07 Basic Div Mult functions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "05ef1c3c-cc68-4633-affd-dda1898cc172",
   "metadata": {},
   "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"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a6b174d3-aa80-4939-bd35-90ee20f6483c",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0db8117a-6de9-4b6f-b50b-f9b61806b2dd",
   "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": "287cd183-7084-47e6-96a0-e4f915bc2076",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# This scrip initializes all variables. \n",
    "import sys\n",
    "sys.path.insert(0, './Libaldo')\n",
    "from Libaldo import *"
   ]
  },
  {
   "attachments": {
    "c15905fe-892f-41fe-a113-d535d29cda49.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAACFQAAAAOCAYAAAALvdoVAAAAtElEQVR4nO3aMQHAIADAMIYZZE46+zhqgB2Jggros9+1BwAAAAAAAAAAx7wdAAAAAAAAAADwN4YKAAAAAAAAAIAwVAAAAAAAAAAAhKECAAAAAAAAACAMFQAAAAAAAAAAYagAAAAAAAAAAAhDBQAAAAAAAABAGCoAAAAAAAAAAMJQAQAAAAAAAAAQhgoAAAAAAAAAgDBUAAAAAAAAAACEoQIAAAAAAAAAIAwVAAAAAAAAAADxAUJBAsA6OPIXAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "6ef2fae7-0aed-485a-97bb-2f3264457711",
   "metadata": {},
   "source": [
    "![image.png](attachment:c15905fe-892f-41fe-a113-d535d29cda49.png)"
   ]
  },
  {
   "attachments": {
    "54df9e1e-714e-4371-a5f2-ffb26663218e.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "e66207d0-7a19-4900-9bc5-08d5272c7ec1",
   "metadata": {},
   "source": [
    "![image.png](attachment:54df9e1e-714e-4371-a5f2-ffb26663218e.png)"
   ]
  },
  {
   "attachments": {
    "51dc8fa0-9c85-4e34-adf7-920a92cdbfb1.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "e36e203d-7aaf-4c32-8677-d29223a9c248",
   "metadata": {},
   "source": [
    "![image.png](attachment:51dc8fa0-9c85-4e34-adf7-920a92cdbfb1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aafbf1c-45d3-4e97-9b95-07ad63265c07",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### playing with division parts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1727d793-c057-4194-b088-c05add78dd36",
   "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": 4,
   "id": "059bc9fe-934d-4aef-bb5b-88d6275d4864",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =3 x^{2} + 2 x + 5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =3 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(3*x*x+2*x+5,'D') # Divident\n",
    "d=MyEq(3*x-1,'d') # divisor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "84a9e5b7-dfb4-46bd-b40e-80af4f812f3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=D.quotient(d,'Q') #  P.quotient(d,'Q') # get quotient between P/d and return in MyEq class called Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7f0376e5-c4b3-40f2-a607-f21173045737",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=D.rem(d,'R') # P.rem(d,'R') # get residue between P/d and return in MyEq class called R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "28ebb621-cc3a-4263-9767-c2e70d36ac49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\left(x + 1\\right) \\left(3 x - 1\\right) + 6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F=MyEq(Q*d+R,'F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0652ebd7-016a-40b9-baee-036c1b448764",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =3 x^{2} + 2 x + 5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0ad5b283-7361-44d7-87a3-636f5284b997",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA4AAAASCAYAAABrXO8xAAABDElEQVR4nK3STyvEURTG8Q9ZkYaNlYWazLwBoaxQk6U3YGFrioWNsvCzsPanWEp5BbY2VuQdYDSllN0UibKRxb2/Gnd+sxh5Nk+dzvfcc3tOX5Zl/qL+gto4TvGCLzzhAKPtTQMJVMYNxnCBe0xjA0uYQ6voxZMIrWMZW1jAPqrYK1q1jFpc7TgZuIMPrGAoBeejX+I7Ad9xjUHMpmA1ekOxHqNXUrAU/a0LmNdHUrAntYP5xFJRY1v9NQUfole6gJPRGyl4Fb2m8wvDQvifuE3BphDFBOoJuCvkdy7k2XFya8LJHWERd5gRMm5gO29MV2piCmcR2BQu6lAIvpU3pi/CM1YL6r/0Lzn2pB/5oi7hEjb8QAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# comprobation\n",
    "D-F"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "544f5a50-711f-4522-9edb-7ffc0139d1cf",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "30f43645-5714-45d8-8dbc-b1f3e54de013.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "bfbc0375-af45-459c-aa3d-f59a8f624dca",
   "metadata": {},
   "source": [
    "![image.png](attachment:30f43645-5714-45d8-8dbc-b1f3e54de013.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b24f40bb-4271-4541-8ff1-d8ffcd4ef60f",
   "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": 11,
   "id": "d32ebc8f-5e67-445a-a403-75273ae95b60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =a x^{4} - 8 x^{2} + 5 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =x^{2} + 3 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =x^{2} - 3 x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =m x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(a*x**4-8*x**2+5*x-1,'P')\n",
    "D=MyEq(x**2+3*x-1,'D')\n",
    "Q=MyEq(x**2-3*x+2,'Q')\n",
    "R=MyEq(x*m+1,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5bac765d-a976-414e-9966-bdd8a55bb8df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R1 =- 33 a x + 10 a + 29 x - 9$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R1=P.rem(D,'R1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b80f2411-5c0c-441c-898a-8be3a9243b72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m x + 1 = - 33 a x + 10 a + 29 x - 9$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(R,R1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "557d4717-f730-4ead-b4ec-cbeead045aea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m x + 1 = 10 a + x \\left(29 - 33 a\\right) - 9$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.factorize(x,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4599ac99-24eb-4039-8e18-66324c6d0952",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle B =10 a - 10$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B=MyEq(10*a-9-1,'B')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "17953284-005c-4298-875b-2d32786329b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a=B.solve(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e5342a1e-3848-47ae-8612-37ec013a4450",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m x + 1 = 1 - 4 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.set(a=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "dcdbf58d-27cf-408f-8e98-a7ee232f72cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m =-4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m=A.solve(m)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAnCAYAAADZ7XK3AAAFkklEQVR4nO3dPY7iXBYG4OPRtxSokVq9AlgBNUlHk04GYZF01tIkk3UCISyhok4aVlCsoNRBm73cL7DB/BlcP1NUtZ9HOhLC2BxfZ6+u780iIgUAAAAAQIv949oNAAAAAABcm6AUAAAAAGg9QSkAAAAA0HqCUgAAAACg9QSlAAAAAEDrCUoBAAAAgNYTlAIAAAAArScojWEsUoqUUuST3rWbeSPVPS+GTz+nPeMEAAAAQFs0CkqHiyIgOyyBWXN1Y1jUIhrnlQAAAADAq7sQlBazCGeDiFhPo59lkWVZZFk/puuIzt2DsPSp9sYxi9EyImIQsyfN7gQAAAAAXtPZoLQ3+RqDiIhYxqg7jtX2yCrG3SLo645XdafTwPx2E5ZGDGZmlgIAAADANZwNSj/fdIoP69/x+BbdtNT8f9NYR0RENz6ZoAsAAAAAb+5sUPr4u4jvonMTnxtfsheTvOk6nLubClWft5VPonfwu+Njp66Xx6R34pxnrQVacz8n//+lOnGzHehT/df9d92YN1lH9hrj9NrPHQAAAABeLtXXMC1SKZ+k3tnfRoreJOXFj9OkV30/rC6y9/3e9feO99IkT0cWw4NjRz3VXS9Srzqptod80tu/n6rxvWPV14s0vDQmh+ecGsfq4E5vh/dS81/bMU8pLYY1Y3F47rXH6bWfu1JKKaWUUkoppZRSL65LPzgItfbCuKZVF7KdCfN2A8DD0G7nWBGiNbhe1IWVl3s7CgZ3Q7uG43EuKL3U13Fo2aTHc302HKeac14+Tq/93JVSSimllFJKKaWUelld2PU+ImIet1kWWb9cR3Mwe8Yr0I9RvcV/+iX+5eg25rtfrH5FXn5cT/8Te3tGre7jZ3m9bs2inkfXi4j5j+WmictLCQy/bDey+n60YdUqxt83OzB9ecEGTMXr6rNB8T/7G2ZVju6/UY9Fn/ebgarp8+w4Nbm3F47Taz93AAAAAHiOBkFpaTWObpZFlvVjuo6Izl08pBSLj7RN++Pvxpsm9T51iw91G1k94Vp7ynFLKUVKD3HXiVhP+5Flx4HlRv7rVAgaMfwyON9jRKzufz69z/cwTgAAAADwhpoHpVurGHez6E+L+GswO974Z7g43NSnCAQ/ks83ZcN7weZOPdzFs25pPY1+lkW2U92Ts0GfIP91cibqW/i/jRMAAAAAvKFnBKWF1fh7FC9VD+LLJintTSJP5avky9FOGFjOQv2ITgSb+9U9/Vr8W+p+uv5O8B9hnAAAAACgxrOD0lOG38rZg+tp9G/rXiS/os835ezGPGreZt/artP5jj1WC7/Wrrna+/e/ymfyM+6bBpV/2DgBAAAAwCXPD0q3m/is4/fh4pRXfBV843hJgF5MvpZrei5/1K4HujX/UcyY7dzFt3e6DuvurN6vk1NzSofxrVzzYP3z/uQzacM4AQAAAMAl9UFp+Rp9SinygxCuN8kjzcqYdGdn8mq39Fm1yVNvEvlV1igdxCzlsWl9uNj0sIxRo9mu87gdlTHk7HjTqu06rPnkiq+9Vz127h4OntMwFmlWhNnL0Zl1UP/scarWy63u8VrHAAAAAHi/6oPS1Ti62SiWUYRwuxv0PNx1ImIZo8ONiOa3ke2EZtffzKcTdw9FH7NBlOto1u8uf2R+G1k5Btv7SdX11tN+ZN3xdWfP7vS4/5yKkHQ5yiK7GHi2YJwAAAAA4IwsItK1m3g91SzK5SiL97hMKgAAAADw/rzqZk4AAAAAAB+RoBQAAAAAaD1BKQAAAADQen/YGqUAAAAAAE9nRikAAAAA0HqCUgAAAACg9QSlAAAAAEDrCUoBAAAAgNYTlAIAAAAArScoBQAAAABa76/0339euwcAAAAAgKsyoxQAAAAAaD1BKQAAAADQeoJSAAAAAKD1/gaSxEAO96KMIgAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "ebe04922-4d94-420e-b23d-6d2ae6e4defc",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "7f21ec51-3c0b-44be-925a-2ed1e29f7872.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "4200be5e-f435-42e3-9fa1-b80271188575",
   "metadata": {},
   "source": [
    "![image.png](attachment:7f21ec51-3c0b-44be-925a-2ed1e29f7872.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "af9e0378-8198-4fab-9927-e3e6425f1560",
   "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": 20,
   "id": "afc145a0-446c-44e9-af96-b6fbb19579b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =m x + x^{5} + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(x**5+m*x+2,'D')\n",
    "d=MyEq(x-1,'d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d05f0f4a-cf72-4d45-b28c-799802bf4619",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =m + x^{4} + x^{3} + x^{2} + x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=D.quotient(d,'Q') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fc1fdce7-be69-45a0-9c63-81340ae9bd8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle m + 5$"
      ],
      "text/plain": [
       "m + 5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q.coef_sum(x) # P.coef_sum(x) # return summ of coeficient value when x is main variable"
   ]
  },
  {
   "attachments": {
    "7cd9c493-2076-469a-a7be-ff50434422c7.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "84afc39b-ccdb-461c-b71b-17621014568c",
   "metadata": {},
   "source": [
    "![image.png](attachment:7cd9c493-2076-469a-a7be-ff50434422c7.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "14d3ff25-d478-445d-830b-1884565cca8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# then m=5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "12ad65a5-aa26-44db-87bb-015c0f92f86b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =x^{5} + 5 x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D.set(m=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b3856529-ba30-4cce-8625-3f33eb094ca5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =8$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=D.rem(d,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "652d24f7-9134-40bd-a141-cfca67e0b4bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =8$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.set(m=5)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "d3d48bae-1447-4a4d-b4d5-19d6b18f39b5",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "c02db77f-0849-45c2-b28f-124d594ed19d.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a69a1e33-f8e6-4d0d-8e1f-fdc91ab38e40",
   "metadata": {},
   "source": [
    "![image.png](attachment:c02db77f-0849-45c2-b28f-124d594ed19d.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0eff636d-cc3c-4b1c-a545-39f5854c83f1",
   "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": 28,
   "id": "42f69688-acce-4632-84e6-835d5f5c891f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =k x^{2} + m x^{3} + 3 x^{5} - x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =x^{2} + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =5 x - 10$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(3*x**5+m*x**3+k*x**2-x+2,'D')\n",
    "d=MyEq(x*x+3,'d')\n",
    "R=MyEq(5*x-10,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "21191203-aa02-410d-ab43-51630b1c24f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R2 =- 3 k - 3 m x + 26 x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R2=D.rem(d,'R2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d2cef6e7-2761-421a-88e3-c2b5761549e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 5 x - 10 = - 3 k - 3 m x + 26 x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MQ(R,R2)"
   ]
  },
  {
   "attachments": {
    "0320622a-6e24-4742-99ab-55081bad8e26.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABKYAAAF7CAYAAADohoOwAAAgAElEQVR4nO3dz2tcabon+K8utS5ok1W10qxCoqoyqY16YSKGm15KNqYz76KoCxoMbQjvJMHFm8EwWiS9MQ0h7yzIBkPChVx0JhiHDL1RNkh4UZ7FJTPv4BOr9mqqEi3mHzizCIUVkkJSRCgijiR/Psmblk6cH+95z4+IePW8z5lLUgYAAAAAZuwfqq4AAAAAAB8nHVMAAAAAVELHFAAAAACV0DEFAAAAQCV0TAEAAABQCR1TAAAAAFRCxxQAAAAAlZhpx1Q9SbmSlM2jkt9PZzvtelL+5fi2ir8k7b8k+d3ktzltzSRl2in7/mumrLpaH71W6ilTHDsuRco0U0xk/ZM47q0kZYrUJ1SnWagnKb9Lir8m+VPVtTk8DmU7ZVl+KM326Ndfq1lPWRTH1lMUZZrtyR+bXhu2v5v4qq+d1p+S8q9JS1sAAMCVc+MipupJ9v6SrHyW5NfHX6v9Oln4dZL/UEHFLmk7yVzuZu7wv+RR1VX66LWT3MteGik+HJe5zGUhc9nOwkS2cZ2OeytJkeLwp8t58S9J5i+9monZTjI3dzdzc3OZm5tLdkY/Du1mcu/5XhpPiw/rmZuby8LCXLbvTuZ86fdZkswnC/O5Ep17V8H6fFL/l6prAQAA9PvVLDe2n2Rupxt98Lw5nW08+X2SXyedJA/+Z7L//0xnO7CSZh4l2c/dqqtyro0kGxPqKJuF1p+S2j93f366l+TfKq3OxKx80cyjnWR/+2qfLzfRxr8l63tJGsmLf04W/kduzHkFAADX3Y2LmOopolOK6fsxnaqrcOOsP+z+20my/XWlVZm4H99N93wptg6HrG0lf+yLkmrW+l77SIezPVrv/ltL0nxYaVUAAIA+U+2Yav6um9epP89T+y/JHy/IK9X8XVKsnM4P1ayfMX+O8kmt/GN32kqOL182u0NpJplfqp6kSPNYjqF2itTTSplWuoO9BmufWO4oL9EZOzmiXl6h/txErZQf1t/NVHT8v5M5iLr5k47nNypSpj6BoVpn1/v0Ntsp0kwrZdo5q03Hac9x9q+dfJg3eZ691E6141XI/XWZ3FSjntdF6ilTZj1laqkd/nT8v/5z76J6p9H9+aJoqXqSot1MWR7lbGoXRerNVsqilTQHnyvdPE/tU3me6s3Jn9ftZj5sIyvPs7deO7bdcXNVDVJPUvvfuj+vN5L1/9b9uZbk+f+Z1A7bdfGMIZLNej1Fu3UsB9ZF7VK2m0dtX5ZJmqeOS7sok/rpENlmPceOQ1GWqTfbadXzYdlWcbptxj3u20my1/35cSMjD29s/VO3Y6/4a5J/Gm1ZAADgbFPrmCrqyfP/1M3r1G/l18n6Pw6x3IkvT7VfJ88/S4opJUwfVTPJXtp5leeZy4MPOYC+ykJe5Ock62cuV6Sd7/P4MBvRUV6iL/Ig7bw4nOtyNpLMZSE7mctOkrk0spG5dAdUJnPZ/pCz6FGSucxlv2+411H+pHeZS+NDPZ+mkRfJ0B0NoyjSzGL20sj3H7bXyFze5UGeZzHd7sbjxm3PcffvbnIs31MjnWP5peYOW7Zq4+amGue8Xsh+5jKXrcylk87hT8f/6z/3zvNF3xf+7R8uqGfZzquF55lrPPiQr+mrBwt58cXPSW3w9XeU5+ld5uYaH5Z7+qCRF1/ksCNkcuf13e0cy0vV2Oocyy81NzeX7buTOV/2kzS+THb+Ncn70693kjz61+Tufz79WruZPN7by6vcS+PB0w91e/W0kb3n91JvDU7OPnd3O3Nzc9l51N2HVj15URR5+u6LzM11j8tK8SjNJ88HbK9M4+lR+zxozGXv8bssPinSSTLX2MrGwvG2Gfe49+wcnlO1D/8b3vrnR8s2Px9tWQAA4HzlpEv79ynLZrc0V46m15OyWDl6rWymzO+PXi/qg5dLUrZ+n7L8S/e1opkyvzt/2+3m5Pfr2HaSsp2yTJqnXqsnZZlWmbSHmn5yva2UZVI/d/tlmmUz5YX17G6zPXCbraQsUpRJa6jp42x/2FKkfu5+Nwfsx7jtOan9K9Ms6ymmep5Nqt2HXW6c83qUdr2wnlspy7+mbP/1gno2U7bLc+pZtHqhSEf1q6csyqJM/Zzj3m6WzfbF7TTsfCeXqbdmc740023HXin+mjJ/Gm9dRatetorz97UbOFWW7W7Y04V1K8r2wOPQO3ZFWQ58fZzjfla7NLdGa4fWP/W15T9N/xgqiqIoiqIoykdUJrvCZs7uXOqV/g6oXsdU/3L1+vjrnlXHVK+jpJ52eVEn0oe6pfel/+z5h+lsSUbroDjq9Bl++kXrbiVlO0U56AviqOW8zrNptOek9u8mdkyNc173t9llOqbqSVl+1/3y3/puiHqW7bLeGr6eRat+YWdSq56yXV58Xl/1jqleB1/x1+Hb9KzSbmaojqmzOowGHYfz1tdu5syOqXGO+7jnmKIoiqIoiqIosykTH8r3x8McTp0k2//34HmeDhjR88e+3E97n+VUfqiyefxJfl9U/Cj57SSN3M2LvEuZFznKUVSkmXYGDQdaSD3vkpw3pKn7ys+pT/Apaq+yn3vpJH25k+pJanmSjeycmr+Wz/I8yck8Qf3/rafMQmpJ/njp+v05SScLyWHrDGvc9pz1/l0n45zXVdhO0pi7mxeL71KWL/pyIhVptgbXs7b4WZ6v5FSOp/6yvnd43OvX97i3/ykf8nQt/Jdk6//q/rw+n3NzI7VbzWP5pXp5n1YeDx7GN67a4mf5+ZxVvvsxyRkPFRjnuAMAAFfbjX0q3yzsJ1nIxoncRgv5Il9NLFfUJGwkqeVpmn35gZ4k2clKkq8GLtPLO3XefwuZO1z79XPT9+8yrst5vZ9k4e5G5uYWPuQaWlhYyBc/f5V28WJgwu1HOzmV4+lkWZibS/av73HvPfjv0V6S/55s/FvS+dezunq6XTll0UruPU/j6atjubcezM1l59WDGdV8OOMcdwAA4OqaeMfUz/9v999akvyHwfN8MSB5eW+5JJn7n8nc9vnl7vakaz45d7OfhTxIK8cT/hbZz2KS8/6q333lj9nPZKMUtrKdL9JJr1NhJa18lU4GRRvtZDtfXFDPSfo5SS1Fctg6wxq3PWe9fzfFWef1pOwnyf/q/nzWk+OGcXd7PwuvHqT14ng9d77fzhcryU0/7hv/lsz9x2S7Lw/4wn9NFv5jkv9+ev4nzWSntp67C4+yv72R/nvCfpL8fHHS+lF03v2YP54TELr4WTJyZvKcfdz7fZYkh+fWz/9r5E0AAABTMPGOqe3kwxOhin9M6ie+A7Z/n6wMeCrfdpLOj92fy3/sPko8fcP76r9LWr9PipXusL7WXyZd89GUaaU+YufRV0lWspV6Xpw5z5MkW1nPWZFM49pIspJXqedxWkk6uZf9vBq7npPU7WP8Pq2s5LxOgyLNw6fldY3bnrPev+tknPN6knpPTVtJzh12VhatM58Ud5avtpOVzlbqret33MutpPxrUvw1yZ8mu+6FP9YPo6xO9/bXk6w8bp2afhlPN/Zzr7aT1E+v96LtjXPc+/U/9fHHETumWn/qOwbnnJsAAMBopjKUr7GT5P/r/s37ZL6ok51S5T8mRTPJ75KF/aRz2Kn1/LOk/E9Hy+39p2T9H5Pa4V+7F399tI7W706vfyWnc1RNujPrRWpppsjJzpR26kleZCNbx6bvJ3mUjeylOLVcPUk7zSRFNvIo5+VNGtdONvIktaynlaep5axhav31bKVI/cTQrV5d2ykyqWFdjWxnPVtpZS8n26WV+mGWo+eHbXO6nqO0ZxX7d52Mel73dIeMvkor6x+W7R2/Iu0UKXNRe37fF9HT/PyCeq7X0mwXp3q/2816sv4iGw8GXH8PNrJ3r0irXaR+YshXvd7Ns9Quiys1HKyZfMgZ9XQvyb9Ndv2vvt3Peq2TZl+HTz3dttgri3Ryb6Lb205SPLqbYm899eZRJ1SznuwV7cPtnTXwcPTj3m/l8JzqJNn/H6PVe/1h999aktb/MdqyAADA+aaWWb31+5TFX46epFc2U7b/krL1u+PTimbK/O5ouebvUhYrx+cpm911tVZS1n9/Yju/Oz3voNL6y+T2rUyrbKYoW2mWRdof0gUXKYd6Wl07zcPUwkfLNVOUg5401XtS2tkpm7ul+4S6s7fbe/pdkbIc5slp9QH1LA/3r5nWwLpe+pxJfeD26hfUd5T2vMz+lWleeBxGfbrgWWXc436Z8+Wy53U9KYu0jm2neyyGf4pa/xPl8qcz5ilaZbNVlK1WsyyKdtlTlGXZLooy9fOvg3arWZZFUfZrF0XZbJ0+7r0nwV1k0FPpynbzwuXSPP98af3p4va49HVXT1kWx/ex147tZj5M63+qYKuewxY/23lP32ue2GZRlmW92S5b9ZRFWQx8Kt9ljnsz3XYs/5qyuTVGG/Ufh3+aznFQFEVRFEVRlI+xzB3+AHAltP6UrP+37s+P9o7nSvoYFf+S1P7542mLVj25t1dkofFqoknoy60kjW601MJ/zsQjzwAAgPF4Kh9wpfSeIpckjxuZeE6l66SepPa/d3/e/qHSqszM4mdJkVqy/+3E1tn6Uz4Mh3zwr9EpBQAAV4iOKeDKefBf8+EhCh+z3lPktt5n4BP1bppWs56V50XuPtrJNPLsbb1P9v/rxFcLAABcgqF8AFdU60/Jvf+WLPyX3LiOqXYzWXl+/O1np5PcfbA10SF8AADA1aZjCgAAAIBKGMrHpbWSlClSjvhfO2WSZtXVnxrtAgAAAOcTMQUAAABAJURMAQAAAFCJqXRM7e7uTmO1AAAAANwghvIBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMVahcS3Kr+3PjTbL/+mouBwAAADANIqaqdHD04/7fr/ByAAAAAFMwlY6pO3fuTGO1N07nl8N/k+RvV3c5AAAAgGkQMVWhYsyopVkvBwAAADANIqbGVK4m5Wa3tDe70+pJiv7pa0nmz17Hu8OopSJJ3g+/7VkvBwAAADANIqbGNPdNMreZ7Lzs/t6aT16sJU9/6U6f20xWDpLm5xev693BxfNcheUAAAAAJulX01jpxxAx1W8lSb5MFr7LsUikuW/OX+7b98l6kp9H7Cia9XIAAAAA0zCXpJz0Snd3dz+azqn2UpL7yd3NqmsCAAAAcL3IMQUAAABAJeSYAgAAAKASIqYAAAAAqISIKQAAAAAqIWIKAAAAgEp4Kt8YWvPJ+sPz59k6SDaezaY+AAAAANfRVDqmAAAAAOAickwBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlRExdE80k5ebx0lytulYft9Z89zjUlye/7mL56DiPs/7rer60lpJy7Xi9i7XrUXdunklcR9O8T1wFN33/xjXNduk/L1trk1//pFyXenIzjft5YpzlZn0fdN+ldw64vx6nXa63X01jpXfu3JnGaj9q20m2N49+L31Rv9EWXid53f1wNI7reL60l5KF+0njZbL/turaXF+t+eTew2Th6yTvq67N9XYdryOup1Gu29552V5K0phB5fpcl3rycRv384TPIZPhc8j0bbxPNja7f8jOYtW1uTq0y/UmYgrGtPE+mdtM9l9XXZObYeUPydOOD4PcLDf9PnHT929c2gWqM+7niXGXm/X17v4C3ERT6ZgSMQWM48dfqq4BAHDdjft5wucQgGpMZSjf7u7uR9E5VU/yYjWp1Y6m7RwkX+0le41kbi/JGX91aS8nK4tJbnV/76T7V5rtbyZTt9Z8sv7w+LStg2TjWffncjVJ7fjrjTfH//rSWkrWG0d1TJLOQfJgb3JRLZOoZ3M+efx5Urt1VNeL6tm/3p0kdzdPH8+dg+TudzkWhtxM8nzz2KryaMjjNk49e846107WbxJmcdx72kvJyv2j3/dqSW4fn2dQ+457/D5sd4jrr55kb607z9ZBsvguWbl9VKcfvzm+vWHPg2kplpNaX9uVD0/P039tJaevr5PXVnL6GA3az2nfz/r3rfEm+eyn5PGXh9fSoWGuh2nXs2ec+0RvHzvpDn9of3p0viXJVifZuKCeszqvL3MfHPf+cpn322Fd9nq4zHH/UIchrtuT6vPJi8+P2qaT5OmbZHuC0RRV1fMy75vjGPc8G7aek3pfmeX79Hnb3DlIvt9Lnt9P5l5mYNuMc98dZ//G/Twx7nKXuQ8mo7fnLO+7474fTeI+MUvN+eT5lzl2bj54mfz5b0ffTc773DTq589x72cn753J4TH44fz9q+I+Mer1fpn2nFW7TOLzGcMrldFLMynLzZSttZSZP5pen09ZrHZfy9Lg5Yq1lM3l06+1l1K2T6zvrFKupmyuXjxfeylle3P09bSXUhabKesn9qF5uH+ttcm252Xr2Vrttn1vemupewzqA9p50HZb86ePyzBtPMpxGKee5Vp3mXLz+HbqSVksd9c56Dy7bD1nddxP1vGi43XZ4zfO9Vcsd9u/vdl9rTnf/b1cO7r+W/NnX/OzLq35w/NiiPtIb/+GOa6Tas9LnSNrKdur3f07uc3etXQV7rvjLtc7dv3nVtK9Z3yYNmC5qs/rad9fxn2/Hadc5nq4zPky6nX7oT3XTrdp73wZ51y9SvW87Pv7qGXc82ycel7m+qvifbpY7d5H+vev3tvHtcH1HPe+O4n9G+fzxGWW6y077DU3TnuOu71x23Pc96P+ZSf5/j/pMqhdevvW+5xxXv1H/fw57v1sYD2Tsn34HeCsYzjr+8RlP2eN256zapfLXA/KSGXyK93d3a16p6ZezutIqad7kp58Uzlr+sn1TupD8YdtnvEGd9YbxzBvKON+QZtkPS8qw3zBaB++IYz7BXoS7XBePXsfUE7eQPvrP0zbDFPPKo77yXWP0zE17PEb9/r70AE4f3zayet/mm0zShn1emnNn98p/KHtTlyfk7yfDX2OrJ3fGTto36u47467XO+L6KB5e1+aJ/W+Msnzetr3l3Heb8ct414Plz1fxu3wOa8zdhqd5VelnsN2II5SpnGenVXPca+/Kt6nL2rrQcdw3PvSpPbvKndMjdOe427vMu05zvvRKNutsjRzdv165+4wHVOX+f4wzDlxXj37j9G0rqNhyyQ+Z43SnlW0y2WuB2X4IsfUmL5/m6xk8KNa95PMPcupkOYnS8nOrdPT+331NllPkqXJ1HM/SedN0hrwRJx7nyavDnIqNPLep92wy/OGxGz9kHxRO/v1WdTzIsXfh5tvJ8ndZ6Ovf1IuqufWwdkht3ffJrVOUv/08vWo4rhPwrDH7zLX36Dz7/vOqDW9mn5+372X9e9zuXb8Mbt/nu+GMOdvR9OquJ8lh+foGdvceH/6eqiqnuPqJNkeEIa+nSQHp6dfl/P6MveXcd5vxzXu9VCVrYMM3PezzpeqTLqew76/j2Ia59l59Rzn+pv1+3Q93SEsG3tnz7OdbiLu/rYZ9750XT+HDGvc9hzXZdtz1Pej6+Lx8tnfK/aT7JxzfPpN6vvDWfeJx8vnH7+N9zl8Mzpu1tfRpD5nDdueVbXLTb0erhI5psa0neTHzcMxsH1jvjsHydN3g3MmLPzm8EZ4jv0kOUjqvzn8eQJe/ZTcu51szOfDxfjhzfHl6flrnyTPa6fHsp/USZK+dc66nj0nxzP36lY7SN5NpmoTMW49v71gJzq/JH9evPzTWao67rNS1fV31W0ned452ufWfJJb3Q8QG0tJ3iaLv02K5Ngxr6o9L0pMe/J6uOnH/brs32XuL+O8345r3OuB6Zjl+/tlzrNZ1XPW79PjdsKOe1+66Z9DZt2pfdPbc1y1T5Kfzzk/3/0tWZjCdke9T9QWkx+H+A7Qv75k9sd91p9Drku7MLqpdEzd9E6pnv0kCwOSnbWXki/WppOYehwb75P1TtL8/Cj53JOlbs/0Wb3bVSRyHrWevSSiO0kaAxKMPllOsjjtWl/sutQzqT6BN9Xo/JJ89kn3nnbv0+558DxJ8w/J9tvuI7Qf3ZAIMapzmfvLLN9vXQ/Vq+p9c9TzrIp63vT36Zu+f7OmPavnPnF1aJerbSpD+XZ3d6ex2mvj7ttk4V3S+vL49OLvyeKtwcv01JPkVrI/4TD1k6GJK43kqzeD59359+rCpEepZy909O6z00Pd9pNkCqH+47hsPf98wZtV7ZOLo6qGUeVxn4Uqr7+rrvh799j3IhS3//3E+XDrdKRSVe352Sfnv37yerjpx/267N+07i9nvd9exjjXA5N11d7fzzrPZl3PWb9P//z+8IFZvx1tuXHvSzf9c8i47Tmum96e/VrzSbnZLe2LImJ+Sf54zvm5OOHjM+59ovNuuM88J836uM/6c8h1aRdGJ8fUmMq1wXkIzvPV22Tl4PzlniwlW8nE8mX0bLw/2nZrPuncSvZ/Gr+e0zJKPRd+k7w7I3S0nm6n1lVw2Xqu30rqZ4zJbs0nndrZbTSKKo/7LFR5/V1137/thq0/WT6KUPzqMN9KazkDP0xU1Z6PazkzR8Gg6+GmH/frsn+Xub+M8357GeNcD0xWFe/v45xns67nrN+nt5OkMzj/Z79i9XgetnHvSzf9c8i47Tmum96e/fo7k876g3bP09fJvVvpDtc6YRrX7bj3iaevDz/zDKhncjjUfEBHy6yP+6w/h1yXdmF0IqYu4cXtpLmaUxdGeynJ7WTju+PT95M8epbsLR4u16ee7tjjNE4vNyk7e8mT28n65+cnf9tP8ui7bj1bq0n9xP7V57t1bW/mzJvCLOr56qdup02z7wbTa8e9zYF57ypx2XpudZK9+8fPmd7y9x4mCy8zkSEsVR/3aav6+puVjffdfAWtL/PhONWTtJaSYi0pBhy/7XSXWbl9lHx3P0k6yfrtwcNpq2rPV2+SonH8ekq6+3fvy9PXw00/7tdl/y57fxn1/fYyxrkeLmuc67YKs6pnVe/vo55ns65nFe/TjW+6OdZaa8fX2Tvu5VpS3DreNuPel27655BkvPYcV1XtWcX9bOUP3X93cnHO1e0kxcukeHj8D7/N+e6Qu0lft+PeJ86qZ/93gM6AhWd93Gf9OeS6tAujm0v38XyMqFxLHr1L/pjk3mJSOwxh7CQpDi7Od3EyAV4n3U6YQeNem7k4UVty+DSDc+ar5+gGuPD1+fXrzf9kQKK+nYPk+wknnB23nq35ZP3L0/W7+13S/m2ycr87rfHm6I2qNZ+sPzy/DlsHycaz49MucxxGrWex3B1C0puW14cJWfv+ArDVSTZ+yKn2uez5MsvjXq5m4F81+s29zLEvgeMev37DXH+9nAD9bdCrS+/49J+jvX256DqchXpOny8XJfDt7VN/e/faehLtOQnlWtJ4l4HXw84Vue+Ou1x54lzrb/P20tE94uRr/WZxXldxf7ns++04Rr0eJvE+Pex1O2hb/e9x/e8fF21zHLOq5zjv75cx7nk2Sj3zejLvK1V8PmstJeuN09v7au/08KR+47w/jHWfGOPzxLjLTeJ6H6U9Z33fncT70TifQ8bV+96QjHY/aM4nz/uu3U6SBy+TP//t8A+/J76DXObz52XuZ8355PHng78DFJ8e/77Qv2wV94lRrvfLfp6fVbtM4npgOFPpmPoYnsoHwGz1OqYm8SUUALj+eh0ck+qEb80P7pgCpkuOKQAAAK6de592/70ot9SwFn+bFIlOKZgxOaYAAAC4dmqfDJdbahitw6FZd19efl3AaOSYAuBKO5mLpmdQvhAAgIuczA+UDJevEpgOOaYAAAAAqISIKQAAAAAqIccUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwxUc0k5ebx0lytulYAAADAVSRiiqkqV5NHSba/qbomAAAAwFUjYgoAAACASkylY+rOnTvTWC0AAAAAN8ivprHS3d3dj6JzqrWUrDeS3Dqa1jlIHuwl+29Pz18sJ7XbR78/6hwNcStXk9SOXmu8SfZfH1++OZ88/jyp3Tra5qDt1ZPsrXXn2TpIFt8lK7ePtvnjN8mL1aRWO12P/jo23iSf/ZQ8/vJwm4d2DpK73yV5f1ELjWbU9jypV/dOkgcD2g8AAAC4ekpl9NJeSllspqwvHZ/enE9ZrKZsrQ1erjXfXS7zp19rzqcs1ga/1tteazVlve/11lLKcjNlffn0MsVy97X24faa893fy7XD+s1361NupsyJ/SjXUrZXu9tsnlh3b5snlxlUytWUzdXptefJOpeb3TLM/IqiKIqiKIqiKIqiVF4mv9Ld3d2qd2qq5bzOpV45r0NmUAdU65xOqYtKsTy4I6ZYPl3PYvmwo+qCupZrh8ue0fk0TBtc1A6Tas/+fSs3Dzu4BnTUKYqiKIqiKIqiKIpytYocU2O492nytJNzh7Jt/ZB8URv82vb75Ol3SfFlUl9K2kvJ4pfJwpjD44q/n/3aq4PT6/y+M9x6n3aSnDGEbuN9Uusk9U+HW9d5LtuePQuvk7nNZGHTMD4AAAC4DuSYGkPtk+R5LXm+ef58nSSZz8AOl+33SZ51c0Ht3EruXrCuJGkvJyuLOZ6DKUntIHk3bOVH8OMv565cMYMAABsnSURBVL/e+SX58+LlO4Em0Z4AAADA9TOVjqmb3CnV058wfFyPl5OdJAsHSX357A6eXjLznSSNAYnOnywnWbxcXao2ifYEAAAArpepDOXb3d2dxmqvjJ1/v3hY2UWK5eTVYnL3WfLgWfJisds5NciTpcOoqmenn063nyTnDOW7jM8+Of/12ifJtxMI1ZpEewIAAADXjxxTY/jqbbJycHZH0kV6nVIbz7q/7+ewc+qTpLl6ev6F3yTvDgavq55kpTFePS7yuJZkafBrrfmkU0v2f7r8di7bnj3FclJuJsXm5dcFAAAATJ+IqTHsJ3n0XbK3mLRWk/r88dfr8918UO3NdHMi9SlWk6efHHVK9a9z4ZvkcU53Tr36KVm/lTT7Olvq6W5jb/Mw99IUvHqTFI3j202S1lJy78tk4WUmku/pMu3Zr3Y4nLGWbu4rAAAA4GqbS/fxfIyhl9/pZELynYPk+3fJdl/OqGZOJ/fuz6tUrqbbo9JbR44nRG/NJ+tfnt7O3e+S9m+TlfvdaY03SV53c1L1zzv3MsnbblRR7Xa3M2vh6yTvj7bdv81yLWm8667rxWpSq53e7slOqUH7OMjJfesZpT0H6d+3B288mQ8AAACuuql0TN30p/J9DHodUzp3AAAAgGmRYwoAAACASsgxBQAAAEAl5JjimF6eppN6OaoAAAAAJkWOKQAAAAAqIWIKAAAAgErIMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRiKh1Td+7cmcZqr7RyLakvW85yAAAAwLBETAEAAABQCRFTAAAAAFTiV9NY6e7u7o3vnCpXk9SSzkFSHHSnPVlMFj5JareS3ErmXiZ5aznLAQAAAIN4Kt8l1JN8Np/88bfJeiPZSfL9XvLj35L995azHAAAAHCeqXRMfQwRU/3aS0nuJysHSeNdsv/acpYDAAAAhlEq45fWfMpiM2Xmj/9sOcspiqIoiqIoiqIoinJhmfxKd3d3q96pmZTmfMpyM2WWjqYVyylba5aznKIoiqIoiqIoiqIoFxU5pgAAAACoxD9MY6W7u7vTWC0AAAAAN4iIKQAAAAAqIWIKAAAAgEqImAIAAACgEiKmAAAAAKiEiCkAAAAAKiFiCgAAAIBKiJgCAAAAoBIipgAAAACohIgpAAAAACohYgoAAACASoiYAgAAAKASIqYAAAAAqISIKQAAAAAqIWIKAAAAgEqImAIAAACgEiKmAAAAAKiEiCkAAAAAKvGraax0d3c3d+7cmcaqb5xyLWm8S/Zf38ztXaRYTmq3uz833ly+Xldt/66j5nzyxafJymKSW91pnYPkwV6y/3a4dXzs5/VJ7eVk5fbR7zsHyd3vkrwfbvmruH/NJM83z5+nk2Th6wy9nwAAwMdnKh1TOqUY1sLrJK+7X7ypXnspWbifPHiZ3P0pHzoUWkvJ3v3k0R+S7W8qreK1Uk+yt5bsJGl8ney/7057sZoUD693p82PSXKQzO0lGdBh2ZpP7j2ccaUAAIBrR44ppqpcTZqrVddiem7a/t19myxsHkZG9XWYbLxNtr5OHteSzFdVu6tj2OP+YjnZuZXcfdbtlEqS/SQL3yR5k7S+nGYtxzfM/u0nmXuWgZ1SSXLv0+TVQYbqeLtp1xEAADA8EVMzVq4mqXWHRhUH3WlPFpOFT5LarSS3krmXOfPL3lXf3qzd9P27SjbeJ+sHSX6bU50NzuvBaovJgzeDX3v1U3LvdrIxn8rbcxpqnyTfvqu6FgAAwFUnx9QlNOeTx58ffVFMLs7FM/dNdyjPZ/PJH3+brDS605/+e/Lj346iKvr152FKkkedo+FUvS+wPSfzNM16e5fVG+ZU69vGefl4rtv+tZaS9UY+nC9Jd/++30ue37/anQ2t+aRzK8nfTr/mvB5s7tmYy12T/TtLM0mnluz/MLl1nty/k9dKeylZuX/0+7T3EQAAmJxSGb20l1IWmylbqynr80fTW0spy82U9eXh1tHeTFmuXTx/a767vcyffq05n7JYG/xaldtLUparKZurQ8y31m3LcvP4/PWkLJYP67J0ffcvSVmspmyvHT9f6r1zZq277719bKb7+7ClvTnd8713Xg+zr87r4Uq5mrK1dvXacxL716vzKG0xyrl11uu96+aie4WiKIqiKIqiKFeqTH6lu7u7Ve9UpaVYvvgLZ/8XyPO+TPaXQV8sW0N+2Zz19npllI6pcjNl/YwvlL2OwLO2e9X376Jz4ip+oW4vHe/8Gqaz1Xk9XCmWh+u4ua77N+ryw85fz/kddMPcexVFURRFURRFuVpl7vAHJqi9lLxrJBtnDONpzifPHx4filIsJ68Wz16mf9nHX3aHCz5JksbFj52f1fZODrU5z8lhNuVaspXz61OuJo1fTg/Puer7V0+yt3m1h+mdp57kyXKycvv84VHO6+GGjxWrSVFL7m5eXMfruH/NJM/POd8vu732UpL7p9vvou0CAABX18R7uz6WiKn28lGkT68Uh0NupvlX+2a625j28K1JbG+UiKmLInKmFQ0x7f0bNtLlqpfm/HSjum7ieX2y9IZz3tT9S0Yfxjfq9s6KmhItpSiKoiiKoijXs/xDpuCmJz6vJynXkiwmjb1kbvOoPNhMdqb8JKrHy8lOkoWDpL483W1Vsb1Zu4r710xSbg5f2hdE30zC9vuk8yZpNaaz/pt8XvfuGa9uJXfHTIg+qqrO65U/JN93prf+/SQ7e8mTvqirerpRWBt709suAAAwHZ7KN4YnS8nOrcFDcfaT5O9JFqez7f6hPPUkL9aSB5ne06dmub0/L56/3mk8fn4W+/fz+2Q9SX6bc4em9dtOsj2Dzqar4iaf1/Uke0MMVZ2kWbdnTzNJasn2y+lu56u3yV6j2+G2/zp5sZxsHcQQPgAAuIZETI1h4TfJu4PBr9Vz9Gj3STuZX2Y/yYNnyYtPkubq9d/e+q2kvjT4tdb84ePnf5rc9ma1f9tJ0rk40qhYTVprk9vupDXTjUqZZudgcrPO6+Z8t1Pq0UE1nVLJ9Nuz3xdL3SitaXcQ9UdNiZYCAIDrbSodU7u7u9NY7ZXx6qduJ0qzb3hMPUl7uZvkehqjWIrV5Oknp7/c7idZ+CZ5nMl+6Zz19pJkq5Ps3T++3l673nuYLLzM0BFHF5n1/jW+6UZNtdaSzB9NrydpLXWHeRW3ko3vJrfNUfWGm7XXTncQtpa6iaUfdSYbdXOTz+te8vLGu2T7mwGvJyk2c+x8uKwqrtt+0x7G1++rt8nKQTcaTLQUAABcX57KN6bWfLL+ZZJbR9N2DrpPvmr/Nlm53502zFOsztN70lS/R52jL7rlapJaXx1y8dO+rtL2+p/Q1XiT5HXyYjWp9W1jq5Ns/JCJdErNev9Oai0l642cOm++2kv2r8gX69ZScq+R1Prq2DnoPuFtUnW86ed1cniPeHj+PJ0kC1/n0ud21ed1Us3TJ9tL3XvtZe+zAABAdabSMXXTc0wBUL32UpL7k+9kAwAAZkfEFADXTi+pfOOdaCkAALjO5JgC4NrpPR1VpxQAAFxvIqYAuPLOy9m1NcOnHgIAAJMlxxQAAAAAlRAxBQAAAEAl5JgCAAAAoBIipgAAAACohIipMdz0/QMAAACYBRFTAAAAAFRCxNQYbvr+AQAAAMyCiCkAAAAAKiFiagw3ff8AAAAAZkHEFAAAAACVEDE1hpu+fwAAAACzIGIKAAAAgEqImBrDTd8/AAAAgFkQMQUAAABAJURMjeGm7x8AAADALIiYAgAAAKASIqbGcNP3DwAAAGAWREwBAAAAUAkRU2O46fsHAAAAMAsipgAAAACohIipMdz0/QMAAACYBRFTAAAAAFRCxNQYbvr+AQAAAMyCiCkAAAAAKiFiagw3ff8AAAAAZkHEFAAAAACVEDE1hpu+fwAAAACzIGIKAAAAgEqImBrDTd8/AAAAgFkQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxdY205pN7D5OFr5O8r7o2H5dyNUmt+/PWQbLx7PQ89SR7m0e/N94k+68vsc21JLcunm8nyd3NC2cDAACAK+dX01jp7u5u7ty5M41VQyXmvkmK5SSLyfqtZGMpydvj8zxZ6pv/5enXR97ms6SZ5PHm2Z2R7aUk9y+3HQAAAKjKVIby6ZTipnqVJJ2k+YfTr600kq03s64RAAAAXF8ipsbUP7SrN5SqnuTFalLrTT9I7n6XU5EuraVkvZFjw7Q6B8mDvWR/QJRNsZzUbvdt++HpeU4OL2smeb45+LX2UrLSF2UzKLpnnP3r1bOTboRP+9Nkpa/eW51k45vTdT9rfztJHlxyONw0bP2QPH6YbM/nw7635pPOreTnn5LcPj7/yeN3sr1PHo9RhgDefZszI7Pq88mLz4+OV3J4DH5Iik+P6nTZIYcAAABwGaUyfmkvpWxvpmzNpyzWUjaXj14rV1M2V0/PX2ymrC8dn96cT1mspmytnb2t1nx32cyPVr/z1lmupczS+cuPsn+9OpZrh9s9rGt9vm/aBXUu11KWm90yzPyzKsXyUX1O7nvv92a69T7Zpr12PGvdZy3XzOljftEx+3CerR0/z+pJ2V7uru+ic01RFEVRFEVRFEVRZlE8lW8CVpIsfpksfJds90WezH2TbPdFCLXmk4X73Wiik5FR2++ThW+S9YOkuTqTag9t2P3rqSV51IvSOowo2n+fPHrWzc+UpdPL9Ou8O/w3ybfvLl39qdj6IXlcSzLfjU5LLdn+97Pn/+ptsnKQ1JcHv/54uRvZdtm8VEm3Pgv3u8er/zzbT3L3dfLq6+NRVAAAAFCVqQzlu+nD+E7aSXJ3wFPaTrr3afK0k3OfqLf1Q/LFw2R7UpWbgGH3r6eTZPuH09O3kzw/uHj5hddJrvjQso33h52InyePf7m4U2k/yc5e8uR+t3OoXzPdYXUbLwcvW0sGDt88y+Pl88+zjffJeidDPfEPAAAApkmOqRmqfZI8rx3lfjpLJ0n68hdxNe3sJY/vJ7Vbw0V2ffU22Wt0o6b6czpdFC3Vy9nVOx/KtfO3U/vk4rp0fomOKQAAAConYmrGHnUGD3/j+ul1NO3cGi55+KCoqXrOj5YCAACAm0yOqRna+ffkC7l9boz9JHPPuk8sHNbJXFMvxsgtNffs+PzlWo7l7er8cvE6homqAgAAgGmbSseUiKnBLkqAPS2LZwzZas7nSg7nKpaTcjMpNmffVtP2IWrqdl+01N5kt/H09VFi9kFa8+kmrgIAAICKiZiaof0kj75L9haT1mpSP9FxUJ9P2stJezMDOxU23ie1g6T15dHr9SStpaRY63bknFzu+7fdp+rV+yJq6knaS8kXXyYZIhn5rNUWD/9N8ufFSqsyFb0Oyhdrk3sSX7/tdJ+8V3w54LgvJ/ceJp3OZLcJAAAA45hLUlZdieumNZ+sX/CUtK2DZOOMJ9nVkzxZTlYWcyxiaecg+f5dsn1OvqJ6kherSa0v4qVzkDw9Z7nmfPL8y6Nt9c9frnWn99d33P3rrWvQPO2lZOX++cv3FMvdSKJOkgdvhsvfNE31JHsn9u1kQvKT+5ecv4+9+Rvn7N/J9jzP3Muc6uCqzycvPj9+rmx1ko0fkuLT5NXi2fUDAACAWZhKx5Sn8sH52ktJ7o+Wn2qSimUdUwAAAFTPU/lgxupJVhrdaCkAAAD4mMkxBTP2ZCnZuVX9EEUAAAComhxTMGXn5ew6Lw/VpA3Kg5Wcn+cKAAAApkmOKQAAAAAqIWIKAAAAgErIMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxNQ10pxPvvg0WVlMcqs7rXOQPNhL9t9WWjUAAACAkYmYuibaS8njh8lXf0/mvkvmNrvl1V6ydz9prlZdQwAAAIDRiJi6AVrzyb2HycLXSd5XXRsAAACA4YiYugE23ie1gyS/rbomAAAAAMP71TRWeufOnWms9sppziePP09qt1JpzqfWfNK5leRvs9smAAAAwGVNpWNqd3f3xndOtZeShfvJq07y7XfJ/uEQutZSN+dT4zfJ/uuj+ZtJnm8Ov/6dJHeHmL+1lKzfTx51YhgfAAAAcK3IMTUFxXLyajHZeDad9beXkpX7R7833hzvBAMAAAC4DuSYmoLi79Nd/9233SfyNTaTnTfJ3u2kvjzdbQIAAABMmoipS2gvJyuL+ZBfKkk66SYi38r0IqZOas4nzx8mcy+TzDC3FQAAAMBlyDE1hnqSvbVuHqjGiUTn9SRPlpMsHl9mWjmmkmT7ffL4TdJqJBs6pgAAAIBrwlP5xvBkKdm5NbjjaD9J/p5THVPbSbZH6JgCAAAAuOnkmBrDwm+SdweDX6snWWnMtDppJqndTr59N9vtAgAAAFzGVDqmbnrE1KufkvVbSbMv4Xg93ZxTe5vdPFOTVE9SriXttaS+dPy11lJ3iOCjjifzAQAAANfLVJKf3/QcU0nSmk/Wv8yxxOc7B8nd75L2b5OV+91pjTeT6zBqLSX3GkmtP9n6QfLgRJ4rAAAAgOvAU/kAAAAAqIQcUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwBAAAAUIlfTWOlu7u7uXPnzjRWXbliOand7v7ceJPsv57t9tvLycrto993DpK73yV5P9t6AAAAAFzWVIby3dROqSRZeJ3MbSY5mO1260nKtSSLSePrbh0am8nCQVI8TDI/2/oAAAAAXJYcU9fEi+Vk51Zy91myfxgdtZ9k4Zskb5LWl1XWDgAAAGB0Iqauidpi8tWbwa+9+im5dyuipgAAAIBrRY6pS6onebGa1GpH06aR92nu2eTWBQAAAHAVeCrfmMq1ZOsgWa8ljzrJ9jfd6fV0h93ldrLwMsnb7vRmkuebw69/J8ndIecvV5OtW8mGzisAAADgGplKx9THEDFVriW5lTReJvtvT7/eXkoW7icLX2eqT8wrlpPi9vCdWAAAAABXhYipMZVryVbOj1IqV5PGL8n+6+nUoVhNippOKQAAAOB68lS+S/j23fmvd35J/rw4nW0Xq0lxS6cUAAAAcH1NJfn5TR/GN45J5ZiqJ9kbIloLAAAA4KqTY2pMVQzl0ykFAAAA3CRTGcp30zuletZvJfWlwa+15pNOLdn/aTLbas53O6UeHeiUAgAAAG4GOaYuYauT7N1PmqtH0+pJ2svJvYfJwstM5Il8zfnk+cOk8S7Z/mbA60mKzSTzl98WAAAAwKx4Kt+IiuWkdrv7c+NNktfJi9WkVjuaZ6uTbPyQiXRKJd3oq/WH58/TSbLw9eS2CQAAADBtckwBAAAAUAkRUwAAAABUQo4pAAAAACohYgoAAACASoiYAgAAAKASIqYAAAAAqISIKQAAAAAqIWIKAAAAgEqImAIAAACgEiKmAAAAAKiEiCkAAAAAKiFiCgAAAIBKiJgCAAAAoBIipq6BZpLnm+fP00my8HWS9zOoEAAAAMAE/GoaK93d3c2dO3emseqP0o9JcpDM7SV5e/r11nxy7+GMKwUAAABwSSKmboBiOXm1mGw8u3jecjV5lGT7m6lXCwAAAOBcckzdALVPkm/fVV0LAAAAgNFMZSjfxzSMr7WUrDeS3DqatnOQfL+XPL+fzL3MwOF3k9JM0qkl+z9Mbp3FclK7ffT7yX1oLyUr949+b7xJ9l9PbvsAAADAx0GOqUsoVpPiVtL4Ltk/TDpeT/LnpeR54/i8wyQw77eT5O4Q83+xlBTJRJOeL7xO2n9Pcn9wHe6+TZpvu/sz7Y43AAAA4OaSY2pMF+V16nVETbvjZtScUcPOX0+yt5Y03g2OhholrxUAAADAIFPpmLrpEVP1JHtXIFroos6vk0PyzjNoOF57KQOjpmbV6QYAAADcbHJMjeHP80knSf5WbT2+WOoO+Turc2jhdZITnU2jRFh99TbZayT15eOdVo+Xk62Ds7cLAAAAMAw5pmZkGjmmVv6QPOpcplbn20+ys5c8uZ/cPeyYqqcbhbXxcnrbBQAAAD4OIqbG8PP7ZD1Jfpuhk45vJ9keoWPqIs0kqSXbU+4gOhk19UK0FAAAADAh/zCNle7u7k5jtVfGdpJ0klbj/PmK1aS1Np06XDSMb1I+RE3d7ouW2pvuNgEAAICPw1Q6pm56xFSSNL7pRk211pLMH02vJ2ktJeVaUtxKNr6bzvZX/pB8P8VhfP2+epusHCQv1kRLAQAAAJMjx9SY9pPMPTvshPoyya2j13YOksZesj+lDpx6MvYwvrkhkp6f1IuaWrmffPtm9OUBAAAABplLUlZdCa6+9lKS+xcnZAcAAAAYlhxTXKieZKWRfCVaCgAAAJggEVNcSLQUAAAAMA1T6Zj6GHJM3WSt+WT94eDXtg6SjWezrQ8AAABwM4mYAgAAAKASckwBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwBAAAAUAkRUwAAAABUQsQUAAAAAJUQMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxNQHlWpJb3Z8bb5L911dzOQAAAICrRMTUJBwc/bj/9yu8HAAAAMAVMpWOqTt37kxjtVdW55fDf5Pkb1d3OQAAAICrRMTUBBRjRi3NejkAAACAq0TE1AS8O4xaKpLk/dVdDgAAAOAqETE1Qe8OLp7nKiwHAAAAcBWImJqAbw+jln4esaNo1ssBAAAAXCVzScpJr3R3d/ej65wCAAAAYDRT6ZgCAAAAgIvIMQUAAABAJURMAQAAAFAJEVMAAAAAVELEFAAAAACVEDEFAAAAQCVETAEAAABQCRFTAAAAAFRCxBQAAAAAlRAxBQAAAEAlREwBAAAAUAkRUwAAAABU4v8H60n5RhkMzb4AAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "3a9e8763-c50e-4e1c-91e3-c9783a1e9a69",
   "metadata": {},
   "source": [
    "![image.png](attachment:0320622a-6e24-4742-99ab-55081bad8e26.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50247ccd-1f4d-4868-8929-dfcfec611c0d",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### solve_coef_list() \n",
    "    * function is aplied in MQ Class\n",
    "    * the number of uknow variable will be < or equal of comprations each to each cefficients...\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f358ec0a-0239-4175-b722-5817499bcff9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m =7$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle k =4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m,k=P.solve_coef_list(m,k) # and voilaaaaaa....."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "65f63467-4ae6-4a39-8b7d-4f988ccb7a51",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAASCAYAAABFGc6jAAAAnUlEQVR4nO3TIQ4CMRCF4W8JGo0kCIIDyy0QeDSSBInoHbgAgnsgOAkJEkXwYKpG7JZNQGyYZNJO809fX9NWKSW/iF6oVzjgggdeONX0F/P9UO8xwxM3TBsOWsxHR1tMMMCmQeQjPjo6F2zeio+OvhZ/ob9Qh4Xih13mhGEeFzjm+R27NnwUmmMd1sY54RqEivl4dQlVTY7a8t17DG81KB6aKULe1AAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 11$"
      ],
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m+k"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a2491b49-fabd-4f2f-90d2-f19917414a58",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "6b2302e4-3485-4f79-8bb8-c74395a32cb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "96134f40-9f26-4a65-b5ef-7efcabb80d80",
   "metadata": {},
   "source": [
    "![image.png](attachment:6b2302e4-3485-4f79-8bb8-c74395a32cb9.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cf0252f7-3559-40ab-8427-8a7c824bf573",
   "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": 34,
   "id": "63a3e138-a5fe-47d7-b1a3-2a67d7fe1271",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =\\left(x - 3\\right)^{3^{m + 3}} + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =x^{3} - 9 x^{2} + 27 x - 26$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq( 3+kpow((x-3),kpow(3,m+3)),'D')\n",
    "d=MyEq(x*x*x-26+27*x-9*x*x,'d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "a753d502-f0c1-4db3-a268-53a419f20b5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =y^{3^{m + 3}} + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =27 y + \\left(y + 3\\right)^{3} - 9 \\left(y + 3\\right)^{2} + 55$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D.set(x,y+3)\n",
    "d.set(x,y+3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ab434927-dfd9-473e-b332-fa7ed4c9b673",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =y^{3} + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "06d43f19-e2e7-47dc-87a7-d10614e3273f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# apply rem teorema\n",
    "y=-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4d8904cb-9a57-4f51-ae8b-3ee05014dd33",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAA9UlEQVR4nJ3SvyvFYRTH8dfl/gcGs90fcWWyGMiIgVFSBqXUN5NNMjAY7j8gg4iFxKSUQZIMsrhJymTwc/g+6vTt271fPvV0Tuc579P5PD21LMv8VV0h78E0dnCHN7ziDFOxtx6gMWzgEcd4QC9GsIWh1PMdoVsMYw9fob6Ic4ymAdtxvSPsFgBoYTPljaKndnpP8aMqVMdEyg+qQivoxz4Oq0CzmMcNxn+L7aAZrOEaA3jpBM1hHVcJaMXLMmgBq7hMwFOxoQgtyY1fYBDPZWvEHzGJZXziVP4IRd2jGaG+FLvlnsp0gmZcL0Otw2mUeaqkf0E/uGsxD4TY4q4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D(y=-1,m=0)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "e0ef4363-5496-4832-be63-dca756c32630",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "9d5058de-072d-4529-8363-6b9b620d412d.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "0d3fa1cc-66f4-42e9-afae-57f4bcb77519",
   "metadata": {},
   "source": [
    "![image.png](attachment:9d5058de-072d-4529-8363-6b9b620d412d.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "2f48f829-8a18-46b0-8dd5-748bc889c44a",
   "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": "027a0ef7-ec5c-4333-be38-8e1928e7ed1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =a x^{5} + b x^{4} + c x^{3} - 5 x - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =2 x^{3} + x^{2} - x - 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =7 x^{2} + 8 x - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(a*x**5+b*x**4+c*x**3-5*x-3,'D')\n",
    "d=MyEq(2*x*x*x+x*x-x-2,'d')\n",
    "R=MyEq(7*x*x+8*x-3,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b78d6fdf-778a-4107-85c3-278c1b8ad1e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R2 =\\frac{3 a x^{2}}{8} - \\frac{a x}{8} + \\frac{3 a}{4} + \\frac{3 b x^{2}}{4} + \\frac{3 b x}{4} - \\frac{b}{2} - \\frac{c x^{2}}{2} + \\frac{c x}{2} + c - 5 x - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R2=MyEq(D.rem(d),'R2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e7033ea0-5232-491d-89e4-d7a3a3058135",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R2 =\\frac{3 a}{4} - \\frac{b}{2} + c + x^{2} \\left(\\frac{3 a}{8} + \\frac{3 b}{4} - \\frac{c}{2}\\right) + x \\left(- \\frac{a}{8} + \\frac{3 b}{4} + \\frac{c}{2} - 5\\right) - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R2.sortdegree(x) # P.sortdegree(x) if P=3*x*x+a*x*x+b*x+3*x+7, return (3+a)*x*x+(b+3)*x+7"
   ]
  },
  {
   "attachments": {
    "e4cb30ca-e176-48df-8ba1-3e8b1cf37f36.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "1b752d26-68bb-47c5-b71c-8ecc001f849a",
   "metadata": {
    "tags": []
   },
   "source": [
    "![image.png](attachment:e4cb30ca-e176-48df-8ba1-3e8b1cf37f36.png)"
   ]
  },
  {
   "attachments": {
    "67839272-37ff-4225-8cee-bf16f9ad904a.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "bda4ed90-d801-4fd4-a8f8-1ca639381d21",
   "metadata": {
    "tags": []
   },
   "source": [
    "![image.png](attachment:67839272-37ff-4225-8cee-bf16f9ad904a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "cbf0a390-82d6-4317-a2f8-a20dacc9b959",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 7 x^{2} + 8 x - 3 = \\frac{3 a}{4} - \\frac{b}{2} + c + x^{2} \\left(\\frac{3 a}{8} + \\frac{3 b}{4} - \\frac{c}{2}\\right) + x \\left(- \\frac{a}{8} + \\frac{3 b}{4} + \\frac{c}{2} - 5\\right) - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MQ(R,R2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "187014e6-8635-484c-9d91-5fdf15425c05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =\\frac{1}{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =\\frac{53}{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c =\\frac{25}{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,b,c=P.solve_coef_list(a,b,c) # and voilaaaaaa....."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "5f9ec4d6-bbf9-4849-b0a3-1ae546a5069f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 20$"
      ],
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+b+c"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "9738fa4f-7c4e-4c66-b05d-f3e338e48015",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "bcb9b43d-7761-4924-9397-a6b0fe29fc9c.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "42845318-ef6c-4fa4-bd3e-2a0a0817ff6e",
   "metadata": {},
   "source": [
    "![image.png](attachment:bcb9b43d-7761-4924-9397-a6b0fe29fc9c.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "3952be21-221f-4419-8453-6d714096e04d",
   "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": 47,
   "id": "d4101845-703d-4095-aa0f-99e78b569aa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =- \\left(x - 2\\right)^{7} + \\left(x - 1\\right)^{7} - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =x^{2} - 3 x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq((x-1)**7-(x-2)**7-1,'D')\n",
    "d=MyEq(x*x-3*x+2,'d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "15be8597-fbf7-4ad9-8e7e-a5f33fafed54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=D.rem(d,'R')"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "10fd38ca-ee5d-4ac2-9190-6defea4f325b",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "26b2fad0-f3dd-4346-b119-add212e5030a.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "8665de1a-2e3d-4af2-9973-623bece38896",
   "metadata": {},
   "source": [
    "![image.png](attachment:26b2fad0-f3dd-4346-b119-add212e5030a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "908220e2-fe6f-4510-9a5f-d02bb1911e7c",
   "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": 50,
   "id": "d41a5794-53f9-4389-bc5d-d4cf18c5d5c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =a x^{4} + b x^{3} + c x^{2} + x + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =3 x^{2} - 3 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(a*x**4+b*x**3+c*x*x+x+3,'D')\n",
    "d=MyEq(3*x*x-3*x+1,'d')\n",
    "R=MyEq(2*x+1,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "3524bd6d-4354-4635-b4b8-7c2667c9cb11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\frac{a x^{2}}{3} + \\frac{a x}{3} + \\frac{2 a}{9} + \\frac{b x}{3} + \\frac{b}{3} + \\frac{c}{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=D.quotient(d,'Q')"
   ]
  },
  {
   "attachments": {
    "dff45343-c539-4605-9092-f5c0dd557e85.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "0ea3985d-d285-4225-a3d1-27ef1f0cdb48",
   "metadata": {},
   "source": [
    "![image.png](attachment:dff45343-c539-4605-9092-f5c0dd557e85.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "1cc258b2-95c3-489c-99f4-a9238e26a5b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\frac{a}{3}, \\  \\frac{a}{3} + \\frac{b}{3}, \\  \\frac{2 a}{9} + \\frac{b}{3} + \\frac{c}{3}\\right]$"
      ],
      "text/plain": [
       "⎡a  a   b  2⋅a   b   c⎤\n",
       "⎢─, ─ + ─, ─── + ─ + ─⎥\n",
       "⎣3  3   3   9    3   3⎦"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mm=Q.coef_list();mm"
   ]
  },
  {
   "attachments": {
    "c2470c88-da75-40fb-b543-eb07ea7d849a.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "6904f00f-ae43-45e8-9df4-29c2edd7b2e2",
   "metadata": {},
   "source": [
    "![image.png](attachment:c2470c88-da75-40fb-b543-eb07ea7d849a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "2ece6595-2cd0-4634-8d09-96c616784330",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle K =\\frac{a \\left(\\frac{a}{3} + \\frac{b}{3}\\right) \\left(\\frac{2 a}{9} + \\frac{b}{3} + \\frac{c}{3}\\right)}{3} - 8$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K=MyEq(mm[0]*mm[1]*mm[2]-8,'K') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "dadea6b0-36e6-4b08-b427-08efc7ee9a94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a x}{3} - \\frac{2 a}{9} + \\frac{2 b x}{3} - \\frac{b}{3} + c x - \\frac{c}{3} + x + 3 = 2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(D.rem(d),R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "d84f2148-9d66-4784-bec1-6169a9e62625",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =3 c + 27$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =- 3 c - 12$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,b=A.solve_coef_list(a,b) # only two variables when two there is two eq equality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "792eed2e-51ed-4021-9ecb-75945d304533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle K =10 c + 82$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K.upgrade(a,b) # upgrade() is used to up finding values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "433cbe49-40da-44c0-8286-6cc3c5c8ba8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c =- \\frac{41}{5}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c=K.solve(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "90f7cc3d-51d3-40c9-85bf-84ac9a278068",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =\\frac{12}{5}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =\\frac{63}{5}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a.upgrade(c)\n",
    "b.upgrade(c)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "b0817ac3-a270-4799-a7f2-478e8755a179",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "6eaa8ca8-d5e0-4418-89f4-4e9cd5a954f9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "375c0565-4ea0-42e3-9b9e-99818539e9f3",
   "metadata": {},
   "source": [
    "![image.png](attachment:6eaa8ca8-d5e0-4418-89f4-4e9cd5a954f9.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "1db27f94-bd14-45bb-b856-b8addf0d3b19",
   "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": 60,
   "id": "6be6f7f2-2097-4165-ba14-194ee0187ca4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =a x^{3} + b x^{2} + c x + d$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d1 =2 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q1 =x^{2} + 2 x - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d2 =2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R2 =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(a*x**3+b*x**2+c*x+d,'D')\n",
    "d1=MyEq(2*x-1,'d1')\n",
    "Q1=MyEq(x*x+2*x-3,'Q1')\n",
    "d2=MyEq(2*x+1,'d2')\n",
    "R2=MyEq(1,'R2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "e5db9956-a8ac-4eba-8086-bee897445170",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a x^{2}}{2} + \\frac{a x}{4} + \\frac{a}{8} + \\frac{b x}{2} + \\frac{b}{4} + \\frac{c}{2} = x^{2} + 2 x - 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{a}{8} + \\frac{b}{4} - \\frac{c}{2} + d = 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(D.quotient(d1),Q1)\n",
    "B=MQ(D.rem(d2),R2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "854a0be0-d112-4b66-9006-93e43ca2e1e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c =-8$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,b,c=A.solve_coef_list(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "ba1f95c7-dde7-43fb-a83f-dd9b06fc2b90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =\\frac{a}{8} - \\frac{b}{4} + \\frac{c}{2} + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d=B.solve(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "0ca420f5-2515-4ca7-aad7-28ba77dc150a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =- \\frac{7}{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d.upgrade(a,b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "a2671a3a-9b00-4c64-8d37-8f1aef80d965",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =2 x^{3} + 3 x^{2} - 8 x - \\frac{7}{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D.upgrade(a,b,c,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "1b419410-8c9f-4f75-8168-4a7e65762dc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{13}{2}$"
      ],
      "text/plain": [
       "-13/2"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D.rem(2*x-1)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "33265f50-6217-4209-a400-55fa3646d939",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "4ec04ef8-5b37-4270-aded-6aff2fd3aa60.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "9e8eb061-cbb4-4bf2-aacd-bb85ae6e2dad",
   "metadata": {},
   "source": [
    "![image.png](attachment:4ec04ef8-5b37-4270-aded-6aff2fd3aa60.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "2aed5121-a1b7-49ae-bda1-4d2c61b63923",
   "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": 68,
   "id": "0ab9fcbd-863a-4b4d-8a6f-abd19e1e4f53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =a x^{4} + b x^{3} + 16 x - 25$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =2 x^{2} - x + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =3 x - 5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(a*x**4+b*x**3+16*x-25,'D')\n",
    "d=MyEq(2*x*x-x+4,'d')\n",
    "\n",
    "R=MyEq(3*x-5,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "391c35d5-7beb-4ae8-94a4-d3fac793c1ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{15 a x}{8} + \\frac{7 a}{2} - \\frac{7 b x}{4} - b + 16 x - 25 = 3 x - 5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(D.rem(d),R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "bc9e5d69-b296-44dc-99ac-8e2686f9b7ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,b=A.solve_coef_list(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "f29559e1-81ad-4c98-abd8-f8c2838f9a16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAAuUlEQVR4nJ3STWoCQRCG4cfgQnfmGBKyF9GNd0hWCq5yjvEYih7Dnxu4nV0OYHIM0YU9MEy6Z8Z80FRTVW/xddGdLMs8q5fSfYlbw7lCtwTlWCWGTzHDMQblCegc4qZqL6V3jPCLfVvoK8Sd8KYmqI95aN4WySboEwOccGkLFdbW5WQd9IYxfnBoC/1ZQBPUwyI076rFFPSBV48fcKkWU1BhbRMrxqAhJiILKNSN5L7RSTiotVerf0F3KJclWZ9117EAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 7$"
      ],
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+b"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "be04da12-d406-4273-ac70-0b558681addc",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "1cdad120-39de-4273-8423-9505a7d171f0.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "550e0843-e6e9-4942-bce7-97db77b4098d",
   "metadata": {},
   "source": [
    "![image.png](attachment:1cdad120-39de-4273-8423-9505a7d171f0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "3660de8a-d62b-4a0c-b44d-b1fbc74fd5e6",
   "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": 73,
   "id": "21a4f1ec-9bcb-4c79-9f94-c2517e7795de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =a x^{2} + b x + c + 2 x^{5} + x^{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =x^{4} - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\frac{a + b}{a - b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(2*x**5+x**4+a*x*x+b*x+c,'D')\n",
    "d=MyEq(x**4-1,'d')\n",
    "P=MyEq((a+b)/(a-b),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "efb46bd0-92a5-429a-aa4a-44c8fcb758e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=D.quotient(d,'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "07a34520-a48e-4e6b-960f-9162951941c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x^{2} + b x + c + 2 x^{5} + x^{4} = 2 x^{5} + x^{4} - 2 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(D,expand(Q*d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "7444927d-0f42-44a7-b38a-e25fcc04e339",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x^{2} + b x + c = - 2 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "f6030f2c-295c-4b9e-9ed6-466e0ad24ad8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b x + c = - 2 x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.set(a=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "5045b666-860e-4009-9f01-e3bc7b603460",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =-2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c =-1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b,c=A.solve_coef_list(b,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "a73ed182-570c-43d6-bf73-92c8c3a46b88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =-1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a=0\n",
    "P.set(a=0,b=-2)"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "11550781-fb3c-4957-b757-b37f5fd48cbe",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "a0b35afa-6b24-4156-9e49-1750b9454963.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "45ad668f-7da6-4cae-a7ac-2b55d8ea449e",
   "metadata": {},
   "source": [
    "![image.png](attachment:a0b35afa-6b24-4156-9e49-1750b9454963.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "67678a64-fb53-49c7-9fa8-70c211a37b76",
   "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": 81,
   "id": "ac808839-da47-49e7-932f-30c43811ac0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =a x^{4} + b x^{3} + c x^{2} + d x + m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d1 =x^{2} + x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d2 =x^{2} - x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R1 =x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R2 =x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d3 =x^{4} + x^{2} + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D=MyEq(a*x**4+b*x**3+c*x*x+d*x+m,'D')\n",
    "d1=MyEq(x**2+x+1,'d1')\n",
    "d2=MyEq(x**2-x+1,'d2')\n",
    "R1=MyEq(x+1,'R1')\n",
    "R2=MyEq(x-1,'R2')\n",
    "d3=MyEq(x**4+x*x+1,'d3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "dda5323b-ccb6-4663-8741-7e4b5c46b800",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x + b - c x - c + d x + m = x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - a x - b + c x - c + d x + m = x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(D.rem(d1),R1)\n",
    "B=MQ(D.rem(d2),R2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "2ce54eef-8b82-414b-9cac-04674bf93b17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =c - d + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =c - m + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  finding a and b in A with solve_coef_list\n",
    "a,b=A.solve_coef_list(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "f366afc5-55f1-4edc-a9c1-8e36087ffff0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c x - 2 c + d x + 2 m - x \\left(c - d + 1\\right) - 1 = x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  replace this value in B\n",
    "B.upgrade(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "ae04f5f7-cf25-43b0-9b57-ce172cacc894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  finding c and d in B with solve_coef_list\n",
    "c,d=B.solve_coef_list(c,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "4050e46f-8a7b-49f4-94ec-8f5883c7c9fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m x + 2 m - x \\left(2 - m\\right) + x - 3 = x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.upgrade(c,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "cf12d1f9-3d2e-4d52-8ccd-6970dc107a6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 m x + 2 m - x - 3 = x - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "2a06c45a-8547-4164-9d10-a6586fc4fd14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# solve m in B if x=0\n",
    "m=B.solve(m,x=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "d8a5ad0d-ef25-4959-adc8-cd97405b86a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m =1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "Upgrade(a,b,d,c,m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "cee509fe-36f1-4e21-b902-707ea9aa99ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle D =x^{4} + x^{3} + x^{2} + x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D.upgrade(a,b,c,d,m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "39c9927a-d939-4aad-909f-d8e676417285",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{3} + x$"
      ],
      "text/plain": [
       " 3    \n",
       "x  + x"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D.rem(d3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09acb79f-05eb-4e50-be85-7e93205ea9d8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}