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@genkuroki
Created June 19, 2017 13:45
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Julia/SymPy in Julia.ipynb
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{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 以下は必ず実行しておく. PyPlot も宣言しておかないと、plot_implict で kernel が死ぬ.\n\nusing SymPy\nusing PyPlot",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# 数式処理用の変数を宣言\n\n@vars x y z",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
"text/plain": "(x,y,z)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "f=x*(x^2-1)*(x^2-4)*(x^2-9)*(x^2-16)-(1+0/10)*y*(y^2-1)*(y^2-4)*(y^2-9)*(y^2-16)",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": " / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2\nx*\\x - 16/*\\x - 9/*\\x - 4/*\\x - 1/ - 1.0*y*\\y - 16/*\\y - 9/*\\y - 4/*\\y \n\n \\\n - 1/",
"text/latex": "$$x \\left(x^{2} - 16\\right) \\left(x^{2} - 9\\right) \\left(x^{2} - 4\\right) \\left(x^{2} - 1\\right) - 1.0 y \\left(y^{2} - 16\\right) \\left(y^{2} - 9\\right) \\left(y^{2} - 4\\right) \\left(y^{2} - 1\\right)$$"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plot_implicit(f,(x,-5,5),(y,-5,5))\naxes()[:set_aspect](\"equal\")",
"execution_count": 4,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026F26E10>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "g=x*(x^2-1)*(x^2-4)*(x^2-9)*(x^2-16)-2*y*(y^2-1)*(y^2-4)*(y^2-9)*(y^2-16)",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": " / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \nx*\\x - 16/*\\x - 9/*\\x - 4/*\\x - 1/ - 2*y*\\y - 16/*\\y - 9/*\\y - 4/*\\y -\n\n \\\n 1/",
"text/latex": "$$x \\left(x^{2} - 16\\right) \\left(x^{2} - 9\\right) \\left(x^{2} - 4\\right) \\left(x^{2} - 1\\right) - 2 y \\left(y^{2} - 16\\right) \\left(y^{2} - 9\\right) \\left(y^{2} - 4\\right) \\left(y^{2} - 1\\right)$$"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plot_implicit(g,(x,-5,5),(y,-5,5))\naxes()[:set_aspect](\"equal\")",
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026A1F550>)",
"image/png": 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n4aSRTX370n7KjDGWk+guaTRsqFw5J08qUxZjTPuePhUdgTR0lzSUmnDXpAnt58wYY5bw9xcdgTR0lTRu3FCurCJFKEFx4mCMWaJLF9ERSENXSePiRWXL69ED2LlT2TIZY0wkXSUNNzegcGHlyuvQATh0SLnyGGNMNF0lDVdX2lNDKfb2QKdOwIoVypXJGGMi6SppBAQoX+aUKcCePfrZYIUxJr1r1wCzWXQU0sgtOgApXbumfJkFCtCm8X5+QKNGypfPmF4kJAAmE60ivWUL3efiQh3ItrZA3rxi47PGlStAmzaio5CGrpLGJ5+IKXfECGDyZE4ajGXHiRPA5cvA9u2Aj0/GjylVCujWDejZE2jVStn4pFK0qOgIpKGr5ilRihUDKlemNz9j7N3Cw4GlS4EPPgBGjwZCQoCPP6avERHpb7/+Crz3HjBwINCgAU+sFUk3NY3r14HYWHHlDx0KTJ1KHwLGWMbu3wcOHABWrqTRjj//TF8dHN7+vG7d6DZuHLBqFTBoENCnD/Ddd9R0pXZGo+gIpKObmkZgoNg2w+LFgbJlgbNnxcXAmFrdu0cXVp99BsTEAEePAps3A3XqvDthpFSoEF2cnTxJC4bOmqWNQSg3b4qOQDq6SRqAsnM0MvLVV8kdeIwx6tSePx+YOJEmwx49CkyYYP1ntVgxmlhrMADffitNrHLy8ABy6eRsq5vmKTVwcABatACWLQNGjRIdjTQePgRu3cr4d05ONHKMsbQMBuCPPwBfX+qzmDRJnpPmkiU0CGXyZGDBAumPz9LTTdIIDxcdAenYERg+nIYOammIYEwMcPs24OVF3589S/G3bZt5e2yePLR0y86dQOnSgKcn8Pw5tT0DQM2agI2Ncn9Dkrlz52LHjh0IDAyEg4MDGjdujPnz56Nq1arKB5PDmM20SsLatdRpPWoUYGcnX3k2NsDcucC0aVTL79tXvrIY0U3SMJlohrZoefJQ9XvrVmDAANHRvF1kJI0fP3oUePUKcHYGPvqIvk6fbvlxRoygr1FRwJ079L/4+29a1DE8nGbqN28OlCtHI2Dk5uPjg1GjRsHT0xPx8fGYNm0a2rVrhxs3biC/REsGREfT1TRASdPenk6OT57Q62lvD/TqlVFsVHurXRuoVYvue/KEXncHB3p9tHSxkSQujv62f/6hbQM2bAByK3R2yZ2bEsf06UDVqoC7uzLlWio6mv7HemFjNutjnuKGDeo6SQ8eDMyZA5QsKTqS9EJCgB07aBOp2rWpNlG8uHzlnT1LtZXDh4H4eKBKFfpgN2yozMiX0NBQuLq6wsfHB82aNXvn441GI1xcXGAwGJA/vzPMZjoZPn8OHDsGtG5NOze6ugJlytBzPD1pIlp2HD1KX69fpyvn6GhKwJUr0//G1VXdI4QePgS++IKaKocOVebCICPPngH/+x8wc6aYGm5mwsJoWfQOHURHIg3d1DTUZsECGk743XeiI0kWHEzJIiYG6N4dqF5dmXKTNsZq146+RkYCe/cCx49TraZoUaBGDfniMfx/leC9TM5mJpMJJpMJABAUBAQEUHvcX38BoaFAxYpUS2rXTp4Lk6RRf2lH/127Bnh7U+3NyYkSe40aQLVq0seQHffuUS0rJgZYvz5ro6DkULQoUK8esHs3vb+ZPLimIaNVq4C6demNLFJkJA1NLFqU+lucnMTGk1JcHE3e+ucfGkKZmEgdpu3b0wibChWsO35iYiK6du2KV69e4WSaGWEXL1IT0+zZM+HtPSvdc1+9MsDFxdm6ACSS8nW6cYOu5p2caHZ06dLKxnLgAH3ePD2BYcMAR0dly3+Xr76ipiolFy99G73VNHSRNBIT6QQ9fLjoSFILCwPGjgU2bRJTvtlMV4DXrwP9+lFTlBYEBdEJ8uhRGoMfEUFDLCMjUy8VU7x45u3/JhO1I0+fPhLe3gcxdepJmM2lYG8PXLgANG0KvHxJycne3oSCBU1vnms0GlG6dGkYDAY4O6sjaaQVFUVNZKdO0QilmjWTa2ulSklf3qtX1E/l50flDBggfoh7Zvz9qXb28ceiIyGcNFQoMhLYuFF9SQOghBEbSzNYlfTiBY1c6dKFRpQo1SkplwcP6AZQs1FCAvWLZHaVazQC//vfaNy/vxurV/uiRInyKFvWsqvylH0aak0aaQUGUk1t3z5q2+/WjU7q7dpRp3xW+0QSE6lvZcMG4OpVOvH166edZp+BA4HVq9Xxvj99mmq0nDRUJDKShor26CE6kvRiY4HevWkxNqXewD4+wDff0Bj2unWVKVNNzGYzxowZg507d8Lb2xuVK1fO0vO1mDTSOnOGFgH08kpekvvTT+mrg0P6E9idOzSSDgC2baNRb0Yjjerq2pW2NtaSv/+mFaiT+tFEWr2a9t0pVkx0JNLgpKGAw4epU3PiRPnLmjcPOHiQhvy6uspfnhp9/vnn2LRpE3bv3p1qboaLiwscLOit1UPSSCkmhpLC6dNUAz14MH2ndVwc3fr3p/6Szp2p6U/No7beJjycBqEsWiQ6EnX2t1pDBZU3/WvfnvpcHj2Sp70ZoKGsX31FQ0IPHsy5CQMAli9fDgBo0aJFqvvXrFmDQUq3E6qAgwP1Q9SoQT9/9ZXYeJRQsCD1WTHp6WQ1FPXr25eajOQQH08zYg8fBo4c0c+6/dllNpszvOXEhJGTtWpFF1BMWpw0FNKyJQ2XvHtX+mNPnUpLNxw9qt4RLYwprVUrGinHpMVJQyGFC9P6/1LXNrZsAZYvz9l9GIxlpGRJGr7NpMVJQ0GffkojmyIipDne1au0P8Hs2bTmDmMsmY0NJY6oKNGR6Isuksa+faIjsEytWrSJzOrV1h8rNhYYOZLmKowZY/3xGNOj4GAaPSZSdLTY8qWmi6QRGUm75mlB27bStLPu309DKGfNknfpaca0rG1bmqgo0o4dYsuXmi6Shr29diax1asnzbIiW7fSKKmmTa0/FmN6VayYuGV89EoXSUNLWrakKx9//+wfIyyMRmI1aaLNvRcYY9rFSUOQ27ez/9yICFpfqGZN6eJhjDFLcNLQMLXtUMYY0z9OGhp2/77oCBhjOQ0nDUGsmYhnb08b8Pj6ShcPY4xZgpOGwi5dop3p0m7tmRXFi1N/xrVrtDIpY4wpRRdJw2ymndq04Pp1wM3N+uP06AHcukWzwhljmdPL5kdqoYukERVF+xZrwbFjtCmTtUaPpiUStm61/liM6dWxY7QKg0jly4stX2q6SBqNG4uOwDIREcC9e7QTmrXs7YFx44A//qB5G4yx9B4/Fh0BzafSE10kjQoVREdgmeBgWkRNqtnrY8bQFrKLF0tzPMb0pmVL2omQSUcXSUMr9uyRpmkqib09sGYN1TaePJHuuIzpgdlM20Dn4rOcpPjlVNCxY8CwYdIes317oEsXYPp0aY/LmB7Ury86Av3hpKGQa9eAAgWA0qWlP/bChbTi7d690h+bMa3y9aUFC5m0OGkoZO9eoHNneY7t7AysWgV89x3w/Lk8ZTCmNffvAx4eoqPQH04aCrlwQdr+jLSaNgXGjgUGDgTi4+UrhzGtOH6cd7SUQ27RAeQEt2/T3hdOTvKWM2AAzTifMQP4/nt5y2LaExNDKwjs2QMYDOl/X7Ys0KwZ4Oio/c7j6GigcmXRUeiTxt8a2vDTT8DEicqVde4cr0vFkh05AgwfTifRZs0oafj4AHfuUB/bhQv087p1gIsL8OGHwJ9/io7aOpGRdKHGpMc1DZlFRwOhoUC5csqVuWkT0KsXMHs20KKFcuUy9QgIoH607duBBg1oFNHPPwO2tjS3J6WUk01NJuDiRWDbNupEHjaMEk6pUsrGb62tW9UzciouDnjxQvzMdKlw0pDZ2bOAp6ey1X1XV/rQfPUVUKcOXT3qSVQUTZRMsn598ve5cgH9+9P3efIAVaooGppwFy4AP/xAcxS6dKF2fWdny5+fNy/QqBHdpkyhwRU9egCTJgF9+sgXt9Tu3AFGjRIdBSlfHvDz088aWLpIGjY29CZRo0OHgK+/Vr7cokXp5NGzJ21sr+XEERFBTW4XL9Jcl+rVk3/XqhXQt2/qx9+5A3h7A3Z2dFXt708n0GrVaHXgIkUUDV92ZjO9NsuX09/27bdA7drWH9fVFfjlF+DRIzr2vn1UWylQwPpjyyk+ntZlU4saNazb3lltdJE08udX53hssxkoXFjcCbtYMWDCBLpS3LUra1ecoiXN5t22jV6/IkWAevWAyZPf/dw6ddKv73X9Ot2mTgUSEoDWrakJz96eLjq0yGym+T/btgGxsZQsypSRvpxSpWhgxZkztKT/2rWpE7faBAZKs5I0y5gukoZa3b4tz2S+rOjUiU6Kf/wBjB8vNhZLhIUBK1fS6J7atYHffpPmuNWr0y2pieXUKZrbEhtLCal9e3VeeGTm6lVg82agUiVg1ixlymzUiGqtS5YAbduqt7nlyhXqx2Hy4KQhI29vahYRrWNH+rpkiXoTx5UrwO7ddBIfPpw2mkrbYSulJk3olpBA7c0rVlBHZc2a6u4HuXQJ2LiRYv/mG8DBQdnyy5QB5s+n0YBBQbRoptrcuZPcr8Wkx0lDRk+f0slPDZISx9KlNAlQLU0yFy7QENDq1YEhQ5QfpWNrm9zxGx1NiWvPHvrd06fqadI7f55GQ1WvDsycSXMpRMmTh/o29u6lPo/Ro9Xzfnr9Wp4mOpaM52nI5OlT9Y0T79iRmjN++YXaw0W6dg0YPJiSxldfUbOR6GGd+fIBn3xCJ2UA2L8fGDSI1vWKjVU+nsREaoaaPZu+Jr1OIhNGSl260FDyn38W/35KcvIk1RaZfLimIZM7d6jdV206daKT4fff0xWi0iNhwsOpfyUuDpgzR12jXNL67DOqaezdC3z5JQ2d7NoVqFhR/rLXrqWmqOrVqYNbrbp0Af7zHxodpIZ5EVevAiNGiI5C3zhpyMTfn5pb1KhTJ7oy7NMH2LIFKFhQ/jKfP6e9Py5fplnrJUrIX6ZUunShxSZv3qSO4BcvqKO1WTNpJ2yFhACrV9MQ1+bNqe8gb17pji+XP/6gxGZnB7i7i40lIoJqjEw+nDRkYjSqpz08I0kr7vbqRctHyHXFbzIBBw/SiKhJk+iK3dZWnrLkZGNDwzjd3Ki25OcHLFpEf1/RojQfJqs1kIQE4O5dGsl14QLNi2jTRjvbFyfJnZu2Hv70UxraLeqkfe2aevszjEbREUiHk4YM4uKUXTYkuzp3pj6OPn2AuXPpyllKgYE0EqpdOxoequUJhikVLEhDdNu3pyvbs2epXd9opL6PRo3oca1bpx4IER9PrwNAr82dO5RoBgwA+vWjK3WtKlqUkmj//sDOnWJiuHyZ/idq4+JCSwnpBScNGezfT5P6tMDNjT7kH31EV7kzZlh/zFu3qAnq6VNqbqlUyfpjqpWTE/VdJfVfhYVREgFoGO/Tp6kf37w5XQ23b6+/VVhr1KD9K9ato34OpZ05A3z8sfLlvkuePOqfRZ8VukkaO3ZQE4Fa2jOlvmqXk6srvX4zZ9IHf9MmoFatrB8nMBCYNw/45x/q5B4wQPtLbGdV4cLJTX9ybbqlZlOm0LIuH31EKzUoxWCghC3n3B5GdPOR7tFDdATJtLiZfZEi1MTSvTvVOH74AXj2zLLn3rpFQ1WbNqXJZgEBdKWptdeAWS93bloZd+pUZcu9eFFd5wA9083HWi01DIDatNUUj6VsbamGsH07LbRYty71d/z9NzWzpL398gvVqJJmVvv60sJ2eum7YNnz4YdU6wwMVK7Mf/9VZhQg01HSUAuTSfsbIH3wAf0NX39NS6H07UsdumlvY8fShDwfH0os1aqJjpypxejRwIYNypXn56fOTnA94hZAiSUm6qeD8/PP6ebjQyupplx+fsAA6kOytxcXH1Ovpk1pUMWECcB778lfnlqWMckJOGnIoHx50RFIq3lzujFmqUKFaCDAiRNAt27ylnX3rrrnROkNN09JLCBAdASMqUO9erSDpNwSE2kODFMGJw2JXbkiOgLG1KFOneQx/pbdAAAgAElEQVQVg+UUH6+fJmEt4KTBGJNFuXLKLImyeTPQsKH85TDCSUNi9vY014ExBkRGKlPbYMrhpCExGxuelcpYSgkJoiNgUuKkwRhjzGKcNBhjjFmMk4bEEhIsX7OJMb2ztaV1zZh+cNKQWGwsTWhiLKeLjaU5FE2byluOnpYd1wJOGhLjZTUYIyEhtBab3Dp3pn3cmTI4aUisVy/RETCmDnfu0KxwJbx6pUw5jJMGY0wmW7fS9q9yy5ePm6iUxDMKZBAWJjoC6cTH0wY3mzZR+3SSJk1oEcNixcTFxtQrMhK4fl2ZmdolSgBXr8pfDiOcNCSWOzdw/77oKKz3+jVtxDRvHnDuHK1a6uREvzObaQOmwoVp740pU4AGDcTGy9TFz48uKpSa6Fq1qjLlMG6eklyePED16qKjsM7t27RfRp8+tMz7iRN01XjvXvLtxAnapOnZMxodM20aYDSKjpypxZ9/0iZdSqlUCTh5UrnycjJOGjI4dw6IiREdRfYEBdEVoosLrdj711+UFIoWTX6MjQ3dN348cOoUcOwYEB1NH9zt28XFztTh/Hna0THle0ZuTZoAL18qV15Oppukcfas6AiSNW+uzfV2/vc/oG1b4Pff6fb++5Y9r1kzYMkSYMsWYNky4OOPgRcv5I2VqZPZDCxcCEyapGy5ZcrQBQ6Tn276NCpVUs8cidy5AYMBcHQUHYnlli2jGsP+/dnf67tlS6qBHDoEtG4NfPcd8OGH1GSX08THU60trZIlk/uG9OjCBaBiRaBgQWXLdXICPDwoafHWr/LSTdLInx/IpZJ6U/PmwO7dwKBBoiOxzPLlwOnTwMaNgIODdcfKkwfo0oWaC0aNouNOn07/Hz0zGChJ7NwJ+PvTpkAZdQLnyUMjfSpXpklpnp60h7YeTnRRUcCKFcCCBcqXnSsX9a/FxQF2dsqXn5PoJmmoScGCwIMHoqOwzOrVwNGjVLWX8sP23nt0zDNngGHDgDFjgEaNpDu+Wvj50Ykyb16gbl2ga1dgzpx3P+/WLeDGDXpd7O1pUmjHjvLHK6edO6mp8r33xJTv4UG15Q4dxJSfGYNBX8PwVXJtrj9ms+gI3m35cuDAAWDbNvmuzho1ov6Rw4eBqVPpSlApy5YtQ7ly5WBvb48GDRrAz89PkuPevUuJYuhQ4Plz+vuWL6fkWL++ZceoUoU269q0iZ7/8CHw+efAhg2ShKi4Bw8AHx/g00/FxdC7NxAaKq78zMTF6WtIMCcNmRQqpO7O4GXLaIjipk3yN43kywfMmEFDePv1A27elLc8ANiyZQsmTJiAGTNm4OLFi6hduzbat2+P58+fZ/uYwcHA7Nk007lJEzrZd+5sfbNorlzA8OE096V8eWDWLErkSqzbJJVffgG++UZsM5uNDf2PmLw4acikTh2qlqpRYCC1q//+OzWrKMHGhppv1q6lzvY//pB3WPKiRYswbNgwDB48GNWqVcOKFSuQL18+/PHHH1k+1v37NCfF25tqA1OmADVrSh+zrS0loxkzAFdX+rprl/TlSO2334D27WkEk2hOTjxfSG6cNGTi6qquYcBJ7twBVq4Eli61vtM7O/LlAyZMoAmQkyfTpEGpm/JiY2Nx4cIFtGnT5s19uXLlQps2bXDmzBmLj3PyJF31HzwITJxIAxsKF5Y21sw0a0ZJIzSUajf//qtMuVl1+zadpFO81EK5u3PSkFu2OsLNZjMiIiKkjsUqMTHqerMULUqdnWqKKS6OZumuXUt7HcTGiovl/feB77+nkVUuLtQfINWic0+ePEFCQgIcHR1hTPEPKFCgAK5fv57qPgAwmUwwpWgL8vKi97a3txETJlCiA8T8L/v2pa+LF1OtsF8/9SzOd+sW1VbnzVPP+zxvXupb6dJFdCTJIiJo8qtaXqOUnJycYJPFNkUbsznr13lGoxEuLi5ZfRpjjDEVMRgMcHZ2ztJzspU01FbTMBqNKF26NB4+fJjlF0BO69bRJLeSJUVHQm3jRqMRY8ao73UCaAa9tzewfj11qFasmP1jxcbGomjRoli/fj06d+785v7hw4fDYDBg8+bNb+6LjweOHjXh7FkT3N2pWSg09Anq16+PGzduoKQa/nkpJCTQUi3370tbO8uK16+BH34AunUzolUr9b2fVq2i10YtgoONqF1bfa8TkL2aRraap2xsbFT3xwOAs7OzquJq146GZFq6HIdcHj2ik8y4cTQvQG2vU5IePWhW+Y4dNDmyf3+aBJcdHh4eOHPmDPr16wcASExMxIkTJzB69Gg4OzsjJobmWBw5QsNkFy1Kfm7SpDwnJydVvk5Dh1Jfwo8/0oi0Dz5Qruy4OOC//wU++ih5gyW1vZ8cHGjkmVr2Jk9aAUBtr1N28eQ+GZUoQfMT5N4j+V3GjqVaT8r9MNSqQAFgyBDqo1qxgq5qGzQAWrXK2nEmTJiAgQMHwsPDA/Xr18eSJUsQFRWFZs0GY8EC4PFjWuLk++/l+TvkVrkyLdPy66/Anj2UQOQWH0/rirVvT3Mi1NhGD1Bt8dEj9SQNvdFF0lDr4oCOjjS8VaTp02lSnaOjej/kGXFwAL74gjrrly2jJpmyZYFOnSxber5v374IDQ3Ft99+iydPnqJMGXd06nQIZ88WRa9eQIUK8v8NcitQgIYCBwQA3brR8vRy7Wvy+jUwcCAl2qFD5SlDKvnyUTNnnTqiI9EnXSSNxMS86NFjBvIqNekgC6pVo9ETIhapCw2lZikPD/o5b968mDFDna9TZuzsKHnEx1Ofx5EjtIJqtWr0mvbunfHztmwBIiNHo2bN0Rg3joZiengAlrQOJL0+WnidbGyAWrWAzZupn+HAAWDECKB4cenKiImhPoLmzVP3Faj1/VShgnV9YlKzs8uLfv3U9zplV7Y6wtUmMhLw8qI2cbU5epSu0lL0xyoiIYGWdFi2TPkVR5UQEEDt68eOUVNTSqVKUd+InR1Qo0bWj500OjA7I0tE27SJmqwmTgR69rR+hrbRCIwcCTRuTAtQasWsWTTPRQ3CwmgRS7WtiZVduqhpqJmHB72BlU4ap09TB7weEwaQPCO7bl2xcahNv340q3zqVBoxN2VK9hInQBNBmzYFvv2WEoeWqKn58dgxy2q4WsEzwmWWL5+yO5glUduwQ6acsmVpheGePWmS25dfZm2V1YgIaupq1owWUNRawgBoCZ+AANFRkLg4/dQyAE4asrOzo6qpkqu7+vjQqprFiilXJlOfHj1oL3eDgTqFu3enGmhma36Fh1NzppsbLcr4zz80z0iLunYFnjwRHYU+cfOUAtq2pQ1qlJqItXq1mI1wmPqUKkW1zuPHqZmpaVNaSbdGDaBhw+THHTxIS75HRdEQ7alTxaxNJhV7e/pbmPR0XdMwmUxwd3eHjY0NLl++LCyOAgVogxol+PvTSKN31TKCg4Px2WefoXz58nBwcEDFihUxY8YMxIpckEolfvvtNwBAkSJFJN2HQ6SWLanWceIE1TguXgRmzky+vXpFy7PfuEF9cG9LGHPnzoWnpyecnJzg6uqK7t2746YS691ngb09Td5Ui3nz5sHGxgbjx48XHYrVdJ00Jk+ejBIlSogOA40bK1dV3r2bxuy/S2BgIBITE7Fy5Upcv34dixcvxooVKzBt2jT5g1SxLVu2vHkNTpw4Ick+HGrSpAnw00+06ZPJlHy7epWWb7FkqK6Pjw9GjRqFs2fPwsvLC3FxcWjXrh2iVHRp7+xs2XweJdy964+VK1eiVq1aokORhlkHIiLM5h07Ut934MABs5ubm/n69etmAOZLly6JCe7/tWunTDn165vNL15k77kLFiwwly9fXtqANKZ+/frmYcOGmQGYDQaDOSEhwVyiRAnz3LlzRYemWs+fPzcDMPv4+IgOJZX160VHYDZHRESYixWrbPby8jI3b97cPG7cONEhWU2XNY1nz55h2LBhWL9+PfIlrWudA0REUFNYdvdoNhgMeE/UBs8qkLQPR4sWLd7cl519OHIaw//vNqa2986VK6IjAEaNGoXatTul2ttF63SXNMxmMwYNGoQRI0bAI2kqtArUqCF/x9yePdlf4C8oKAi//PILhg8fLm1QGhIWFoaEhAS4urqmur9o0aJ4+vSpoKjULTExEePHj0eTJk1QI7sTQmRy9arY8jdv3oyLFy+iT5+5YgORmGaSxtSpU2FjY5PhzcnJBj172iAwMBC//PILIiIi8NVXX4kOOZWXL+Xf/vX+fSA4OPPXKekWmGZBrJCQEHz44Yfo3bs3hvHkDpYFo0aNwrVr11ItN68WIrefffjwIcaNG4eNGzfCzs5eXCAy0MyQ24kTJ2LQoEEZ/i4qisafV6hQAf/88w/OnDmTbp0XDw8P9O/fH2vXrlUgWjFOnAA6dZqIhQsHvfVxFVJMl338+DFatmyJxo0bvxk1lFMVLlwYtra26Tq9nz17hmI86SWd0aNHY9++ffD19UWpUqVEh5NOs2biyr5w4QKeP3+OunXrwmymrYITEhLg6+uLX3/9FSaTCba2tuICtIJmkkaRIkVQJJO1jiMjgQcPaCLdzz//jDlz5rz53ePHj9G+fXts2bIFDeRaAlRFnJ2LwM3NsjWhQ0JC0LJlS9SrVw9r1qxBrlyaqXjKws7ODvXq1YOPj8+b+xITE3Hs2DGMHj1aYGTqYjabMWbMGOzcuRPe3t4oX7686JBUp3Xr1gj4/ynpe/fSzPzBgwfDzc0NU6ZM0WzCADSUNCxVJk2d1NHREQBQsWJFVV4NiRISEoIWLVqgbNmyWLhwIUJDQ9/8LidfVU+YMAH/+c9/AAA3b97E77//jqioKAwePFhwZOoxatQobNq0Cbt374aTk9Ob/h4XFxc4aHlGoIScnJze9PFcvkx9mvnz50ehQoVU1/eTVbpLGswyXl5eCAoKQlBQULpkatb+wsfZ1rdvXzx48ACTJ09GkyZNUKdOHRw6dAhFRSwgplLLly8HgFSjzABgzZo1mTYhM/3QfdIoV65cjjkJNmli+WMHDRrEH/BMDB8+HJMnT0ZYWJjmlkZXglY+TydP0vYAauHt7S06BEnk7EZsBb33nvzLI5cvD5w/L28ZjGlFcLDoCPSJk4ZCrl2jLVflVL06tZ+qdftbxpSUg+b1KoqTho64uwNPn2Zt7wTG9Oqjj0RHoE+679NQg0ePaElqJfTqBfj6Zr53NmMANd2kXPi5WbPsLz/DchauaSjg5Ena10AJI0cC//ufMmUxbQkPB5YupQuYqlVpk6akW8mSNJdg7VpAD6vjh4bSNqtMelzTUMCVK8CkScqUVbo0kD8/dYiraOktJlB4OG3/Ons29Xc1bQp8/XXqx8TGAn//TTOXd+ygZdK1/P4xm4HOnUVHoU+cNBQQGAg4OSlX3sSJwNy5wPbtypXJ1Cc+nmoWP/9MTU+LFwMtWmS+Z8acObRx0apVtGnTmDG0QZOdnZJRS0Ppz1xOws1TMouMpKv/PHmUK7NlSxp+K3qVTyaOry/QvDk1N82fD1y6BHzyybs3Wapfn5LGmTPUvNOjB23SpDW3btG+6GpgMOhrKDzXNGT26BFQsaLy5U6eTB/4U6eUL1tJly/TCsIpVa8O5NQJ3NHRwLRptCf4nDlAx45AdpY5qlGDFgGdO5fev3v3quckbInwcCCTpeoU5+FBfSx6wUlDZrTyrPLluroCn3+evAe0Hrx4QVfAvr60l3VcHE2Y9PRM/bg1a4Dnz6lZ5f33qUnGzQ1IsbivLq1ZQ30Xn38OzJtH+2Rbw9YWmD6dLj5GjKCmrrp1pYlVbmkvJESqWFFd8VhLF0kjTx5AZfvav3HqFCBqi4pPPqGE4e1NJ04tevWKEu/x43QSLFYM6N+fksG72tpNJmrbvn8fWLCAPritWgHdu9Nx9MLPD/j1V0qM69ZJ/7dVrw78+SfVXKpVoz4zNS+IHBZGTcIstdDQUNSsWRNjx47FtGnTAACnT59GixYtcPDgQbRu3dqi49iYtbKQzDts2AAMGCA6itQMBrr6Gz9eXAyhocB//0sfehcXcXFkhdkMBARQR/6//9KInubNaVSYtc6dA3bupGTUpg1dRadtvjEajXBxcYHBYFD12lNhYZQMQ0KARYvkb5JLSACGDAFq1QImTABsbOQtL7uuXqVY1dKcFhYG+PsDHTqIjgQ4cOAAunfvjtOnT6Nq1apwd3dHt27dsGjRIouPwUlDRrduUduq6G08wsKAGTPoSrFgQbGxvMuVK3QCLFIE+PJLeWsEFy7QnJaaNWkYatIQUy0kjdWraYLeRx/RSgBKmjgRKFsWGDtW2XIt9euvQL9+6pmsqKakAdDS9kePHoWHhwcCAgLg7++fbtO6t1FxJVP7jh+nD5dohQvTFfX/10hV6dIlOhndvUtDRBculL8JqV49OvkOHEhNPJMn08+RkfKWa41t24CePelqf9Ys5RMGAPz0E7XTL12qfNmWePlSPQlDjRYuXIj4+Hhs3boVGzduzFLCADhpyOrZM/W0nbdpA3TrBixZQs0/auHvD3z7LXDnDp0Ee/RQvhmtYMHkQQM1a9KIIYASWHy8srFkxs+PaosA9Vt4eortV+jUCahUiRK8mt5PMTFi9wbXgjt37uDx48dITExEcDaWAubmKZk8fQrs3g0MHy46ktQOHqTRR1OmAAUKiIkhMZH6LHbvpg/4xx9bP9JHSknNU7NmGWAyOaN6deo8V3rV1Lg4YM8e4NAh2itFba8TAOzbB9y7B4werY4+Di8voFAhdY3yUlPzVGxsLOrXrw93d3dUrVoVS5YsQUBAAFxdXS0+hi5GT6nR8eNA27aio0gv6Y37xRfUd6B0H8eVK9TEUqYM1TDUbPx4GtJ76xYtA1OmDF3ht2olb7lPnlDTT+7c1GexapW85Vmjc2dKHL/8oo4+jmvXaHgwy9jXX38Ng8GAn3/+GY6Ojjhw4ACGDBmCffv2WXwMThoyiY0FypUTHUXGOnSgTt9evWgcfsuW8pYXGwucPUs1iwYNaF0jLS1NUaUKsGwZ8Po1XTFOmZI8OqdmTepfsNa5c9SvExhIiXzKFGqmU/PQ1iSdO9O8kLlzga++EhuL0QjwNuUZ8/b2xpIlS3D8+PE3AzzWr1+P2rVrY/ny5Rg5cqRFx+HmKZnMnq3+K+nnz2lElZ0ddZJL3XkYFUWJYtcuat7p2lX+jaikYMnoqYgIOsmfO0cTDmvUoGa3/v3pRG9rS23+aYWEJHe0798P3L5NfScNGlB/jpubNk96sbFU06hZExg1SkwM+/ZRn4batgUIDwfWr1dHTUwKuqlpxMZSh5wa2lW9vbXRGefqSh2Zu3dTU1q/flS1t2Y+REICJaMff6STYffuNEdEb7uoOTnRHhTNmtHPz54BDx5QEjh6lCacOjlRQklSuTIl5levqNmrWze6iVhmRmp2dvRe+vZb6q+qWVPZ8hMTaV7PypXKlmuJggX1NZpLN0nj6lW6ylDDyenyZWDoUNFRWK5bN5oxPmYM7bMwejQNf83qIotbt1KCiIujpq+FC7XRvCKFokWTJ9d17So2FlHs7IDvv6da05o1yiaOiAiq2Wqp2VOrdJM0PvhAdATJoqOBLA59Fs7FhVZEvXmTTv4VK1Knb716tPIpQM0txYvTsh5J9uyhFTyjo2lxvDlzaO6AGmp8THm2trQfR58+wPLlys3K3riRaspMfrpJGmoRE0PNFEouhS4VGxtqU//mG2p/PXuWEsLEifR7R0dqb09asbNePVoD6rPPqIaituGgTIwyZWg01fTpwJYt8vdjmUzAP/9QvyaTHycNiV2/ThPptM7FBWjfnm5pd3lj7F08Paljv18/qo3K6eZNGqnIFy3KyCEtzsq5di25c5SxnKx/f6px//mnvLPGf/yR+tCYMjhpSOyvv2hUEmM5nYMDNRlNnQocOSJPGeHhNCO9YUN5js/S46QhMbWNEWdMJAcHqmmMHCnPRkQnT6prEExOwElDQo8f877cjKX14Ye09MrkydIfe/58GqnFlMNJQ0Lx8dyfwVhGpkyhSaRSdooHB9PSLm5u0h2TvRsnDQl5e3N/BmMZqVyZ1jyTcmmdvXtpPpEWl13RMl0ljWfPxJb/6JHY8hlTs5kzad+U9eutP1bSsiHNm1t/LCVs3kwx64GukoaXl9jyS5RInj3NGEutQgWavzFvnvUn0LAwwMeH5oJoQY0aoiOQjq6ShmiHD/MEI8bepndv4MYN4MAB646zZw/NAdHCqsmA8gs4yomThoTkGFLImJ4kjXQ6f96649y7R6OynJysj4llDScNxphi8uShZcJPnbLuONY+n2UfJw3GmGKcnbnfT+s4aTDGFJOQQHMrmHZx0mCMKebVK5rPZO3mXDllcy814peeMaaYpLlM/ftbd5x+/YCnT2mXSKYsThoS8vQUHQFj6vb33/TV2vWiPD0Bf3/a9EwLkjYu0wNdJQ3RY6GdnQE/P7ExMKZWYWG0d/gnn1i/HbKbG5AvH7BrlzSxye3wYdERSEdXSaN2bbHl29hwJx9jmfnmG9qaddky6/eQz5sXGD8euHBBmtjk1q6d9X+zWugqaYjWty9w/77oKBhTnwMHaK2o7duBggWlOWb37rTp2ZMn0hxPTkWKcNJgGcibF7hyRXQUjKlLaCgwaRIweDDQooV0x/X0BNzdgWPHpDsmezdOGhIqWpRW8WSMkefPgbZtgU6dgO+/l/74M2YAS5ZIf1yWOU4aEmvaFLh1S3QUjIn37BnQsSPt2jdvHpA7t/RlNGkCVKlCI6mYMmT4N+Zs3btTu60cW1uKcPNm5h/I996jkwJjaYWF0aZLH3wALFokb1mLFtHnbd06ecthhGsaEitbFggJoa1ftcjPD5g2DWjfnnZFGzuWNs1JSEj9uJAQYOlSelzNmsCAAcAvvwAnToiJO0lwcDA+++wzlC9fHg4ODqhYsSJmzJiB2NhYsYHlIKGhdPG0dCnd5FasGO1lc/Gi/GUxHdU0vLzUcdWbOze9iU+elLbTT0737gG//QZcv05LTXfrBnzxBY2Dz58/8+dNmUJfY2KAyEjg7FlaImLOHOqgLFQI6NwZqFZNkT8DABAYGIjExESsXLkSlSpVwrVr1zBs2DBERUVh4cKFspb98iXtW22pIkWA0qVlC0eIgwfp4uHHH4FGjZQr98svgXHj6AKHlxiRl43ZbDaLDkIKGzbQ1a4aGI1UZZ45U3QkmYuLA44fp5P8ixfA8OFA9erWT7pKYjDQngknTgD//gu8/z7QujUlE6X3QPjxxx+xfPly3L1716LHG41GuLi4wGAwwNnZOdXvYmOprT4+Hti9GyhcGNixg5ph8uShGliBAkCXLpkff9Mmqrm99x4l3FOngF696Nhdu9JGXkWKWPMXK+/VK2DBAno9PvsMcHFRPoYNG2hHwP/8R/my3yY8nJLZ2LGiI5GGbmoaauLsDJQsCTx8qL4ryYQEwNcXWL6clqj+8ks6eUnNxYWSROvW9PPTp0BgILBqFRAQQPf36kU1Mzk6SFMyGAx4Lxt/ZFwcTdbcvx+IjqYk6+lJE9Tc3YE2bWgbz6xerMyZk/H9/v7A7ds0e7h4cUpANWvSkhtKvE7ZkZAAbN1Kr83kydSkKcqAAfSe+uijt9eQlZaQAFSuLDoK6XBNQyZhYTQUMLMThAjHjtE2mY0a0RVtvnziYrlzh9qgb92ik6GbG9CwIQ1bllJQUBDq1auHhQsXYtiwYRk+xmQywWQy4eVL4MwZICDAiLlzS2P4cAMaNXJGwYL0eonwzz9UE5T7dcoOLy9g3z7ap1stTbEBAUBQkLr2Dg8LowuCDh1ERyINThoy2rWLmntEv1n276dY+vWjIcF58oiNJ63Xr4GICDoB+fsDdeoADx4kv2716wPTp0/F/Pnz33qcf//9F25ubm9+DgkJQfPmzdGiRQv8/vvvb+6/cYOaU16+pMmY/v4zsXv3rHTHy6h5SqTXr6np88ABwMcHqFABqFePhpxWqqRMDIGB1F936hQwcCANeVXb+2nkSBrMoZZaPicNFTKZgMWLgalTRUeSWmwsJbI1a8RUlx88oM7qhg2BTz+VpxlKLg8f0ut34gQtv+DvH4rw8BeoVYt+HxJC1f4GDZKvukuXrgA7Ozs8fAjs3fsY69a1gJtbQwwb9ifOncsFZ2dqTnr8mJowAOp/cHSkmkYSo9GI0qVLqy5ppBUWRn/L0aN0Mnd1pb6QTp0AR0cakGGtqChapmP/fuDSJXr9evemUYJqdecO9TNNmiQ6EsJJQ4UiI6mqrKYqaZIHD2gm7NKl1MGphOBgYOVKuvrs3p1GMenNxYuUVDLy/HkIRo9uiWrV6mH//g2wtbXN0rHf1hGudpcuAVev0okzadXlTp2oJleiRHIfU2aePqXPUmIiJYoaNeiCp3t3oG5dZf4GKfz4I9Czp9g+liTbttFAkOrVRUciDU4aCtiyBfjzT7r6cXCQr5z792nUVkwMDZl9/335ylKrkJAQtGjRAmXLlsXatWtTJYxiFl56azlpZMRkAo4coe9fvKDmrcz0709DVitU0PZJzmAAhg1L3r9DJDU2nVtDheMx9KdvX/rapw+tyunoKO3x794Ffv2VriYnTgSqVtXPippZ5eXlhaCgIAQFBaFUqVKpfqeD66NsyZs39RDgQYOEhaIYFxfqnD9zRtn5IjmBLqbBvHolOoJ369sX+PhjuuJI2vLSGgkJwLVrwNChdBsyhIazurnl3IQBAIMGDYLZbM7wxnKWkSPpYioqSnQk+qKLpHH4sHKjR6zRvz/VNjw9qcYRHZ31YxiNNHu7Wzdg9mza3OXQIWp7Zowls7Ghfo2NG8XGobel23WRNPLmFb/Vq6X69aO5El9/TUNL16yhTsfMLoQTE+l25Ai10dasSZPzFiyg9to+fQA7O2X/Bsa04qOPaHSZyNaIdw0+0Bru0xDA05P6IVasoPTN+aYAAA5FSURBVA7yIUNo/kSZMukfe/EiPbZVq+Rl16Va6oOxnKB3b5q1nsncTpZFnDQEGjGC3sihocDmzbRhTdIol7JlaT2jtm1pNrKW5lgwpiY9elDT8McfK7/u2dOnNOxeT3SRNI4d0+6QNltbmoQ1fjz9/MMPYuNhTG9y56aksW4dMGqUsmWHh9OUAD3RRZ+G3toMGWPSatKEkkbafWGU0LOn8mXKSRdJgzHG3qZQIWrq3blTdCTax0mDMZYj9O4NLFumbG1j82blylIKJw3GWI5Qsyat//bsmXJl5sqlv9GOmk8aBgOt9MkYY2+TKxfN21ByPaqKFbUzh8xSmk8aL1+K6dxijGlP587A3r2io9A2zScNgOYzMMbYuxQrRvMmLNwu3mobNihTjpJ0kTQYY8xSbdrQSgtK0OM6mZw0GGM5SrVqtOUvyx5OGoyxHKVuXVrEUAkVKihTjpI4aTDGcpynT5Upp3FjZcpREicNxhhjFuOkwRhjzGKcNBhjTCa3bomOQHqcNBhjOcqDB0CzZsqU5eenTDlK4qTBGMtRfH2BevVER6FdukgaBoPoCBhjWnHwIC0nwrJH80kjVy56EzDG2LscOUKLCJYurUx5HTooU46SNJ80ypYFGjYUHQVjTO3i44Hp04Evv1SuzOho4PZt5cpTguaTBmOMWWLzZqBwYVp7SilOTvprPs8tOgAphIeLjoAxpmZ37wI//USJI08e5cpt0wZ49Ei58pSgi6ShVQYDEBUFHD4MhIZm/rhq1Wi9nLx5aa9jxpjl7t0DBg4EVq8GqlZVtuzcuakfpW1bZcuVky6SRoECQGIidYqrXUQEsG0bcPo0cOkS7eplawv065fx41++BLZvp9vr1/Rz9er0vObNqUMvd27AxkbZv4MxLXjwgD5by5bRhZfSKlcGHB2VL1dOukgadeoAu3cDPXqIjiRzly8DS5cCL14ALVtSh1zZspY9t1ev1D9fu0a3bdtozHmVKoCzM+DhAbi7A6VKSR8/Y1rz8CEwdiywciVQq5a4OGxtxZUtBxuzWfvbhERGAn/9BQwbJjqS9C5dot27KlUCunUDihaV/k0UEwOYTMCxY8CrV8CePVQdfvaMxqM7OlLtRGtCQ+XbYc3FBXBzy/h3RqMRLi4uMBgMcHZ2licAiTx+TCfHlA4dopp35cqp7z95kppq3qVOHaBGjeSfL1ygoaMuLvRzuXL0Plar6Ghg0yZayXbyZMDOTmw827ZRE3O1amLjkIoukkZiIl1NjBwpOpJkfn7Avn1A7dpA+/ZiqqgPH1JCCQigr3fvJq/vn5CQepvc996jZj4pxcQAT56kv9/Xl5rUUkoZWxKDgR7XsqW0cQHAjh0Z18iMRsBgMGLaNBf89psBDg7JSSN3bqB+fcuOX7Ik9UGlFRVFyfxd/Pzo9UvbaZv2dXr5kk7yaU/ijo5AiRKWxfouQUH0GQOouScwkN4rKWMpVIj6CxwdAVdXacrNqshI6j+4eJEu0Dw9xcSRVlgY8M8/QJ8+oiORhi6SBgDMnw+MGwfY24uLITERuHKFNq4vV47eJCLjeZvgYCAkhL5//JhOACVLJv/++XPqoM+TB+jbN+NjvHhBEysz65N59Yqu8tLWckqVsrxpToTMaho3b9IJ4G1On6bX0t0dyJ8//e9fvKCTrrMz0LXr249Vty7g4JCNP0AAPz8gLg64epWGmfr5URJxcKB5VGXKUL9bRq+JNSIj6TN35AhQsCBdYNSuLW0Z1oqLA1asAMaMER2JNHSTNLZvpzdox45iyr98GVi8mK7ehw4VEwOThpaap9Tu3j06qT97Bpw5Q0NQT5ygWdlJtRQbG+Cjjyw73t691BQbFEQ/P3pEx2zWjGrLavXdd8DXX2tjsM676CZpJCRQp9eyZcqW++wZNXU8fgyMHq3utl5mGU4a8jKZkpu79u6lZsikGtWuXTTCMK1WragmHBNDNdc6dagWq5VO5o0b6W8oXlx0JNbTTdIAgLlzgREjqJoqt9ev6Q1+4AAwahTQoIH8ZTJlcNJgUouKAv78k84VWqeDylKy5s2B9evlL+f6deqviI4G1q3jhMEYe7v8+amWlFTD0jJdJY3Gjand9MULeY5/8yb1V6xeDSxZAgwZIk85jDH9MRrfvvKDVuiqeQoAvL2p/XDVKumO+eoV8PvvwKlTwPjx1OnGM7D1i5unmBwuXKC5I506iY7EOrqqaQBAixbUObZ1q/XHCgujWdytWlGS+PtvagLjhMEYy6p69QAvL9FRWE93SQMAvvmGmo/Oncve81+9ohUxGzWiIX1eXsDEicqujskY0x9HR+03UekyaZQsScNgx40D5syhzVfexWwGYmNpPLW7O8272LsX+PFHXlmWMSaNpk1peL6W6TJpADRfYtcuWpOqenXqk8hIWBiNgOrWjZZ9ePSIZkKvX5/52kSMMZYdDRrQGmBaptukAQDFigHnzwM9ewI//EALrrm4AJ9+SjNSXVxoOYvFi+kK4NUrWsNK6TX3GWM5Q8GCgL+/6Ciso7vRU5kxGmkhM2/v5PuS9qMoW5b7K1gyHj3F5LRsGS13VL686EiyJ8ckDcYsxUmDyenyZeDsWVq9Qot03TzFGGNqU7UqzQ7XKk4ajDGmIAcHWvlXqzhpMMaYwlq0oL1HtIiTBmOMKaxKFdqMS4s4aTDGmMI8PICjR0VHkT2cNBhjTGG2trQFrhZx0mCMMYXZ2lLzlNEoOpKs46TBGGMCVKlCa95pDScNxhgToE4d4PZt0VFkHScNxhgT5OxZ0RFkHScNxhhjFuOkwRhjzGKcNBhjjFmMkwZjjDGLcdJgjDEBTp8G+vUTHUXWcdJgjDEBnj/X5uZvnDQYY0xhcXFArlyAk5PoSLKOkwZjjCnMywto21Z0FNnDSYPplslkgru7O2xsbHD58mXR4TAGAHj9GlixAujTR3Qk2ZNbdABye/gQuHcP2LEj88e4uwM1atD35csDhQopExuT1+TJk1GiRAlc0fI2aUx35s8HpkwRHUX26TJpBAcDGzcCvr5AqVJAsWJA9+70NSOXLgE7d9L3ZjNw4QJQvTpQogRQpAjtsgXQ8/PmVeIvYNY6ePAgjhw5gu3bt+PgwYOiw2EMAJ2XypUDmjQRHUn26SZpxMcDp04Bf/5JJ/cOHYBp0wAbm3c/180t4/uvXAEMBuD+fWDXLqBSJcDZGTh2DGjdmh5jMgGffJL8HFtbTiyiPXv2DMOGDcOuXbuQL18+0eEwANHR8h07Tx71j0J6/RoYO5aSxcCBoqOxji6SxrFjwJ49QNeuwJo10h23du3k75s1S/5+wIDk70+cAFJeyN6+TbWblB49AnLnBipWlC62twkMBEqXVqYstTGbzVi4cBAaNhyBwEAPhIYGAwD27weuXcv4OXFxJsTHm978HBNDmxxs2QI4OMgdsRgJCfSZAYD8+YF27eQtb9cuoEsXwNFR2uP6+dGFWrVq6X/3+DFQuXLyz7lyAd26SVv+u0REAL/9Rhe1X38NlC2rbPlysDGbtbiiO7lzB/j1V3ojNG1KJ2Y1ioujGolS7OzopidTp07F/Pnz3/qYf//9F0eOHMHff/8NHx8f2NraIjg4GOXLl8elS5fg7u6e4fNmzpyJWbNmpbvfYDDA2dlZkvjVxmwGoqLoexsbShx6ExNDyTFJUFDqC4eULQZRUVQbqFcv+fd58wKenlkr8/x5Oo63Nz3f0RHo1Em7u/RlRJNJw2AAfv8dKFgQ6NGDvjJ9Cw0NxYsXL976mAoVKqBPnz7Yu3cvbFK0SyYkJMDW1hb9+/fH2rVr0z3PZDLBlCKrG41GlC5dWtdJg6UWGwuEhCT/HBZGe3inrbEfOACkfRtWrAg0bkzfP3wItGoFuLpSrSKXDsenaippxMdTBj96FBg8GKhaVXRETG0ePHgAY4o9NB8/foz27dtj27ZtaNCgAUqlbTvMgNFohIuLCycNxjKg0gad9J4+BRYvBjw8gHnzREfD1KpMmnYAx/9vRK9YsaJFCYMx9naaSBqXLwMrVwILFmhz2j1jjOmFqpPG69fAH3/Q9z/9BPDoSZZV5cqVg4ZaYBlTPdUmjdu3gdWraengWrVER8MYYwxQYdIwm4Hjx4Hdu6nvQq/j5BljTItUlzTWraP5FkuXio6EMcZYWqoZRRwVBUyaROs99e8vOhrGGGMZUUVN4/JlYPNmYMQI5ZbaYIwxlnVCk0ZiIs2w9PUFvv9e/YuOMcZYTie0eWrZMur4XrCAEwZjjGmBkKTx6hUwbhwtDtali4gIGGOMZYfizVMPH9LOVdOnZ74pEmOMMXVSNGmcOkXLEc+cCRQurGTJjDHGpKBY0tiwAbh7F/j2W6VKZIwxJjVF+jRmz6Z9cb/5RonSGGOMyUXWpPH8OTBlCm1K0rSpZft1M8YYUy/ZmqeePqW5F3PmAC4ucpXCGGNMSbIkjQMHaMP32bM5YTDGmJ5InjT27wfu3KERUowxxvRFsqQRF0cbJplMwOjRUh2VMcaYmkiSNGJjqe+iRw+gTh0pjsgYY0yNrE4a9+/TGlIff8wJgzHG9M6qpPHwIS02uHAh77DHGGM5QbaTxrlzwPr1wOLFgJ2dlCExxhhTq2xP7rt+nWoZnDAYYyznsDGbzWbRQTCmJkajES4uLjAYDHB2dhYdDmOqopo9whljjKkfJw3GGGMW46TBGGPMYpw0GGOMWYyTBmOMMYtx0mCMMWYxThqMMcYsxkmDMcaYxThpMMYYsxjPCGcsDbPZjIiICDg5OcGGN7ZnLBVOGowxxizGzVOMMcYsxkmDMcaYxThpMMYYsxgnDcYYYxbjpMEYY8xinDQYY4xZjJMGY4wxi3HSYIwxZjFOGowxxizGSYMxxpjF/g//z1qObzxQXwAAAABJRU5ErkJggg=="
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Edwards curve\n\nedwards=x^2+y^2-1+20x^2*y^2\n\nplot_implicit(edwards, (x,-1.5,1.5),(y,-1.5,1.5))\naxes()[:set_aspect](\"equal\")",
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026A390F0>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n=10\nphi = x*prod([x^2-i^2 for i in 1:n])\nphi -= n*subs(phi,x,y)\ndisplay(phi)\nn += 2\nplot_implicit(phi,(x,-n,n),(y,-n,n))\naxes()[:set_aspect](\"equal\")",
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": " / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \nx*\\x - 100/*\\x - 81/*\\x - 64/*\\x - 49/*\\x - 36/*\\x - 25/*\\x - 16/*\\x -\n\n \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \n 9/*\\x - 4/*\\x - 1/ - 10*y*\\y - 100/*\\y - 81/*\\y - 64/*\\y - 49/*\\y - 36\n\n\\ / 2 \\ / 2 \\ / 2 \\ / 2 \\ / 2 \\\n/*\\y - 25/*\\y - 16/*\\y - 9/*\\y - 4/*\\y - 1/",
"text/latex": "$$x \\left(x^{2} - 100\\right) \\left(x^{2} - 81\\right) \\left(x^{2} - 64\\right) \\left(x^{2} - 49\\right) \\left(x^{2} - 36\\right) \\left(x^{2} - 25\\right) \\left(x^{2} - 16\\right) \\left(x^{2} - 9\\right) \\left(x^{2} - 4\\right) \\left(x^{2} - 1\\right) - 10 y \\left(y^{2} - 100\\right) \\left(y^{2} - 81\\right) \\left(y^{2} - 64\\right) \\left(y^{2} - 49\\right) \\left(y^{2} - 36\\right) \\left(y^{2} - 25\\right) \\left(y^{2} - 16\\right) \\left(y^{2} - 9\\right) \\left(y^{2} - 4\\right) \\left(y^{2} - 1\\right)$$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026A1FBA8>)",
"image/png": 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"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "#psi = sqrt(x*(1-x))/(x+y)\npsi = sqrt(x*(1-x))\ndisplay(psi)\nintegrate(psi,(x,0,1))",
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": " ____________\n\\/ x*(-x + 1) ",
"text/latex": "$$\\sqrt{x \\left(- x + 1\\right)}$$"
},
"metadata": {}
},
{
"output_type": "execute_result",
"execution_count": 9,
"data": {
"text/plain": " 1 \n / \n | \n | ____________ \n | \\/ x*(-x + 1) dx\n | \n/ \n0 ",
"text/latex": "$$\\int_{0}^{1} \\sqrt{x \\left(- x + 1\\right)}\\, dx$$"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "integrate(x^y,x)",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": "/log(x) for y = -1\n| \n| y + 1 \n<x \n|------ otherwise \n|y + 1 \n\\ ",
"text/latex": "$$\\begin{cases} \\log{\\left (x \\right )} & \\text{for}\\: y = -1 \\\\\\frac{x^{y + 1}}{y + 1} & \\text{otherwise} \\end{cases}$$"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@syms k\nsummation(1/k^6,(k,1,oo))",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": " 6\npi \n---\n945",
"text/latex": "$$\\frac{\\pi^{6}}{945}$$"
},
"metadata": {}
}
]
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"kernelspec": {
"name": "julia-0.5",
"display_name": "Julia 0.5.2",
"language": "julia"
},
"language_info": {
"file_extension": ".jl",
"name": "julia",
"mimetype": "application/julia",
"version": "0.5.2"
},
"gist": {
"id": "",
"data": {
"description": "Julia/SymPy in Julia.ipynb",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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