute the polar representation of the curve defined in ``watt``." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-5.15000000000000*x^4 + 5.15000000000000*y^4 + (x^2 + y^2)^3 + 5.12000000000000*(x^2 + y^2)^2 - 14.7456000000000*y^2" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "watt" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-5.15000000000000*r^4*cos(t)^4 + 5.15000000000000*r^4*sin(t)^4 - 14.7456000000000*r^2*sin(t)^2 + (r^2*cos(t)^2 + r^2*sin(t)^2)^3 + 5.12000000000000*(r^2*cos(t)^2 + r^2*sin(t)^2)^2" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r, t = var('r, t')\n", "pwatt = watt(x = r*cos(t), y = r*sin(t))\n", "pwatt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe the $\\cos(t)^2 + \\sin(t)^2$ which can be simplified to one. Let us simplify before solving." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1/4044180699863300*r^4*sin(t)^4 + r^6 - 1213254209959/40441806998633*r^4 + 2/25276129374145625*(130172066276849975*r^4 - 186355846649700864*r^2)*sin(t)^2" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spwatt = pwatt.trig_simplify()\n", "spwatt" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[r == -1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 + 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633), r == 1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 + 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633), r == -1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 - 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633), r == 1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 - 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633), r == 0]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = solve(spwatt,r)\n", "sol" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(sol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe that ``r == 0`` is one of the factors. So we see that the curve passes through the origin." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 + 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1 = sol[0].rhs()\n", "f1" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p1 = polar_plot(f1, (t, 0, 2*pi), color='red')\n", "p1.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f2 = sol[1].rhs()\n", "p2 = polar_plot(f2, (t, 0, 2*pi))\n", "p2.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 - 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f3 = sol[2].rhs()\n", "f3" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (3839: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 198 points.\n", "verbose 0 (3839: plot.py, generate_plot_points) Last error message: 'math domain error'\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 0 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p3 = polar_plot(f3, (t, 0, 2*pi))\n", "p3.show(axes=False)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0,\n", " -1.31743435377368e-16 - 2.15153357636002*I,\n", " -1.98892849598223e-16 - 3.24816673242766*I,\n", " -1.98892849598223e-16 - 3.24816673242766*I,\n", " -1.31743435377368e-16 - 2.15153357636002*I,\n", " 0,\n", " -1.31743435377368e-16 - 2.15153357636002*I,\n", " -1.98892849598223e-16 - 3.24816673242766*I,\n", " -1.98892849598223e-16 - 3.24816673242766*I,\n", " -1.31743435377368e-16 - 2.15153357636002*I]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[f3(t=2*RR(pi)*k/10.0) for k in range(10)]" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1/10*sqrt(1/80883613997266*sin(t)^4 - 20827530604295996/40441806998633*sin(t)^2 - 1/80883613997266*sqrt(sin(t)^8 - 83310122417183984*sin(t)^6 + 1735144124291545345496293968519864*sin(t)^4 + 954572963783593651936794875955136*sin(t)^2 + 14719857779832372547816810000) + 60662710497950/40441806998633)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f4 = sol[3].rhs()\n", "f4" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0,\n", " 1.31743435377368e-16 + 2.15153357636002*I,\n", " 1.98892849598223e-16 + 3.24816673242766*I,\n", " 1.98892849598223e-16 + 3.24816673242766*I,\n", " 1.31743435377368e-16 + 2.15153357636002*I,\n", " 0,\n", " 1.31743435377368e-16 + 2.15153357636002*I,\n", " 1.98892849598223e-16 + 3.24816673242766*I,\n", " 1.98892849598223e-16 + 3.24816673242766*I,\n", " 1.31743435377368e-16 + 2.15153357636002*I]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[f4(t=2*RR(pi)*k/10.0) for k in range(10)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The third and fourth component cannot be plotted because of the complex values." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pt = point((0,0), color='red', size=50)\n", "(p2+pt).show(axes=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a *real* curve, the origin is an isolated point!" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.3", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10" } }, "nbformat": 4, "nbformat_minor": 4 }