04 Basic samples and functions Polynomies.ipynb

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   "cell_type": "code",
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   "outputs": [],
   "source": [
    "# These examples was solved  by Mathematician Professor  ROBERTO CARLOS ALCANTARA CONDORI\n",
    "# Link\n",
    "# https://www.youtube.com/watch?v=K9Jms_whis8&list=PLGbSw9USRLuSK4bwHlp_ZCngyyJa58zxB"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42808ce5-9b3d-4ad6-abf5-ba832fb3a599",
   "metadata": {},
   "source": [
    "#### Library :  Libaldo.py\n",
    "* This library include:\n",
    "  * sympy.py The best symbolic math library for me\n",
    "  * numpy as np, matplotlib.pyplot as plt IPython.display  \n",
    "  * libaldo_math2.py this module have some util tools for classic math functions  \n",
    "  * libaldo_algorith.py some algorith to manage simple math functions\n",
    "  * lib_MyEq , this module manage maths Eq\n",
    "  * lib_MyEqEq , this module will be MyEq=MyEq\n",
    "* Also include the most used variables like   ,x,y,z,alpha,mu..   etc... mayby 150 variables  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a2216eb6-f040-4269-9fad-5605682d2865",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
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   "source": [
    "![image.png](attachment:c15905fe-892f-41fe-a113-d535d29cda49.png)"
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"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"
    }
   },
   "cell_type": "markdown",
   "id": "62113f01-2b30-4c22-ae09-0fafadcc309f",
   "metadata": {},
   "source": [
    "![image.png](attachment:c72f9718-3788-401b-92ec-b5c1ed4b1e1f.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "07375c4f-06d8-43b0-a7bd-750668b85603",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =x + y$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq(x+y,'e1') # P=MyEq(expr,'P') return Equation class with name P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b43eb100-d150-45f0-b269-90190bb6ce55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(x + y\\right)^{3}$"
      ],
      "text/plain": [
       "       3\n",
       "(x + y) "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ppow(e1,3) # ppow(e1,a) return e1**a , e1= symmbol, class, numeric..  wathever"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "12c3cba4-4708-45c4-a393-1bf936bdfa83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{x + y}$"
      ],
      "text/plain": [
       "  _______\n",
       "╲╱ x + y "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rpow(e1) # rpow(e1,a) return e1**1/a , e1= symmbol, class, numeric..  wathever"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9a35ed45-e7bb-4c34-96aa-0254c20d8972",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt[3]{x + y}$"
      ],
      "text/plain": [
       "3 _______\n",
       "╲╱ x + y "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rpow(e1,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d9724ee9-d2db-458a-8f39-00a110bb0f5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAAAcCAYAAADlXHhOAAAElElEQVR4nO3Ze4hVVRQG8N/kQJpCgb3LKdLSCGLEbAwyijSjqKSISNDsARH2sKzQ1Boqe0pJD3xAMFJRmUaRRYXSA8ciS80SE4rsAZaVZu+0mv5Y5zhnrufcuaPeaYT54LC5a7/W/vbaa629b01jY6NuVA/7/N8KdDHcjTf35IDdBLfFYKxup80czKp0wG6C26Ieq8rU1+B8vFjpgEUEz8cm9K50oL0AQ9CCqwrqD8bh+AdL8buw5pMzbYZiXyzLyKZhDX7F92hCr7Qyj+ChGIv78FtHV9GF8aGwvLvQJ6e+Pikn4U7hLr7B86hN6kbjFfyd6VeLa3ACLsVITEwr8wiegZ8xu+Nr6PK4F4fi+py6emzHhXgb63Er6tA/aXOBnd1DI5rxJZaIDRiUVpYSfBxGYAH+2MVFdATjxbE9vRPmgvfxKa6289oH4wVsyMi2JGUPDMAxeD1T3w+P4GNsFm7icmH55ExyhXDkz+Uo94Yg46ISeY3wOy3CrXQWbkrmnFRQPxB/4Z0S+bPCKkeWyOuxskQ2TJD2mXAPS7W6zb5YIU7EzRiOk/CnTCZSSvAI4eTfy1H4FvwrfFiPjHwmLsM8TM7pVy00J+WwgvpHhZ7XFvTLEryfOL3ZddWIzXsK2+zsHs5FT1wirHotGoR/X502yhLcW+ziOvnB7SM8ieNFEITbhCUtEI6+M7FSuLGGnLqLBYGPiwifxYqkPC0jO1EYzzixYQPEWuswHQcl8pczfX4UZI5O2l8nTvAvwuLRluAjxA5uLLOo6eII3CEsY4bYvbGJgp2J7YKsfjgsI++Nh0SaeXtOv61iDXUZWT0+x1RhLGtEqtWAH3BeMtd3mT6vYq5IaZfjWDyd9G1JG9VmOvRNyi2K8bW4xUwWR3C5iLrbyvRJsQFHFdTlXU/niyBYDs3CEk8RAYog9UgRbLYW9NuMQzK/5ySfzDhZ5GUPLZiQfIXIEpxmDT3LdRDJdIorRUJeCWbhgBJZvVB+vrbRm/avrLT60wZBzCDciHeTMYvQS8eypGY804H2O5AleFNS9s1rmGCMCGrfiuh5g8p976wc2XhBcBPeqnCcLJYLS0oD3WPCzU2QOaYl2Eds9BcdmOeBXdBtx2QpNgrrHFjQ9hxBxCciKKwX186i9p2BLSIoDxGbf6bwi+XeEwaKDGF1tZWjLcEtImc8UETFLE7FQpFAjxIbMU2cgPurr2ZZLBOBba4ISFPbaZ9a+x59lixCaR68KClHZWT1WCwCxkitWcZCfCCO+PDqqdguUj/cB1OUD9Jwlsj1X6qmUinyCN4k8kHCkl8T1j1KpDJZTEnKB6ulYAVIfekKPNFO2/1F3rpYZERVR23J720iGN0j7uarRDArwhLhz3YVTcm3O0hvmOUCW4pxIkuauZtzVoy817SH8ZV4suvqGCMuAbO13tCK0EucuEXavudWFaUWTNxyxuIMETy62ptwnSC2v7DIteJZsT0cLd5LmqqlWB7yCCayidJXqK6Cs8W77k8iUE1U2WVnnXi77VQUEdyVMS/59gp0/+lZZXQTXGV0E1xldBNcZfwHppb0gVC1tnEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left(x + y\\right)^{\\frac{b}{a}}$"
      ],
      "text/plain": [
       "       b\n",
       "       ─\n",
       "       a\n",
       "(x + y) "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rpow(e1,a,b) # rpow(e1,a,b) return e1**b/a , e1= symmbol, class, numeric..  wathever "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "51803d24-ba2e-4424-8e01-abfb31fbf960",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =\\left|{x + y}\\right|$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e2=MyEq(abs(x+y),'e2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8c059a12-eed8-43db-acbb-ac24264e7107",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x + y$"
      ],
      "text/plain": [
       "x + y"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kilabs(e2) # killabs(|e1|) return e1  , e1= symmbol, class, numeric..  wathever"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5effde09-5aac-493a-ad0a-efa8893e00e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e3 =\\sqrt{3 x + y^{z}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e3=MyEq(rpow(3*x+y**z),'e3') # P=MyEq(expr,'P') return Equation class with name P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "51f6aaf0-2179-46a6-b5c6-1e2bc912b730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3 x + y^{z}$"
      ],
      "text/plain": [
       "       z\n",
       "3⋅x + y "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insideroot(e3) # insideroot(sqrt(a)) return a  , a= symmbol, class, numeric..  wathever"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2ed06843-ee44-4e47-b84e-641836145724",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(3 x + y\\right)^{z}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4=MyEq((3*x+y)**z,'e4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "619cd25e-75b4-4964-aed8-8575295ffdc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAyklEQVR4nK3RsUpCURzH8Y+mIET0Bg0+hIGD0OzaAxhNiZvtXVoCsbEaDQenhmhoioZw8lF8AxdtuPfG4XC8EPiD/3A45/vne/7/WpZl/pt6dF5iV1E/0Iigd3wlml/hDN8paJoApgUww31KL0wNzxjjCdfYVkFHeMUNJhjJ/ySlB00scIm7UilMDLXwhj5u8ZjSCKFjfOACQ7zsUf+DTvGJcwww3weE0AJdrNBGlnj7gE0J1dErLjpFxVmHjRry2Z9U6cSpWu5hoV9E2yQa48yFcAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle z$"
      ],
      "text/plain": [
       "z"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getexponent(e4) # getexponent(a**b) return b  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b1eae486-6cbb-4da1-95fb-5b42595ac9f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3 x + y$"
      ],
      "text/plain": [
       "3⋅x + y"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getbase(e4) # getbase(a**b) return a"
   ]
  },
  {
   "attachments": {
    "54df9e1e-714e-4371-a5f2-ffb26663218e.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3UAAABACAYAAAC9UV6jAAAX+ElEQVR4nO2dP2ibx//H3/nxjQtyA4pS0CIPBiuGtpsWo0BW49RDu3TwksEgTyZZsgVMoFsXh042ZMiSoUs7ODZZCzZevCUFR4IO9iJoVEEqQ5XBv0GS/Tz353nu0d3peR7l/YJCI0v3fO6eu899Pnef+9wNAJcghBBCCCGEEJJL/i9tAQghhBBCCCGEjA+dOkIIIYQQQgjJMXTqCCGEEEIIISTH0KkjhBBCCCGEkBxDp44QQgghhBBCcgydOkIIIYQQQgjJMXTqCCGEEEIIISTH0KkjhBBCCCGEkBxDp44QQgghhBBCcgydOkIIyRQFNNbmcbm1iMvNChppi0MIIYSQzEOnjhAy1dRrFTS3FnG5NY/tWtrSxFNfLmOnOjP4R2kW3+dAZpIVCtgeLgg014ppC0M8kje9RgjxD506Qsj0Uinj5eosFgAAM3i0mHVDt4Af786EPql+VUhJFpI36stlPBouCCxUy9insT+d5E6vEUImAZ06QsjU0rhfHBo+Q+58gXpawphQuYXvSuGPmn9fpCMLyRlFPF0KLwis0NifSnKn1wghE4FOHSFkSini+6rw0Yf/cJSKLIaUb4aNNfTxvp2SLCRfVL6A2N3JNJJDvUYImQh06ggh04nCyG196Kciiin1r24Kn3zCn+epiBLD9dmt8ZO5uChjGhmzXaQFgez3dzIGmdFraY/ftJ8fR9blI9MInTpCyFRS/6Yg7Xq9fpflUEb5PB06n/A2HWEiCZ7dQmkWO2Mk5XBRxjQybrvICwJkGsmKXkt7/Kb9/DiyLh+ZTujUEUKmkm/vCA5SZne9RszgrnCeLqthVXLbplPGNOKyXXgec/rIil5Le/ym/fw4si4fmU7o1BFCppACvr4jfNT8F7upyGJIZsKq4pDP9CSX00UZ08j47SIbkTyPOX1kRa+lPX7Tfn4cWZePTCt06ggh04cii+TBaTcdWUxRJEnJZLho7UushD4YQ04XZUwjY7eLwtjP/M40SUxW9Fra4zft58eRdfnI1EKnjhAyfeQwi2RekqRIcnYu8GtCOV2UMY04bZeMnsckFmREr6U9ftN+fhxZl49ML/9LWwBCyOdHvVa5ujy3dXyG6hu3q5h5nFSl8LlMhosqkrkkPvfnooxpxKZd5POYrfcf2aZTRjb0WtrjN+3nx5F1+cg0Q6duSqjXynhaL2CldK1MWp0eXh918Pgkm9v+SpmbXTx81Z6oAhxLjkoR+z+UsVIC0Oni3i/xMjfW5rFTnQHQx/MXf+Gx8WRcQL12Kyxjp4fnv53Hl1EpY/+HIlZK6bStTqaRQwcAC0tlbL/TtEelgMb9Mp5UZ66+32p28fMfbexG1F1ykBJOqpPvm3L4nPoMRgGNtWB79HGw18aDBGPcqm4uwr88hJBlRZdYYdMuivOYk0mSYqGbckt6dfai15LaCWmHgKb9/Dgmpd8ybt+RdLgB4DJtIYgFAaNdS6zTUcT+Znlo+LdRfeVZQQYdIiU9bDw7979LMbYcBWxvzuFR4HcHe6d4cBLxrFoFl6uzBmWHCe5oycQ7h/XleRwuBSYC3a5YqC36ODhu40Hc7lmliO37t6/SNhsb0VJbqNqvgMZyCU+Wxqn7GO9nRGp9s4j9rXLgHIZcv/pyBS817WFUv6R1q1XQ1Pa9AJ0+WqP/L83Efz9pGVH6y/Z9Beqo77+yI91q/oOHr7rjO4wu2jbYLtKYUo0PcUwZjnMNtrpp4vOOA+zrbIONXhvTTnDdT5Pi4/mhMW/Q74ILo+L86bt9nNh35HOCZ+ryTK2C5nrMgAeAUhGHm2XUlX8sYHvz2ihaqN7GdkX+Vr1WQXNzcXCR5tYimmu68kxkjjLCAGACd7pYySGHOlW/KkSUU8B2fTbi72oaa/M4jJwwZvBofRGXm2Xji00X7t6S3lu9VsFlqC1msLI0h+ZyRJ0qZTTXA/fwAFioRvWzwPNi79MaGC87WoduIOOjdd2FruL7MTx3kmbflHZagufpCtjeXMRhRHusrMZcbjtG3RqLBsYKMDBSRv+ZfD9pGaWb+Fb1G9v3VSmHDLKFahFPa4rvbM1hpxqUawYL1bJRX9fhpG117QLIYXmVIvalMWUwzjXY66YJzzsO8KGPk2Gj18azE7z30xjcP7+I/dCYL2NfHPMhCtgOOFULS6XQu/XaPk7sO/K5QacurwxXZo2NqFIRL1WTtyJUIMzQoFydxULge6YGfIgkMle/9DQx+pFjIeJOmvpyObS6CiD2vFRjbXEYqmlAqYjvNRNT7F05tQoOV9UOp8oBHFDE/npR3X4lhWEcS8A4qRSxvzUnt5eSWXW9Ix0kDWn3TTEBwlWSC3l1Xo2mLYCx6/Y2Iym4W8cdeaw4eF+qS5xDRvLQqNI+Q6dTDXDRtsF2kRZKgmF5wwUYnXEoGqpxONFNk5x3HOBKH1vhW68BUp923U+T4vz5ijDlyAXZmH7qrX1c2Xfks4NOXS4ZrDaF6eNg7wz3np3ixrNT3NvrXm/3D1FO3lI2rSAxBmUSRTJcFZdkPm4PZH7RxoFZSXY4kaOP9x3hoztfqA2NWiUU/jigh42IkI+BASF82Onh+d7Z4N0eW0wkorGncegAAKUCflSsnjfWykK65jDRu5YqRsZJEfvrQtmBet/Y65k9S+sgachA31Qb5fL4azW72HhxihvPzvBc6IPKtrCo29GbNp43zftaq9NHq9nDwXEXG1e66My6DClc2NH7irzEWdjF0xG1mBOFi7YNtotYl+vzmBELMFdELAgIONNNk5p3HOBVHychqV5zYCe47qdJcf58Rb+LOnsqLfwIbe6nfRzad+Szg4lScohsVMux/EcnbVRxUzhnMZi8d01i8AE01uJ3CBaWSmi8uYhZiVMZFoLM5wNH6Wo12Us6bldyXODX9308CjprwxCKUFy7xvh8/kJ/xqe+PK8wIMIx80fvLtBaCoZxmKe1vjb2BmEl0cbeDO6WAQRXg2sVWT6Bhbu3UH9zkTgj4vam6NAJZwVO/sXB6mykQ6kkMplANvqmyigPj78+nu+1A4fiL/DnBwCR49O2bhd4/OovPEYB9coFjsqKc1shmVS4KMNlnSK42j1XPKPTw8Zv59hFOXr3zhiX7SIm2bm+EytuAWbEYEEg+lm+ddMId/OOPZOq81jEJElxYye4Hr9Jcft8OfS/h9+19pCcxVLOKOu+fSZl35HphDt1eUNhVLeO2+rD2Sf/SivW8bsow9Vq6Tm9wQ6BtFtyE18rdnOC1JdvS4bFwZ5woFwMc/CQAtilHEfvLoSVMnG128D4FKmU8VLc1TM6BK0Lw5EzKl6tStZKguHUx/MX8u6PWJ54NvBg70xeqU56hqLzCV+LhlyzPfbh7/gze4HvZqJvKi6OvlsOjL9hvwkZBhHvdoi7ul3g6FyTTt3YWHFRhss66bONSkZVp4t7v5wPsq2et1F90cVBBwD6eP6HbXIPF+0inrXS6fDBXHHv2Rk2muHPY3ccnesmzfcczjvWeK9zMpLoNfd2gpvxOz5unp/s2hj57Lx+V89R+3i378i0Q6cuVygSbnS6eKgNb5DDBM3ChcTt/+Hu0jmAk45g+M/gu2+iE2qIE2Pr+EzI2FXEfmjXyIWx5FmO8494LbTtSn101kPMZDgoSzI+Q6icwB42VAaEcRiO7mC9HN4xkG24+6NDdASbg1T6R39/Er6Y0OAqFfEoOJE127inyixomLZdH4omlpeRvqkwHhauUlfrFgLk34TwUDfbdOrWZTitkzw2Xr+7kI0qlRF/3saDX05x45m7TId27SKMi84nvFWM8UHmvi6OcIHdUzmUWY8P3aR5jqt5x5pJ1dkcY73m0U5woQNssHu+vJATedVA7UtpDo/bgbWVbzL2HZlm6NTlCdX9J0eOU9l2PgHCanjYGZEN/yhF0rgvhjEJSqpyndZ6hHZlygL3clzg8ZFgGJWKeFoblhP6w8Chi0o9rd6BUIdpNhYFxa+bODQH66VnNdta2a5X/sQJJ2Astz9J8f1RRCZv6XTVDh2gOA+hCp2J38EakZW+qXJWR2gXAqTfhNvCfd2K+F5cQU6cJMCuDL/v6xP+PBedCo0R7xzLthXHxYf/8K2429hsh8/uiGNWdyYYnnSTiON5x5aJ1DkR5nrNn53gQgek+HypXaJDL+WM1XE7sK7l82DfkamHTl2OUBk1PyWMnxaVjBgu0HoPfB9cDVcY/OYZnxRK7iomvYDGsiIluWh8OMGTHCfnUhjTyqqYZS7eoTPbgbj+7pNxJ47hCv7T0LPCSVu071accJr/BM4w/YdwMwzP4iUmyohWrWLarIhnpW9CnzQiwtmWdUGwLTzUTXIir89tGWNVhuM6KXa3ZKdiAndlqmRJ2LaiDj/48EVYRwwXSkKIY1YXMu1JN/mddyyZlD72hA87AYAbHWCD7fNFPRsVeikdT4BBwi07+by9N/JZwUQpuUFxBkQ6tCuSJCZ8yN1C+AJkRejSINwuMOkNV3klWRThC03cwvZa+H6zEd4uoPUox+4fXTyp6hInmF1GK6dW7+FnpTFqktwkgGIFf1zDNTzhxIcg6hMvKM6PmciimGTVq5gxYYlX5WWkb2qJypAa5eDAT90kx3OMc0M2Zfh+Xx9uxjoV3rBs2/DOdx/Vu8JY/c1ktX8YMi0815tuEnE571gysTonwlCv+bQTXOgAGyyfL+6oJgpfNcFKvgnZd2TqoVOXF6SteYNVIMkQksMNxFC467M8CUKXVJkfoTrYPYOVpRlFNrY+DvYG57N84FWO84943SkqsrWZOXSQds709/oo77uDXpFLq+Efvgg/y9RwFVejg7t0AEax/bGXpEYRKYsixbPxKqb6HERW+qZalmgHVw4NCxudPuomJwBIvktqU4b391UNZlWNvnLENXZtKxqDM6F73fQ6XByziky3HnWTz3nHDn91dovmfJcnOwFwowNscDtO9O2izb4aE1ZrJZ/H90Y+L+jU5YXEq0CK1aaYC6/D6FYncXUe41oe9Spv7MXXGKyoP9SdoXKETzkaa+qJ3XiVTqGYVe1eX55X3HeXjOadm4kN14U7M4l36YCoaw1UK85RZSquOoD9WYOs9E2lLFEOqzI0LGx0+qhb2klSnNcp4p40m8uSx8GubSN2cCKTLMhIu+sT1E1xzwBgPO9YkUqdHeLRTsh3khRNhlgRgyt7dFjJN3H7jkwrPFM3pciriCrDecxQONszVMOLW+89O0VVmeWwiP3NRVxuVfxepmklR2F4Ka1uYp/Fzma8/Care3XlBebJWaleTwLGhmu1HJ7kpF06QJXEING1Bp0L/Kq5kkF1CbH2fAugONeQ9b6pyMimdVhV4V4RRrDI2HXTp/83x0UZCpy/rwTt6QTLdtEm2YkLu1QkHrl7K5QsxZ9uSmneMWCS+jgRtnpNg5mdAHgbv8Y4fr5qF61WCd8r2+kNry5JQb4YzN8b+dzgTl1u0a9SKicdpTGuWeWNDW2Tw+1MLq9Fs4t7r2J2WCrBy309rMQ6kqOxNiffJ9Pph8KIUJrFzmYZbyMy6MWt7skrwj1s7AE70qXmSdAbrtK5lRD6iePthz4QcnBn8WS5gF3xOSojVHOPmMqhS7r7YExW+qY2bba6PYzORFrXzfQ8D1BfruDl0ixwfCYkKXFRRgBf72viq92W7aLZcTQJYZTGbKmIp7XrMGh/umnC804C0tHHPnFhJwDOx29i/D6/Xqvg5eqscBa1A/wQCMuOPMPpWj4X762AxloZT6ozV/VqSc80+Q7JE9ypywtS2nj1Sl19eR6H0gSjCbXTrPLGh7ZFrPJWimjUBmnwpWxl1ajdmwIaa/O4DN4NpN3BSYZrOQY7dOFftY7PUP3lLykbJkpFHG5W0DC9t22UWny4wxBW3sN7m4Sf6C4c1YWsRe7SRV1PoJ3wobirDlhYmkNzrRxOla4yQqu3sV+7vjqhXquguaV26Ma9kFwkK33TLCxI4+BqziGmU7dBOYdLA8NovHTz+jImVafIe6tSQ98uygupDRc+jt5dSGP9+q5NBa50k+d5xykO9fFE8GEnGONCB9iQ4PmlAn6sBH4Tcug0iyJJok+SyufFvrsVctYAYGGpjO1Kwu+QXEGnLi9IoSfAymrAWagUsb+pivNXTzwA1Aa2YQIKycgqFXG4tYjL9TJ2VgdKQTb0BztXQQenXilie20eza05IZTRNGtbPC7lqC/PyzH3gdTpu6/OhEtyMdixW58POC4RBNpRvBpBl3hFDJuKJia8TNHPRr+LnPBP/sWB4uOFahEvl+PqPYOV1Tlcbi3icmtOmmABWDl0KiMrK30T6OL3UIPP4slacfg+h6n6dQ6u5n24r5vikttAn6vXytjfDJcjO0d2ZUzmfaWRaMCuXVQLN8bnTc/b+FmxCKUdr650k+d5xyne9fH4KJ1HH3bC8O/2OsAG2+eLv5/Bo/XBfCMdobiaz8VFhOHumQ/5vL03EZOz/hPOakqcwvDL3NDF780yVkIOxSx21hexo/1NdAZGZdY9Q4Pg6N0FWkszmmQDQ6Vw/i8OVmfDB89LReysFyNkjpc7MSeO5FAkqZCN6ws8/qWNu1tico+B49Jc7OLnP9rYHZa5e9rDTjUudEeQQ0wYUCriae2jUca/+LN0qn5mEubXxU/Ht7GimHSCWbyUOwsx2IaDDFZEhd+76hMO2H11hq8DO3EL1TIOtyIOzMQ5uM7rNjRugkZtqYjDraKylJZyB9GyDNd1kpJuYOLZ/AbYtIvibFrCu62irmTxpZu8zzsWTFof26DUax7shAEudIANts+/wOOjHh7Fhck226H5PByiPIPvving8bnqvdrK5+u9hb8fP4+bfIdkGe7U5YjdV23lboiSTm8M4zPBSrVqlXfItVLo4sFeL4kAQKeHDcdGsxs5VEkqdDsAXTx4oX5XC9Uidu4HFL3iAvMgrWYX954J7aFc1ZvD5Vp4ApEv6zVLArH76gzPm6Pf9nGwF5GYJMDRm79w77h3HUaieJfinVoHzYjD5J0eNl6cJnPotDuNIlnpm4Ay0YyGVrNtsGPpvm67p2blRd0PZ1eG4zqp+smEs/mNcNG2IxJnhT1vo/qifZ0QIhi66VE3hXE971gwsTonxFiv+bMTXPbTcbB+fuS77ePg+Aw3hGRLYojywtKcNuLGVj7n7+38I153wt+X5nGT75BccQPAZdpCkASEDv+rMU7tXavgMrhy1WzjRiJlXAhf/tvpYeO386tdqBFm6Z/7ODj+Bz+98ZdC3koOVbvHtVeliP0fxLAdzWHl5RKeLI3CDvtoNS9CO3omdZHKtX6/rhHPhvWw8awDrJUDYSmjun/ErnJFNB7xzOPB3ql2ospK34wf18nvX3NdN9VZ0qTy2Zbhrk7yOcU0EwSM3S6VMvZ/KGKl5MuY9qCbJjTvjI8nfWxJEr3m1E6IkCGM/zs9XTx/lKjk+t3+g4d/dHFkmoE5IlLCWj5P7418PtCpyyVyxiJ0+jh4/w9+eqdTTmoaa/NDg9p9WFmIShHb92/ju9Ch3D5anU94fdTBryeqO80yJIdoiBi3V9hAcGd4BQ0bvRE7sfdrRBH7wbBUh4lPQgQmRiPDKmN981Hg3EWr07OTwWndRGMX13rH2OF1UIarOtXKaK4Wr8ZluoaSi7bNCvG6KVt6yQVm+tiKpHrNoZ0QKjPVfprC80MLJ108jMy660hHOn9v5HOBTh0hJograKnveuUQtiEhhBBCiBd4po4QE87beLjXQ6sD8KLP8ah/U4gMKyGEEEIIIePB7JeEGHJ0co4qDxGPjZh+vSUlciGEEEIIIePAnTpCyASQ0683/04nKQUhhBBCyLRBp44Q4p/KLXwnXN77vp2WMIQQQggh0wWdOkKIf8o3eZ6OEEIIIcQTdOoIId6pf3VT+OQT/mRqZkIIIYQQJ9CpI4R4R0ySgs4nvE1HFEIIIYSQqYNOHSHEM3KSFHz4L2cXKhNCCCGEZBc6dYSQicPrDAghhBBC3EGnjhDimQs8/q2Ng87gX61mFw/f8DoDQgghhBBX3ABwmbYQhBBCCCGEEELGgzt1hBBCCCGEEJJj6NQRQgghhBBCSI6hU0cIIYQQQgghOYZOHSGEEEIIIYTkGDp1hBBCCCGEEJJj6NQRQgghhBBCSI6hU0cIIYQQQgghOYZOHSGEEEIIIYTkGDp1hBBCCCGEEJJj/h+j/tUSZd3PzAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "2ea8fdad-5403-40cb-b5c7-77a7caba4e4e",
   "metadata": {},
   "source": [
    "![image.png](attachment:54df9e1e-714e-4371-a5f2-ffb26663218e.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0ef9a09f-06b2-4470-97ce-d6d272104e7d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "23363714-2584-45f4-b708-eaa68a8efab8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =3 x^{a} + 4 y^{b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq(3*x**a+4*y**b,'e1') # P=MyEq(expr,'P') return Equation class with name P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "eef30889-aa0c-406a-97a2-fdfbbb3c3c7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3 x^{2} + 4 y^{b}$"
      ],
      "text/plain": [
       "   2      b\n",
       "3⋅x  + 4⋅y "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1(a=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "aedc5e77-6285-42de-84e5-3b4215021ae3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3 x^{2} + \\frac{4}{y}$"
      ],
      "text/plain": [
       "   2   4\n",
       "3⋅x  + ─\n",
       "       y"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1(a=2,b=-1)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "ea4f7568-8a10-40ea-9bd1-901f6b98cc82",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "6c980f8f-9767-41e7-a121-721a9944b3f6",
   "metadata": {},
   "source": [
    "![image.png](attachment:364a3b5a-4f08-44a6-8c43-bd9b032d1eb2.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "3c4108bf-78f3-49a0-a7fb-f1b0209deb96",
   "metadata": {},
   "source": [
    "![image.png](attachment:18eae8fa-e1f5-494a-bfb4-ff382d9deb43.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "36306f2c-46aa-4152-bbe9-533e49fd7e0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will find F(x) in the upper example\n",
    "e1=(x+1)**2\n",
    "e2=2*x*x+4*x+5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "bc6e0ce0-e28c-443d-9074-76018fab747b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle If\\;we\\;have\\;that\\;...\\;f(\\;\\left(x + 1\\right)^{2}\\;)=\\;2 x^{2} + 4 x + 5\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE([ 'If we have that ... f(',e1,')=',e2]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e74e185b-4fe4-488e-a41d-38e616e670da",
   "metadata": {},
   "outputs": [],
   "source": [
    "# f((x+1)**2)= 2*x*x+4*x+5 , f1= 2*x+3\n",
    "# procces, x--> Add(1) -->['A'],[1]  -->x+1  -->Pow(2)  -->['A','P'],[1,2]  --> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3130c521-4a47-4a1d-9bd8-a54c56de321e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2 x + 3$"
      ],
      "text/plain": [
       "2⋅x + 3"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "findFunc(2*x*x+4*x+5,['A','P'],[1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bf7a45ca-4407-4242-a208-421c93412794",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =2 x + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now ..we check ...\n",
    "F=MyEq(2*x+3,'F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8d9198d7-ceec-43a1-8cc3-972fccfc3e6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2 x^{2} + 4 x + 5$"
      ],
      "text/plain": [
       "   2          \n",
       "2⋅x  + 4⋅x + 5"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# is ok\n",
    "expand(F(x=(x+1)**2))"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "3a3d1b7a-ac72-4114-8df8-d45dacadc99e",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "d79bf349-e98b-4c1f-8bf3-5fe11659ddb7.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "415c9ec4-5941-4770-91d8-b8eeb6b4f427",
   "metadata": {},
   "source": [
    "![image.png](attachment:d79bf349-e98b-4c1f-8bf3-5fe11659ddb7.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8504a2b9-b256-4f33-b208-1376471c798e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# import Libaldo each you initialixe and  clear all variablea  \n",
    "import sys\n",
    "sys.path.append('D:\\Libaldo\\SolveLib\\Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "16733a6b-0b39-4a4b-b916-a9300693c28f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = x^{2} - 4 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(P,x*x-4*x) # Q=MQ(expr1,expr2) return Equation Equallity  class with name Q--> expr1=expr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a0e93dbc-169c-457c-beea-e8768d47484e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P + 4 = x^{2} - 4 x + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Add(4) # Q.Add(a) = Q+a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ac458bdf-1cae-4f68-8329-ac75c0525925",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P + 4 = \\left(x - 2\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bb77003a-f546-4f86-a0e1-9deb58fdfbd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = \\left(x - 2\\right)^{2} - 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Substrac(4) # Q.Substrac(a) = Q-a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "9d53317e-52ec-48be-9edd-a63fef49e4b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\sqrt{x + 4}$"
      ],
      "text/plain": [
       "   _______\n",
       "-╲╱ x + 4 "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "findFunc(x-2,['A','P','A'],[-2,2,-4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f8f9a502-1036-4f6b-a945-b29321f073ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\sqrt{x + 4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now ..we check ...\n",
    "F=MyEq(sqrs(x+4),'F')"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a5c68bf1-78e7-42b7-8d51-cf750948819d",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "e4a9332c-f33d-44f4-99fb-9459d7b2dd5c.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "56087cd8-6598-489d-8d74-c2e739efd34d",
   "metadata": {},
   "source": [
    "![image.png](attachment:e4a9332c-f33d-44f4-99fb-9459d7b2dd5c.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "495e3474-2b21-4338-b3a1-59ad32874aad",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5b98cb52-b1d0-4908-b6ba-44dab6e832cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def P(x):\n",
    "    return a*x+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d44ed0d7-7f10-478a-a899-5b26c16f8432",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a \\left(a \\left(a x + b\\right) + b\\right) + b = 8 x + 7$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MyEqEq(P(P(P(x))),8*x+7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5c5ecc71-4997-4845-ae47-8187f9fab730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{3} x + a^{2} b + a b + b = 8 x + 7$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f6fa3672-350d-456c-8d7d-3e17e8305443",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 7 b + 8 x = 8 x + 7$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# deducce that a =2..then\n",
    "Q.replace(a,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b8c6c345-117f-48f4-b3c7-851164ecf7b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b=Q.solve(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "684baa60-3964-4443-8719-3190a463c061",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P(x)=\\;2 x + 1\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE(['P(x)=',2*x+1])"
   ]
  },
  {
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    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
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   },
   "cell_type": "markdown",
   "id": "d44c64f5-075c-4025-ab61-a3de42185d0a",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "a83c8712-d2f2-4afd-8b75-41223a9648db",
   "metadata": {},
   "source": [
    "![image.png](attachment:4f9d63fe-76eb-4b0c-8711-394904505eb2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ecf088ff-1600-40cd-a1a0-97d0898b42dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "febde9e3-7ba1-422d-ae3a-c8fa495a158b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{m} + 1 = y$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(x**m+1,y) # Q=MQ(expr1,expr2) return Equation Equallity  class with name Q--> expr1=expr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b7e1e01b-24fa-431c-8669-4287d9628514",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{m} = y - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Add(-1) # Q.Add(a) = Q+a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "78309a96-e607-4f81-80f5-56e0d9306bb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x^{m}\\right)^{\\frac{1}{m}} = \\left(y - 1\\right)^{\\frac{1}{m}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Rpow(m) # Q.Rpow(a) = Q**(1/a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "3ca70a18-b2a2-4c0c-9532-745d5ccdc994",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\left(y - 1\\right)^{\\frac{1}{m}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.mulexpo() # Q.mulexp() if Q=(x**a)**b return x**(a*b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "31127df6-82f5-450d-9211-833bb1d18454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Y =\\left(y - 1\\right)^{\\frac{1}{m}} - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Q.L = return Q left side\n",
    "# Q.R = return Q right side\n",
    "Y=MyEq(Q.R-1,'Y',var2=y) # var main default is x, change to y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "bcb8adf1-4a5b-47f1-9f4a-45d303ee669a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2^{\\frac{1}{m}} - 1 = - \\frac{7}{8}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# cfrac(a,b) return a/b without mat solve\n",
    "Q2=MQ(Y(3),cfrac(-7,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "19c7edc7-1b3d-4c6d-a27d-73a8594b03c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2^{\\frac{1}{m}} = \\frac{1}{8}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2.Add(1) # Q.Add(a) = Q+a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "eb9924bf-ee3a-4dde-becb-11c97a075eee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m =- \\frac{1}{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m=Q2.solve(m)"
   ]
  },
  {
   "attachments": {
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   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "60ad879e-34ad-4948-aed9-db18b8b745b5",
   "metadata": {},
   "source": [
    "![image.png](attachment:70776850-5863-406f-9b1b-3b6d6489d0f0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "1523f1be-3684-4c4d-ad5d-02e160537728",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "a8020491-c1c7-427f-b7be-db952385e245",
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    return factor(simplify(expand(x*(1+x*x)/(x-1)-x*x-x-1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "4c0c3562-5627-4cf4-b62c-cb71f9f6707f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x + 1}{x - 1}$"
      ],
      "text/plain": [
       "x + 1\n",
       "─────\n",
       "x - 1"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#m=1\n",
    "g(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "6a82a5a6-ce35-40d9-850a-27e078efc228",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA8AAAAPCAYAAAA71pVKAAAA90lEQVR4nKXSsSuGURTH8c/LO/oDjAYli/wBjHrLohiUkoHFpJR6iTwlRQzKZlI2vaMBmU0WZVFMFGWyGAwvw73D03Uf6nWWe8+5v+895557akVR6NS6Ev8SX5hK4jUcx7OdKngFbWyhuxTfxxyO0KyCb3GCQczG2BqWcYrFsrieecoGprGJHmzjIl7WLgvTzPCEA/ThENeYxGcqzMHwVtrP4yMnysEzQoNeo79UkeAHPC58yR2GcI8FDPwFj6CFZzRi6etCU3d/g4dxhneM4SXGW7jBBEZzcD/Ohelp4DHRrMZ1L4XreEBvrqxoV8J4Vpbdkf0L/gZMHiyGjZDamQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle x$"
      ],
      "text/plain": [
       "x"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#m=2\n",
    "g(g(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "3834c6ac-9d31-47e4-be13-5a6bac9cbd8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x + 1}{x - 1}$"
      ],
      "text/plain": [
       "x + 1\n",
       "─────\n",
       "x - 1"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#m=3\n",
    "g(g(g(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "0869c831-1772-4cb6-8ecf-6746397bb2e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x + 1}{x - 1} = \\frac{a x + b + 1}{a x - b + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2*m+1 even then\n",
    "Q=MQ(g(g(g(x))),(a*x+b+1)/(a*x-b+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "8a62fa44-7c86-41ca-bca4-5a435c892ba2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x + 1\\right) \\left(a x - b + 1\\right) = \\left(x - 1\\right) \\left(a x + b + 1\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.crossMul() # Q.crossMul() return.. if Q= (a/b=c/d).. return a*d=b*c "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "934f3389-c95d-42da-8509-b4edd3adbd60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x^{2} + a x - b x - b + x + 1 = a x^{2} - a x + b x - b + x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "40ba5068-0145-421a-8251-337036f127f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x - b x + 1 = - a x + b x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "629c33f2-f054-4d8d-a4c9-5d6251f649f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =- \\frac{1}{a - b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=Q.solve(x)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "3fb9c8f2-0932-41b4-b12f-7f30fa13bba4",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "5bd3f1a3-6019-4ba6-bb21-5546f255adea",
   "metadata": {},
   "source": [
    "![image.png](attachment:f20bb931-d137-424e-9a10-891563c402aa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "8b76083f-9617-463c-aef1-2db442dd4c08",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "ad77ebb1-c976-457e-9216-e88fc64f86aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x}{2 y} + \\frac{2 y}{x} = 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MQ(cfrac(x,2*y)+cfrac(2*y,x),2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "5072d8d0-e9f8-4611-9868-6aa56f46fd70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x^{2} + 4 y^{2}}{2 x y} = 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "805aca33-5bdb-4245-b2df-3660fe385a0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} + 4 y^{2} = 4 x y$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.crossMul() # Q.crossMul() return.. if Q= (a/b=c/d).. return a*d=b*c "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "d4b25f7c-a4c5-4f40-8c05-31570ac4c418",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} - 4 x y + 4 y^{2} = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Add(-4*x*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "ccf7bd65-ba63-4a51-931b-287ffa13be93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x - 2 y\\right)^{2} = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5eda2c99-bd47-4b0b-9460-daaf4be1b1b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x - 2 y = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Rpow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "fd6181a0-711e-4901-811e-1e20e64f89aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = 2 y$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Add(2*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "bc02fe4b-8e1f-4be8-975b-851ae8714118",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{x^{8}}{y^{8}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=MyEq(ppow(x/y,8),'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "99ef447b-7185-4b6b-8b71-ff91bf631051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =256$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.set(x=2*y)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
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   "cell_type": "markdown",
   "id": "67c23f07-b248-4c1d-ac86-18304db5b949",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
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"
    }
   },
   "cell_type": "markdown",
   "id": "b07a2a3f-a8e0-4220-9090-052ac8d3e43d",
   "metadata": {},
   "source": [
    "![image.png](attachment:ee98dee9-c41f-4fe1-bf36-11e628efaf67.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "cadd6986-34f4-47fd-876a-e7eca0ee50ef",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "3e34c75c-f07e-42ef-b571-8758c21b8749",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y =\\frac{2}{x - 3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y=MyEq(findFunc(x,['D','P','A'],[2,-1,3]),'y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "9bf574d8-120e-4f79-9028-ec8db3044fa8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def msec(n):\n",
    "    return 2/kpow(2,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "710f737f-09b6-4a6b-ba16-c6ecad2bf8a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2}{x - 3}\\;,\\;\\frac{2}{x - 3}\\;,\\;\\frac{2}{x - 3}\\;,\\;\\frac{2}{x - 3}\\;,\\;\\frac{2}{x - 3}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE([y(4),',',y(5),',',y(7),',',y(11),',',y(19)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "6d154ca3-072b-4603-871a-88fb8751d7b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2\\;,\\;1\\;,\\;\\frac{1}{2}\\;,\\;\\frac{1}{4}\\;,\\;\\frac{1}{8}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE([msec(0),',',msec(1),',',msec(2),',',msec(3),',',msec(4)])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a77acaaa-547d-4847-818f-fea0d952f906",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA4AAAASCAYAAABrXO8xAAAAyklEQVR4nL3SMWpCQRDG8Z/B0ivYBiyTxsbKc9gEUnuAQJItbQQDFoEoEr2JCDlDUqZPl2CstHj7yKI89Qnmgy12d/7zzexOJYTgFF0cuO9gHdftsWAdQ3yXcaxggi88lwG7aOMGP8eCDfTwhHlB4h2wihk+cVcE5YGpHnCFFpb7wNSxGV36eNsHpWAVU3zg/hCUgjVcyh7m19+nr/EYY17ifpA7wQrjguTXsr4XeM/byMGlrZFKFCL4itF2qaV1VjDIZneUHv5/qRu2oCPfAqwKjwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 4$"
      ],
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summation(msec(x),(x,0,oo)) # summation() is sympy function..put  summation?? to get help"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
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   "cell_type": "markdown",
   "id": "3b73197a-17e9-47f3-addc-48bcfd1d8473",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
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gV1dXuTR9fX3S1dWVa2G9du0ade7cmby9vSk9PZ2kUikVFhbSwoULCQDNnj1brhXu+vXrct+V+vr69NVXX1FMTIzYXp1LWloaOTo6ko+PDz179kwu7d9//6WYmBi6e/euWJeTk0Pjxo0jALRr164q95+enk4A6PTp05Xme/jwofgO9/T0pFmzZpGJiQlt376dHj9+TLGxsSo7J6dPnyYTExMaN26cQtr169cpJiaGkpKSxLp79+5RkyZNCACtW7euxuLYtm0bASBTU1Py9/cnMzMzcnd3Fy23VS0//PAD9erVi1JTU6tVbmZmJg0ePJgAUJcuXSg6OpqGDRtGK1asqLSFWSKRUHR0tNwyevRoMjU1pUOHDlF0dDQlJiYqbKdsyyQAufeiOhdW93Bl8iXw8OFDateunfhAW1pa0sKFC+n06dMKlcXCwkLy8/MTeetSZbKgoIDmzJlDLVu2VKgkjRw5kgCQhYUFJSYm0smTJ8nZ2Zm0tbXJzMys2mW5urpSYGCgUnkXLlxI7733nuhakpycTEREt27dIhsbG2rTpg05OzuTr69vlftyd3cnExMTunXrVrVjlrlz547oZlP2PK1Zs4YAkLW1NV28eJESExPJzs6ONDU1afr06ZSVlfXc5VYmMzOTzp8/Lyr7a9euJSKi+Ph4atKkCbVr146cnZ1pzJgxtVK+MlJTU6lt27YEQO61Ki4upsTERPLy8iIA1K1bNyIiSk9Pp/Hjx5OpqSk5OzuTs7MzxcbGqit8xpQWHx8vbnKVffzh7t275OTkRADIx8enyn2lpaWVeyPowIED4nckLCxM7PvNN98U64uKiuT2079/fwJAI0aMoPz8fCIi+vHHH0X+q1evKpQvu3CeP3++3HoDAwPRTbAqGzZsEGXcvn1brM/JyZGrTMq+t1TtyZMn5OfnR48ePZJbv3XrVnHTVFmzZ88mADR8+PAq8z59+pQA0JkzZ6rM++WXX8qdq/379ysd0/PYtm0b+fn5UWJiotz6Y8eOEQA6ePCgUvtJT0+n3r17EwBycXGh7OzsGonv6tWrZGtrK87HoEGDKCMjo0b2XZWDBw/KvRZRUVFVbpOamkpfffWVWMaMGUMAqE+fPmLd7t27FbZLTEwU5Xz33XcK6bJrDgCUmppaI8fHXj1cmXxJxMfHU4cOHeS+YABQ79696dmzZ3J5V69eXScrk48fPyYA1LZtW4W0v/76i3744QcKDg6WWy97fkDZiqFM27Zt6euvv1Y6f3Z2tjhn//vf/ygpKYk6depEa9asoRs3bii9n549exKAam1T1meffUYAaPTo0ZSbmyuXFhUVRQ4ODnI/LgkJCeLCcvr06c9drjJk7y1nZ2c6d+4ctW3blrp3716t518///xzeu+99ypcDh8+/FyxyVq9UcHzuLdv3xZ3mk+ePEljx44lAHTixInnKo+x8qjizvy3334r3us9e/ZUSM/IyKDU1FSF1i7Z8uTJEzp58iSdPHmSBg4cSABIS0uL1q9fL/KU1zK5fft2sc7Ozo6Kiork9puVlUWpqamilVQqldKWLVvENleuXFGIZdCgQQSAbG1t5dbr6+sTAJo6dWqF50F2DDNnzpT77MvSS3+vt2jRgpKTk1XeipKSkiJ+F+Li4sT64uJi8vPzIx0dHdq0aVO52xYWFopjfP/998nCwkJUsrW0tMrdJiIiQjxP2LhxYwJKnrns2bMneXt7k7e3t9zrI1suX74sztWGDRuqPK6CggLy9vamUaNGkYWFBXl4eJCjoyNZWFhQv379yNvbu8LnGB89eiQqgGWfx5VV4AoLCyssOywsjIYPH04WFhZkbm4u4m7durVci/NXX30ljrmipbJWV9lno3Xr1pSVlaWy90xhYaE4punTpyv9zGXZ91bfvn3LfVa59MItk6wmcGXyJSKRSGjv3r1kYmIiV6E0MjKixYsXi3x5eXlkZ2entsrkjRs36MCBA5SQkCC3XlaZ9PLyUnpf+/btIwDUt29fevDggdLbVbcy+ezZM+rcuTMBIB0dHbK0tKRff/2ViouLld4HUfUqk48fP6YDBw7I3d0n+v/KZHl3CWWxljVs2DACSh6Sr02//fYb1a9fnwCQnp4e2dvbV/tOcHZ2NmVmZla45OXlVTuuY8eOka6uLhkaGtK2bdvKfd1Kt/Dr6uqSubk5HTlypNplMaZusm59AOiPP/5Qervk5GTy9fUVF8lll+XLl4u85bVMlr6hGRQUVGV5+fn54jtx6NChCj0tiP6/ZbLsTUYDAwOqV6+eXJd6IqKdO3eSr6+v3OMfpZeKWiZL/0aqkr+/v4ihdAukrMLQuHHjcrc7d+6c6IJsZmZGgYGBtHjxYrEvbW3tcre7d+8eBQYGUmBgIH3//ffi2Ktq3YqOjhb7rs7N25ycHAoMDKT09HQ6f/48BQYGUnx8fKXblH5vlb0ekFUOy/4uEpX0IvL19SVtbW3S1tYWxynr2eTg4ECZmZlKx14V2Y0OY2NjOnToUI3ttypFRUXi/JRtsa/Mjh07yNfXl3x8fAgADRw4UHxW/vzzz3K34ZZJVhN4apAXQCqe70ZfXx+enp5o2LAh0tPTMW/ePKSmpiInJwdr1qzBF198AQDQ0dGBpmbJ2EobN27EihUrVBbjkydP4OnpiatXr2LdunWYP3++SJNN1TBv3rwKz11hYSEOHDiAvXv3Aih5CB0oGSo8JiYGAwYMKHe7/Px8+Pr6QltbG/n5+UhNTUVQUBAuXrwIAOjVqxdmzpxZYdx6enqYOXMm3n//fRQUFMDa2lpM1FvV6zx58mQUFhaiuLhYDFn+4Ycf4o033gAAzJo1S2Fo++LiYkybNg0HDhzA2rVrsWDBApFWVFQEDQ0NaGlplVu2rq6uGCgmICAA4eHhuHTpkoi1onhXrVolBgUoz4ABA+Dj41PpsY4cORLLli3DtWvX0KZNG+zfvx+GhobV+iwYGhpWmac6+5NKpVi3bh2KioqwYcMGjB8/vtx9mJmZwdvbG0uWLEF+fj5+/vlnDB48mOetUrNXbUAFVbyfnJyccODAAVFeVWXm5uZi+vTp2LNnD4qLi/Hpp5/izz//BFAyxZRsaoXS+yq9T9l6R0dHXLt2TelygZLpLQCgU6dOMDExUdhG9ndwcLBCmdL/pgbp2bMnAMDf3x8ffPABGjdujL59+4p9f/vtt/Dz81PqGFRtxowZ2L59OyIjIxEeHq4Qm6Ojo0JcFy5cQO/evSGVSvHjjz9i0qRJ0NLSAlAyiJ2/v3+Fx9OkSRP4+voCADIyMjB79my4ubnB3t6+0uM/e/as+P/UqVMxfvx4paafMDAwEOW9+eabePPNN+WOrzzvvPMORo4ciX379smdk0WLFuHRo0f4+eefxRyTMp999hnWrVsHAFi5ciUWLlwo4rt37x727duH0aNHo379+jXyOicnJ4vB7TIzMxETE4Nhw4a98H6VERkZKf4fFxeHp0+fiuneKlNYWIjc3FxERkaiRYsWaNiwoRhUsKioqNzzYmRkhA4dOuDatWvlvqfqwmeorFftN+OVUCtVVKYSCQkJoqVFR0dHLk3W7dHV1VWlMQUHB4u7WOvXr5dLk92BvnDhgsJ2J06coICAAGrTpg0BoJEjR9KUKVPEUNiOjo6UkpJSYbl5eXkUHBxMjx8/pilTppCxsTE5OjpW6xnCsLAwcVd08+bNyh/0f0JDQ8X2fn5+leZdtGiROE+jR48W62V3CR0dHcvdLiYmhpYtW0ZAyfOlU6ZMoSlTplCzZs1U0jJJ9P/vLTs7uxfqzltTpk6dSgBo7ty5VeZdsWKFOO+//vqrCqJjrOadPHlSvI9dXFyqzB8XFyfyT5o0Sa77vOyZSSjRMhkVFSXWdenSpdzWo7Jkz0x+8skn5abLfhf+/vtvufUGBgakqakpWkv27NlDRkZGBJQ8k1maMs9MqqtlkqikRwf+a+GSPQuYkZFBAOj48eNyeWXdRwFQgwYNFPYle2ayopbJ0pR9ZjI3N5c6deokfm8B0NOnT6txhNV35swZAkBNmzYV6+bPn0/29vYKgwympKSIAYIAKPSGkT3vaWdnVyNx5+TkkL29PRkaGoru1osXL65WT6X8/HwqKCiodtl///03WVpakomJCWlraxMAioiIUHr7goICGjVqFF2+fFnpbSrrDSVrmfT19VV47IYxGZ4a5AXQf3dp1LXY2Njg4MGDMDAwQGFhIdasWSOXDgAzZ85UaUyWlpZiUmV/f388ffoURIQTJ07g/Pnz8PT0hK2trdw24eHh8PLywrRp06ClpYWwsDBs27YNAQEBWLVqFQDg3LlzuHLlSoXl6ujoYMKECWjUqBECAgLQuHFjjB07FkZGRkrHnpWVJVr8/P39kZ2dXa1jd3FxgY2NDQBgypQpleaVDelf3vsIABo2bKiwPiEhASNGjMDy5cthbGyMnTt3IiAgAAEBAejcubNK3pNZWVkoLCwEAMTGxuL06dPV3kdCQgJcXFwqXLZt26bUfvLy8rB48WLs2rUL33zzDWbNmlVp/qKiImRmZorP708//aTSzwYv5S+s+po2bYp27doBKPluPHXqVKX5S/fKaN++PfT09J6rXFNTU9jb2wMAYmJicPz48UrzFxUVITQ0FABw8eJFpKWlVZh3xowZCus0NDRgamoKoGQS+JycHADAli1bnit+denatSuAkhYu2fRJFfWUSUpKQlRUVI2Uq6Ojg9mzZ4uW5/Lk5ORg7Nix0NDQwJ49e2BgYFBpfDVFdk5ycnJw5swZPH78GJcvX4aZmRmaNWsml1cikSAxMbHc/WRnZ4uWvDfeeEO04FbXo0ePcPnyZSQnJ8PFxQXPnj3D+fPn8eWXXwIAvvzyS6SkpCi1LyLC1KlTMXfuXERERCgdQ3h4ONzc3NCpUyc8ffoUb7/9NoDqvRbHjx9HTk6O+Jwqw8HBAcbGxjh16pTc9FgSiQSnT58GANjZ2T339wZ79XFl8gWoak6dI0eO4NChQ+Wm2draQltbG0QkN6eYrBvA3bt3VTr/j6urKz766CMAJfMSFRYWQkNDA48ePUJ6ejqaNm2KBg0ayG2zdetWPHnyBEDJRYKLiwsMDQ2hoaEBOzs7lZzvwsJCbN26FVlZWQCAf//9F4GBgc89B1JVeWxsbLB582YAwI0bN5CYmAgNDQ3R9ey7775T2GbmzJm4desWzMzMcPDgQbz99tvVLvdFluzsbIwdO1Z05X3e8gwNDeHk5FThYmVlpdR+Fi5ciJUrV+Knn37C3Llz0aZNm0rzb968GWvXrlX555eXyhdWfW3btoW7uzuAki6sP/30k8IcuYmJiUhISABQ0kVQ5vHjx2L+3uzsbNE9tDKyxw2aNWuGMWPGiAt2f39/hfl3k5KSEB8fD6lUCk1NTbRo0QIAcOLECURHR8vlDQoKkuvSV5ZUKhWVr4YNG6JevXoA/n+uWaCkwvr48WOFWMv+X50sLS0xbdo08bdEIkF2djbc3NzQo0cPuby2trbitZVIJPj000+Rm5uLtLQ0HDlyRDwCQkRVHp+BgQE2btyIli1byq2PiIiAo6Mj/Pz8MGvWLMTGxmLlypXw8PAQN4NPnDiBrVu3iq6lNU1DQwPm5ubIyMjAoUOHcPfuXYSFhZU7t7K1tbVct9bExETEx8cjPj4e06ZNE7+bKSkpSlf4ypo8eTI8PDwwaNAgpKSk4PDhw2jfvr1cHg8PDzg6OlY5HzERYfv27di0aRPGjBmDuLi4CvPeu3cPjo6OcHR0xJgxYzBo0CDs2LEDAMS5uHXrFhwdHeU+xxUxMDDA+++/X2W+0tzc3NCxY0f8/vvvSEpKEuvj4+Nx8OBB2NjYiMdHGCsXseemilGrIiMjycTEhAYOHEgZGRkK6Xfu3CFDQ0PS1tYWI209ePCAbGxsCABFRkaqfKSt0l0Jz507R1JpySiAxsbGdO/ePYX8ssGC8F9Xp9JpXbp0EWlHjhxROgYPDx2p1ksAAAoiSURBVA/asWOHUnnT09PJ29ubRo8eTUePHhXlLVy4sNIR5cpbvLy8qHHjxnT79u0q84aEhIiyDhw4QFKplJycnMT0JGXzv/322wSUjCz34MEDuTTZPIqtWrWq0dcyIyOD0tPT6cmTJ+Tu7k7m5ub0119/0cSJEwkomaamuufoRReJREILFiwgLS0tWrlypVxabm4uffLJJzRhwgSSSqWUlJRExcXFtH79ejIxMaGlS5fSL7/8QkDJwFWHDh2qtKwff/yROnToQLNnz6bs7GyVHufrsrDnJxv+HwBNnjyZlixZIhYdHR0aN24cEZVM7ePq6io3qMeSJUtoxIgRYh1QMtBZQEAAERGNHz9erK9fv75cd8zSo6d6eXnJlWtsbEzDhg0TU4NcunSJ5s2bR0DJ1Eul85Yuu1GjRqKr68GDB0UXv9JTg8gGoLGxsRH7WLBggdx+rK2t6cKFC3T16lUxVRBQMvds2ak5VGn58uUElEwxsXfvXgJAEydOrDC/bD5J/Nc1uW/fvgSAhgwZQnp6eqKr8c2bN6sdy6FDh8S+LSws5NJmzZol0vT09Gp1kLKAgAACSkYknjZtGgGodKC9b775Rm5qGvzXFXj58uVibu2BAwc+Vyyl31sxMTFifWRkJFlYWIj31vLly6vsvlpcXCwX46VLlyrMe+vWLZFv8ODBJJFIRNqDBw9Emqura61OTZKSkkI9evSgNm3aiM9WixYtqGfPnrRp06ZaK5e9GngAnhegirvqEokEGRkZOH78OCIiIhQeAF+1ahUkEgkmTpwIKysrACV3e2/evAkAWLJkCU6cOFHrcZbm6uqKjRs34uHDh1iyZAmOHTuG3bt3Q1tbGxYWFgr5V6xYAU9PTwCQa604ePBgua1gyti/f3+l6UeOHEFISAiAkrtvx48fx59//okePXpg0KBBOHbsGNatWwd3d3cYGBigW7duSpXr7++Pa9euoXnz5lXmLX0spVtqpk+fDmtr6wrzJyYmIjg4GIsWLQIAREdHIzY2Vm4/NWXGjBnIyclBQUEBzp07hz/++AN9+vTByZMnAZTcVfXz84OhoaHKBnqKi4vD+vXrAZR0C5K1agMlg4kEBQXhrbfewm+//YalS5diwIAB2LhxIz766CMsX75cDFaUk5ODTZs24e+//8a0adNEt8HS5s6di9zcXFy7dg1jxoxB7969VXKMjCnj559/xqpVq3D8+HFs27ZNfA8AwKVLl0SrYIMGDbB3717MmDEDKSkpojXQ2dkZN2/exLFjx7B9+3YUFBSIAVTu378PZ2dnsb+EhAQxANr69evh5+eHM2fOwN/fX7QeAsDRo0fRvn176OjoAAC6deuGzp07w9raGr/++qv47pCVX1pSUhIaN24Mf39/ODg4AADu3LmDuLg4tGvXDkuWLIGOjg6OHj0q9lO/fn3cvHkTqampoldMamoqGjRogDfeeEOUUVxcjGfPnr3oKX9uTZs2hZ6eHo4dOya6sbZu3brC/AEBAaKLZWmNGjXC06dPIZVKAaDc39SqNGzYEM7Ozujbt69CF0pfX19ERUXByckJc+bMEe+h2nTmzBmcOXOmynxz587Fu+++i+zsbLFOS0sLzZs3x6RJk1BYWAh9ff3nimHJkiWYPHky9PX15c6pk5MTzp8/j4KCAujp6cHS0rLKfWloaODmzZuYOHEibt68Wemgc02bNhXXa40aNRLdjGV/y9LeeOMNGBsbP9exKaNp06Y4fPgwvLy8xGfLzs4O27dvR6NGjWqtXPaKUHdt9mWmirv2J06ckLuDeOzYMbF8//33pK+vT6ampqJFLzc3lyZPniy26dq1q1rmBpK1Nnbr1k1MQty3b99y8+bm5tJHH31EQMkE3FOnTqXNmzeTvb09DRgwQAyDX5OtbtnZ2WRpaUkAxBQRsrQdO3aIubxatWpFISEhtXKO8vPzycvLS9yx9/PzowYNGlBwcHC5+dPT08XdfCMjIzI3Nydzc3OytbUVrZZaWlo0Y8YMkkgkNRKjbFh/S0tLOnXqlFi/ZcsW0tHRIaBkaPsRI0ao7L118eJFubu+5S29evWir7/+mjQ1NUlTU5NWrlxJ+fn5JJVK6caNG2RtbS3yDhgwgM6fP19uWQ4ODiJf6ePnpeYWxl4XsgHmZN/VrztZy6RsGTlypFzL3Mvs7Nmz1LRpU5o3b566Q2Gs1nHL5AtQRctkhw4dEBwcDKCklXLQoEFy6T4+Ppg4cSL69u0LoOTua9++fcXfQMkzNap+NmnmzJmYO3cuoqKiRMwfffRRuXHo6elhxYoVCs8n7Ny5E+3bt0dERASSkpKgq6tbY8dhZGSE7777DhKJBNbW1nBxcRFp3t7eMDQ0RFZWFqysrNCvX78aKbMsHR0dcRf1wYMHWLt2LVq1alXh9BwNGzbE2LFjFe5mN2/eHM7OztizZ49YJ5te5EXt2bMHYWFhaN26tRieHwCmT58OExMT5OXloUWLFujTp88Ll6WsFi1aiM9ERczNzTF48GCYm5uDiODt7S3SbG1t8dtvv4lWnMqmQ9m7dy88PT1x6dIlfsaPMcZqkI+PD4KCgsQgLz179pRrmXuZxcfH49GjR+jQoYO6Q2Gs1mkQ8XB6z0sdp65smXX14jYqKkp0l5I5fPgwhgwZoqaI6iYigp6enhghtWXLlqJbC6sbRo4ciatXr+KPP/5A27Zt1R3OK6eufocxVtM2btyIOXPmACiZi/jrr79Wc0Tq5+rqipCQEGhoaGDDhg348MMP1R1SjUhOTkZMTAyGDx+u7lAYq3XcMvkC1HER9LJceJWN08XFBQ4ODi9N/KpStrXLz8+Pz1EdcvToUURGRuLdd98t95lKxhhTVumRW8uO4vq62rp1K6ytrdGlS5dXpiIJlPQYUmbsBMZeBTw1CKsVZmZmYh4poGRodDMzMzVG9HLo0qWLukNgpYSEhGDChAnYsGGDukNhjL3k7OzsMHnyZAwdOrTWHp942WhpaaFp06blTgnCGHs5cDdXVmvmz58vuvEkJCRUOnLd62z16tX45JNP4OnpiaCgIBgZGak7JMYYY4wxxqrELZOs1gwZMkQ8TN+qVSs1R1N3DR8+HG3btoW5uTlXJBljjDHG2EuDWyZZrUpJSUFxcTGaN2/OzwJW4tGjR9DS0uL5nBhjjDHG2EuDK5OMMcYYY4wxxqqNu7kyxhhjjDHGGKs2rkwyxhhjjDHGGKs2nmeSMcYYqyH85AhjjNUeHn+j7uHKJGOMMVZD+EKHMcbY64Qrk4wxxlgN4ZZJxhirPXzDru7hyiRjjDFWQ/hChzHG2OuEK5OMMcZYDeGWScYYqz18w67u4cokY4wxVkP4QocxxtjrhCuTL4DvQDPG2It51Spf/LvAGGO151X7zXgVaBD/8jHGGGOMMcYYqyZNdQfAGGOMMcYYY+zlw5VJxhhjjDHGGGPVxpVJxhhjjDHGGGPV9n8Y+gnocMEGFQAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "922f422d-6618-46ec-b6f3-2b81d371ecd6",
   "metadata": {},
   "source": [
    "![image.png](attachment:b01d67d8-e757-467d-999f-01e484a728f6.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "f7b9b28f-6c59-4a21-9c2d-1a7a228ff23f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "66767ec7-ce36-4711-a383-d3ad41c41962",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{a + x}$"
      ],
      "text/plain": [
       "  _______\n",
       "╲╱ a + x "
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1=sqrs(a+x);e1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "1a0081d5-e641-43dd-a0e1-edf971523a2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{a - x}$"
      ],
      "text/plain": [
       "  _______\n",
       "╲╱ a - x "
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2=sqrs(a-x);e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "83e9d9eb-324b-425e-99a5-41c50b0aa9e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{a - x} + \\sqrt{a + x} = 2 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(e1+e2,2*x) # Q=MQ(expr1,expr2) return Equation Equallity  class with name Q--> expr1=expr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "709e1474-5c3e-4573-abdf-8eac727ffa7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\sqrt{a - x} + \\sqrt{a + x} = H$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2=MQ(e1-e2,H)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a7b60b3-44f3-401b-905a-5ca422b87a40",
   "metadata": {},
   "source": [
    "##### If Q1= MQ(a,b) and Q2= MQ(c,d) we handle... two Eq with..\n",
    "     Q1.Add(Q2) => a+c=b+d\n",
    "     Q1.Mul(Q2) => a*c=b*d\n",
    "     Q1.Div(Q2) => a/c=b/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "d1f2554e-6396-49b2-92b8-127404500bcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(- \\sqrt{a - x} + \\sqrt{a + x}\\right) \\left(\\sqrt{a - x} + \\sqrt{a + x}\\right) = 2 H x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Mul(Q2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "2dbb070d-03a0-4428-96f9-6ce8e886b0c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 x = 2 H x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "dd6b01f9-4b38-4494-89b0-cdbf73311e7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle H =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H=Q.solve(H)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "aefeccc5-0c2b-4f99-9592-cae660282337",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "d080d00a-f383-4733-bc4e-92ba47e877c8.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "bfc191ad-361f-4012-9b15-2176e3bb3fb5",
   "metadata": {},
   "source": [
    "![image.png](attachment:d080d00a-f383-4733-bc4e-92ba47e877c8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "2bba3afd-ab60-4ee3-b36e-c08c55de1754",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "46e2555c-b0c7-4c6f-89e5-dfe191053e33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{m} b^{- m} + a^{- m} b^{m} = 11$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "am=a**m\n",
    "bm=b**m\n",
    "Q=MQ(cfrac(am,bm)+cfrac(bm,am),11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "9f3b9635-0532-4fef-8708-0c5db475f2fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{m} \\left(a^{m} b^{- m} + a^{- m} b^{m}\\right) = 11 a^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Mul(a**m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "e837acb6-8041-4b46-bf21-ecfc2069da2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2 m} b^{- m} + b^{m} = 11 a^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "8e8c29ae-6b73-4069-b405-6aabee1f5adb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b^{m} \\left(a^{2 m} b^{- m} + b^{m}\\right) = 11 a^{m} b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Mul(b**m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "0ac2ce22-5bec-4cc1-aea5-f2cee07319b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2 m} + b^{2 m} = 11 a^{m} b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "4d4f0086-09f2-46e3-895b-8a248967e732",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = a^{- \\frac{m}{2}} b^{- \\frac{m}{2}} \\left(a^{m} - b^{m}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F=MQ(P,(a**m-b**m)/(a**(m/2)*b**(m/2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "b359ea80-797d-482c-8860-b05ce4941be9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P a^{\\frac{m}{2}} = b^{- \\frac{m}{2}} \\left(a^{m} - b^{m}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.Mul(a**(m/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "b326f23b-57a8-4170-b823-9f82b99bd9bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P a^{\\frac{m}{2}} b^{\\frac{m}{2}} = a^{m} - b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.Mul(b**(m/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "44ad6689-ee15-4fda-9127-02ec848662a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{2} a^{m} b^{m} = \\left(a^{m} - b^{m}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.Pow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "45c15386-325f-4120-a79a-666c1a80bc2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{2} a^{m} b^{m} = a^{2 m} - 2 a^{m} b^{m} + b^{2 m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "9a50e690-8c96-4c8d-931e-9b851b045859",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{2} a^{m} b^{m} + 2 a^{m} b^{m} = a^{2 m} + b^{2 m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.Add(2*a**m*b**m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "cba28a19-df61-4056-9080-fe4c4b95e3a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{2} a^{m} b^{m} + 2 a^{m} b^{m} = 11 a^{m} b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.setR(Q.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "2b4f56a4-5072-4d94-aed8-415a54eae49e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{2} a^{m} b^{m} = 9 a^{m} b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.Substrac(2*a**m*b**m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "da3701a9-0315-44aa-92ed-19d365ffe19b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{2} = 9$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "9ef9464e-84e7-41ca-9383-ab397a0fef26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=F.solve(P)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
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