Лекция 10. Задание 1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "700b9582",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "from sympy import symbols, exp, sin, cos, solve, Function, Eq, dsolve,\\\n",
    "    sqrt, trigsimp, integrate, pi, init_printing, Rational, diff,series\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "46f2d11e",
   "metadata": {},
   "outputs": [],
   "source": [
    "q,p = symbols('q p')\n",
    "Q, P = symbols('Q P')\n",
    "k, eps = symbols('k varepsilon')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ae8e2862",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - k q^{4} \\varepsilon + \\frac{p^{2}}{2} + \\frac{q^{2}}{2}$"
      ],
      "text/plain": [
       "                     2    2\n",
       "     4              p    q \n",
       "- k⋅q ⋅varepsilon + ── + ──\n",
       "                    2    2 "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H_old = Rational(1, 2)*(p**2 + q**2) - eps * k * q ** 4\n",
    "H_old"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dac8dc8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 P Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{P k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}$"
      ],
      "text/plain": [
       "       2           2 ⎛   2      2⎞                  ⎛   2      2⎞\n",
       "3⋅P⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠   P⋅k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠\n",
       "────────────────────────────────── + ────────────────────────────\n",
       "                16                                3              "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G1 = Rational(1, 3) * k * P * (2 * P**2 + 3 * Q**2)\n",
    "G2 = Rational(3, 16) * k**2 * P * Q * (5 * P**2 + 3 * Q **2)\n",
    "G = eps * G1 + eps**2 * G2\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "87de9989",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Poisson(x, y):\n",
    "    a = diff(x, Q) * diff(y, P)\n",
    "    b = diff(x, P) * diff(y, Q)\n",
    "    return a - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "068a1b29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Xcnxqv/uZZRc+7+JvfdKf0K/4yKNIC/QhN7rGVwhs6+gQ+afr2CjLW77rateyhmKIutSWJs9mZeXzTZdtsuDX92PQoy7HLfLFKXHVua66DMLGvNo9LGVtLgtmWdfuY9JNEIfvqg5qRqw6CPy3U/vQQW1rFIin/2TBLGNsd9N2hXH0HdvEfqzt89p3rH3HtoTyFdC+Y1t85bQ6mkH7jmcsmGUf2uhc66ayc63Ylh3EeDfy7ey2OD7z/58hQXozcDRyow402x6OjNQEeLNZ/hF54+M8ZFT6qaz8xvxcRRnujySCO4GLLcr8eLO8KLVuS2TK6uuQEcnbIxXKR0qOU1WuhKMQYXgh4gQ3IU51ToNjgoyS3ho4I7XuWOCdyBSiH0S+Mb8b8C7g08gUr8dWHHcJuZ95nJ2z7hTEYYt4LPIGzQbspsz15SdQz84u9suzSZpkJPT2yPTCJyB++Fyq3wJZol27uJRrjDFWlStjyH1FLNGdr0A7/gJu15/UdXdl1lfFpAuJP8whb80kDxo/R2x9GfAU5CGkKNct0a5tfOc0F81wBOL7lwKH5GyvEwcaA/YUxQD4rZvaYIlie+XxaeQtoyLK/NZVk4Bbvgc3X4+9fgX7nKEa1j3P+c7hUJwbyuLkM0iMPRtptPgScCvSALML8hmiXZl9AiW0z4O9v/VNf0J/4iOPMi3Qh9zoGl8JS3SrOyBM/uk6Nsryls+6uk5Z0yyhujRNW89nTZ7NysqXZon2bddlmyz48/1Y9KjLcYt8sWmdu0S7fuOqy0LGvNp9xhLd6qymdg+pm8Df/bLVTbH47hh0EHRr7y50EPhvp/ahg9rWKBBH/0ns7W5jb1cYS9+xTexr33F/Ykz7jvMJ4SsJ2nfcbd+xq2bQvuP+ttG51k1l51qxLTuIcRm4b0FB2uTDiEPul1qXTAU6Bf6+xXNtZ5Y3kf8t7zRzwIvM32mD7IXcqy2QaSw/RXkg2zKHGPYqZDrZ3c36X7Rw7AOBO5DRxyAjuN+NXNdRqf0uZJYkj0Zsc2XJcaesnJZ0AvwVEqxLmW0XlxxrNZJcLgPeWrJfGl9+Au52drVf1iZFXIvY6ULk3nwCGYFexpT27OJarjHG2DL1cmXI3FfElO58BdrxF1cSWy1n1tvGpA2/N8sruecbzCBvrXwDeDny8F0kRKe0axvfOW0Zuzh4DTL19SXAOmazQ6QJGQdTNAbS+Kyb2uAK3N52+03F9mXy/baOJikjL9+Dm6/HXL8m5/RRx6qGFXzncCjODcsU5/e7kDceX480LByCNBz8AHgp0ti9K7O39EP7vAt905/Qj/jIo0oLxJ4bm9h0Sre6A/znH1t8xsYy7s9nbdTVTZmiujRNW89nTZ7NysqXZkr7tlumuzZZ8Of7Q9Cj0E6dO6Vdv3HVZSFjXu0+Y0q3Oqup3UPqJvB/v6p0Ux99d5l+6qDkPNtm1k0IY+8udBD4b6f2oYOWCaNRQPuO0+cbc7vCmPqOXWJf+47jj7FltO+4DJ++UgftO24/py1jHwPad9y9Ng3Zd1x2rhXbsoMYNzIbzeqTpPFkq9S6xAnzRk034Uaz3Bb4M+SN1CJeCOyBTJH9udT6x5jl0cgo6RcjI5OnDct2IjJN8IeAQ815b294TJARzs8DvsPs+p9rlnkjhW9FviN/IDIla5UQzbKIBPDJwHcdyrk1MoIaigcofMT8ez9wJP78BNzt7GK/PJtUcRWSuCdI4rqhZN+8Mi5Szy6u5RpjjNXNlSFzXxHTnHWLhPGVG2jHX1zZBhGD16bW1YnJMn5plssF2xOheu+SY0xz1i1S3zY+cxrYxcGRwL8gb5Sto/jTEyHjYJqzbpHxxQD4r5vaYF3Lxyvy2zqapIy8fA9uvh5z/Qp+6ljVsDN853Aozg1V+f1O5E34DZn190Zyw23I26QQ3udd6Jv+7Et8ZDmSai0Qe25sYtO8Yy4STneA//xji6/YgHrPZ23U1U2Z5qxbRHVp0+ezJs9mReXLMs1Zt0gz23XZJgv+fH8IehTaqXOnOesWaeY3LrosZMyr3WdMc9YtEk5nNbV7SN1EwXEXab9uLNJNffNd6K8Ogm7t3YUOAv/t1D50UCiNAtp3nDD2doWx9B3XjX3tO443xrTv2A4fvlIH7TtuX9/bxsCRaN9xDNo0ZN9xWXvbim2rMjtcADzCsiBNWGuWacHjywmvRQJmDnh6yX4PB05CPrFxOPLmasIas7wA+BskkDcg316vy4OAVyMjrF+NNCi11YC/H/Id9PTI2y3M8oEFv0nW39FSGWy4Hfj3gn+JH5xr/p+MPveZrFzs7Gq/PJvY8GCz/FPpXuFJl2uMMVY3V4bMfbGQ9eE2/MWV3RCb3Z1aVzcmi/g+0nmwK7B5zvbkrYOlls5ng8+clhy3LA7egIjQi4GnUixCYdhxEGsMwPDqJhuK/LaOJikjL9+Dm6/HWr+CvzpWNewM3zkcinNDXZ1zCPI5is8y88PQPu9C3/RnX+Ijja0WiDk3+rSpD/LqaJ/5xxbf97FO3mqjru4bQ9SleTR5NisqXwi6bJMFf74/BD0K8de5WfJ0WciYV7v7x1ZnNbX72HRT33wXVAfZEoMOAv/t1D50UCiNAtp3DNquAOPpO24S+7G2z2vfsfYd29K2r9RB+47b1/c2MaB9x0IM2jRk33FZe9uKbdlBjN8EHp2zvg57IN/uzrIj8jkLkOlJk3JMEKdvYzrsLFOzfB+zm5fmucB/AvdBpi7NvnGyBhn9eSlwi9n/aqT8a6nHg5Drvi/534YvG3FdxUHIJ0W+mFp3jlkeDvx5Zv9nA09E3mj5QYPzunIb8IqCf18y+5xi/n8q/v3Exc6u9suzCUhQ7sBKVgHvMOf5AbOR+KFwLdfULMcSY2W5MqbcF4I6Pjw1y7r+4sreiMBKUxSTdbkByVPbAMdltj0deCbytsKZLZ3PBp85Dcrj4K3ACYj4XUf524B9j4O+xgC0XzedjIjMxfpF9U6R37pqEnDL91DP16dmGVP9Cv7qWNWwM3zncCjODVXPhHmfhNgXyfs3A/9k1nXh8y70TX/2JT4SbLVA7LnRp03r4FpH+84/tvi+j0V5K0RdHRND1KV1aPJsVlS+EHTVJgt+fX8IehTirXNtdVnC1Cx9x7za3S8ubS7QzO5j0k3QP98F1UEJfdBB4L+d2ocOalOjQFz9J1OzjKndTdsVxtN3XBb72ncs9C3GtO94RmhfqYP2Hbev76s0g/Ydx6VNQ/Udl50rd9vqzA5XAT9CnPeCzLYF849U4dYiHdYgTnZMav+DgX9Abt5G5PvduwAHIG+Cfg14r9l3d2R66B9T/Y3vOnwAuaaXIgH5ReBXyBskTwQeiYxuXWAmgBI2R0ZBX8Rs1Og1wHMQJ/kSch8udyzTL5Hvgq9FptY8C0lS2yEV2WXAyxyPmbCAOMi1qXWnA98CnoYE+hnIdeyOOPwcYq/f1TxnCHz6iaudXe23wEqbADwLeA8yEv8K5P5vDzwF2NmU4bBWrtAN13KNLcbKcmVMuS8EdXy4ib/UYS0y3XOaBfJjMr19wfxtU+cBHAU8Dngz8pbC+cgDyIGIbx9G8ZThbeM7p0FxHLwU6Sj5E9IIckRO+ZaY3cu+x0FfYwDar5uSB5OY7ViWv11xyfdQz9djrF/BXx27gGpYCJPDoTg3VMXJWUhDx88Qv9/DlO125AE3eWs4tM+70Ef9uUB/4sNFC8SeG33atA6udbTv/GOL7/tYlLdC1NUxMURdmmxbMH/7fjYrKl8IumqTBX++PxQ9CvHWuba6LCFEzKvd/eLa5gL17T423dRH3wXVQQl90EEQpp26bR1U1UbgWr6Y+k9ibHfTdgV3+tp3vEBx7GvfcT9jTPuOZ4T0lbpo37HQpr4viwHtO45Pm4bqOy47V+627CBGkAB6CSsda4LcsDQ7m38gTpkOyrOR6UL3NifeCgnAc4FPmn93m32Tb69fXFDwpiSzAp2B3LhnIFNgJiOG3wO8HfhDzm/3BDZj5TSllyCNQd8Avo5cY9Vbj2n+iIwwPg4ZaZ1M93kNcCHwcYdjpdkXeAgyDWuau5AE9BpkatgDke+pb0IqxhOR0dEx49NPXO3sYr8im4A8HPwbknj2Qr5zfwuS9D+J2GVTw2urg2u5xhRjCUW5MqbcF4I6PtzEX1zZB6lor0qtK4vJhAludR7IlNePA96C5NjHIw8iXwXeBZznXPr6+MxpafLi4GFmeS/gyILffY+ZEO17HPQxBsBP3bQnM5+PmaL87YpLvod6vh5j/Qp+6ljVsDNC5PCi3JBQFienI7Z4MfK25W+AjyJvUS6l9gvt8y70TX/2LT5ctEDsudH3M4UrrnW07/xjS4j7mJe3QtTVMTFEXQrhns2q6sYQdNEmC/58fyh6FOKtc211WUKImFe7+8W1zQXq231suqlvvptGdVD8OgjCtVP70EFlbQSu5Yup/yTGdjdtV3Cnj33HVbGvfcf9i7EE7TsWQvpKHbTv+J60qe+LYkD7juPSpiH7jst0Zu62ufXr1+cV+sPAmwpOMiSORka1n4VM13p3+e694J3AG5FkubHjsijCmG0yxBhLM5ZcGQof/vIBZArja1LrxhyTPtA4aI9QMQDtx8G2yFs3G4BjWzieb/rut0OsXzU3h6UoN6SJKU6G6PMuaHzYMXY/UeLKW32nz7q0LjZ1YwjUj7sjFl/sgjHXoWr3cdp9iGj90R6+YiPmduq+tRH4Zoj5MRZfU4Sx22OIMZZmTPnSN2Osk4eAxkC79L2Nrkxn5m4rGsS4DfBK4J9bKlisrEKmK30C8Drgg90WpxV+gXwyZNJxOZQZY7bJEGMszVhyZSja9pf9kLcGz8ysH3NM+kDjoD1CxQC0HwfPA04DdqL7jl8b+u63Q6xfNTeHoyw3pIkpTobo8y5ofNgxdj9R4spbfafPurQOtnVjCNSPuyMGX+yKMdehavdx2n2IaP3RHj5iI+Z26j62EfhmiPkxBl9TZozdHkOMsTRjype+GVudPBQ0Btqlz210Zecq3Jb3OWmQb5mfBswxvNHvae5CpjM9BPnkxiqzrs/s3nUBlBWM2SZDjLE0Y8mVoWjbX34NXJGzfswx6QONg/YIFQPQfhx8Gdiy5WP6pO9+O8T6VXNzOMpyQ5qY4mSIPu+CxocdY/cTJa681Xf6rEvrYFs3hkD9uDti8MWuGHMdqnYfp92HiNYf7eEjNmJup+5jG4FvhpgfY/A1ZcbY7THEGEszpnzpm7HVyUNBY6Bd+txGV3auwm1FMzEqiqIoiqIoiqIoiqIoiqIoiqIoiqIoiqIoiqIoiqJ4ZVXXBVAURVEURVEURVEURVEURVEURVEURVEURVEURVEUZZzoIEZFURRFURRFURRFURRFURRFURRFURRFURRFURRFUTpBBzEqiqIoiqIoiqIoiqIoiqIoiqIoiqIoiqIoiqIoitIJ/w/PMxrZlcYhyQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\left( \\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}, \\  - \\left(\\frac{45 P Q k^{2} \\varepsilon^{2}}{8} + 4 P k \\varepsilon\\right) \\left(\\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 P Q k \\varepsilon + \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right) + \\left(\\frac{15 P^{2} k^{2} \\varepsilon^{2}}{8} + \\frac{9 Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 Q k \\varepsilon + \\frac{3 k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right) \\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}\\right)\\right)$"
      ],
      "text/plain": [
       "⎛    2    2           2      2                     2           2 ⎛   2      2⎞\n",
       "⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅P ⋅k⋅varepsilon   3⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠\n",
       "⎜────────────────────── + ───────────────── + ────────────────────────────────\n",
       "⎝          8                      3                          16               \n",
       "\n",
       "                ⎛   2      2⎞    ⎛        2           2                   ⎞ ⎛ \n",
       "   k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠    ⎜45⋅P⋅Q⋅k ⋅varepsilon                    ⎟ ⎜9\n",
       " + ──────────────────────────, - ⎜───────────────────── + 4⋅P⋅k⋅varepsilon⎟⋅⎜─\n",
       "               3                 ⎝          8                             ⎠ ⎝ \n",
       "\n",
       "    2  2           2                             2           2 ⎛   2      2⎞⎞ \n",
       "⋅P⋅Q ⋅k ⋅varepsilon                         3⋅P⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟ \n",
       "──────────────────── + 2⋅P⋅Q⋅k⋅varepsilon + ────────────────────────────────⎟ \n",
       "         8                                                 16               ⎠ \n",
       "\n",
       "  ⎛    2  2           2      2  2           2                         2       \n",
       "  ⎜15⋅P ⋅k ⋅varepsilon    9⋅Q ⋅k ⋅varepsilon                       3⋅k ⋅vareps\n",
       "+ ⎜──────────────────── + ─────────────────── + 2⋅Q⋅k⋅varepsilon + ───────────\n",
       "  ⎝         8                      8                                          \n",
       "\n",
       "    2 ⎛   2      2⎞⎞ ⎛    2    2           2      2                     2     \n",
       "ilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟ ⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅P ⋅k⋅varepsilon   3⋅Q⋅k ⋅vare\n",
       "───────────────────⎟⋅⎜────────────────────── + ───────────────── + ───────────\n",
       "   16              ⎠ ⎝          8                      3                      \n",
       "\n",
       "      2 ⎛   2      2⎞                ⎛   2      2⎞⎞⎞\n",
       "psilon ⋅⎝5⋅P  + 3⋅Q ⎠   k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠⎟⎟\n",
       "───────────────────── + ──────────────────────────⎟⎟\n",
       "    16                              3             ⎠⎠"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = Poisson(Q, G)\n",
    "a2 = Poisson(a1,G)\n",
    "(a1, a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "38a99357",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left( - \\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} - 2 P Q k \\varepsilon - \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}, \\  \\left(- \\frac{27 P Q k^{2} \\varepsilon^{2}}{8} - 2 P k \\varepsilon\\right) \\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}\\right) - \\left(\\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 P Q k \\varepsilon + \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right) \\left(- \\frac{15 P^{2} k^{2} \\varepsilon^{2}}{8} - \\frac{9 Q^{2} k^{2} \\varepsilon^{2}}{8} - 2 Q k \\varepsilon - \\frac{3 k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right)\\right)$"
      ],
      "text/plain": [
       "⎛       2  2           2                             2           2 ⎛   2      \n",
       "⎜  9⋅P⋅Q ⋅k ⋅varepsilon                         3⋅P⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q\n",
       "⎜- ───────────────────── - 2⋅P⋅Q⋅k⋅varepsilon - ──────────────────────────────\n",
       "⎝            8                                                 16             \n",
       "\n",
       "2⎞  ⎛          2           2                   ⎞ ⎛    2    2           2      \n",
       " ⎠  ⎜  27⋅P⋅Q⋅k ⋅varepsilon                    ⎟ ⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅P\n",
       "──, ⎜- ───────────────────── - 2⋅P⋅k⋅varepsilon⎟⋅⎜────────────────────── + ───\n",
       "    ⎝            8                             ⎠ ⎝          8                 \n",
       "\n",
       "2                     2           2 ⎛   2      2⎞                ⎛   2      2⎞\n",
       " ⋅k⋅varepsilon   3⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠   k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠\n",
       "────────────── + ──────────────────────────────── + ──────────────────────────\n",
       "     3                          16                              3             \n",
       "\n",
       "⎞   ⎛     2  2           2                             2           2 ⎛   2    \n",
       "⎟   ⎜9⋅P⋅Q ⋅k ⋅varepsilon                         3⋅P⋅k ⋅varepsilon ⋅⎝5⋅P  + 3\n",
       "⎟ - ⎜───────────────────── + 2⋅P⋅Q⋅k⋅varepsilon + ────────────────────────────\n",
       "⎠   ⎝          8                                                 16           \n",
       "\n",
       "  2⎞⎞ ⎛      2  2           2      2  2           2                         2 \n",
       "⋅Q ⎠⎟ ⎜  15⋅P ⋅k ⋅varepsilon    9⋅Q ⋅k ⋅varepsilon                       3⋅k ⋅\n",
       "────⎟⋅⎜- ──────────────────── - ─────────────────── - 2⋅Q⋅k⋅varepsilon - ─────\n",
       "    ⎠ ⎝           8                      8                                    \n",
       "\n",
       "          2 ⎛   2      2⎞⎞⎞\n",
       "varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟⎟\n",
       "─────────────────────────⎟⎟\n",
       "         16              ⎠⎠"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b1 = Poisson(P, G)\n",
    "b2 = Poisson(b1, G)\n",
    "b1, b2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "26a5b7ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle - k \\varepsilon \\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + Q + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3} - \\frac{\\left(\\frac{45 P Q k^{2} \\varepsilon^{2}}{8} + 4 P k \\varepsilon\\right) \\left(\\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 P Q k \\varepsilon + \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right)}{2} + \\frac{\\left(\\frac{15 P^{2} k^{2} \\varepsilon^{2}}{8} + \\frac{9 Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 Q k \\varepsilon + \\frac{3 k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right) \\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}\\right)}{2}\\right)^{4} + \\frac{\\left(- \\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} - 2 P Q k \\varepsilon - \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + P + \\frac{\\left(- \\frac{27 P Q k^{2} \\varepsilon^{2}}{8} - 2 P k \\varepsilon\\right) \\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}\\right)}{2} - \\frac{\\left(\\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 P Q k \\varepsilon + \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right) \\left(- \\frac{15 P^{2} k^{2} \\varepsilon^{2}}{8} - \\frac{9 Q^{2} k^{2} \\varepsilon^{2}}{8} - 2 Q k \\varepsilon - \\frac{3 k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right)}{2}\\right)^{2}}{2} + \\frac{\\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + Q + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3} - \\frac{\\left(\\frac{45 P Q k^{2} \\varepsilon^{2}}{8} + 4 P k \\varepsilon\\right) \\left(\\frac{9 P Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 P Q k \\varepsilon + \\frac{3 P k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right)}{2} + \\frac{\\left(\\frac{15 P^{2} k^{2} \\varepsilon^{2}}{8} + \\frac{9 Q^{2} k^{2} \\varepsilon^{2}}{8} + 2 Q k \\varepsilon + \\frac{3 k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16}\\right) \\left(\\frac{15 P^{2} Q k^{2} \\varepsilon^{2}}{8} + \\frac{4 P^{2} k \\varepsilon}{3} + \\frac{3 Q k^{2} \\varepsilon^{2} \\left(5 P^{2} + 3 Q^{2}\\right)}{16} + \\frac{k \\varepsilon \\left(2 P^{2} + 3 Q^{2}\\right)}{3}\\right)}{2}\\right)^{2}}{2}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               ⎛                                                              \n",
       "               ⎜                                                              \n",
       "               ⎜    2    2           2      2                     2           \n",
       "               ⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅P ⋅k⋅varepsilon   3⋅Q⋅k ⋅varepsilon\n",
       "- k⋅varepsilon⋅⎜────────────────────── + ───────────────── + ─────────────────\n",
       "               ⎝          8                      3                          16\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                   ⎛        2           2     \n",
       "                                                   ⎜45⋅P⋅Q⋅k ⋅varepsilon      \n",
       "2 ⎛   2      2⎞                    ⎛   2      2⎞   ⎜───────────────────── + 4⋅\n",
       " ⋅⎝5⋅P  + 3⋅Q ⎠       k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠   ⎝          8               \n",
       "─────────────── + Q + ────────────────────────── - ───────────────────────────\n",
       "                                  3                                           \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              ⎞ ⎛     2  2           2                             2          \n",
       "              ⎟ ⎜9⋅P⋅Q ⋅k ⋅varepsilon                         3⋅P⋅k ⋅varepsilo\n",
       "P⋅k⋅varepsilon⎟⋅⎜───────────────────── + 2⋅P⋅Q⋅k⋅varepsilon + ────────────────\n",
       "              ⎠ ⎝          8                                                 1\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                 2                                            \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " 2 ⎛   2      2⎞⎞   ⎛    2  2           2      2  2           2               \n",
       "n ⋅⎝5⋅P  + 3⋅Q ⎠⎟   ⎜15⋅P ⋅k ⋅varepsilon    9⋅Q ⋅k ⋅varepsilon                \n",
       "────────────────⎟   ⎜──────────────────── + ─────────────────── + 2⋅Q⋅k⋅vareps\n",
       "6               ⎠   ⎝         8                      8                        \n",
       "───────────────── + ──────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "          2           2 ⎛   2      2⎞⎞ ⎛    2    2           2      2         \n",
       "       3⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟ ⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅P ⋅k⋅vareps\n",
       "ilon + ──────────────────────────────⎟⋅⎜────────────────────── + ─────────────\n",
       "                     16              ⎠ ⎝          8                      3    \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                            2                                 \n",
       "\n",
       "                                                                              \n",
       "                                                                          ⎛   \n",
       "                                                                      4   ⎜   \n",
       "            2           2 ⎛   2      2⎞                ⎛   2      2⎞⎞⎞    ⎜   \n",
       "ilon   3⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠   k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠⎟⎟    ⎜  9\n",
       "──── + ──────────────────────────────── + ──────────────────────────⎟⎟    ⎜- ─\n",
       "                      16                              3             ⎠⎟    ⎝   \n",
       "─────────────────────────────────────────────────────────────────────⎟  + ────\n",
       "                                                                     ⎠        \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    2  2           2                             2           2 ⎛   2      2⎞  \n",
       "⋅P⋅Q ⋅k ⋅varepsilon                         3⋅P⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠  \n",
       "──────────────────── - 2⋅P⋅Q⋅k⋅varepsilon - ──────────────────────────────── +\n",
       "         8                                                 16                 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "     ⎛          2           2                   ⎞ ⎛    2    2           2     \n",
       "     ⎜  27⋅P⋅Q⋅k ⋅varepsilon                    ⎟ ⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅\n",
       "     ⎜- ───────────────────── - 2⋅P⋅k⋅varepsilon⎟⋅⎜────────────────────── + ──\n",
       "     ⎝            8                             ⎠ ⎝          8                \n",
       " P + ─────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       " 2                     2           2 ⎛   2      2⎞                ⎛   2      2\n",
       "P ⋅k⋅varepsilon   3⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠   k⋅varepsilon⋅⎝2⋅P  + 3⋅Q \n",
       "─────────────── + ──────────────────────────────── + ─────────────────────────\n",
       "      3                          16                              3            \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "   2                                                                          \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                   2                          \n",
       "\n",
       "                                                                              \n",
       "⎞⎞   ⎛     2  2           2                             2           2 ⎛   2   \n",
       "⎠⎟   ⎜9⋅P⋅Q ⋅k ⋅varepsilon                         3⋅P⋅k ⋅varepsilon ⋅⎝5⋅P  + \n",
       "─⎟   ⎜───────────────────── + 2⋅P⋅Q⋅k⋅varepsilon + ───────────────────────────\n",
       " ⎠   ⎝          8                                                 16          \n",
       "── - ─────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "   2⎞⎞ ⎛      2  2           2      2  2           2                         2\n",
       "3⋅Q ⎠⎟ ⎜  15⋅P ⋅k ⋅varepsilon    9⋅Q ⋅k ⋅varepsilon                       3⋅k \n",
       "─────⎟⋅⎜- ──────────────────── - ─────────────────── - 2⋅Q⋅k⋅varepsilon - ────\n",
       "     ⎠ ⎝           8                      8                                   \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "               2                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                            2                                                 \n",
       "           2 ⎛   2      2⎞⎞⎞    ⎛                                             \n",
       "⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟⎟    ⎜                                             \n",
       "──────────────────────────⎟⎟    ⎜    2    2           2      2                \n",
       "          16              ⎠⎟    ⎜15⋅P ⋅Q⋅k ⋅varepsilon    4⋅P ⋅k⋅varepsilon   \n",
       "───────────────────────────⎟    ⎜────────────────────── + ───────────────── + \n",
       "                           ⎠    ⎝          8                      3           \n",
       "───────────────────────────── + ──────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                    ⎛        2\n",
       "                                                                    ⎜45⋅P⋅Q⋅k \n",
       "     2           2 ⎛   2      2⎞                    ⎛   2      2⎞   ⎜─────────\n",
       "3⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠       k⋅varepsilon⋅⎝2⋅P  + 3⋅Q ⎠   ⎝         \n",
       "──────────────────────────────── + Q + ────────────────────────── - ──────────\n",
       "               16                                  3                          \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "           2                   ⎞ ⎛     2  2           2                       \n",
       "⋅varepsilon                    ⎟ ⎜9⋅P⋅Q ⋅k ⋅varepsilon                        \n",
       "──────────── + 4⋅P⋅k⋅varepsilon⎟⋅⎜───────────────────── + 2⋅P⋅Q⋅k⋅varepsilon +\n",
       " 8                             ⎠ ⎝          8                                 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                  2                           \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "      2           2 ⎛   2      2⎞⎞   ⎛    2  2           2      2  2          \n",
       " 3⋅P⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟   ⎜15⋅P ⋅k ⋅varepsilon    9⋅Q ⋅k ⋅varepsilo\n",
       " ────────────────────────────────⎟   ⎜──────────────────── + ─────────────────\n",
       "                16               ⎠   ⎝         8                      8       \n",
       "────────────────────────────────── + ─────────────────────────────────────────\n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                    2                                                         \n",
       "\n",
       "                                                                              \n",
       " 2                         2           2 ⎛   2      2⎞⎞ ⎛    2    2           \n",
       "n                       3⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠⎟ ⎜15⋅P ⋅Q⋅k ⋅varepsilon\n",
       "── + 2⋅Q⋅k⋅varepsilon + ──────────────────────────────⎟⋅⎜─────────────────────\n",
       "                                      16              ⎠ ⎝          8          \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                             2                \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "2      2                     2           2 ⎛   2      2⎞                ⎛   2 \n",
       "    4⋅P ⋅k⋅varepsilon   3⋅Q⋅k ⋅varepsilon ⋅⎝5⋅P  + 3⋅Q ⎠   k⋅varepsilon⋅⎝2⋅P  \n",
       "─ + ───────────────── + ──────────────────────────────── + ───────────────────\n",
       "            3                          16                              3      \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "         2\n",
       "     2⎞⎞⎞ \n",
       "+ 3⋅Q ⎠⎟⎟ \n",
       "───────⎟⎟ \n",
       "       ⎠⎟ \n",
       "────────⎟ \n",
       "        ⎠ \n",
       "──────────\n",
       "          "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_subs = Q + a1 + Rational(1, 2) * a2\n",
    "p_subs = P + b1 + Rational(1, 2) * b2\n",
    "H_subs = H_old.subs([(q, q_subs), (p, p_subs)])\n",
    "H_subs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "73318ea6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{P^{2}}{2} + \\frac{Q^{2}}{2} + \\varepsilon^{2} \\left(- \\frac{15 P^{4} k^{2}}{8} - 16 P^{2} Q^{3} k^{2} + \\frac{45 P^{2} Q^{2} k^{2}}{4} - 8 Q^{5} k^{2} + \\frac{45 Q^{4} k^{2}}{8}\\right) + \\varepsilon \\left(- Q^{4} k + 2 Q^{3} k\\right)$"
      ],
      "text/plain": [
       " 2    2               ⎛      4  2                     2  2  2                 \n",
       "P    Q              2 ⎜  15⋅P ⋅k        2  3  2   45⋅P ⋅Q ⋅k       5  2   45⋅Q\n",
       "── + ── + varepsilon ⋅⎜- ──────── - 16⋅P ⋅Q ⋅k  + ─────────── - 8⋅Q ⋅k  + ────\n",
       "2    2                ⎝     8                          4                     8\n",
       "\n",
       "4  2⎞                               \n",
       " ⋅k ⎟              ⎛   4        3  ⎞\n",
       "────⎟ + varepsilon⋅⎝- Q ⋅k + 2⋅Q ⋅k⎠\n",
       "    ⎠                               "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H_new = H_subs + Poisson(H_subs, G)\n",
    "H_new = H_new.simplify()\n",
    "H_new = series(H_new,eps,0,3).removeO()\n",
    "H_new"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.2"
  }
 },
 "nbformat": 4,
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}