{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Manifold graphics in SageMath" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates some plotting capabilities of manifold objects in SageMath.\n", "\n", "More examples can be found on the [SageManifolds page](https://sagemanifolds.obspm.fr/examples.html)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The 2-sphere example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us consider the sphere $\\mathbb{S}^2$. In SageMath, we declare it as a 2-dimensional \n", "differentiable manifold:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)\n", "print(S2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then introduce the standard spherical coordinates $(\\theta,\\phi)$ as a chart on $\\mathbb{S}^2$, denoting the chart as `spher` and the coordinates `th` and `ph`.\n", "We shall be lazy here and consider that the spherical chart covers the whole manifold $\\mathbb{S}^2$; this amounts to authorize coordinate singularities:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (S^2, (th, ph))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher. = S2.chart(r'th:[0,pi]:\\theta ph:[0,2*pi]:periodic:\\phi')\n", "spher" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "th: [0, pi]; ph: [0, 2*pi] (periodic)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For 3D plots, we shall require the Euclidian space $\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Euclidean space E^3" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E3. = EuclideanSpace()\n", "E3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us call `cartesian` the chart of Cartesian coordinates $(X,Y,Z)$:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (E^3, (X, Y, Z))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cartesian = E3.cartesian_coordinates()\n", "cartesian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The canonical embedding of $\\mathbb{S}^2$ into $\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Phi: S^2 --> E^3\n", " (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi = S2.diff_map(E3, (sin(th)*cos(ph), \n", " sin(th)*sin(ph),\n", " cos(th)), \n", " name='Phi', latex_name=r'\\Phi')\n", "Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot of a chart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each chart is endowed with a `plot()` method.\n", "For instance, we may use it to plot the chart of spherical coordinates plotted in terms \n", "of itself:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More intersting is to the plot the chart of spherical coordinates in terms of $\\mathbb{E}^3$'s Cartesian coordinates, via the embedding $\\Phi:\\; \\mathbb{S}^2\\to\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a better image, let us increase the number of coordinate values:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can customize the color of coordinate lines:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can fix the value of some coordinates, thereby obtaining a partial plot:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " fixed_coords={th: pi/4})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or limit the range of some coordinates:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " ranges={ph:(0, pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can also restrict the coordinates of the ambiant chart; here is a example of plot of the chart `spher` in terms of the coordinates $(X,Y)$ of $\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 22 graphics primitives" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " ambient_coords=(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Same thing with only the coordinates $(X,Z)$:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 22 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " ambient_coords=(X, Z))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us introduce the chart of **stereographic coordinates from the North pole**:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (S^2, (x, y))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN. = S2.chart()\n", "stereoN" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x = -cos(ph)*sin(th)/(cos(th) - 1)\n", "y = -sin(ph)*sin(th)/(cos(th) - 1)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN = spher.transition_map(stereoN, \n", " (sin(th)*cos(ph)/(1-cos(th)),\n", " sin(th)*sin(ph)/(1-cos(th))))\n", "spher_to_stereoN.display()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " th == 2*arctan(sqrt(-cos(th) + 1)/sqrt(cos(th) + 1)) **failed**\n", " ph == pi + arctan2(sin(ph)*sin(th)/(cos(th) - 1), cos(ph)*sin(th)/(cos(th) - 1)) **failed**\n", " x == x *passed*\n", " y == y *passed*\n", "NB: a failed report can reflect a mere lack of simplification.\n" ] } ], "source": [ "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of spherical coordinate in terms of the stereographic ones:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=stereoN, number_values=15, ranges={th: (pi/8,pi)},\n", " color={th: 'red', ph: 'green'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of stereographic coordinates in terms of spherical ones:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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Q9S0pZSddYw9hKZYotUbgdDpR0OGU9WQdTgPEA9Q11wrLYenxTaJduylul7n2WujZQ2xel5UBqS8LT5T+TzZ7iFdd5S66agNN/g7Yept4but+V7P70VAf6hNc2XGMeit6ZyFZ1mFIih1C2mMwIOLfwroC4kdvt0POjk9Eu1phOpIE06eDU4aF/86Fg/8WlsmQjviCq66CTz6BlSvh3ntBKT0BP/8BogbCiHfdtiw0fj+oTnCZqSLdeJe4dCyGYRj1dsqlLhiNkBB6CGuECLuJi4Xrry6kg/57V8tzf+DR0RAWChEnnhV+mH0e8+lYr75apOf7+EMLOZ9eJpLOjv+ywe0GjdaL6gR3/EA6JRVhdIjJotCWhF4nk1nYGaPBSWRIMbtP1bj0P3bDx+il+syFEBbq4M6LFrF8/5N+2QubeYuVvQuvwezMYNnpbyCojc/70FAPqhOc3H0OM98RqdZzskQtuNSMzugUOxX2YFb97Np/UxT6mBaz+ejEeq6moHNYKJW6cduCv7B1q68Ha4dNf6Rz6EaWZnzJzbN78803Pu5DQ1WoTnB9+kC/xANYKmMJc+zFqRg4ciwMZDsFjr5s3uqKzC7ai1S0h/yIWwGo8JQCz5ICso3wi16jVx8Tjz/uw4HKTthyK5z+Fmnc58x6ejyXXw433giHvEz6rNF6UJ3gYmNhTK+dpBUMY0j7H1EkIzp7DiBjiOtfs5l94mMI78nw6eMA2LKl1oUc5cJBWWdG3/ESnn1WOCGvX++DQcpO2H4HnPwERi+H9tPQ6UQcXfv2cOWVHjbdNX4XqE5wAGV0IjVnKImxp1AkE307HkAB4pJ6EBbqOil7PfS8j44dxS2eI6R9z4CjVEQVAFdcAUOHwhNPNK1WYzVOG2y+EdI/hJEfQKcZ1YciIuDLL+H0abjllrNS8Wn8blClp8mawjdJz2qPzWHEKRsZ2PkAsmxEbzQyYoTrJL0Zut5a3WbXLsitqsFYsAsO/gvaXFSdO0SS4LnnYNMm+OGHJg7MUQEbrhI1AcaugKRz83X27AnLlsFXX7k25jV+V6jS06RPHxjQZi2/ZozG6ZRpF3kam1M8u40dVQGALf6yc9ymVq5EGDK23g5RA87J3HXJJSIR7EsvNWFQ9mL4aZqYWcd/DYlX1Xnq9Onw4IPCn3P//ib0paFaVLmkTO7hYHyv9RwsnIxOseKQTdjsRmQZLurxJQB7im50azNkCHz8MZD6T7DshxH/qSnk6EKShMf/+vWNKPBxNhVnYN0kKNwNE36AhCkNNnnhBejRQ3iiWOuotqXR+lCl4Hq2P0yIuZz0ykkY9ZWUm/qiKJCX6yS6UESCbtvn7jEyZgwUpB9A2fcs9HrILXXC2Vx1FSQlwb//3cjBFB2AH0aK/CeTfoI2jUvtFRQkjCgpKfD0043sS0P1qFJwCcl9iL2nELNJwqBzVjsBl5/eg1QpEsTu2ePe5oLhdj6cdRMWZzfo/3Sd1zYY4IEHhC/kiRMNDCRrDawZLZauU7ZBzOAGGrgzeLAoJPLSSx6sqBqtElUKzmSCuLahDI3/GKeso9jZDUkHMfb11SnMU1Lcy0/FFn1A344pPP/j0gZdq/78Z2FRfOutus5Q4Mjb4pktbjRcvBFCm1bZ9eGHhXX03nsbiKHTaBWoUnAA3bs5GNF2OVa7mbx8HWajgwhjtkjGg3Bc3rnzrAYZK9hgeZ63PxlUdx04F6Ghwmz//vuuKjy1SXsHdswS1W3Gf92smDa9Xgh7716op5CsRitBtYKbPnQtUUE52JxB5OUpmPSVnMzvDNFiWRcSIkz82F3JIyP7EzfuIcrKRNnhhrjjDsjOhq/PTrtX5iqXnLMBRr4Hwxc2KoNzQwwfDnfeCU89BYWFDZ+voV5UK7h+nQ6yL2MgimTAVHkIneTk2z1TKbSIqIDkZPj1VwX2zBUN+vyNfv31xMc3zpukf39RGXXJEtcX2ethrfBaYcBz0HWmT+/nmWfAZhPR6BqtF9UKLjfmrwyetxO9DnpFrUFBT9qZ7hw/Lo4nJ0Mfw1tw+n/iC3NbdDqYOLHxeST//GdYt9ZB2Zan4cfJEOkqAOKKufMl7drBQw/Ba69BZqbPL69xnqBKTxOADh3AKRswGqy0Cc8CfTCSJHHcVeHmgl6pPDblQawdZ7q1mzhRVDttjC/jNZdmsG7uRIKPPQf9noQLV/lk7HXx0EMQHNyEdHsaqkGVniYgnIAlScakK+PImW4g6YmOpnqGG2V+jL0nB7LX4R4CMHGiSHmwYUMDHWR8QczWgfRKTOfBb36C/k/55HmtPiIiRCKixYvPckPTaFWodknZvj1cO2IFesnJ2v0XI8vQpg0cPyE8jw0Uc8s7n7LvgNmtXbduEB8vsiZ7xFEBO2YLn8g2F/G9tJc3PhlHdrafb8jF/fcLj5c33wxMfxqBRbWCCwly8uy1T+OQTZzM74SsCCENDP8QAGnA04TEd+HIEfd2kiTqAWzf7uGiedvg+8Fw9D8w/C0Y9xnTroxBUQhY4GhsrHD3Wry4ji0JDVWjWsEhSby75UmszlAkSYS6dI0/zK0jXxHH24wnORmOHTu3aZXgqqNwnFbYM094jRgiYNpuUchDkoiLE/UD1qwJ1I3BrFmQlSUiCjRaFyoWnI69lhtwOA2Eh4Miy/QO/ogtR0ZVn9KzJxw7em7TCy4Q+10FBYjogdXDRbhO/2dhyuZzMnxdfDGsXRu4+LWBA0UprHffDUx/GoHDK8E9/fTTSJLk9mrXrp2/xtYgbdqArEBcjBWTrgxFF8Lcj2s2spKTITvn3HbDh4PJYMWRuR6seYAEU3dAv8c9GkYuvhjy8mDfPj/eTC1uuUXMqprxpHXh9QzXt29fsrKyql/7AvkrrEVMjJh1piSvRELG1mEmxZU1blbJyZ7bxTo3su+lwcQrv4gU6FN3QPTAOvsZNUp4rvz0s6/voG5muALFP/sscH1q+B+vBWcwGGjXrl31Kz4+vt7zrVYrxcXFbi9fERMDQYZyOkcdoNIRQnBsO4xnTVDdutVqYLPA9lmwdhwOXQQ/pN8DxvAGa2qbzeI5zqsYuWbSpo3Ywli5MnB9avgfrwV35MgR2rdvT1JSEtdffz3HPFklzmLBggVERkZWvxITm+ZV74khbf9HiKmMtJKJ2B1GdBK0aVtzPCpKxJ0BkLcJvukDxz+CoW+wKG0TaRltPV7XE8OGwe5ffTb0RnHZZWK/UAtQbT14JbgRI0bwwQcfsHr1apYsWcKZM2cYPXo0+fn5dbaZO3cuFoul+pWRkdHsQVehhPekwhbMKeckZJfJMTa25rgkwYAerpKo+58TReunp0DyffTqrScvv/EJg4YOheMNxcf5mKlThX+lT+qIa5wXeCW4adOmMWPGDPr378/kyZP5xrU59X499XbNZjMRERFuL19hjOlJaWUYRoMEiogni4p0HZTtkPISS2+7SHzu+zhc+GV13FpSknj+a6zlcdgwnw270fTsCZ07a3ksWxPN2hYIDQ2lf//+HKm9uxwgYkTFqqrEW5SVQWSU6+DmG2Dv42zJull8jh/nVkCjk6siVZ2lh2vRvTs1KfgChCTB6NE17moa6qdZgrNaraSmppKQkOCr8XhFqEsAOtdd2MqKuLnvw+KDKQam7WFLqefyU94KTqfzYIQJABdcIKIHmpMqU+P8wSvB/e1vf+Pnn38mPT2dbdu2cc0111BcXMytt97acGM/EBIi3nU4MRutxGb/g06hLsvG8Hcgqh/R0Z7bRkQIg4qjkYID6NoCghs+HOyOmrqSGurGK8GdOnWKG264geTkZK6++mpMJhNbt26lc+fO/hpfvQQHg9Fgp5/xNYKMlRSbRrK6UqTJU1zlqcLDcX0+l7AwkZW8sSQlNXPATaC/KwRP1qa4VoFX8SYff/yxv8bRJEJ1p4kIKaJE7oLdaiUr+A8YgsIAMSuYEDMZMlRUQEit9sFB3qU1b+9aOSt4qjbnHyIixH8M2gzXOlCvLyUQHNOewrJoUux3Iss6bLaafTerK1FQpMsoWlZ2bvugYO/8I9u2rfta/iQ+TpvhWguqFpzRCA7ZAIqYb2w2MFcJzrVZHO4SXGnpue2DvRRcG1ctRYuliQNuItExzSwwonHeoNoUC1Bj5a8SjcMBQa5400qX4EymmmO1CQryTnBVBpgyD+L1J6EhmuBaC6pNsVCFhPuP0ewSXNUMV+Vb6Ulwev2539VHsOsh0Gbzrl1zCQlB2xdoJah6SemGJISndwmsauaq+uxpv02n8+53HOJK2GxtAcFpemsd+DcrTiCQFEKlTPQ6JyHKKYIqUwEwVx6EAh0htjMAGK1HoMA9siHKdBqDzg4FjfNKDraWua51rNFtfEGEIQOdJAe0z9ZCcCV0bxsO9GjpoQAgKUpgnw6Ki4uJjIzEYrH4xK+ycEkM0aFaumKN+jnQ9TB9R7a86FQ/wzllPbtLZ9Pd8D5H5NsJ7zKSHjk3cLLjh3Tq14fTx87Q/vB0DoW/QfKY0W5tty9fTDfjZ8Res7pRfRXmlxG940IOGBfQd1LDNeB8xc7Pl9PP+AZBl28OWJ+thfS9qSRl3YxOLmnpoQCtQHAKEiXODjh1esrkjhiMIh+JLagXxAyhzBUO5AjucU5NuMKK9jgNxjprxdXGVi7+0SoNXRvdxhcUVm5ENugC2mdrodLc8DmBRP1GE8XlvKyI2m5Ol7Gk2qHZZeAwePivxe7AK5eRUteGtznA/4jlFYHzbNHwL6oXnEKNed9gqPEwqfI4sbsEZzSe29bh8O6HXLXhHegwnfIyt8giDRWjasE5HIACkusuDEbhMwlnuXjVIzi7zbsfcpHLNhMSYMGVlqJNca0EVXuaWCsVQoPKCNGJXHIGfU3V02CX4KpcukJqey4jlmo6L/4G8lyZJKoiEAJFXj7oNMG1ClTtaWItPkOQsVKE55gqMRls1YKr8qksKhLvYWHnti8v805wmafEe5WYA4Esi5yYkqrXIhpVqPqfsUJJIL80lix5AmaDla7WfxDnEDnJq2aEqucus4dMeGXl3gnu1KlmDrgJZGaKGgPaDNc6ULXgKisBBTLskyipDMdh7MC4MFeKhbLjQN2e/YrimuG88Kc8ebJZw20Sv7qcS7QZrnWg6n/GKjEpCsiyjoqE21hx7HXx5abrYc88yorLPbbNzRXpFfRe/A0cPtzMATeBHTvEM6NmpWwdqFpwVc9nVdHQwcGw4+SF4kPXP8OhV5jVc4LrbHcPtnRXpVRP+3OeqKiA9OPNGm6T2LEDOnfSjJStBVULrrAQJEmp3uw2B9WIkO53wfQDpOX0FZ9/ewrKapLQVgmusSE6qamBj0mzWmHTppbJpaLhH1QtuJiS5cSEFaBzliBJwrBQdLYfc1hXZn/wX/Hn0jSR6vzQGyA7SU8Xe3WNNZps39742dBXbNok0jn07t3wuRrqQNWCO1R4EQB9QpZWGxUKCmqO22yQU1Xu6YIlkHQL7PoLrBlDWeY+t7ToDbFlCwzo75NhN5rVq0Vah/YdAtuvhv9Q9cb3qfwESiojiTBkEmyswOGo2ZwGUUW0ehloCBVlhC/eCI4SnhoxhIt6rW30OnHzZpGUNVAoCnzxBUybpm0JtCZUvfFdUACyYmDTiSsx6m1YM7e46afqOc2N+DE4Jv/K/K+eoEfUZrDmQt7WevvJzRUFNUaM8NnQG2TPHmEVvf76wPWp4X9UvaQ8c0Y8g+06PhSHbCK44AsGd6mJij540PNz1+GjZp5e+SRZYbMAHawZA3vmilrfHtiwQbwHUnDLl0NcHEyaFLg+NfyPqgWXlSU2rkuKwUEwpXIX/n3jQ9XHDx4U1Wdq89tv4j06IR7McTDgOTj4b/h+mMc0Bt98IwwXPixtVy92O3z4IVx3nWenaw31ol7ByXbmT7kUk76SikrxnLO76BZsssvRUbZx8CB091APYMcOUcwjJBixwdV3HkzdKep7rx4B+54BWaT5kmX49luYPj1gd8YXX4jZ+557AtenRmBQreAUyUieJRyTrgy95ETSQXZ+GG9sfFmccPBVUlOhu4c0Fps2wZgxtb6MHgBTtkHfuaJ447qLoOwEe/aIH38gBbdoEYwdW1NXQKP1oFrBFRbCUyufQkJBJUgFAAAgAElEQVRmaNed6HTCuEGEa9MqYwUj239yTompigrhn3iO4EDU+h7wLEz+RWySfzuItPWfERFRx/l+YMcOWL8e5swJTH8agUW1gsvKgtTMPjgUMxP7rEcnQU4OdHF5ZRSYp7DkjjsZ0tPdVLljh3hGqldA8aPh0j0o7SZxXcI1rJp3N0bJs0+mr5k/H3r0gBkzAtKdRoBRreBOu0p3W52hhAeVgGyjrAySuojv12bN44wlga757g9CGzcKZ+AGl2umaHaHrOCud99hfOIHsHo4FB/09W24sW+feH577DHvs0JrqAP1Ci49j4l91+N06knLHwxyJUaDjaSu4vi+1FCe/XEFUukxt3Zr1sD48Y37QS9bLvHlgbtQpu4EJFh7kc/v42zmzhVVVm++2a/daLQgqvU06Vj2OqseuAqnDOkVE0FRGN1jC51cpvvUVIjqMgD6Pyu+yNtESYmY4S65pOHrOxxiL+yPfwRDbF+YshUSpoqDx5dWWzF9xc8/i+2H+fNrCpBotD5U62ny9f6biAi2oJesBEXG4FRMTOz7Eya9yLFw4gQMGQJ0drlqHHqVTWuzcDgaJ7j//U8sW2+7zfWFMQxG/p/4c+bX8NM0qMzzyb04nfDAA6K88LXX+uSSGucpql1Sbt6XzNGi4QQZKomNAavDTLCpDDK/AoQv4ujRnBW5aSAx8za6d1fOsVx6YtEiGDkSBg8+68uqa/X9OxTuEc91ltRm38uiRcKVa+FCLdC0taNawaWnw/acmzAZbLSJLcfu0JFrHwBH/w8QtdySk2vOV3o9RN+Y1cyf+WaD1z5yBH74AWbNquOEqH5wyU7hEP3DKDizrsn3kZUFf/873HFHYJ2jNVoGVQqupMDC5X3/y57saQAEVe4HBSoiJ0KlMF8OHuQ+W6QVDmPhD7O5OulhsNRvbVy4EGJjG1jehXaGizdB7AhYfwkc/a/X96EocPfdIi5vwQKvm2uoEFUK7tQxC/+963aidQewyyZ0xXsAiE9sjzNGFOwYPMQ97GbDBnhp9T/QhSXC9jvqrFKflwdLloiN5+DgBgZiioSL/gfdbodtt8NvT3sVFv7RR/D11/D223gVm6ehXpoluAULFiBJEn/96199NZ5Gse9YJw5n9aBH+FocchBhHEevlwkNhaPKnwEY18u90syGDTB1egjSiCWQuwmOLPJ47ddfFzPjffc1cjA6IwxfBAPnw/5n4NeHGiW6w4fh3nvFFsCVVzayLw3V02TB7dixg8WLFzNgwABfjqdRpKbCxqOTGdB2LYrOhN1pwGS0A/DTb0MB6GBf5tbm9GnXErHteOh+N+x5DOzuOfRKSsRy8q67vJxxJEn4YA57Ew69AtvvAtlDyVUXFRUiEqB9e3jrLS/60VA9TRJcaWkpN910E0uWLCG6qtJ8ADl2uJTMiuH0aHsYg17hSHZPjDohuE2bxIObVLDdzYIYHg4TJ7o+DHoJjJFw6iu36779thDdgw82cWA974WR78Ox/8Lmm8DpuTbxX/8Khw7BihWBT5uu0bI0SXCzZ89m+vTpTJ48ucFzrVYrxcXFbq/m8vjw0VyQtAFZltBhY9/JvugkJxXFxfy2z3WSKRoOL6zO6DVu3FmxZaZIsQwsTQOn2LezWODFF+H225sZ99b1TzB2BZz6HDZdB7Ld7fCyZbB4MbzxBrTA4kCjhfFacB9//DG//vorCxppVluwYAGRkZHVr8RmRnE6nbDt8BC6Rv/G7pPDkBQbR7J7oQD5x/YhV9lCEq+G9PfZtkEIfErtgqUdL4fwnmAvBkc5//43lJfDE080a3g1fY9bBae/hS23Vi8vt20Tgr7lFvGu8fvDK8FlZGRw//3389FHHxEU1LiKFnPnzsVisVS/MjIyGm5UD+npsC1tGF2ifiOteDw6bMTGByFJBoxl+2sCTjvOAKeVzG0rAOjVy8PF2l8CipPSnf/k5ZeFZbKDrzJkdZgOo5fByU9gx90cT5f5wx9g6FAxw2kb3L9PvMq0uGvXLnJychg6dGj1d06nk19++YWFCxditVrR1/IKNpvNmH1YMjRj/0HaRGZj1NsxxXRBJyn07ZaDojMSF3SUieNciSmD4rG1m8HgrI+AOjIXm2LBEIbpyIt0iZ/Jo496yMfQHDpdA87/gy1/Yv3SKMLC/sWqVTW16zR+f3gluEmTJrFv3z6372677TZ69erFo48+eo7Y/ELuL8z7w3zsDgPxsQ4UBbonnEBWjEhUcMnQDeCqCff9kdv5Q7tP6r2cnTByLTo+f+JvxMau8PlwKxNuYcmWIuaM+guXXteN+Pi63Fc0fg94taQMDw+nX79+bq/Q0FBiY2Pp16+fv8boxoQremPQy6RldyeSfThkA/Ghx7HZJU5bOpIUugkQW2FPL5pIXnn7Oq+lABaLxOu/vEjPoJUNpsvzFpsNrrkGHv3PHDLD7qdtxhw4/b1P+9BQF+rzNHGlUMgp7UCkYwdO2YjRegK7HSxyL3T5WwDYvQd279FTGn2NaCdXnnOpAweEKCbdfiNE9oO9j/tsmE6n2NReswZWrYIOl/0b2l8KG6+Dwt981o+Gumi24H766SdeffVVX4ylcQTFYamMwxQcQvuQAyLTlq0QRVYIaZcMDmGV/OQT4bzcaazLITJ3k9tlystFKvGgIJgyVQ8DX4DsH+HM2mYP0eEQYT2ffy7GMXUqIp/f6GUQ3h1+uRJsRQ1eR6P1ob4ZDsi19SY2phKD3oneIG7BoHfQsWcnMIid5J9+ElZHXZjLEJL1g9s1nnpKFMqIiHB90eFyiBsFe+Y1q0yO1SqyJS9bBkuX1nLbMobBuM/AVih8LwNdjkejxVGl4LoP6UNMkIgKMOhlLJVRmAwOjCadEA0QZIY//emsRkW/QWUOIBIJvfwyTJhwVmZmSYL+z0DBDshuWrhNeTlccYUIXl21SkSLn0NYEox8DzI+h8MLm9SPhnpRZ4qFiN5ESGmcLk5CkR0cz05Erxeby7bIkQDMuLK0ltuUBBmrsNnEpvOgQa4A1bNpNxlihsKBF70eksUiIsk3bhSpEi6/vJ6TE6+E5L/C7ocgf6fXfWmoF1WmWHCG9cakt2I1JCE7neSUdEDCCYrCDzvEHuGN0/a6N4oeCCdX8I9/QEoK/Oc/HsoNSxL0eUzMcPmNH2dWlvDT3LdPGEkaVQ9g0EsQPViURnaUNbovDXWjyiXlsVyRTjk8Lh5JcWCObo8EOCvyWPheJwDidHvcG8WPRclez6JXc3n4YTHDeaTjVRDeA1IaN8vt2yeKfJw5I54bR41q5E3oTTDqI6jI9Kl1VOP8RpWC6zEwEUXS49SFotfJdOoeA8CJ1Eyyzrh8Sgrdi3LYosYgy3DHJV/w1FP1XFynh95/g4xVUHq83nF8/71IKBsbKyqkDhzo5Y1E9BBxdIdeP8eKqtE6UaXg0BmQQhJJPyasfJ0SSlCQyDt5igvHuc6xpICjorrJ+8ui2JI2mgf++F3DrlVdbgJjBKQt9nhYAd58Ey67TOS43LChGT6YPf8CMcNgx70+T72ncf6hTsEBckgSuadFAKnOnoeCgShzJn+u8sJXHJC/vfr8zz4Dpd0lRFWsPSdk5hwMoZD0Jzj2H4814xYtEhHh990nMiWHhTXjRnR6UZm1aB8cbjjBkYa6Ua3gMi1daRd+EgUdijUfu0NPYtxpBlc9m+mDIH87Ra6g7gEDYMw1l4CjBPK2NNxBj1liGyFjVfVXJ0+K982bRf22V1/1UUry2GEiCn3f02AtaPB0DfWiWsFlFCbRo306SHqK8wpwOHUEG8trPDjCk1EKdvHYY+Ljww+DLnYwmOMb588Y2RviRsPxDwFYuxYuvFAcev45P6Qj7/+0mJVTtPRdrRnVCm70xUlEBeeDpKOiKB9Jck01Za5qORG9sKTv4ptvxMf4OEDSQcIUyGqkA3GXm1CyVrPg6VymTKlJCtuliy/vxEVwW2GsOfSGKJWl0SpRreAI7QKAU9YRYc7HZHbdisuyeKqkN1H6NGbfVSulQ9sJULRXRHo3QIbuOpwOicwtK3juOVi50ofj90SvB8EQIsofa7RK1OlpAhCcAIDdJhFirsRgUMAUUz3DLXhThHg/dPsB93ZxY0ROygZCcT77DAYMj+OXI1OYf9cyHn88ACWkjOHCapm2uNoNTaN1oUpPEwCC2gFUJwlCkSGoDYprhjt0qguyLghjeYp7u4hkMMfWue9VXi6yIV9zDUyeDCOvvYYI62aozPXNuBsieY5Y+moWy1aJapeUDoIproyscT5WFDDHYzl9AoCnntGji+gJJUfdG0qSmOU8CG7zZuGB8uGHIu/Ip59CSPdpgNL4577mYo4VWxJHlzS8faGhOlQrOJ0OCErAZFQQGUtkcoqiMCvZAIwbC0T0EqnwahM/GvK3IbawobISHnlEpNKLjRWVbO6805XoJ7id2JjO/CYwNwZiS6IiC059Gbg+NQKCqgUX0TYBnSSDIQxZllm3IZpg01mR3RG9oPTouY2jBoGjFGyF2Gwik9Zrr4liiBs3Qs+etc5vPx2yVgfOEySqv9iSOPpuYPrTCBiqFRwAQQmgyMj6CBx2BRtR7scjeoPVw7NXtMjA+tv2bPLywGyGXbvg0UfrMIwkTAV7kbBuBoqkW0T0eaCeHTUCgsoF1xYFmcycCCRJ5tIra6Vdj6g9VQl+2d6OgrI4CjLPEB4uErTWmwMpZgjozG6uYn4ncYZ4z/D3XoRGIFG34ExRKLJCZk4EBr1MfLtQ0J1VIDvEPctzUZEo1DH+IoljhQMYOTib8PCzUqDXhd4sAlPztvn+HuoiKB7aToKTmuBaE6oW3L5D0UjItO0QgoQirBzm+JoTzHFiZgJ+2QC9e4ukPm+9BUMn9idI8WKvK350YGc4ENmbczd4dKDWUCeqFlybjlFIEnTuaqLK4ojprGWlJGE3iv26F14QwaEpKaKUsBTeTTyXNZa4UVBxyneDbwwJU8XWQMmRwPar4TfU62kCtE0U4tLpXJtxirNacDa7sDru3C8SwT75pEhbVx23FpYkzlfqruPmRvRgn4270YT3FKWNSw4Hvm8Nv6BeTxMAY5VV0hXl7aio/u7660UqvJA4IbgxtRMGhSaJ93oKJ7qf3xl0DdUg9jFVm/QNRJ5rqAdVLykxuQvOUljB+s3iuzZtYO9eGDg8znPbsC7ivbEznKSDyOSmj7WpxA4P/FJWw2+oW3AGEWrtVMTm2dL3KziaIZaUi96CPn0QlU49tg0VBpXGCg4grFvD5/ia2AtcS1+54XM1znvULTi9SE6yZq24jSGDKrnltlDgrPpr1ctODz9YQ4jn7+siuGPTxtkcoqo2CLUsza0BVQsuK0cILiRE/BhHXuDAHOx6zlJcblgm1wx3VkKhavSh3s0cIVWCC+BsY4xwjVMTXGtA1YJL6CgEN26s68coO6pnPRwun8qqJaWj5NwLGEK8E1ywy8Rp93AtfxIUT0BFruE3VC24qk1tqerHqJwlOKdrRjOEiHfZw+axPhivfshm1x5foDMlm2K0Ga6VoG7BVT2oKWcLzrWkrKoHJ7n8tpweYst0Bu8ejapnywALzhCC9gzXOlD1xrdAqrE0yvYaX0qnTbzrXfXFFQ+hNZIBr37I1YIrb9JIm4w+JLD9afgNdW9810aRzzJPutC5ZjjF0wxnxCvB6eoRrz/RazNca8HQ8CnnNwpQXAwRiJJRhcclkoBj6QpFBRBabiIZyMywk13LUNmjVE+YorD713Ov6wmjXU9/4MwZJ6cb2cYXJFl0REGjx6lRw5l06C01fF6gUL3gADZulLh0EKz/SWLlNlg6G+bNU/hkK4zqobD5aXjjDXjpf+7t1j+uMDZZRHw3hg7Rek4thKVLZf621Oe3UScr7ocZwxs/To0aBneBS1+A0PNkVd4qBDd2LFAGF10kMehyIAsWzIdHIiG03Akn4b6/GLjuGfd2PU7I6Cskdu1qXD9GuwJH4eabJCY86Ou7qJukUwqU0uhxatQQXAkch06dWnokAtULTkIhMlKCMoiOkohOlCALkpIUkroAZ+xwEjp21NOxd63GeTJUwpAhjezMUgFHoW2CmbZ11ZfzB8V2KPVinBo1FADHW3oQNah7W+AcJJBd1knJZa2sigaQPPzfojipjjRoDE6XdVJvqv88X+Msx6txapy3eCW4RYsWMWDAACIiIoiIiGDUqFF89913/hqbF7h+jJKuZv+tejvAZZ2UPGQHkh00SXBV1spA4dAE11rwSnAdO3bkxRdfZOfOnezcuZOJEydyxRVXcODAgYYb+4OqDW/JdRs6Q006girBVXmc6D2IxFlx7jZCfVRl0DJGeD/W5uAo1fTWSvDqGe7yyy93+/zCCy+waNEitm7dSt++fT22sVqtWK01blXFxQ0X0WgsiqMSCSgu0REBYtO7SnA6l4uXzdWfwUPVRGdFjVgbg9WVA6WukB9/Yc2j1a3+f6c0+V/R6XTy8ccfU1ZWxqh6KskvWLCAyMjI6ldiYmKd53pL9mmxxFv3o/hsc5rAWWtJ6agSXOi5F3BW4NVfQVWBDV0An+EU2SU4bYprDXgtuH379hEWFobZbOaee+5h1apV9OnTp87z586di8ViqX5lZPiu9lm7OLFc7C0K5bB0uYnU/S4/x6pntqqyVJ5E4u0MV3ayiSNtBuWZwrPFm6WvxnmL14JLTk5mz549bN26lVmzZnHrrbeSkpJS5/lms7nayFL18hkuI0YvV+aDmDgzv6wTmbiOueoy1hlKo8giZMcbwZUea+JAm0Ghy73Em3FqnLd4vQ9nMpno3r07AMOGDWPHjh289tprvPPOOz4fXIPUciK+4koTp9MsYIcbb4ALr4LnL8vF4wKwMtvle+nFX0FpesPn+Jr87WAID7z/poZfaPZ/m4qiuBlFAkpVUGnVj9EQQvtYMcPdeScsXAib1mWJU2q3rVoeetou8NhXeU0540CSvwNCzxM3CY1m45Xg5s2bx4YNGzh+/Dj79u3j8ccf56effuKmm27y1/jqx1og3qvCc/TBYBOCu/12kfS1S9szAPz973D8+Flty70UXOEeAu6x77SKOnZhXQPbr4bf8Epw2dnZ3HLLLSQnJzNp0iS2bdvG999/z8UXX+yv8dXL1g35AFRW2AFJGBbslurjXbpAUltRL+7ECejbF155BRwORDZjXVDjjREFu2qCWQNF7ibxnBrRK7D9avgNr57h/vOf//hrHE2iT7cC5DSJQynlDGgvCcO59ax6AbKj+vPixRDzGjz0ECxdCj88k0pMUHzjn40Kdoq6bYUBjJHJWg1BbWtyqWioHlWbviLMBUiShGIvR5YlFKcDbIU1J1RkUbUMDAmG118XZYWtVkjfk8KpvHjkxq4SC3ZCdAA9lhUFTq2C9pdqWwKtCFULDlsBkqQjKbEMp6zj120W9+MecvKPHAm/7pIZ0DmVlKPx5OYIEdZLRTZYUiBupO/G3hCFu8Wyt/P1getTw++oO6eJNR8kiciQYnQ6iR2ba1XDKT7k0exvrEzDqKtgxPg26PQinu6RR0Stb49krxPvbSb4buwNcWK5KLfVdmLg+tTwO+rOaVJ5BgUd2CzoDTp6dKkluJLDoghHbVx13iLbdSAuFl58UdT4HjoUdu700M+ZNeL5Lbit78ZeH04bpH8oZjed6kMWNc5CtUtKux3OHMvE6RQhOZKkY+wFRVgqhGOx1YaY4UI9mNTzt4tSUPpgJEnMbrt2QVCQWHI++aS4PiCepbJ+gHYBtMSe+kJszHe/J3B9agQE1QrOaFCIDTmNzV4TC2dW8jBFinTkL7+MEFx4HYKLvcDtq379YOtWeOIJUVfuwgshPR0o2gsVp0VxxEBx5C2IHwdRniMwNNSLagWHNR+j3nZWQmIJKnMJjusCwOpvSoRnSEStvApOmzBI1BIciFrfTz0FGzfCmTMwaBCkfL9CFHlsG6Dnt7ztkPMzJM8JTH8aAUW9gqs4DYDBALKMeJaz5kBoFwD+dIWwUJ4s6efeLn+bSMMQX7tCYw0jR8KePTBtmoLh9Ao2Hr+KsooAbXqnzIeIZOh4dWD60wgoqhec0aBQUhmBzaaIcBuX4G6+4iAV9mDufKBWTbfsH0UJq6j699QiI2H5W3vpmXCEf356HcOGCVcxv1L4G5z6Evo8BrpGupxpqArVCq44+xQKEjpJxkocdrsr3UKYKCVsqjiEEjmQY+m1frhn1onlYSN+0NKJZWCK4aX3J2I0wgR/ryr3PAbhPaBLC/mmavgd1Qpuz8Z0Mgs6oChOItrEocMpnudCXBHlxQcJ6TCYF54XHzduQhThyN/auL0tpw3S34ekW+jV28iWLTB9ujj04Ycuf0xfkr0esr6DgfNr0rNrtDpUK7jBPY6SdqYrKA6CwuMwGp3kl8ZR6XClVihLh5hhXHut+Pjqq5Cf+rMo+NFuUsMdZH4tUip0uwOA0FCociX95luYMgVyc310M7IDfn0QYkdA4gwfXVTjfES1nibhHMOubyccls2xGHROThV04Isvzjopfly1G6LRCFtWfoUS1q1x3vdH34XYkWeV/K1xaXzyCThwAIYPF+/N5shbULgXhi3U/CZbOer1NCk7RvvOIhNXhRKLhBMlqAPv/5/ruCkawrtXn/63h2QGx3/Nntw/NPyjLj4kPPV73O3xcJ8+wiMlIgJGj4Y1a5pxH+Wn4LcnoPvdEDusGRfSUAOqXFIW5VrAmk/HDhKKAocPi824xOT2nM5ynRQ9yE1YQ3um0SHmNI++/gdSUxvo4ODLIiym8w11npKYKPbrRo+GadNgyZIm3Igiw9bbRAqFQfObcAENtaFKwVXkimQ+JYUWZEVPzkkRZBrXsQPjxwmfLLm22T9vK4oxmtP2Mdx+OziddVy8MgeOvQ/Jf/GcPPYsIiLg66/h7rvhrruEl4pXlYEPvwln1sLI98SMrNHqUaXgEsKOAmArOgU6A0Z7FgoSGMO496b9AOw9MdC9Ue4vSB0vZ9E7wuL41lt1XPzwmyLtQnfPy8naGAwid8o//gHPPw/33y824hvEkgp7HoGecyChZSLmNQKPKgVH8UFK7dHEmVLR6Q10istAVsS+WnKMCG5799NahpHyU9D5RsaNg3vvhblzoahWcAH2EjjyJnT7M5hjGj0cSYKHH4a33xbiq3cGBbHlsOUWEckw6MVG96OhflQpOHteCuX6bkQEWVAwkBibgcMpwlikvC0AbNuud/cMMUZWbwcsWADR0WI56LYCPPS6EF3vR5o0rrvvho8+Evt0N9wANlsdJ+66H4p+g1EfgeE8qRSoERBUKbi03alkF8QCYgPaqLdjcxiwFJSDRSwpY2PEbFNdrqrNhdWxZRERYjY6kgaVVWWIbUWQ+i+xlAxtejr2G2+Ezz6DL7+Ea645K8ynevCLIe1tGPaWZpX8HaI+wclOusUdxFKsp7gyCqfTiSLpccp6sg4fqT5txgz44AMoy9gmvqgVrT19usjYXFwM5eUIy6RcCX3nNnuIV1whBPf993DzzWctL3M3w877oMcs6H5Hs/vRUB/q2/guO45JX4liKyHPMQBJsUNwBwwGUCyHq3M4Xn21SBZ0euvHol1k7fKncMklQgwL/5UNB1+FHrMhOKF54zvr2p98Ima7O+4AuSQDNswQ3iRDXvVJHxrqQ3Ub3yf3iwezzvHHKTYMw6i3U0YnjEZoH5ZKZbgIu4mLg1tvKKCT4VtXy3M3u2NiICwMYjOfwKkYoO+8Zo2tNlddJWbZr1YWkPPpVFFQZOzKwFdQ1ThvUN2S8mRqBpaycDrFZlBg64peJ3O6qDNGg5PIkBJ2nqxZOj58zYdI1G+jDwu1c9u4d3lv19NeWSYby43XlXPgzcswOHL46PQPgcuLonFeojrBKT3u5Za3PwQgL7sMRYEDJ5PQKXbKbaF8vcm14a0o9NQvYUPalPquhs5RTInUk1kvz2LLFh8PVrbDxutoF/QbH536llvnJPPNNz7uQ0NVqE5wvXvD4C57sFTGEmLdh4yBtGPBINspcPZl8xZXnFvRb0iWAxRGCPesSk/1RiypINsIH/8yffoamTfPS0+R+pAdsPkm4ZM59jPmPH0Bl18O118vosk1fp+oTnBxcTCm1w6OFg5lSId1KJgwOHMBGWN8X6orGp/4GMK6c8H0cYDwe3TDXgynvwWdGV2HabzwAvz0UzMdkauQHbD5RshYBWNXQPup6PUixXpysni2Kyxs+DIarQ/VCQ7AIncnNXs47aOzUHRG+nRIQQHik3pQXe8x+0fo9Vc6dRK3+MMPtS6y93GxDWCMBEli+nThiNzsWU62w+aba8SWeGX1odBQYbUsKoI//9mHs6mGalCl4NYVvsqJnHbYHEacspGBXfbhlI3oDEaqy43rQyDp1uo2+/ZBdrbrQ95W4TPZdmJ1qgVJgmefFfkpmzzLOcrhl6vg1Ocw9lM3sVXRuTO8/z588YVIPqvx+0KVguvdG/rGrWPPqZE4nTLtIrKwO0VagnEjRY1vW7urwBhW3UaS4PPPETPQ9rsgZogIMD2LiRNFUOmLTXFvtBbAj5Mh5ycY/z9IvKrOU//wB3jwQZGAdvv2JvSloVpUKbg+vRyMT15PSsFk9EoldtmMzW5EVmBMly8B2Ft0nVubgQNh5Uog5SWwHIALFp9TN1uS4LHHYP162LbNiwGVn4K140Rq9Yk/QkJ9llHBiy+K1Oo33ABlZV70paFq1OdpAvTueBiTwUZa2RSM+krKTf1QFMjLlYku+giAbXvbubW58EKwpP+Ksu8Z6DNXzHAeuPJKYdho9CxXtB9+GAP2Upi8EeLOTTDrCaNRODlnZYnIBY3fB6rzNAFol9yH+HsLCDKDXicjRYvYt/LM3UiVIl/l7lp1E0eNsPH+PbeQ7+gH/Z6s89o6Hfztb8IXMr2hkt6nvoIfRoEpCqZsgkjvKpV27y4iF8jgQFIAACAASURBVN54w4MVVaNVosolpcEAbROCGNFuOU5ZR4GtKzodxNrXQfyFABxIgYqKmjZRBe/TIyGN59Z+2KBr1Y03ioiCd96p6wwFDiyAX64URT4u3gQhHZt0L3PmwIgRMGuWh8gCjVaHKgUH0K2rg2FtPsFqN5OXr8NktBNuzK32wnc4aj2HZXzGBssLvLeqX91xai5CQmDmTJEWz+ppw/zQG7B3HvT7O4xb6Wac8RadTkSfp6S4wok0WjWqFdz0IWuIDsrG5gyiIF/BpK/kaE4PiBoACNFs305NCeLIfkSPeoCSEhrlwnXPPZCX57JsVlF2Urznb4fRy2HAs+cYXprCkCGiv2eegfz8Zl9O4zxGtYLrnXiE3SeGoUgGzLZD6CSZ1XsnUehKm5CcDL/+qogEqwB9HmXQYD3x8SJOrSF69RKVUT/80PXFqa9hzVjx5wHPQBfflgJ+6ikRKjRfS97VqvFKcAsWLGD48OGEh4fTpk0brrzySg4dOuSvsdVLQdxfGPr4NvQ66BW1DgU9x3K6cvy4ON6rF/Q3vVpTLtgcj04HU6c2TnAgnuV+XGenbNMj8MsfIM61qx7Wrf6GTaBNG5EXZeFCyMjw+eU1zhO8EtzPP//M7Nmz2bp1K2vWrMHhcDBlyhTKWmAjqXNnUBQdRr2VtuGZoA9C0kkcd1kWR/Y6wMOTH8WaeKdbuwkTYO9esFga7uOPl5/ix3kXEXz8ZRj8LxjzsR/upIYHHxTuX//8p1+70WhBvBLc999/z8yZM+nbty8DBw7kvffe4+TJk+zatctf46uThASQJBmTvoy0M11RJAMxMXDMJbgLzPPYfXwwv1Y+6tZuzBjhw7h1awMdnFxJzNaB9Gh/kns++wV6P+T3NORhYSLN3pIlkJPj1640WohmPcNZXNNETEzdgZtWq5Xi4mK3ly9ISIA/jvwEveRkzf4pyDK0iYfj6SLg1KBYuHXJxxxIdd8C6NlTRBxs2lTHhW0W2HIrbLwW2k5grXEP734x2neFOxpgzhyx7fHGG4HpTyOwNFlwiqLw4IMPMnbsWPr161fneQsWLCAyMrL6lZjY9IxYZxNkcvDctU/hkE2czO+EIkNcPIyOXwyANPB5zDFJHDvq3k6SRFSAR8HlbIDvBgpP/5H/B2NXMHFaLIoC333nk2E3SEwM/OlP8O679aTZ01AtTRbcfffdx2+//cby5cvrPW/u3LlYLJbqV4avLAKSjjc2LMAqhyJJICvQLS6FG4a/LY7Hj6VXL0g7em7T0aPFHp1cFR7jtIpiiGvHi/pyl+6FrreCJNG2rXBo/vbbc6/jL2bNEjXG3SoBabQKmiS4OXPm8NVXX7F+/Xo6dqzfw8JsNhMREeH28gmSjv2WGTicBsLDAFmmd/Ay1qeMrz6ld29ISzu36eDBwmG4qBARPfD9EJEmb+B8mPRTdRXVKqZPh9Wr/VCEsQ769RNbEu++G5j+NAKHV4JTFIX77ruPzz//nB9//JGkpKSGG/mRhASRxz822opRV4asC+fvnz5ffbxXL89FEwcMgGBTOcrp78GaB/pQuGQX9PVcW3vqVBE0umevP+/GnZtvhnXrNONJa8Mrwc2ePZuPPvqIZcuWER4ezpkzZzhz5gwVZzstBpA2bYTgpvZeiYSMLXEmpdbw6uM9e3pu15b1pPyzP1HOHWCIgCmbIap/nf0MGQJmc2Bj12bMEG5fK1cGrk8N/+OV4BYtWoTFYuGiiy4iISGh+vXJJ5/4a3z1Eh0NQYZyOkcdoNIRQkh0W8xnGSU7darVwGaB7Xcj/TgRi70j3x29F4yh1SnQ68JkgmHDYLs3MXLNJC4OJk/WBNfa8HpJ6ek1c+ZMPw2vfobEf0GouYy00snYHEYkCeLb1ByPjYWgqhJvOT/DN73h+DIY/hbvn1rP0VOxje5r1Cgvg1J9wKWXirAdjw7UGqpEtb6UALbQAZRZQ8h0TKhOyBN9Vl1DSYLhfVw74SkLhGvW9BToMYuu3XQUFTY+kc/o0XAq07fjb4ipU0XIzpEjDZ+roQ5ULThjdFfKKkMxGCRQhPNvdJTroPz/7Z15eFTV/f9fd/Zskx3IAsiSBBCEyCIgm2KhVGhpXetP6tb6VRHlx/P0a9AqVFHUtiiWxWotuBS1FlD6sxRQWUQEQZOyL7KGJYSwzGSdzHJ+f5yZJEMmZCaZGbjxvp5nnsnce8/nnMvMm3PuOZ/z+Thg+wwW33OT/NznWRi+tC4zTpcu4PYEmTwRObMZbXJy4Kqr4DK5q2pEAFWGWPCR5BWXz+Oqurr+GBvvgN2zWX/cm8k01T/0gW+CNdip/k6dIDamde0NFUWRrmhHj0a3Xo3IocoQCz58w0fflrSa8gvc3fu38kNMBxj3X76pCJxc8aqr5PslM5U2QKeTW36izcCBciirhbBsG6h6SBnv3Wht0LswGx2klLxMxzivI/WAhZDYk8TEwGVjY+WESrBDSpAxSKLNwIGyFxYhtFPjykXVgjObwWSopY/hVSzGGmyGIfynUobJ840zfUNMT4AuIjYuNMFltSxsSavwuakGar+G+lC14GI4SWKsDQfJlNckcEo/AUOMXPj2PZv5eriqqsbl42LlxEmwdPQKLpo/fqsVEuK1Hq6toGrBmZMyOVeZwl7n/Xg8OlwusHgnNmpq5LtPcBUVjcvHxtWnAA+GzEz5Xl7e8ja3hLR0rYdrK6hbcGZwu/UIjxw+ulxgschzPm+z2Fj57hNgQ2JiQkuo4ZukifYG9+RkLfFHW0HVglMUQKl/DnO6pIigXmBGmXIg4PS/wRDaD9nXW0ZbcHGxmuDaCqoWHEjRudyAAi4nmLwCc3g3b/p8KwMJzhii4HwTMNEWXGwc2rpAG0H1gmuI29047IjRK7hAUY1D7eHMXr/MaO2L8xEbo+mtrXBpN/kwMn/+fObPn4872JXmIFEQJOhOoNe5iec4Mc49AJhq9sI5HXHOEgAM1QfgXLpf2STzSQw6J5z7rpHdQBirZNdmcR0Kukw4sBqK0SmeqNbZZrDtudwt8EMRIrpPB3a7ncTERGw2W1h2f59/M4XkOC1/r0YzjN8P1pzL3Yro9XCRwuXRU1Q5mW76tznIA8R3Gkz30l9yLOtdOvXpxYmDJWQduJkDiX8mZ8hQv7Kb//4GOZalpN6yKqi67OcrsW4ZwQ79bPr8qPkccOFi27L36W38M5YJm6JWZ5vCkHBFiA3agOAQCpUiC7dHT5WSjd7cE4Aacw9IuZbKYzJokdOS0ygn3AVHJm6TsclccRdTUV6OFXBbugZdJhycr9mIx6CLap0akaHtTJoIOWHi9M5O+mYr3d4JDn2AOw3FrQugyru2ZzJf+rpwU1UFkQ1BqxEtVC84Qf3MpKJAjXd3tG9G0ekTXIC+3OkMLZhyZYW/7WhRVRXxoM8aUULVgvN4AFEfaMtoBId3wbvO48TrQxlIJDXVcttNsJSVyfdwRfoLlooKtC6ujaBqwdVUC+ItFcTqTgMy2I8v/ofZKzi71+8xPkDOxOqa0NK7nfaGrGtqy0+kKCsDnSa4NoGqBVd9oQSToZbexteIMVVjMVY3GlL6UhnExQUoXx3aD9kXI9L3fBgNPB4puDDkfdS4AlD111jlyeBcZQrH3WMxGWrpUvMS7Z0yPrhvksQnuEAiqQ5xSFl8rJUNbgHHj8vnUK2HaxuoOqZJVRUgoMQ9Anu1lVpzLkPiZsqT5fsBsDeRB87jgXI76BsHWm6SQ4da1dwW8Z3XuUTr4doGqo5p4ttUKgAhFCrT7uKd/W/Jg5smwbfTsJ8LsBEOOH1abj690gW3dStYE7RZyraCqv/f9G0E9a21xcXBzhP95YfcR+D715nc8wbv1f4ebMe8w8NgBVdZCUcuQ/Ssb76REcM0vbUNVC24s2dBUURd5C1LDFzwDSG73APj97D/9DXy8/anoaK+iwpVcEVFoS+UtxaHAzZtgq7hTymucZlQteCSbX8nJf4cisuGopMTC7YLDS6I68yU97xDzMqj8OnVsPN58Dg5cECu1QX7bPTtt9Ff8N64UQ6be/aIbr0akUPVgtt1VkZVvjruvbpZvNIG6alcrgafr3sTch+DHTPgPwOpOv4d7dKDH6p9+y30vjpsTQ+KVaugQ4f6WCoa6kfVgjte1p7ymkQSjKexGKtwOQXnztWfP3mywTBQZ4H8l2CszDk1c+ggRuStCXoH6rZtkB9F32EhYPlymdBDmzBpO6hacOfOgQcDG4/+AqPeieP4l37n9+8PUCjlWjxjtjLrk9/TLfFrcJyB0o2XrOf0adi9GwYPDmPjm+G772T21jvvjF6dGpFH1YI7e1Y+t/33aD+cHjOxF/4fg7t/XXd+//76IEINOXDQyO//+RQnYh4CdPDZCNg2BVyBg5V89pl8v2FU+O+hKd5/XyacvOGG5q/VUA+qXvg+dUqg04HNBm4s2D25vPzL+lwC+/ZB586Ny/kymaZntwNzGlw7Bw6+BSvzoaxxmtM1a2Sa4nbtGp2KCLW18O67cMcdMu6KRttBvQvfHicv//gmTIYaqmuki1aR7a76lMOeWvbtg25dGxf95huZjjgmBjlr0mMqjCsEYyKsGQo7ngWPXNwTQgruRz8KT7ODYdky6bf50EPRq1MjOqh2SCkUI8Vn2mPSVWLQudApUHImlgVf/0lesHcO+/ZBlyYEN2jQRQeteTLX99VPws7fw5rhUP49RUVy8mXs2IjfUh0LF8LIkdCrV/Tq1IgOqhXc2bPwzEczUfBwXfct6HReb/5EGWKB4qUMzfx7ox+twyEXsRsJDkBnhGuehZs2ysmUlf04uGYRKSkwalSEb8jLli2wYQNMmRKd+jSii2oFd/IkHCjJxSUsjOy5DkWBM2egy1XyfJn5J7zxwIPkd/NPH7pli3xGGjq0kcl60ofAuCJEpzu4Nft+Vjx5L0YlOtFfn38eevSAn/88KtVpRBnVCu6EN9+2wx1HjLEaPA6qquoTLX52YjqHyrrR+fT/+JX74gsZq79fv2YqMMZTZH6LSQvfYXDGR7BqENj3hv0+GlJUBP/6FxQUhLZtSEM9hPy1btiwgQkTJpCZmYmiKHz88ceRaFeznDtRwthrVuF269hfNhA8DkwGR53gdu2zMGvtRyjVJ/3Kff65HB4G40O5ZAms3DMJz1jvRM+akWG9h4spKJCTOXfdFdFqNC4jIQuusrKSvn37Mm/evEi0J2g6VLzOR4/fhtsjOFY7EoRgSM5mOnaU5/fuhbSuefKZDODMRiorYfNmGD26efu1tfD22zBpEhhTe0kPlY4T5cmDfwVPgNjpreDzz6Ur1wsvBF471GgbhCy4cePGMWvWLH7xi19Eoj1B88n2X5FgKceg1BKXlIRbmBjVaz1mg4widOQIDBgAdLpDFtj3Kpu/OI7LFZzgVqyQz4S/+Y33gCEOBr4u/y75HNaOBcfZsNyLywXTpklPlsv8z6oRYSL+pOBwOLDb7X6vcLB5Z1f2nRuK2VBDWho4XGbizBVwXA5xhYDhw6l3RNSZyTr2K3Jz3OTlNW//zTflxIrfLKfPVp+n4cIOWHUd2Ha3+l7mz4cdO2DePM1vsq0TccHNnj2bxMTEuldH35ivlRw8CFvP3IXJUEt6ciVOl47S2n5waBEAqSnQrcE+Mk+P/yU3cR1//PWcZn/Ue/fC6tXw4INNXGD1DjH1MbBqMJz4d4vvo7gYnn4aHn4Y+vdvsRkNlRBxwU2fPh2bzVb3Ki4ubrVN25nz3J6/kF1npfuHqWoHCKhJGg01MmRev37+vcWBsr7MWTmNm7OfBvu+QGbrmDMHMjKacRyO7yIXytuPgvXj4cDCkO/D44F775Vh955/PuTiGiok4oIzm81YrVa/V2spPlzBwvsfIU2/HafbhM7+XwDSO7bHnS69ffv28992s3kzzPnsOZT4TrD5/iaTe58+De+8A489FsSGU2MCjPgYcqfA1kekS1gIyYj+/Ge5TLF4cX2yR422jSpXe/Ye68ieEz3oFrcalzATz1H0eg9xcfC9624Ars/72q/Mhg0wZlwMyuC3oGwTHJgf0Pa8edJh+H/+J+Dpxig66P8q9H1ebm7dNqVJMTdk92544gl4/PHgJnE02gYhC66iooKioiKKiooAOHz4MEVFRRzzBQmJAnv2wIYDY8jPWA06M063AbNRTtN/9q3cJdrJs8SvzPHj3vWtdsMh91Eomg61/nnl7HZYsAAeeEAujgeNokgfzEFvwvcLYdNd4K5t8vLaWrj7bujaFWbPDqEeDdUTsuC2bdtGfn4++fn5AEybNo38/HyeeeaZsDeuKY4euMApx7V0Tj2KQe9h36keMpMpsGmTfHBTzm6BC7vqyiQlwY03ej/0nQ2WdnBihZ/duXNldK7f/raFDev+axi2VM6UfnV7k6KbMgV27YL33vPuWND4wRCy4EaNGoUQotFr8eLFEWheYJ7oP5whXddT6zKio5adxVejU9xUXTjPLt8svTkV9r2K2xtiYeTIBnvLjPEwYL6M4uWW63bnz8Of/iSHktnZrWhcx4nyue7kyoCi+8tf4I035I6Aa7V0bz84VPcM53bDV3sH0T21kMKjA0E4+b40DwGcO7yrfs6i0+1w+F22bZLDxkY7p7N+Agl54LSBq5I//UkO9aZPD0MjM8f5i87rlbJxIzz6KEyeDPffH4Z6NFSH6gR35Ah8vX8QnZN2cKh8KDpqSWtnRlEMGKt20t239pb9c8BD8aalgPTAb0TmOBAeKra8wNy5UgwdOoSpoZnjYPhyOPlv2PwAx456uOUWuZj+yithqkNDdahOcMd27CI7tRiDzk18Wnt0iqBn1zKEzkia5RA3DvMGpjQl40ifyDWJ7wNNhMMzJYMhHvPhP9Ij6wAFBWFubNZPYPA7cORd1vzhCWJj4aOPNF/JHzKqi2milG3iyZ/OpqbWRGqKGyEgJ+Mwbo8RBcHNgzbUXfvp3t+Q2+HAJe05RTwnzmbwfsF0UlJa1bSAVKbfyZz1c3lg6B/55u0/Ri0uisaViepimoz62dXodR4OlnYjQezF5THQLu4wTpfCifOd6WxZD8j152cWjOZMVdOuZAKw2RVe3/Qs3U1LAwYQag1OJ9x2G8xY8hinUp4k/fhvoXhZWOvQUBeqG1KSKL2Jz1e1x+oqxO0xoq85jNMJdnJRzm0BYPt22LVbR2Wq1z/L3XjH9u7dcqJk1L3/BxJ7w38LQvIUuRROJ/zylzLE3rJlkDF2FnS6Db7+FVzYGZY6NNSH+gRnSqKsKouYOBOZ8bsQOiOK0w4eD7EZeeCS6ane/wBycqDTsFtluTOb/MzYbPDvf8v8Aj8ep4e+L8DptVCyptVN9IltxQr45z+9Eb8UBQYvgviusGFio0V3jR8G6hMccNbVi5SkGox6FwaDnA7R691k53QEgwyT98UXMHUq6GIzZKHTa/1sPPmkDChUl687azykXy89UFrRyzmd0qPFJ7af/rTBSUOcXC6oPQ9f/TIoFzCNtoUqBZfXPxeruQyPR8Gg92CvScRkcGM06SD1OgDi4+GeexoUOl8I1XInwddfy4Xnm0Y3CLWgKNDnWTj/HZxa1aJ2VVZKgX3ySQCx+YjvCsM+lD3pnpdbVI+GelGl4EjIIZ5DHLd3R7hdHD2TjV4vA7c6rEMAuPMWO3FxDcooOjj2D5xOuc9twAAYdN1FdtvfAKmDYPeLITfp7FnphLxxI6xc2YTYfHS4CXo+AdufgXOFIdeloV5UKTh3XA5mQw0OY3eEx8VpezYKbhAeVm6VGTduv+miH3Jyfzj2IbNnS+fnN94IkKheUaBXAZSuhzNfEyzFxXJ3+aFDsG5dkN7/fWZCUm/4+u469zKNto8qBXe4LAeA5PYpINyYkjqiAO6qUt54VyZTSxL/9S+Ufj3izCZef7WUp566RJi87J+BtUfQvdz27dJ7pLoavvoqhF3behMMeRfKD0LRk0EW0lA7qlv4Buje9yqEYsCDCb3OQ6ecVACO7S3mxElvt3W+yK+Mw3odQsCD4z/ld7+7hHFFBz1/Cyf+5ZeiOBAffyzFlp4uxZaTE+KNJPWGfrNh3ytQuqH56zVUj+oWvgHQGVHiu3D0sPTE75RRjkBHWfGp+pDk9t3gqq4rsvjvSWz5fgjTbl/RvGtV5ztlYo8Dfwl4WiBDIvz85zBuHHz5ZSuylOY9DmlD5I7xMIfe07jyUOWQEsATn8OFUrmWpXOeQaDDairh17/2XiDccK5e3MuXg6vDT7FWrvYTYkAMsdD1Xjj0N3A7Gp1+bS787ncwcyZ8+CH+kzOhouhg4AKw74F9r7XCkIYaUK3gis92Ii3uJAIdoroUp0tPdmoJfXp7L9DHwpmvOOddX+7TB66/7WZwV8GZL5u0W0fOQ+Aog2P/rDt05Kh837pNOiHPmBGmkOTJ/SDnEdj5LNSUhcGgxpWKagV38kJHurQvBkVPedkZXG49caby+uCs1h6Ic4VMmyY/PvEE6JKvBkt7OP1F8xVY8yB9OBx5D5Bra8OHyVPPPQe33hrmG+r9jFxw3/VCmA1rXEmoVnBDRnciKeYsIKixnwfFu4Jt84ZVsOZx4fB3fP65/JiWipz2b38jlAQhOICr7kKUrGHGE6VMnAjDR8jDXa4K333UYUmHXv8rgxtVHo1ABRpXAqoVHLFyF4AiXMSbzmM26+Tz0IUdABTb8kg2HOT/PmrzL9dhNJz/FmovNFvFcd1tuF0Kth0f8uqr8Pf3wn4X/uRNlaH3dv8hwhVpXC7UK7i4+m03seYaDJSDKQUqvgfgxQVyi/djk/yXB2h/IwgPlF76Oe7DD6HPgFTW7h/HrAeW8PjjUQhDboyH3MdlspDqkghXpnE5UK/gYrL8PwsPmFIR5XLtbN+Jznh0MRhs3/lfF3cVWDrA2S0BzV64IEPY3XknjBkDQ26/hXjHFqgpjcBNBCDvUdCZYP/lzU6kERlUKzinx0xZxUXbp82pKFXy+efZ5wzoEnvK6faGKAqkDoSzjTebrlsH11wjkyK++y588AHE54yTJ0+ujMBdBMCUDF1+BQffvGRsSw11okpPE5Ah70wJXsEp8jZOna+PkTB0CGDNDZxHIHUQnN0qe0WgpkbGorzxRhmcdft22cspCjJ+ZepAOPlpWNodFDkPyx71+PLo1akRFdTpaYIUg7VduvxgkPkKPv8yzf+ihDyoPNy4cOogcF6Aiu+prYX8fBkE9qWXZGLEzp0vuj7zZrllJ1qeIElXyyWJg3+NTn0aUUO1Q0oAzFJwHn08AE7loihA1tzA5VIGAHB6zzbKyuQm1MJC2csFTEWcMRacdrmnLlp0uVuuF3r38Gm0DdqE4E6WSsGN/8VFmXmsgTMvrtmQQok9k/Yx+7BapePx1Vdfop7kfNBbGoVpiCgdbwF0UPzPZi/VUA/qFpxFPsOdOiMFl94+1v98fDe/jxcuyEQdY8bAifKe8pL4Jnq1huhNkNIfyoLfI9dqzKnQ4Ud+rmUa6kfVgivcI3u4dpleoV28UGZMrPvzi7Uy+vJHH8n4/tfe0IuQSBsq01xFk8yfwJmN4CyPbr0al2T16tVMmjSJ++67j9tuu43a2uBnk1UtuKyuch9cp6u8+22EAF2DLIqKgkexAHJCZMQIudv7wQdBSZQ9HB5XcJWlDZF5CKJJxlgQrkYBkDQuH3PnzmXp0qW88847LFq0iMTERGbMmBF0eVULrl2mjNCl+G7DXQUxMkpXjUNuoTl4SqbCeX4W/OMfkOVbL4/rIt8dZ4KrLDk/XM0OnoTusp2nP49+3RqNWLlyJfPmzeO1115D8Y6m8vLyWLJkSTMl61G14DDIZzeEt5dyltc9191xO/zhD2CwSoUNGHBR2bhOodUV6vXhQFEgfWj069VohM1m47777uOpp57C3CAXtc1m49ixY5SXBzfsV7fgjLKHQ8j4juXnyynaLZ/bsrJgxw7o0jMrcNnYpkOgB0TRNTnrGVFSB8l3j+Z1cjl57rnnMBgM3H333X7HCwvlUtEVJ7hwe5oAdT2cxyV3Za9cYef4aau3PsjNBcxNZOjwiTUU4kMNWhIGUrz/XkILGnu5sNvtvP7669x7770Y6rJ6Qm1tLRs2yFg0SUlJQdkyNH9JeJg8eTKTJ0/GbreTmJjYfIEgEPoEFGD3rlp6Z0KfHuV0790OihtMWBp9/xCe1ld4OYaVSZdaINSIBsuWLaOyspJPPvmEzz77rO54eXk5FRUVZGVlERsbewkL9ah6SFlyVvZS1lgZo6RndzvGWK+YfW5YJq/gvDkHWoVvGCrCIN5gMVqbv0YjoqxatYrY2FgKCwvZvHlz3euOO+4AYMiQIUHbUrXgMrJMAHTM9g63XBX1P1CnXb771uKC2HDaLLHe50GHFnfkh8T69evp37+/33ASpBABJk6cGLQtVQvOF1ZBEd7eTLhkwgyo79FMXsGFYw3N5H0e1DLf/GBwOp2UlJTQ76LIwSdPnmTz5s0kJyf/kATnfVDzTSh4nHLzJtQvFejkwnegcHchY0qW784w9JYaqqCsrAwhBBkZGX7HlyxZgsfj4ZFHHiEuhDiJLRLcggUL6NKlCxaLhf79+/Pll0GEnYskPnF5nKAz1v8NDT6HYVrd9zwYjuFpKBjDM8mkETrJyckoikJaWv3WLyEEb7/9NhkZGTzxxBMh2QtZcB9++CFTp07lqaeeorCwkOHDhzNu3DiOHTsWqqnw4RNXQMGZ/D+3Bn2MfHc3E0g23GTeHN36NOqwWCxkZWVRU1OfcGXZsmXs3r2bv/3tbyQkhLa8FPKywJw5c3jggQf4tTfE8auvvsqqVatYuHAhs2fPbnS9w+HA4agfztnt9lCrRAjR9MJiFTILohMQTqgU8lh5FdjtUO29plrIzw0x9gDb3sbHm8JpkrbihgVfJhz0mgtdCqJbZxsmISGhzjUrGO68806++UaG5Dh+fs+xJQAABlFJREFU/DhTp07ltdde48c//nHolYsQcDgcQq/Xi2XLlvkdf+yxx8SIESMClpkxY4ZAhuP3e9lstqDrtdlsAW1oL+3Vklcovz0hhCgvLxe33nqrmDRpkhg7dqxYvXp1SOUbEpLgTpw4IQDx1Vdf+R1//vnnRW5ubsAyNTU1wmaz1b2Ki4tDvmmPx+Nnw2azidzc3BYd89VfXFwcctlI2w+mznDbv/hYpO2HUkek7Hs8nlB+9mGlRZ4mF3fHQogmu2iz2ezn7NnS+qxW/wVgvV7f4mMAVqvV73gwZSNtP9g6w2m/qWORth9MHdH4jqNNSJMmaWlp6PV6Skr8g5SWlpbSvn37sDasOSZPntziYy21F2n7wdYZTvvB1hFp+4Gui8Z3HHVC7RIHDRokHn74Yb9jPXv2FAUFBUGV9z2PhTqODheRrl+zf/nruNy/sUuhnzlz5sxQBGq1Wnn66afJysrCYrHwwgsvsHbtWhYtWhSUx7TD4eDFF19k+vTprR5qthS9Xs+oUaMauepo9qNjPxp1ROMeWoIihBChFlqwYAEvv/wyp06donfv3rzyyiuMGDEiqLK+3QI2m+2yj6c1NKJNiwTXGoR3TS3UtRANjbZA1AWnofFDRt3OyxoaKkMTnIZGFNEEp6ERRdqk4ELZPrR48WIURWn0augdHgwbNmxgwoQJZGZmoigKH3/8cYvaHqqddevWBWz/3r17Q6p39uzZDBw4kISEBNq1a8fEiRPZty9Aqq8I2AnXd7Bw4UKuueaaOg+TIUOGsHJllPL6BUmbE1xLtg9ZrVZOnTrl97JYLCHVW1lZSd++fZk3r3WZS1tqZ9++fX7tz8kJLcLY+vXrmTx5Mps3b2bNmjW4XC7GjBlDZWVlVOyE4zvIzs7mxRdfZNu2bWzbto0bb7yRn/3sZ+zatSskOxHlMi66R4RBgwaJhx56yO9Yjx49mvSEWbRokUhMTAxrGwCxfPnyqNhZu3atAMT58+dbXV9DSktLBSDWr18fcTuR+A58JCcni7/+9a8Rsd0S2lQPV1tby7fffsuYMWP8jo8ZM4ZNm5pOxFFRUUHnzp3Jzs5m/PjxdcE91UR+fj4ZGRmMHj2atWvXttqezSZjwKSkNBHXM8x2wv0duN1uPvjgAyorK0OKqhVp2pTgysrKcLvdjRyp27dv38jh2kePHj1YvHgxK1as4P3338disXD99ddz4MCBaDS51WRkZPDGG2+wdOlSli1bRl5eHqNHj64LUNoShBBMmzaNYcOG0bt374jbCed3sGPHDuLj4zGbzTz00EMsX76cXr1CzJQUSS53FxtOfPv1Nm3a5Hd81qxZIi8vLygbbrdb9O3bV0yZMqXF7SCKQ8pAjB8/XkyYMKHF9T7yyCOic+fOori4uMU2WmOnNd+Bw+EQBw4cEFu3bhUFBQUiLS1N7Nq1K2Q7kaJN9XDh2D6k0+kYOHCganq4QAwePLjF7Z8yZQorVqxg7dq1ZGdnt7gNrbHTmu/AZDLRvXt3BgwYwOzZs+nbty9z584N2U6kaFOCM5lM9O/fnzVr1vgdX7NmDUOHBpeFRghBUVFRo7BoaqKwsDDk9gshePTRR1m2bBlffPEFXbp0aVHd4bATzu9ACOEXU+eyc1n71wjwwQcfCKPRKN566y2xe/duMXXqVBEXFyeOHDkihBBi0qRJfjOWM2fOFP/5z3/EwYMHRWFhobjvvvuEwWAQW7ZsCane8vJyUVhYKAoLCwUg5syZIwoLC8XRo0fDaqegoEBMmjSp7vpXXnlFLF++XOzfv1/s3LlTFBQUCEAsXbo0pHoffvhhkZiYKNatWydOnTpV96qqqgq7nUh9B9OnTxcbNmwQhw8fFtu3bxdPPvmk0Ol0rYpBEm7anOCEEGL+/Pmic+fOwmQyiWuvvdZvSnrkyJHinnvuqfs8depU0alTJ2EymUR6eroYM2ZMo2fAYPBNz1/8alhXOOzcc889YuTIkXXXv/TSS6Jbt27CYrGI5ORkMWzYMPHpp5+G3P5AdQJi0aJFYbcTqe/g/vvvr/ve09PTxejRo68osQkhhLZbQEMjirSpZzgNjSsdTXAaGlFEE5yGRhTRBKehEUU0wWloRBFNcBoaUUQTnIZGFNEEp6ERRTTBaWhEEU1wGhpRRBOchkYU+f+Xil/7oDEv0AAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN.plot(chart=spher, number_values=15, plot_points=200,\n", " color={x: 'blue', y: 'orange'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the embedding $\\Phi$ in terms of the stereographic coordinates is computed by Sage:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Phi: S^2 --> E^3\n", " (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))\n", " (x, y) |--> (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1), (x^2 + y^2 - 1)/(x^2 + y^2 + 1))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This means that we can use $\\Phi$ for a 3D view of the stereographic chart:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN.plot(chart=cartesian, mapping=Phi, number_values=25,\n", " color={x: 'blue', y: 'orange'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The hole at the North pole is due to the default limitation to $[-8,8]$ for the plot range of coordinates that span the whole real line. We can change it to $[-20, 20]$ via the argument `max_range`:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "