{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cálculos de ceros de sistemas\n", "#### https://meet.noysi.com/metodosnumericos1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Método de Newton-Raphson" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En primer lugar, vamos a resolver aproximadamente la ecuación \n", "$$\\begin{cases} x^5+x y=1,\\\\ y^5+2 x y=1.\\end{cases}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Necesitamos transformar el problema en encontrar los ceros de una función. En este caso, lo más sencillo es pasar todos los sumandos al mismo lado de la ecuación:\n", "$$F(x,y) = ( x^5-xy-1,y^5+2xy-1).$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y \\right) \\ {\\mapsto} \\ \\left(x^{5} + x y - 1,\\,y^{5} + 2 \\, x y - 1\\right)$$" ], "text/plain": [ "(x, y) |--> (x^5 + x*y - 1, y^5 + 2*x*y - 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f(x,y) = x^5+x*y-1\n", "g(x,y) = y^5+2*x*y-1\n", "F(x,y) = ( f(x,y) , g(x,y) )\n", "show(F)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para aplicar el método de Newton-Raphson, es preciso considerar un punto inicial. Por ejemplo, vamos a tomar el punto $(1,1)$. Lo definimos como vector, puesto que queremos realizar operaciones con él (suma)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1.0, 1.0)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v0 = vector(RDF,[1.,1.])\n", "v0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "También necesitamos la matriz jacobiana. En Sage se puede calcular con el método `diff` sin introducir ningún parámetro." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "5 \\, x^{4} + y & x \\\\\n", "2 \\, y & 5 \\, y^{4} + 2 \\, x\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 5*x^4 + y x]\n", "[ 2*y 5*y^4 + 2*x]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "DF = F.diff()\n", "show(DF(x,y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Como nuestra función de variables no está definida sobre puntos sino sobre coordenadas, para evaluar una función de varias variables en un punto hay que transformarlo en sus coordenadas. Para ello usamos el operador `*`." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(\n", "[6.0 1.0] [6.0 1.0] [6.0 1.0]\n", "[2.0 7.0], [2.0 7.0], [2.0 7.0]\n", ")" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "DF(*v0), DF(RDF(1.),RDF(1.)), DF(v0[0],v0[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora podemos aplicar el método de Newton-Raphson. Recordemos que $v_1$ está definido por\n", "$$ J_{v_0} (v_1-v_0) = -F(v_0),$$\n", "donde $v_0$ es el vector inicial y $J_{v_0}$ es la matriz jacobiana de $F$ evaluada en $v_0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Si $x$ es la solución de $ J_{v_0} x = -F(v_0),$, entonces \n", "$$v_1-v_0=x,\\quad v_1 = v_0 + x$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "v1 = v0 + DF(*v0)\\(-F(*v0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Los siguientes pasos son análogos." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(1.0, 1.0),\n", " (0.875, 0.75),\n", " (0.8674615838407234, 0.5883877512370015),\n", " (0.8783073191378743, 0.5437936013364996)]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v2 = v1 + DF(*v1)\\(-F(*v1))\n", "v3 = v2 + DF(*v2)\\(-F(*v2))\n", "puntos = [v0,v1,v2,v3]\n", "puntos" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0002938404595224098, 0.002787983990069298)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F(*v3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Por último vamos a representar las ecuaciones, la solución y las aproximaciones. Cada ecuación define en este caso una curva implícita y las soluciones serán las intersecciones de ambas curvas." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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4cUPsOFTHWOZUa1q3bo2ffvoJKSkpGDt2LBQKBQ4fPgx/f3+89tpriIyMFDsikc6wtLREp06dAPBQuz5imVOtc3R0xI8//ojU1FR88MEHMDQ0xJEjR9C9e3d0794dR48eFTsikU7goXb9xTKnOmNnZ4c1a9YgNTUVQUFBMDQ0RGRkJHr06IHu3bsjOjpa7IhEklZxEVxsbCwkcNcxaRDLnOqcra0tVq1ahStXrmDChAkwMjJCZGQkjhw5InY0Iknz9vbGsWPHkJqayttC9QwnjSHRZWRkYMmSJZg/fz4aNmwIADh16hRKSkrQtWtXccMREYlEZ6ZzJf3QokULLFu2TFXkgiBg2rRp6NatG0JCQsQNR0QkASxz0jrFxcXo2LEjLCws8Pbbb6uWFxUViZiKSBrKy8sxefJktG7dGnfu3BE7DtURljlpHRMTE6xcuRIZGRlo2rSpavmbb76Jvn37ckY5omcwMDBAZGQkLl26hD///FPsOFRHWOaktRo0aKD676tXr+Lw4cMIDw+Ht7c3BgwYgAsXLoiYjkh7Vdyi9scff4ichOoKy5wkwcHBASkpKRg1ahTkcjl+/fVXdOjQAUOGDEFSUpLY8Yi0SkWZHzp0iLeo6QmWOUmGo6MjfvrpJyQmJmLo0KGQyWTYuXMn3NzcMGLECFy+fFnsiERa4ZVXXoGZmRmysrJw8eJFseNQHWCZk+S4uLhg27ZtOH/+PAYOHAhBELBlyxa4uLjggw8+QHp6utgRiURlbGyM7t27A+Chdn3BMifJateuHXbv3o24uDj069cP5eXlWLduHZycnDBp0iRkZ2eLHZFINBWzwXFqV/3AMifJ8/DwwIEDB3DixAn06NEDJSUl+OGHH5CZmSl2NCLR9O7dG7a2tnBzc+N5cz2gEDsAkab4+vri8OHDOHLkCKKiouDp6an6XsUjWB+/Qp5Ilzk5OSEtLY3TuuoJrZ7ONSQkBCEhISgvL8elS5c4nSvVyPXr1+Hk5ARzc3OcP38ezZs3FzsSEdFz6cx0rhMnTkRSUhLOnDkjdhSSsOzsbNjb26NDhw4sctI7ZWVl/DdUD2h1mRNpQufOnZGYmIitW7eqluXk5MDLywvbt2+HUqkUMR1R7SkuLoa1tTU6deqEq1evih2HahHLnPSCQqGAlZWV6uvvvvsOcXFxGDZsGDw8PHDw4EFeJEQ6x9jYGC4uLgAeTSBDuotlTnpp1qxZWLhwoeo8er9+/dC9e3ecPHlS7GhEGvX4bHCku1jmpJcaNGiA//znP7h69SpmzJgBY2NjREVFwdfXF2+++Sb++usvsSMSaURAQAAA4PDhwygtLRU5DdUWljnptUaNGuGbb75Bamoq/vWvf0Eul2P//v1o3749Ro8ejevXr4sdkeiFeHp6wtLSEnl5eYiNjRU7DtUSljkRgBYtWmD9+vVITEzEoEGDIAgCNm/eDGdnZ0yfPh05OTliRySqEQMDA/Tq1QsAD7XrMpY50WNcXFywc+dOnD59Gq+++ipKSkrw3XffoWfPnrxAjiSLj0TVfSxzoip4e3urnp/u7u6OGTNmqGbSKisr47lHkpQ+ffpg3rx5WL58udhRqJZo9QxwFdSZBYdI0yruQ5fLH/3tu3btWixZsgRLly7F66+/LmY0ItJh6nQf52Yneo6KEgcAQRCwcuVKXLp0CVeuXBExFRHR//AwO5EaZDIZoqOjsXjxYowfP161PCYmBomJiSImI3q24uJi7N69GzNmzOD1HzqIh9mJXlBpaSnc3Nxw+fJljBkzBgsXLuQc8KR1Hj58CEtLSxQVFSEpKQlt2rQROxI9h848aIVICvLy8uDm5galUokNGzbAyckJn376KfLy8sSORqRiamqKrl27AuBV7bqIZU70gho1aoTdu3cjJiYGr7zyCh4+fIjg4GA4Ojrihx9+QElJidgRiQD8bza4iIgIkZOQptWozFeuXAl7e3uYmJjA09MT0dHRz1x/y5Yt6NChA8zMzGBtbY333nsPd+/erVFgIm3l4+ODqKgo7Nu3D61bt0ZOTg4mTZqEtm3bYteuXTxPSaKrKPNjx46huLhY5DSkSWqX+fbt2zF16lTMmTMH8fHx8Pf3R9++fZGenl7l+sePH8eoUaMwduxYJCYmYufOnThz5gzGjRv3wuGJtI1MJlPN7b5q1Sq8/PLLuHz5MgYPHgw/Pz/ExMSIHZH0mJubG5o2bYrCwkIcP35c7DikQWqX+dKlSzF27FiMGzcObdq0wbJly9CiRQusWrWqyvVPnToFOzs7TJ48Gfb29njllVcwfvx4nD179oXDE2krhUKBoKAgXL58GXPnzoWZmRlOnjwJPz8/DB48GDdu3BA7IukhmUymGp1zalfdolaZl5SUIC4uTvXLUCEgIOCpIw5fX1/cuHEDYWFhEAQBt27dwq5du5452UZxcTHy8vIqvYikqEGDBliwYAEuX76McePGQS6XIywsDAYGBmJHIz1VMbXrpUuXRE5CmqRWmefk5KC8vBxWVlaVlltZWSE7O7vKbXx9fbFlyxYMHToURkZGaNq0KRo2bIgVK1Y89XOCg4NhYWGherVo0UKdmERax9raGuvWrUNCQgLWrVsHa2tr1ff27NnD85dUZwIDA5GWloa9e/eKHYU0qEYXwFXMUV1BEIQnllVISkrC5MmTMXfuXMTFxSE8PBxpaWkICgp66vvPnj0bubm5qldGRkZNYhJpnXbt2uHdd99VfR0ZGYm3334b7dq1Q1FRkYjJSF80aNAAdnZ2YscgDVNrOtfGjRvDwMDgiVH47du3nxitVwgODoafnx8+/vhjAED79u1Rr149+Pv744svvqg0QqlgbGwMY2NjdaIRSVJ+fj6aNWuGnj17wsTEROw4pGeeNRAjaVFrZG5kZARPT88n7lGMiIiAr69vldsUFhZWmtsagOp8IW/VIX33xhtv4NKlS/jyyy9VyxITEzF06FBcvXpVxGSky27evInAwEC0bt2a/w7rCLUPs0+fPh0//vgjNmzYgOTkZEybNg3p6emqw+azZ8/GqFGjVOsHBgZiz549WLVqFa5evYoTJ05g8uTJ6NSpE5o1a6a5n4RIourVq4eGDRuqvp45cyZ27NiBNm3a4OOPP8a9e/fEC0c6qVGjRjh8+DBSU1Px119/iR2HNEDtMh86dCiWLVuGhQsXwt3dHVFRUQgLC4OtrS0AICsrq9I952PGjMHSpUvxww8/wM3NDYMHD0br1q2xZ88ezf0URDrkq6++Qq9evVBSUoJvv/0WrVq1wooVK/gMddIYY2NjdOvWDQBvUdMVfNAKkRYSBAHh4eGYMWMGkpKSAAAuLi749ttv0a9fP57npBe2dOlSfPTRR+jduzfCw8PFjkNV4INWiCROJpOhb9++OH/+PFatWoXGjRvj77//xhtvvIGAgABcuHBB7IgkcRXzhURGRvJOCh3AMifSYo/PJDdz5kwYGRnhzz//hLu7O95//33cunVL7IgkUW3btoW1tTWKioo4tasOYJkTSYCFhQW+/vpr/P333xg8eDAEQcCPP/4IJycnhIaGih2PJIhTu+oWljmRhNjb22PHjh04fvw4vLy8kJ+fDwcHB7FjkUT169cP3bp1Q5s2bcSOQi+IF8ARSZRSqcTx48fRtWtX1bINGzagffv28PLyEjEZEWmCOt3HMifSEWlpaWjTpg1KSkpw7tw5uLu7ix2JiF6AOt2n1nSuRKS9TExMMGTIEGRnZ6NDhw6q5Zyyk54nJycHV69eRadOncSOQjXEc+ZEOsLa2hqbN2/G77//rirvu3fvwtPTE9u3b+e0nVSlmJgYvPzyyxg4cCB/RySMZU6kY4yMjFT/vXTpUsTHx2PYsGHo2rUr4uLiRExG2qhjx44wMjJCZmYm/v77b7HjPFdWfhbe3f0uWv/QGvIFckwNnyp2JK3AMifSYXPmzMGCBQtgZmaG48ePw9vbG++99x6ysrLEjkZawtTUFP7+/gDwxEO0tFFxeTGamDXBHP856NC0w/M30BMscyIdZmZmhrlz5yIlJQUjR46EIAjYtGkTnJ2dERwczJm/CADQq1cvANpR5mvOrkHzpc2hFJSVlvcP7Y/R+0bDrqEdlvddjlEdRsHC2EKklNqHZU6kB2xsbLB582bExsaic+fOePDgAT799FO4urpiz549PFeq5yomjzl69ChKSko08p5FZUVYEbsCXx3/CtkPsqu93eC2g5FTmIOjaUdVy+49vIc/rvyB4e2GaySbLmKZE+mRTp06ISYmBj///DOaNWuGtLQ0vP3223jttdc437sea9++PZo0aYKCggKcOnVKI+/ZP7Q/JodPxuzDs+Gz3ge5RbnV2s7S1BJ9WvXB1otbVct2Ju2EpaklXrN/TSPZdBHLnEjPyOVyjBgxAikpKfjss89gYmKCo0ePomPHjpg/f77Y8UgEcrkcPXv2BKCZQ+15xXmIuPq/97l2/xrisqp/8eXwdsOxO3k3isuKAQBbLm7BsLbDYCA3eOFsukqryzwkJASurq7w9vYWOwqRzqlfvz4+//xzJCcnY9CgQVAqlWjVqpXYsUgk48ePx8aNG/Hvf//7hd+rvlF9NK3fVPW1odwQtha21d4+0DkQSkGJA6kHkJGbgejr0RjRfsQL59JlnAGOiAAAp0+fhpeXF+TyR3/j79+/H8bGxujdu7fIyUiKzmWdw5TwKXhQ8gBz/OdgkOsgtbYfs28M8kvy0bl5Z2yI34C/P3zytrnum7rDvak7lvVZpqHU2oUzwBGR2h6f/Ss/Px/jx49HdnY2du7ciUGD1PuHmMjD2gPR70XXePvh7YYjMDQQibcTnxiVJ2QnAAAelDzAncI7SMhOgJGBEVybuL5IZEnjyJyInpCfn4958+YhPDwc8fHxMDY2FjsS1YH09HTs2rULpqamGjnc/iLKleVo8V0LZD3IwpXJV+Dw0v+eDihb8OT0xLYWtrg29VodJqx9fNAKEWlEcXGxqshLS0vRt29fjBw5EiNHjlQdjifdsX//frz55pto1aoVUlNTxY6j99TpPv7fSERP9fiI/KeffsLhw4cxZswY+Pj4IDY2VsRkVBu6desGAwMDXL58GdevXxc7DqmBZU5E1TJy5Eh8/fXXqF+/Pk6fPo0uXbpg9OjRnBpWh1hYWKiundCG2eCo+ljmRFQtxsbGmDlzJi5duoQxY8YAADZv3gxnZ2csXrwYxcXF4gYkjaiY2vXPP/8UOQmpg2VORGqxtrbGxo0bcfr0adXUsJ988gnc3Nzw+++/c2pYiaso88OHD0OpVD5nbdIWLHMiqhFvb2/ExMRg06ZNaNq0KS5fvozAwEC8/vrrSElJETse1VDnzp1Rv3595OTk4Pz582LHoWpimRNRjcnlcowePRopKSmYOXMmDA0NcfDgQbRr1w5z584VOx7VgKGhIbp37w5jY2NJPN+cHmGZE9ELMzc3x9dff43ExES8/vrrKC0tFTsSvYBVq1bh3r17eOedd8SOQtXE+8yJSOPCw8Ph7++PevXqAQDi4+NRWlpaaZY5Ino23mdORKLq06ePqsiVSiXef/99dO7cGRs3bhQ5GamLF8FJA8uciGpVYWEh3NzcYGFhgX79+okdh6opNDQUHTp0wH/+8x+xo1A1sMyJqFbVr18fmzZtQmpqKqysrFTLp06divDwcBGT0bOUlJTgwoULOHTokNhRqBpY5kRUJ5o0aaL67/DwcCxfvhx9+/ZF//79cfnyZRGTUVVee+01AEBcXBzu3bsnchp6HpY5EdU5Hx8fTJ8+HQqFAr/99hvatm2L2bNn48GDB2JHo/9nY2MDFxcXCIKAI0eOiB2HnoNlTkR1zsLCAkuWLMGFCxfQq1cvlJSU4KuvvoKLiwu2bdvGWeS0RM+ePQE8mg2OtBvLnIhE06ZNG/zxxx/Yt28f7O3tkZmZiXfeeQfdunVDfHy82PH0XkWZc5527afVZR4SEgJXV1d4e3uLHYWIaolMJsObb76JxMRELFy4EKampoiOjoanpyeCgoKQk5MjdkS91b17dxgYGCA1NZWPRNVynDSGiLRKRkYGPv74Y2zfvh0A8NJLL+Hzzz/HhAkTIJPJRE6nfwYNGgQzMzP85z//gZOTk9hx9Io63ccyJyKtFBUVhUmTJuHChQsYOnQotm3bJnYkojqlTvcp6igTEZFaunbtiri4OKxduxZvvPGGanlWVhZKS0vRsmVLEdMRaRetPmdORPpNoVBgwoQJlYp7+vTpcHFxwS+//CJiMv2iVCqRkJCAW7duiR2FnoJlTkSSUVRUhJs3b6K4uBhubm5ix9EbQ4YMQceOHXmqQ4uxzIlIMkxMTHDs2DHExsbC3d1dtXz9+vVISkoSL5iOq3jaHW9R014scyKSFJlMBi8vL9XXycnJCAoKQvv27TF16lTcv39fvHA6quJ+88jISJSVlYmchqrCMiciSTMzM0NgYCDKy8uxfPlyODk5Ye3atSgvLxc7ms5wd3eHpaUl8vPzcebMGbHjUBVY5kQkaba2ttizZw8iIiLg6uqKnJwcjB8/Ht7e3jhx4oTY8XSCXC5Hjx49AHBqV23FMicindCzZ08kJCRg2bJlsLCwQHx8PF555RUMHz4cmZmZYseTvIqnqPG8uXZimRORzjA0NMSUKVNw6dIljBs3DjKZDFu3boWzszMWLVqEoqIisSNKVsV585iYGBQUFIichv6JZU5EOufll1/GunXrcObMGfj5+aGwsBCfffYZXF1dsW/fPj6VrQYcHR3x5ZdfIjw8HEZGRmLHoX/gdK5EpNMEQcDWrVsxc+ZM3Lx5E56enjh9+jTkco5lSLup0338bSYinSaTyTB8+HCkpKTg008/xfLly1VFXlhYiHv37omckOjFscyJSC/Ur18fixYtgp+fn2rZV199BScnJ85sVk2CIOD333/HtGnT+EeQlmGZE5FeKi8vx8GDB3H37l0YGhqKHUcSZDIZPv74YyxbtgzHjh0TOw49hmVORHrJwMAAJ0+exI4dOzBw4EDV8oiICFy/fl3EZNqt4hY13m+uXVjmRKS3FAoFBg8eDJlMBgC4d+8e3nnnHbi4uGDu3Lm8BasKLHPtxDInIvp/ubm5aNeuHYqKivD555+jdevW2LJlC29le0z37t0hl8vx999/czIeLcIyJyL6f3Z2djhy5Ah27doFOzs7ZGZmYsSIEfDz88PZs2fFjqcVXnrpJXh4eAAAjhw5InIaqqDVZR4SEgJXV1d4e3uLHYWI9IRMJsPbb7+N5ORkLFq0CPXq1cPJkyfh7e2N9957Dzdv3hQ7ougq5mlnmWsPrS7ziRMnIikpiU/pIaI6Z2Jigk8//RQpKSkYOXIkAGDTpk1wdnZGcHCwXk8NW3HePDk5WeQkVIEzwBERVUNsbCymTp2KU6dOAQDs7e3xzTffYODAgaoL6PRFUVERMjIy0KpVK7372euSOt3HMiciqialUonQ0FB88sknyMzMRNOmTXH58mXUq1dP7Gikg9TpPkUdZSIikjy5XI7hw4djwIABWLx4MZydnVVFrlQqcffuXTRp0kTklKSPtPqcORGRNqpXrx4WLFiA4cOHq5aFhobC0dERK1asEDFZ3bl16xYGDx6Mtm3b8tY9LcAyJyLSgN27dyM/Px8PHjwQO0qdeOmll3DgwAEkJSUhMTFR7Dh6j2VORKQBu3btQmhoKKZNm6Zadvr0aZw7d07EVLXHyMgIr7zyCgDOBqcNWOZERBogl8sxbNgwmJiYAADKysowduxYeHl5YcyYMTo5W1rFLWpHjx4VOQmxzImIakFBQQE6dOgAQRDw008/wdnZGQsWLNCp+d4rJo85duwYysrKRE6j31jmRES1wMLCAr/88gtOnToFX19fFBYWYv78+WjdujU2b94MpVIpdsQX5uHhobp1Kj4+Xuw4eo1lTkRUizp37ozjx49j+/btqvneR48ejU6dOiEyMlLseC/EwMAA3bt3B8Dz5mJjmRMR1TKZTIYhQ4YgOTkZX331FRo0aIC4uDh0794db731FlJTU8WOWGO9e/dGly5d0LRpU7Gj6DXOAEdEVMdu376N+fPnY+3atSgvL4dCocDEiRMxd+5cWFpaih2PtIQ63ceRORFRHXv55ZexcuVKXLhwAf369UNZWRlWr16NvLw8saORRHE6VyIikbi6uuLAgQOIiIhASkoK7OzsVN87efIkunTpIpkHmeTm5uLOnTto1aqV2FH0Uo1G5itXroS9vT1MTEzg6emJ6OjoZ65fXFyMOXPmwNbWFsbGxnB0dMSGDRtqFJiISNf06tULH374oerr2NhY+Pr6wt/fHyUlJSImq56dO3fC0tISH3zwgdhR9JbaI/Pt27dj6tSpWLlyJfz8/LBmzRr07dsXSUlJaNmyZZXbDBkyBLdu3cL69evRqlUr3L59m/ckEhE9RUpKCszMzODk5AQjIyOx4zxX+/btoVQqERMTg6KiItXEOVR31L4ArnPnzvDw8MCqVatUy9q0aYMBAwYgODj4ifXDw8MxbNgwXL16tcYXdvACOCLSN1lZWZDL5bCysgIApKamIiQkBJ999hkaN24scrrKBEGAjY0Nbt68iSNHjuDVV18VO5JOqLUL4EpKShAXF4eAgIBKywMCAhATE1PlNvv374eXlxcWL16M5s2bw9nZGTNmzMDDhw+f+jnFxcXIy8ur9CIi0ifW1taqIgeAWbNmYfny5XB0dMRXX331zH9D65pMJlMVeG1M7boneQ96/dwLTb5pAvNgc/is98Efl//Q+OdImVplnpOTg/Ly8kq/YABgZWWF7OzsKre5evUqjh8/jr/++gt79+7FsmXLsGvXLkycOPGpnxMcHAwLCwvVq0WLFurEJCLSOf/+97/h7u6OvLw8zJ49G87Ozti0aRPKy8vFjgYAqjKvjcljoq5HoZdDL4S9G4a4D+Lwqt2rCAwNRHwWZ51TEdSQmZkpABBiYmIqLf/iiy+E1q1bV7lNr169BBMTE+H+/fuqZbt37xZkMplQWFhY5TZFRUVCbm6u6pWRkSEAEHJzc9WJS0SkU8rLy4Wff/5ZaNmypQBAACC0b99eOHjwoKBUKkXNdvXqVQGAoFAohPz8fLW2XX1mtdBsSTOhXFleaXng1kBh1N5RVW7jGuIqLDi2oMZ5pSA3N7fa3afWyLxx48YwMDB4YhR++/btJ0brFaytrdG8eXNYWFiolrVp0waCIODGjRtVbmNsbAxzc/NKLyIifSeXyzFixAikpKTgm2++QcOGDXHhwgX07dsXPXv2xNmzZ0XLZm9vDzs7O5SVleHHvT+qte3gtoORU5iDo2n/O0R/7+E9/HHlDwxvN/yJ9ZWCEvnF+bA05QQ7FdQqcyMjI3h6eiIiIqLS8oiICPj6+la5jZ+fH27evIkHDx6oll26dAlyuRw2NjY1iExEpN9MTEwwY8YMXLlyBdOnT4eRkRGOHDkCb29vDBs2DFeuXBElV/O+zYHXgWkJ0zBy78hqb2dpaok+rfpg68WtqmU7k3bC0tQSr9m/9sT6S2KWoKC0AEPaDtFIbp2g7rB/27ZtgqGhobB+/XohKSlJmDp1qlCvXj3h2rVrgiAIwqxZs4SRI0eq1s/PzxdsbGyEQYMGCYmJiUJkZKTg5OQkjBs3rlYONRAR6Zu0tDRhxIgRgkwmEwAIhoaGwvfff1+3Ge6lCZiPSq+UnJRqb7/9r+2CRbCFUFRaJAiCIHTd2FWYenDqE+ttvbBVMFtkJkRcidBYdm1Va4fZAWDo0KFYtmwZFi5cCHd3d0RFRSEsLAy2trYAHt1OkZ6erlq/fv36iIiIwP379+Hl5YXhw4cjMDAQ33//vYb+HCEi0m92dnb4+eefER8fjz59+qC0tBQdOnSo0wwmChPI8L/Z6mSQwVRhWu3tA50DoRSUOJB6ABm5GYi+Ho0R7UdUWmf7X9sxdv9Y7Bi0Az0demosuy7gg1aIiHRMfHw8OnbsqPp6yZIlMDQ0xPjx42FsbFxrn/vdye/w0baPIFwR8OFbH2LF2BVqbT9m3xjkl+Sjc/PO2BC/AX9/+Lfqe6EXQ/Gv/f9C6NuhGOAyQMPJtZM63ce52YmIdMzjRZ6dnY25c+eisLAQ9vb2CAwMrLXPneYzDefXncdPB36CSRv1Z4Eb3m44AkMDkXg7sdKoPPRiKEbtG4XlfZaji00XZD94dBG2qcIUFiYWT3s7vcKnphER6bBGjRph6dKleOutt/DGG2+oll+/fh21cWC212u9ANRs8pge9j1gaWqJlLspeLfdu6rla+LWoExZholhE2G9xFr1mhI+RWO5pY6H2YmI9Exubi4cHR3h4uKC4OBg+Pv7a+y9MzMzYWNjA7lcjrt376Jhw4Yae299w+eZExHRU8XGxqKgoAAnTpxA165d8frrryM+XjOzqTVv3hxOTk5QKpWIiorSyHvS87HMiYj0TEBAAC5fvozx48fDwMAAYWFh8PDwwNChQ5GSkvLC71+b87RT1VjmRER6qHnz5li9ejWSk5Px7rvvQiaTYceOHXB1dcXYsWNx/fr1Gr83y7zuscyJiPSYk5MTtmzZgoSEBAQGBkKpVGLDhg1wdnbGpEmTnvoQrWepKPPExETk5uZqOjJVgWVORERo37499u/fj5MnT6JHjx4oKSnBDz/8AAcHB3zyySfIz8+v9ntZWVnhyJEjuHv3bqXnclDtYZkTEZFKly5dcPjwYRw+fBg+Pj54+PAhfv75ZygU6k1L8uqrr/LuozrESWOIiOgJPXr0wIkTJxAWFoaioiKYmj6amrW8vByrVq3C6NGj0aBBA5FTUgWOzImIqEoymQyvv/463n77bdWyHTt2YNKkSfD09IRSqXzqtkqlErNnz4avry/u3r2r8WzH04/Db4MfGi1uBNNFpnD5wQXfnfxO458jFRyZExFRtZmbm8PJyQmjR4+GXP5oPCgIQqXRO/Do2ev79+9HUlISoqOjMWDAAI3mqGdYDx96f4j2Vu1Rz6gejqcfx/jfx6OeUT184PmBRj9LCjgyJyKianv99deRlJSEjz76SLUsLCwMDg4OWL58OR4+fKha3r17dwDAsWPH1P6cNWfXoPnS5lAKlUf//UP7Y/S+0eho3RHvtHsHbV9uC7uGdhjRfgR6O/ZGdHp0jX4uqWOZExGRWhQKBUxM/vcglfXr1yM7OxtTp06Fo6MjVqxYgaKiIlWZ1+R+88FtByOnMAdH0/637b2H9/DHlT8wvN3wJ9aPz4pHTEYMutl2U/8H0gFaXeYhISFwdXWFt7e32FGIiOgptm3bhjVr1qBly5bIysrC5MmT4ejoiPjER1PEXrhwAa+uehX5xdW/vc3S1BJ9WvXB1otbVct2Ju2EpaklXrN/TbXMZqkNjL8whtc6L0z0nohxHuM094NJCB+0QkREGlFSUoKNGzdi0aJFyMjIeLRQDkAJ4G1g9r9n48vXvqz2++1I3IEPfvsAt2bcgrHCGN02dYNHUw981+d/F7ql3UvDg5IHOHXjFGYdnoUf+v6Ad9q9o9kfTCR80AoREdU5IyMjjB8/HqmpqVi1ahVMG5k+KnIA2A8cDT2KwsLCar9foHMglIISB1IPICM3A9HXoys95xwA7F+yRzurdnjf831M6zIN8yPna+4HkhCWORERaZSxsTGCgoKwPWo7ZF4yQAagFDi1/hTs7e2xbNmyar2PqaEpBrYZiC0XtyD0r1A4N3KGZzPPp64vCAKKy4o180NIDG9NIyKiWhHoGoiE/QlIuJmAzBOZWLdsHdLS0nDx4sVqv8fwdsMRGBqIxNuJlUblIadD0NKiJVwauwB4dN/5tye/xaROkzT+c0gBz5kTEVGdKC0txZYtW+Dv7w9HR0cAwF9//YUdO3Zg6tSpsLS0fGKbcmU5WnzXAlkPsnBl8hU4vOQAAFgRuwJr4tYg7X4aFHIFHF9yxPse72O813jIZbpx0Fmd7mOZExFRrRMEAffu3XuisIcNG4bt27djxIgR+Pnnn0VKp514ARwREWmNkydPonnz5ujRo8cT3xsyZAg6duyIGTNmqJZlZma+0PPU9RHLnIiIapW9vT2ysrJw4cIF3Lt3r9L3Bg4ciLi4OHTo0EG1bP78+WjVqhXee+89pKSk1HVcSWKZExFRrWratClat24NQRAQHf3kdKsymUz130qlEjdv3kRZWRk2bdqENm3aYPDgwTh37lxdRpYcljkREdW66k7tKpfLceDAAZw8eRL9+/eHIAjYtWsXPD090bt3bxw7dgwSuNSrzrHMiYio1nXr9mjO9MjIyGqt36VLF/z666+4ePEihg8fDgMDAxw6dAivvvoqfHx8sHfv3mc+glXfsMyJiKjWVZR5QkIC7t+/X+3t3Nzc8MsvvyA1NRUTJkyAiYkJYmNjMXDgQLi6umL9+vUoLtbPiWIexzInIqJa16xZMzg7Oz/1vPnz2NvbIyQkBNeuXcOnn34KCwsLpKSkYNy4cRg6dGgtJJYWljkREdWJ9957Dx999BHs7e1r/B5WVlZYtGgR0tPT8e2336J58+YYM2aM6vu5ubnIzMzUQFpp4aQxREQkWSUlJVAoFJDLH41NFy1ahAULFmDu3Ln47LPPRE73YjhpDBER6QUjIyNVkQOPzsmXlpZWGv2XlZXp/BXwLHMiIqozBQUFOHz4MC5dulQr779z507ExsZiyJAhqmUrVqyAp6cntmzZgtLS0lr5XLGxzImIqM5MmjQJPXv2xMaNG2vtMzp16gRDQ0MAj+aEX7duHeLj4zFixAjY29tj8eLFal1RLwUscyIiqjNdu3YFUP37zV+UTCZDdHQ0vvjiC1hZWSEzMxOffPIJbGxsMHnyZFy5cqVOctQ2rS7zkJAQuLq6wtvbW+woRESkARX3m585cwYFBQV18pmNGjXCnDlzcP36dWzcuBFubm4oKCjAihUr4OTkhLfeeguRkZGSPq/Oq9mJiKjOCIIAW1tbZGRkICIiAj179hQlw+HDh7F06VIcPHhQtdzd3R1Tp07FsGHDYGxsXOe5/olXsxMRkVaSyWR1fqi9qgw9e/ZEWFgYkpKSMH78eJiamiIhIQFjxoyBj4+P5EbpLHMiIqpT6s7TXpvatGmD1atXIyMjA8HBwWjevDkGDhyoepJbWVmZJJ7YxsPsRERUpy5duoTWrVvDyMgI9+/fh6mpqdiRVEpLS1FaWgozMzMAwN69ezFw4EAEBgZi//79dZpFne5T1FEmIiIiAICTkxNWrVoFHx8frTg3/ThDQ0PVbW0AkJqaCkNDQ7i5uYmY6vk4MiciInqG7OxsKBQKNG7cuE4/lyNzIiIiDWnatKnYEZ6LF8AREVGdKykpwfr16zF27FidnWK1LrHMiYiozikUCsycORMbNmxAXFyc2HEkj2VORER1Ti6Xw9/fHwAQHR0tchrpY5kTEZEoKiaPiYqKEjmJ9LHMiYhIFBVlHh0djfLycpHTSBvLnIiIROHu7o769esjNzcXf/31l9hxJI1lTkREolAoFPDz8wPAQ+0vimVORESiqTjUfvXqVZGTSBtngCMiItHcvXsXMpkMlpaWYkfROpwBjoiIJKFRo0ZiR9AJPMxOREQkcSxzIiIS1eHDh9GtWzd88MEHYkeRLB5mJyIiUSmVSkRFReH69etiR5EsrR6Zh4SEwNXVFd7e3mJHISKiWuLj4wMDAwNcv34dGRkZYseRJK0u84kTJyIpKQlnzpwROwoREdWS+vXrw8PDAwDnaa8prS5zIiLSDxUPXeHkMTXDMiciItHxCWovhmVORESie+WVVwAASUlJuHPnjshppIdXsxMRkegaN26MV155BS+99BJyc3PRpEkTsSNJCsuciIi0Ag+x1xwPsxMREUkcy5yIiLRKeno6ioqKxI4hKSxzIiLSGl27doWtrS0PuauJZU5ERFrD1tYWAM+fq4tlTkREWqPifvPjx4+LnERaWOZERKQ1Ku43P3XqFEpLS0VOIx0scyIi0houLi6wtLTEw4cPce7cObHjSAbLnIiItIZcLleNznnevPpY5kREpFV43lx9NSrzlStXwt7eHiYmJvD09Kz2X08nTpyAQqGAu7t7TT6WiIj0QO/evfHhhx9i3LhxYkeRDJkgCII6G2zfvh0jR47EypUr4efnhzVr1uDHH39EUlISWrZs+dTtcnNz4eHhgVatWuHWrVtISEio9mfm5eXBwsICubm5MDc3VycuERGRJKnTfWqXeefOneHh4YFVq1aplrVp0wYDBgxAcHDwU7cbNmwYnJycYGBggH379rHMiYiInkGd7lPrMHtJSQni4uIQEBBQaXlAQABiYmKeut3GjRtx5coVzJs3r1qfU1xcjLy8vEovIiLSHw8fPkRkZCR+/fVXsaNIglplnpOTg/LyclhZWVVabmVlhezs7Cq3SU1NxaxZs7BlyxYoFNV7SFtwcDAsLCxUrxYtWqgTk4iIJO7EiRPo3r07pkyZInYUSajRBXAymazS14IgPLEMAMrLy/Huu+9iwYIFcHZ2rvb7z549G7m5uapXRkZGTWISEZFEde7cGQYGBrh+/Tpu3Lghdhytp1aZN27cGAYGBk+Mwm/fvv3EaB0A8vPzcfbsWXz44YdQKBRQKBRYuHAhzp8/D4VCgSNHjlT5OcbGxjA3N6/0IiIi/dGgQQPVnU8nTpwQN4wEqFXmRkZG8PT0RERERKXlERER8PX1fWJ9c3NzXLx4EQkJCapXUFAQWrdujYSEBHTu3PnF0hMRkc6qmDyG95s/X/VOYj9m+vTpGDlyJLy8vODj44O1a9ciPT0dQUFBAB4dIs/MzMTmzZshl8vh5uZWafuXX34ZJiYmTywnIiJ63CuvvILly5dzJrhqULvMhw4dirt372LhwoXIysqCm5sbwsLCVI+ty8rKQnp6usaDEhGRfvHz8wMAXLx4Ebm5ubCwsBA5kfZS+z5zMfA+cyIi/eTo6IirV68iPDwcvXv3FjtOnVKn+9QemRMREdWVkJAQNGrUiNOAPwfLnIiItFafPn3EjiAJfGoaERGRxLHMiYhIq+3atQvvv/++Ws/00Dc8zE5ERFrtl19+wa+//orWrVvz3PlTcGRORERareIWNc4E93QscyIi0mqPl7kE7qYWBcuciIi0mqenJ4yNjXHnzh1cvnxZ7DhaiWVORERazdjYGF5eXgB4qP1pWOZERKT1eN782VjmRESk9SrK/ObNmyIn0U68NY2IiLRer169cPv2bTRp0kTsKFqJZU5ERFrP1NQUpqamYsfQWjzMTkREJHFaXeYhISFwdXWFt7e32FGIiEhk58+fR8+ePfXuUajVweeZExGRJFy+fBlOTk4wMjJCbm4uTExMxI5Uq9TpPq0emRMREVVwdHSElZUVSkpKEBcXJ3YcrcIyJyIiSZDJZPD19QUAxMTEiJxGu7DMiYhIMirKnJPHVMYyJyIiyaiYPCYmJoYPXXkMy5yIiCTDw8MDRkZGuHPnDq5cuSJ2HK3BSWOIiEgyjI2N8dprr0GpVKKwsFDsOFqDZU5ERJISFhYmdgStw8PsREREEscyJyIiScrOzsbDhw/FjqEVWOZERCQ5vXr1grW1NY4ePSp2FK3AMiciIslp3rw5AN5vXoFlTkREklNxvznL/BGWORERSU5FmZ85cwalpaUipxEfy5yIiCTHxcUFDRs2RGFhIS5cuCB2HNGxzImISHLkcjl8fHwA8KErAMuciIgkqqLMT548KXIS8XEGOCIikqTevXsjKysLvXv3FjuK6FjmREQkSZ06dUKnTp3EjqEVtPowe0hICFxdXeHt7S12FCIiIq0lEyTwQNi8vDxYWFggNzcX5ubmYschIiItUVxcjHPnzqG4uBjdu3cXO45GqdN9Wj0yJyIiepZdu3bB19cXs2bNEjuKqFjmREQkWb6+vgCAc+fO6fVDV1jmREQkWXZ2dmjatClKS0tx9uxZseOIhmVORESSJZPJVKNzfb7fnGVORESSVlHm+jwTHMuciIgk7fGZ4CRwg1atYJkTEZGkeXh4wNDQELdv30ZaWprYcUTBGeCIiEjSTExMsH79ejg4OMDGxkbsOKJgmRMRkeSNHDlS7Aii4mF2IiIiiWOZExGR5CmVSmzZsgUffvghCgoKxI5T51jmREQkeTKZDDNnzkRISIheTh7DMiciIsl7fPIYfbzfnGVOREQ64fH7zfUNy5yIiHTC49O66tvkMSxzIiLSCR07doSRkRFycnJw+fJlsePUKZY5ERHpBGNjY3h5eQHQv0PtLHMiItIZXbp0AQAkJyeLnKRuyQQJnFjIy8uDhYUFcnNzYW5uLnYcIiLSUpmZmZDL5bC2thY7ygtTp/u0ejrXkJAQhISEoLy8XOwoREQkAc2bNxc7gig4MiciItJC6nQfz5kTEZFO2bVrF/r164eVK1eKHaXOsMyJiEinXLt2DQcPHkRERITYUeoMy5yIiHTK4zPBSeBMskawzImISKd4eHhAoVDg1q1buHbtmthx6gTLnIiIdIqpqSk6duwIADh16pTIaeoGy5yIiHROxaF2ljkREZFE6dsT1FjmRESkc7p06YJ69erB0tJSLy6C0+oZ4IiIiGrC1tYW9+/fh0KhHzXHkTkREekcmUymN0UOsMyJiEjHPXz4UOwItY5lTkREOunvv/+Gs7MzXFxcxI5S6/TnGAQREekVGxsbXLlyBUqlEllZWTrxWNSn4ciciIh0Uv369eHm5gYAiI2NFTlN7apRma9cuRL29vYwMTGBp6cnoqOjn7runj170KtXLzRp0gTm5ubw8fHBH3/8UePARERE1dW5c2cAun+/udplvn37dkydOhVz5sxBfHw8/P390bdvX6Snp1e5flRUFHr16oWwsDDExcXh1VdfRWBgIOLj4184PBER0bN06dIFgO6PzGWCmnfTd+7cGR4eHli1apVqWZs2bTBgwAAEBwdX6z3atm2LoUOHYu7cudVaX50HtBMREVVISkpC27ZtYWZmhtzcXEndrqZO96k1Mi8pKUFcXBwCAgIqLQ8ICEBMTEy13kOpVCI/Px+WlpZPXae4uBh5eXmVXkREROpycXGBubk5CgsLcfHiRbHj1Bq1/kTJyclBeXk5rKysKi23srJCdnZ2td5jyZIlKCgowJAhQ566TnBwMBYsWKBONCIioifI5XK88847KC8vh4mJidhxak2NjjfIZLJKXwuC8MSyqoSGhmL+/Pn49ddf8fLLLz91vdmzZ2P69Omqr/Py8tCiRYuaRCUiIj23evVqsSPUOrXKvHHjxjAwMHhiFH779u0nRuv/tH37dowdOxY7d+5Ez549n7musbExjI2N1YlGRESkt9Q6Z25kZARPT09ERERUWh4REQFfX9+nbhcaGooxY8Zg69ateP3112uWlIiIqIZKS0sRFxeHgoICsaPUCrVvTZs+fTp+/PFHbNiwAcnJyZg2bRrS09MRFBQE4NEh8lGjRqnWDw0NxahRo7BkyRJ06dIF2dnZyM7ORm5uruZ+CiIiomdwd3eHl5cXTpw4IXaUWqF2mQ8dOhTLli3DwoUL4e7ujqioKISFhcHW1hYAkJWVVeme8zVr1qCsrAwTJ06EtbW16jVlyhTN/RRERETP0KFDBwDA6dOnRU5SO9S+z1wMvM+ciIhexPLlyzF16lS88cYb+O2338SOUy21dp85ERGRFFVM6xobGwsJjGHVxjInIiKd17FjRxgaGuLOnTu4du2a2HE0jmVOREQ6z9jYGO7u7gCAU6dOiRumFrDMiYhILzx+qF3XSGfGeSIiohcwaNAgNGvWDL169RI7isbxanYiIiItxKvZiYiI9AjLnIiI9EZWVhZ27NiB48ePix1Fo1jmRESkN9auXYuhQ4fq3JPUWOZERKQ3Kq5oP3PmjMhJNItlTkREesPb2xsAcOnSJdy7d0/kNJrDMiciIr3RqFEjODo6AtCt0TnLnIiI9EqnTp0A6NYT1FjmRESkV1jmdSwkJASurq6qcxxEREQvqqLMdekJapwBjoiI9EpRURF+++03dOrUCS1btoRMJhM7UpXU6T7OzU5ERHrFxMQEgwcPFjuGRmn1YXYiIiJ6Po7MiYhI79y8eRM//fQTHjx4gEWLFokd54XxnDkREemd5ORkuLq6wtTUFHl5eVAotG9sy6emERERPUPr1q1hbm6Ohw8fIjExUew4L4xlTkREekcul6tue46NjRU5zYtjmRMRkV6qKHNdmNaVZU5ERHqJZU5ERCRxFTPB/fXXXygsLBQ5zYthmRMRkV5q3rw5mjZtCoVCgdTUVLHjvBDtuxafiIioDshkMpw4cQItWrSAoaGh2HFeCMuciIj0loODg9gRNIKH2YmIiCSOZU5ERHqrvLwc48aNQ/v27XH37l2x49QYy5yIiPSWgYEBoqKicPHiRUnfosYyJyIivVZxixrLnIiISKIqyvz06dMiJ6k5ljkREem1ijKPjY2FBB4kWiWtLvOQkBC4urqqptwjIiLSNHd3dygUCty5cwfp6elix6kRrS7ziRMnIikpSdLnMYiISLuZmJigffv2AKR73pyTxhARkd7z9vbGgwcPUFZWJnaUGmGZExGR3lu5ciXkcq0+WP1M0k1ORESkIVIucoBlTkREpFJeXo6SkhKxY6iNZU5ERARg0qRJaNiwIXbu3Cl2FLWxzImIiPDoUPuDBw8keUU7y5yIiAhQzWnCMiciIpKoijKPj4+X3C1qLHMiIiIATk5OMDc3x8OHD5GYmCh2HLWwzImIiPDonLmXlxcA6R1qZ5kTERH9v4pD7VJ7ghpngCMiIvp/3bp1w4ULF1QjdKmQCRJ43lteXh4sLCyQm5sLc3NzseMQERHVOnW6j4fZiYiIJI5lTkRE9A/Z2dm4fv262DGqjWVORET0mK+//hrW1taYP3++2FGqjWVORET0GFdXVwDSuj2NZU5ERPSYiivZk5OTUVBQIHKa6mGZExERPcba2hrNmjWDUqlEQkKC2HGqRavLPCQkBK6urqqb+ImIiOqC1GaC0+oynzhxIpKSkiSzM4mISDdUlPnZs2dFTlI9Wl3mREREYpDayJzTuRIREf1Dp06dMGnSJHh7e0MQBMhkMrEjPROncyUiItJCnM6ViIhIj7DMiYiIqlBYWIjjx48jLCxM7CjPxTInIiKqwsmTJ+Hv749JkyaJHeW5WOZERERV8PDwAABcvXoV//3vf0VO82wscyIioiq89NJLcHBwAACcO3dO5DTPxjInIiJ6ior7zePi4kRO8mwscyIioqfw9PQEoP0zwbHMiYiInoIjcyIiIomruAguLS1Nqy+C43SuRERET9GwYUNs2LABrVu3RoMGDcSO81QscyIiomd47733xI7wXDU6zL5y5UrY29vDxMQEnp6eiI6Ofub6kZGR8PT0hImJCRwcHLB69eoahSUiIqInqV3m27dvx9SpUzFnzhzEx8fD398fffv2RXp6epXrp6WloV+/fvD390d8fDw+/fRTTJ48Gbt3737h8ERERLWtoKAAP/30Ez777DOxozyV2k9N69y5Mzw8PLBq1SrVsjZt2mDAgAEIDg5+Yv1PPvkE+/fvR3JysmpZUFAQzp8/j5MnT1brM/nUNCIiEktFBwHA7du30aRJkzr9XI0/Na2kpARxcXEICAiotDwgIAAxMTFVbnPy5Mkn1u/duzfOnj2L0tLSKrcpLi5GXl5epRcREZEYzM3N0bp1awBAYmKiyGmqplaZ5+TkoLy8HFZWVpWWW1lZITs7u8ptsrOzq1y/rKwMOTk5VW4THBwMCwsL1atFixbqxCQiItKoffv2ITc3F927dxc7SpVqdAGcTCar9LUgCE8se976VS2vMHv2bOTm5qpeGRkZNYlJRESkES4uLlp9mletW9MaN24MAwODJ0bht2/ffmL0XaFp06ZVrq9QKNCoUaMqtzE2NoaxsbE60YiIiPSWWiNzIyMjeHp6IiIiotLyiIgI+Pr6VrmNj4/PE+sfOnQIXl5eMDQ0VDMuERER/ZPah9mnT5+OH3/8ERs2bEBycjKmTZuG9PR0BAUFAXh0iHzUqFGq9YOCgnD9+nVMnz4dycnJ2LBhA9avX48ZM2Zo7qcgIiLSY2rPADd06FDcvXsXCxcuRFZWFtzc3BAWFgZbW1sAQFZWVqV7zu3t7REWFoZp06YhJCQEzZo1w/fff4+3335bcz8FERGRHlP7PnMx8D5zIiLSN+p0nyTmZq/4e4P3mxMRkb6o6LzqjLklUeb5+fkAwPvNiYhI7+Tn56tmoHsaSRxmVyqVuHnzJho0aFDlvel5eXlo0aIFMjIyNHoY3tvbG2fOnNHa99P0e3I/cj9q03tyP3I/atN7irEfBUFAfn4+mjVrBrn82derS2JkLpfLYWNj89z1zM3NNbqTDQwMtPr9aus9uR81g/tRM7gfNYP7UTPqej8+b0ReoUYzwOmLiRMnavX71dZ7ahr3o2ZwP2oG96NmcD9qhqYySuIw+/PwanfN4H7UDO5HzeB+1AzuR83Q9v2oEyNzY2NjzJs3j1PAviDuR83gftQM7kfN4H7UDG3fjzoxMiciItJnOjEyJyIi0mcscyIiIoljmRMREUkcy5yIiEjiJFPmK1euhL29PUxMTODp6Yno6Ohnrh8ZGQlPT0+YmJjAwcEBq1evrqOk2k2d/bhnzx706tULTZo0gbm5OXx8fPDHH3/UYVrtpe7vY4UTJ05AoVDA3d29dgNKhLr7sbi4GHPmzIGtrS2MjY3h6OiIDRs21FFa7aXuftyyZQs6dOgAMzMzWFtb47333sPdu3frKK12ioqKQmBgIJo1awaZTIZ9+/Y9dxut6hlBArZt2yYYGhoK69atE5KSkoQpU6YI9erVE65fv17l+levXhXMzMyEKVOmCElJScK6desEQ0NDYdeuXXWcXLuoux+nTJkifP3118Lp06eFS5cuCbNnzxYMDQ2Fc+fO1XFy7aLufqxw//59wcHBQQgICBA6dOhQN2G1WE32Y//+/YXOnTsLERERQlpamhAbGyucOHGiDlNrH3X3Y3R0tCCXy4Xly5cLV69eFaKjo4W2bdsKAwYMqOPk2iUsLEyYM2eOsHv3bgGAsHfv3meur209I4ky79SpkxAUFFRpmYuLizBr1qwq1585c6bg4uJSadn48eOFLl261FpGKVB3P1bF1dVVWLBggaajSUpN9+PQoUOFzz77TJg3bx7LXFB/Px48eFCwsLAQ7t69WxfxJEPd/fjNN98IDg4OlZZ9//33go2NTa1llJrqlLm29YzWH2YvKSlBXFwcAgICKi0PCAhATExMlducPHnyifV79+6Ns2fPorS0tNayarOa7Md/UiqVyM/Ph6WlZW1ElISa7seNGzfiypUrmDdvXm1HlISa7Mf9+/fDy8sLixcvRvPmzeHs7IwZM2bg4cOHdRFZK9VkP/r6+uLGjRsICwuDIAi4desWdu3ahddff70uIusMbesZrX/QSk5ODsrLy2FlZVVpuZWVFbKzs6vcJjs7u8r1y8rKkJOTA2tr61rLq61qsh//acmSJSgoKMCQIUNqI6Ik1GQ/pqamYtasWYiOjoZCofX/y9WJmuzHq1ev4vjx4zAxMcHevXuRk5ODCRMm4L///a/enjevyX709fXFli1bMHToUBQVFaGsrAz9+/fHihUr6iKyztC2ntH6kXmFfz76VBCEKh+H+qz1q1qub9TdjxVCQ0Mxf/58bN++HS+//HJtxZOM6u7H8vJyvPvuu1iwYAGcnZ3rKp5kqPP7qFQqIZPJsGXLFnTq1An9+vXD0qVLsWnTJr0enQPq7cekpCRMnjwZc+fORVxcHMLDw5GWloagoKC6iKpTtKlntH6Y0LhxYxgYGDzxV+bt27ef+KuoQtOmTatcX6FQoFGjRrWWVZvVZD9W2L59O8aOHYudO3eiZ8+etRlT66m7H/Pz83H27FnEx8fjww8/BPColARBgEKhwKFDh9CjR486ya5NavL7aG1tjebNm1d6JGSbNm0gCAJu3LgBJyenWs2sjWqyH4ODg+Hn54ePP/4YANC+fXvUq1cP/v7++OKLL/TyyGVNaFvPaP3I3MjICJ6enoiIiKi0PCIiAr6+vlVu4+Pj88T6hw4dgpeXFwwNDWstqzaryX4EHo3Ix4wZg61bt/KcGtTfj+bm5rh48SISEhJUr6CgILRu3RoJCQno3LlzXUXXKjX5ffTz88PNmzfx4MED1bJLly5BLpfDxsamVvNqq5rsx8LCQsjllf/pNzAwAPC/kSU9n9b1jCiX3amp4taL9evXC0lJScLUqVOFevXqCdeuXRMEQRBmzZoljBw5UrV+xS0D06ZNE5KSkoT169fz1jRB/f24detWQaFQCCEhIUJWVpbqdf/+fbF+BK2g7n78J17N/oi6+zE/P1+wsbERBg0aJCQmJgqRkZGCk5OTMG7cOLF+BK2g7n7cuHGjoFAohJUrVwpXrlwRjh8/Lnh5eQmdOnUS60fQCvn5+UJ8fLwQHx8vABCWLl0qxMfHq27x0/aekUSZC4IghISECLa2toKRkZHg4eEhREZGqr43evRooVu3bpXWP3bsmNCxY0fByMhIsLOzE1atWlXHibWTOvuxW7duAoAnXqNHj6774FpG3d/Hx7HM/0fd/ZicnCz07NlTMDU1FWxsbITp06cLhYWFdZxa+6i7H7///nvB1dVVMDU1FaytrYXhw4cLN27cqOPU2uXo0aPP/PdO23uGj0AlIiKSOK0/Z05ERETPxjInIiKSOJY5ERGRxLHMiYiIJI5lTkREJHEscyIiIoljmRMREUkcy5yIiEjiWOZEREQSxzInIiKSOJY5ERGRxLHMiYiIJO7/ANFrwXfFYlf5AAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "implicit_plot(f(x,y)==0,(x,0,1),(y,0,1),linestyle='--',color='black')\\\n", "+implicit_plot(g(x,y)==0,(x,0,1),(y,0,1),linestyle='-.',color='black')\\\n", "+points(puntos,color='green')\\\n", "+sum([text('v'+str(i),puntos[i]+vector([0.05,0]),color='green') for i in range(len(puntos)) ])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Ejercicio 1. \n", " \n", "a. Crear una función que reciba $F$, $x_0$ y $n$ y aplique $n$ pasos de Newton-Raphson partiendo de $x_0$.\n", " \n", "b. Aproximar soluciones de $e^{x+y}-x y=0$, $x^5-x-y=2$ contenidas en $[-3,3]\\times [-3,3]$. \n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def NR(F,x0,n):\n", " DF = F.diff()\n", " xn = copy(x0)\n", " for _ in range(n):\n", " xn = xn - DF(*xn)\\F(*xn)\n", " return xn" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "F(x,y) = ( exp(x+y)-x*y , x^5-x-y-2 )" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0 = vector(RDF,[-1,-1])\n", "implicit_plot(F(x,y)[0],(x,-3,3),(y,-3,3)) + implicit_plot(F(x,y)[1],(x,-3,3),(y,-3,3),color='red')\\\n", "+ line([NR(F,x0,k) for k in range(6)],color='green')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cálculo de extremos, tangentes, etc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "El método de Newton-Raphson está diseñado para determinar los ceros de una función de $\\mathbb{R}^n\\to\\mathbb{R}^n$, pero se puede aplicar a cualquier problema que sea equivalente. Por ejmplo, determinar el mínimo de una función de clase 1 de $\\mathbb{R}^n\\to\\mathbb{R}$, ya que este se alcanzará en un extremo local (o en el borde) y el método de Newton-Raphson permite encontrar los ceros de la derivada y por tanto reducir el problema, bajo ciertas condiciones, a evaluar la función en un número finito de puntos. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Por ejemplo, calculemos el máximo y el mínimo de $F(x,y)=e^{x^2+y^2}+x - 2y$ para $-1\\leq x\\leq 1$ y $-1\\leq y\\leq 1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comenzaremos calculando y representando la derivada de $F$ en dicha región." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G(x,y) = exp(x^2+y^2)+x-2*y\n", "F = G.diff()\n", "implicit_plot(F(x,y)[0],(x,-1,1),(y,-1,1))+implicit_plot(F(x,y)[1],(x,-1,1),(y,-1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Si alguno de los extremos se alcanza en el interior, será en el punto de intersección de ambas curvas, que podemos calcular con Newton-Raphson." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.06688023968137236, (-0.30961045795161296, 0.6192209159032259))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v0 = vector(RDF,[-.3,.6])\n", "DF = F.diff()\n", "v1 = v0 + DF(*v0)\\(-F(*v0))\n", "v2 = v1 + DF(*v1)\\(-F(*v1))\n", "v3 = v2 + DF(*v2)\\(-F(*v2))\n", "G(*v3),v3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora basta estudiar la función en los bordes y tendríamos los dos extremos:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(G(-1,y),(y,-1,1))+plot(G(1,y),(y,-1,1))+plot(G(x,-1),(x,-1,1))+plot(G(x,1),(y,-1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Ejercicio 2. \n", " \n", "a. Aproximar los extremos de la función $G(x,y) = e^{x^2+y^2} +x -y$ para $-1\\leq x\\leq 1$ y $-1\\leq y\\leq 1$.\n", "\n", "b. Aproximar el mínimo de $f(x,y)=x^4+y^4-x^3 y+x^2 y^2+x-y-1$\n", "mediante 5 pasos del método de Newton-Raphson. Elegir un punto inicial conveniente.\n", "\n", "c. Calcular los puntos en los que la distancia entre las gráficas de $f(x)=e^{x^2}$ y $f(x)=\\sin(x)$ sea mínima.\n", " \n", "d. Calcula la distancia entre las gráficas de las curvas paramétricas\n", "$$t\\to ((1+\\sin(t))\\cos(t),(1+\\sin(t))\\sin(t)),$$ $$t\\to (3+\\cos(t),2+\\sin(t)),$$ \n", "con $t\\in[0,2\\pi]$.\n", " \n", "e. Calcular una tangente común a las curvas paramétricas \n", "$$t\\to ((1+\\sin(t))\\cos(t),(1+\\sin(t))\\sin(t)),$$ $$t\\to (3+\\cos(t),2+\\sin(t)),$$ \n", "con $t\\in[0,2\\pi]$.\n", "
" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G(x,y) = exp(x^2+y^2)+x-y\n", "contour_plot(G(x,y),(x,-1,1),(y,-1,1),labels=true,contours=[0.5, 0.6 .. 11],fill=false)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F = G.diff()\n", "implicit_plot(F(x,y)[0],(x,-1,1),(y,-1,1))+implicit_plot(F(x,y)[1],(x,-1,1),(y,-1,1))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "((-0.3765445824898374, 0.3765445824898374), (0.0, 0.0), 0.5747748470154906)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0 = vector(RDF,[-0.3,0.3])\n", "xmin = NR(F,x0,6)\n", "xmin, F(*xmin), G(*xmin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## c)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(exp(x^2),-1,1.2,aspect_ratio=1,ymax=2) + plot(sin(x),-1,1.2,color='red')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p1 = (0.1,exp(0.1^2))\n", "p2 = (0.5,sin(0.5))\n", "plot(exp(x^2),-1,1.2,aspect_ratio=1,ymax=2) + plot(sin(x),-1,1.2,color='red')\\\n", "+point([p1,p2],color='black')+line([p1,p2],color='black',linestyle='--')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "p1(x1) = (x1,exp(x1^2))\n", "p2(x2) = (x2,sin(x2))\n", "distancia_al_cuadrado(x1,x2) = (x2-x1)^2 + (sin(x2)-exp(x1^2))^2" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((0.3398534064835867, 0.7029682147028288),\n", " (-1.1102230246251565e-16, 1.1102230246251565e-16),\n", " 0.3583806064913039)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F = distancia_al_cuadrado.diff()\n", "x0 = vector(RDF,[0.2,0.8])\n", "xmin = NR(F,x0,6)\n", "xmin, F(*xmin), distancia_al_cuadrado(*xmin)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p1 = (0.33985340648358675,exp(0.33985340648358675^2))\n", "p2 = (0.7029682147028288,sin(0.7029682147028288))\n", "plot(exp(x^2),-1,1.2,aspect_ratio=1,ymax=2) + plot(sin(x),-1,1.2,color='red')\\\n", "+point([p1,p2],color='black')+line([p1,p2],color='black',linestyle='--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### e) \n", "\n", "Calcular una tangente común a las curvas paramétricas \n", "$$t\\to ((1+\\sin(t))\\cos(t),(1+\\sin(t))\\sin(t)),$$ $$t\\to (3+\\cos(t),2+\\sin(t)),$$ \n", "con $t\\in[0,2\\pi]$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c1(t) = ( (1+sin(t)) * cos(t) , (1+sin(t))*sin(t) )\n", "c2(t) = ( 3 + cos(t) , 2 + sin(t) )\n", "pp = parametric_plot(c1(t),(t,0,2*pi)) + parametric_plot(c2(t),(t,0,2*pi),color='red')\n", "pp" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('t1') \n", "pp + arrow(vector(c1(2.)),vector(c1(2.))+vector(c1.diff()(2.)),color='gray')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('t1') \n", "var('t2') \n", "pp + arrow(vector(c1(2.)),vector(c1(2.))+vector(c1.diff()(2.)),color='gray') \\\n", "+ arrow(vector(c2(1.)),vector(c2(1.))+vector(c2.diff()(1.)),color='gray') + arrow(c1(2.),c2(1.),color='gray')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(((sin(t1) + 1)*cos(t1) - cos(t2) - 3, (sin(t1) + 1)*sin(t1) - sin(t2) - 2),\n", " (cos(t1)^2 - (sin(t1) + 1)*sin(t1), (sin(t1) + 1)*cos(t1) + cos(t1)*sin(t1)),\n", " (-sin(t2), cos(t2)))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w = c1(t1) - c2(t2)\n", "u1 = vector(c1.diff()(t1))\n", "u2 = vector(c2.diff()(t2))\n", "w, u1, u2" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((sin(t1) + 1)*cos(t1) + cos(t1)*sin(t1))*((sin(t1) + 1)*cos(t1) - cos(t2) - 3) - (cos(t1)^2 - (sin(t1) + 1)*sin(t1))*((sin(t1) + 1)*sin(t1) - sin(t2) - 2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# producto vectorial de w con u1 (tiene que ser 0 si son tangentes)\n", "w[0] * u1[1] - w[1] * u1[0]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(t1, t2) |--> (((sin(t1) + 1)*cos(t1) + cos(t1)*sin(t1))*((sin(t1) + 1)*cos(t1) - cos(t2) - 3) - (cos(t1)^2 - (sin(t1) + 1)*sin(t1))*((sin(t1) + 1)*sin(t1) - sin(t2) - 2), ((sin(t1) + 1)*cos(t1) - cos(t2) - 3)*cos(t2) + ((sin(t1) + 1)*sin(t1) - sin(t2) - 2)*sin(t2))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F(t1,t2) = [w[0] * u1[1] - w[1] * u1[0], w[0] * u2[1] - w[1] * u2[0] ]\n", "F" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "implicit_plot(F(t1,t2)[0],(t1,0,2*pi),(t2,0,2*pi)) + implicit_plot(F(t1,t2)[1],(t1,0,2*pi),(t2,0,2*pi),color='red')" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def NR(F,x0,n):\n", " DF = F.diff()\n", " xn = vector(RDF,x0)\n", " for _ in range(n):\n", " xn = vector(RDF,xn - DF(*xn)\\F(*xn))\n", " return xn" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "h = 0.5\n", "tangentes = []\n", "for t1 in [0.,h .. 2*pi]:\n", " for t2 in [0.,h .. 2*pi]:\n", " tangentes += [NR(F,vector(RDF,[t1,t2]),5)]" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(-0.22776682179769436, -1.127048396085469),\n", " (-1.5707912982414163, -13.830200266194176),\n", " (1.3226126003092824, 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-1.9430738161087917),\n", " (4.249204975595583, 8.730007656467102),\n", " (12.338603792564205, 5.156136911089687),\n", " (10.995574289218109, 5.019356681900534),\n", " (10.177146520601164, 5.055543865413189),\n", " (-146.54723982149807, -35.25228961665235),\n", " (6.055418485384622, -1.1270483960898987),\n", " (4.712359376753193, -13.842345821722605),\n", " (7.605796630071659, 4.340111484716224),\n", " (6.542720635131838, 2.7454974821207196),\n", " (6.542720635131833, 2.745497482120696),\n", " (6.54272063512943, 2.7454974821042177),\n", " (6.542720635449821, 2.7454974811738455),\n", " (6.542720634994765, 2.7454974814209883),\n", " (18.621789099755954, -32.5429749319851),\n", " (6.055418485384619, 5.156136911089687),\n", " (6.055418485384619, 5.156136911089687),\n", " (6.055418485384619, 5.156136911089687),\n", " (6.055418485384619, 5.156136911089687)]" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tangentes" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "tangentes = [ p for p in tangentes if p[0]>0 and p[0] <2*pi and p[1]>0 and p[1]<2*pi and F(*p).norm(2) < 10^-3]" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t1,t2 = tangentes[5]\n", "pp + arrow(vector(c1(t1)),vector(c1(t1))+vector(c1.diff()(t1)),color='gray') \\\n", "+ arrow(vector(c2(t2)),vector(c2(t2))+vector(c2.diff()(t2)),color='gray') + arrow(c1(t1),c2(t2),color='gray')" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 445 graphics primitives" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum([pp + arrow(vector(c1(t1)),vector(c1(t1))+vector(c1.diff()(t1)),color='gray') \\\n", "+ arrow(vector(c2(t2)),vector(c2(t2))+vector(c2.diff()(t2)),color='gray') + arrow(c1(t1),c2(t2),color='gray') \\\n", " for t1,t2 in tangentes])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 4 }