10220 GCD LCM mcm MCD.ipynb

{
 "cells": [
  {
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    }
   },
   "cell_type": "markdown",
   "id": "3c0cf20d-b424-42bc-a373-c03e3c71e466",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "0dd49af4-5de5-46c0-a009-76ff4288fce5",
   "metadata": {},
   "source": [
    "![image.png](attachment:fe4d89c2-2fe0-4968-89ec-eacf08018c0b.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "dabc8a7e-8c99-470f-8a34-2ded63f56aee",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
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   "cell_type": "markdown",
   "id": "21775fd2-7409-48ff-ae5b-6cf3a22db536",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
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"
    }
   },
   "cell_type": "markdown",
   "id": "4d28ca6a-ff30-4b60-8ffa-82ffdb316d63",
   "metadata": {},
   "source": [
    "![image.png](attachment:5a18c037-4336-4662-ad36-271ce3ba79d4.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4af5a143-18c1-483a-89ad-2183af31268f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(x + 3\\right) \\left(- 2 a + x^{2} + x \\left(a - 2\\right)\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\left(x - 2\\right) \\left(3 b + x^{2} + x \\left(b + 3\\right)\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq((x+3)*(x*x+(a-2)*x-2*a),'P')\n",
    "Q=MyEq((x-2)*( x*x+(b+3)*x+3*b),'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f691cb35-7381-41bc-b2af-53eefdb6a9af",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(a + x\\right) \\left(x - 2\\right) \\left(x + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\left(b + x\\right) \\left(x - 2\\right) \\left(x + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.factor()\n",
    "Q.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "467d1103-36f2-4d23-8f93-65ec6d4bae28",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle mcm =\\left(a + x\\right) \\left(b + x\\right) \\left(x - 2\\right) \\left(x + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcm=P.LCM(Q,'mcm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c3c5c42b-9050-49d4-963f-0cb0c8fadbbb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle MCD =\\left(x - 2\\right) \\left(x + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MCD=P.GCD(Q,'MCD')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "be1d79ab-36a5-42bc-8a74-8ad6dc4a8275",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =a + x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Div(MCD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "6bfb77f7-e111-4bf5-bed2-30752b217199",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(a + x\\right) \\left(b + x\\right) \\left(x - 2\\right) \\left(x + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Mul(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d3bfec1d-e373-4725-a8d8-a462abd6aeb0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =a b x^{2} + a b x - 6 a b + a x^{3} + a x^{2} - 6 a x + b x^{3} + b x^{2} - 6 b x + x^{4} + x^{3} - 6 x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3cf8d432-fc9a-4aa1-bb96-ad40c2e29fe4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =- 6 a b + x^{4} + x^{3} \\left(a + b + 1\\right) + x^{2} \\left(a b + a + b - 6\\right) + x \\left(a b - 6 a - 6 b\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.sortdegree(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "323773f5-3e1a-4366-8b1a-e2666ba3fb2b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle mcm =a b x^{2} + a b x - 6 a b + a x^{3} + a x^{2} - 6 a x + b x^{3} + b x^{2} - 6 b x + x^{4} + x^{3} - 6 x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcm.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a3be1d8f-1afc-4f37-a2b7-6ed18beb086c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle mcm =- 6 a b + x^{4} + x^{3} \\left(a + b + 1\\right) + x^{2} \\left(a b + a + b - 6\\right) + x \\left(a b - 6 a - 6 b\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcm.sortdegree(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "0c4a5710-ab25-47a0-ac38-6b8f8bb58ffc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 6 a b = 120$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(-6*a*b,120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "08762230-3f89-45df-afd2-f46de4f1f6fd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =- 6 a b + x^{4} + x^{3} \\left(a + b + 1\\right) + x^{2} \\left(a b + a + b - 6\\right) + x \\left(a b - 6 a - 6 b\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.s()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "33d58aa6-8372-41df-9e02-f32f26982c1d",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b + 1 = 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2=MQ(a+b+1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "8fe1986b-ed36-449d-b596-f1e58bd570cf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a1 =-4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a2 =5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b1 =5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b2 =-4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a1,a2,b1,b2=simplesolve(Q1,Q2,a,b,'eQ')"
   ]
  },
  {
   "attachments": {
    "9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "f3b6474f-ee7f-4dbd-8eff-125875b4a283",
   "metadata": {},
   "source": [
    "![image.png](attachment:9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "d01cff8d-f052-4a7e-ab82-c41fa3647f3d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "0f97d688-aa2a-425c-b6c2-849e68d2ada4",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "38e78f27-8041-4dbd-b15d-d700e4d254c1.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "78a616e4-4fb6-451f-ad61-985351035d3a",
   "metadata": {},
   "source": [
    "![image.png](attachment:38e78f27-8041-4dbd-b15d-d700e4d254c1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "eb843406-2669-44a0-af08-e01cdc123554",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =x^{6} + 2 x^{5} + x^{4} + x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2 x^{4} + 7 x^{3} + 9 x^{2} + 7 x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F=MyEq(x**6+2*x**5+x**4+x+1,'F')\n",
    "P=MyEq(2*x**4+7*x**3+9*x*x+7*x+2,'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "8c1ecf84-4939-402f-9f79-880c7b006494",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\left(x + 1\\right) \\left(x^{2} + x + 1\\right) \\left(x^{3} - x + 1\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "6aff2aea-30e2-4e04-9ae5-a987a44926d3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(x + 2\\right) \\left(2 x + 1\\right) \\left(x^{2} + x + 1\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "9db609e1-3085-4105-86f4-af695be792f3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle MCD =x^{2} + x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MCD=P.GCD(F,'MCD')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "891efb40-9394-4f62-a706-da2b10bd10b4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle MCD =\\sqrt{2} + 2 + \\left(1 + \\sqrt{2}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MCD.set(x=sqrt(2)+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "dad10f08-6307-4fbc-9d96-fc48e57fd07a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle MCD =3 \\sqrt{2} + 5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MCD.expand()"
   ]
  },
  {
   "attachments": {
    "9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "6069968f-ab4a-4266-b354-ca0f141aeb54",
   "metadata": {},
   "source": [
    "![image.png](attachment:9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "a168fd39-22c5-475e-bf9c-5267bee7d1f3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
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   "cell_type": "markdown",
   "id": "384f91ca-c64b-4b12-b063-20d0636fd9fa",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
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"
    }
   },
   "cell_type": "markdown",
   "id": "2b4ef98f-bb2c-4e8a-a82b-b4b5d52c27a7",
   "metadata": {},
   "source": [
    "![image.png](attachment:2e7554e8-ce76-4d1c-aeae-b460d003011d.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "859a7e89-82ab-4f65-ade8-3ffc62e475e5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(x^{2} - 2 x + 1\\right)^{4} \\left(x^{2} + 3 x + 2\\right)^{8}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\left(x + 2\\right)^{8} \\left(x^{3} - 3 x^{2} + 3 x - 1\\right)^{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq((x*x-2*x+1)**4*(x*x+3*x+2)**8,'P')\n",
    "Q=MyEq((x**3-3*x*x+3*x-1)**4*(x+2)**8,'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "01682488-ef7d-46f1-bb5d-89f32f4ef815",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(x - 1\\right)^{8} \\left(x + 1\\right)^{8} \\left(x + 2\\right)^{8}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\left(x - 1\\right)^{12} \\left(x + 2\\right)^{8}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.factor()\n",
    "Q.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "f42d43b0-b4de-421a-bf02-35c59db3a846",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\left(x - 1\\right)^{8} \\left(x + 2\\right)^{8}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F=P.MCD(Q,'F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "b3e5a933-9d23-4ac0-9998-5cc587dab2a9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\sqrt[8]{\\left(x - 1\\right)^{8} \\left(x + 2\\right)^{8}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=8\n",
    "F.Rpow(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "14545bb2-7cd5-42cf-b5e5-8cee56bca807",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\sqrt[8]{\\left(x - 1\\right)^{8} \\left(x + 2\\right)^{8}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "c562b71c-924d-498e-8caa-bda709539242",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\sqrt[8]{\\left(x - 1\\right)^{8} \\left(x + 2\\right)^{8}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "b085858d-92af-49ab-83f4-c89c54107352",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F =\\sqrt[8]{x^{16} + 8 x^{15} + 12 x^{14} - 56 x^{13} - 154 x^{12} + 168 x^{11} + 700 x^{10} - 328 x^{9} - 1791 x^{8} + 656 x^{7} + 2800 x^{6} - 1344 x^{5} - 2464 x^{4} + 1792 x^{3} + 768 x^{2} - 1024 x + 256}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.expand()"
   ]
  },
  {
   "attachments": {
    "2687061f-64c5-49bb-8920-75a1862fd540.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "4f521597-ef08-4cc4-90ba-0669422472a0",
   "metadata": {},
   "source": [
    "![image.png](attachment:2687061f-64c5-49bb-8920-75a1862fd540.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "591ccccb-fccf-4294-94d3-0d66781e34c1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "a=1\n",
    "b=1\n",
    "c=-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "5b984957-1b51-4713-80dd-9e0573c56645",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVQoFXWRwQ2CQBBFBS1AvXmFDpQ6PBmtgFgCeuNmLIESDJbAgQakBDow0gG+vzCEkDDJz/z983d2dtdr23YxjjRNn+M1/IVWrUxkEcBzkMAL6WSthdCX0IcE7XamXluTa3FPR1M8wWXcwBsVpmEdrxSaOZM22YwRvMa4J1/AF4QgR3OjmFGzKCIKSUfdZX6sY/BeIsp0AzuEo5mUy7LUS9zJmc0o3d1OZBQfuBpFPl3slpZHvoEG1lEDa+dc1GbMcGieaRwQ9GyFM+pWCAV5+Ge4TjiDGHQ/I6LojTbCFumBVqn2B44LUrfH/UOvAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle 6$"
      ],
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*b*c+n"
   ]
  },
  {
   "attachments": {
    "9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "48abf563-bffe-4ad3-893b-236604eb71d6",
   "metadata": {},
   "source": [
    "![image.png](attachment:9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "88001327-208f-4185-b36d-fc6e974f7b47",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "fc4358bb-fbab-4b72-a3d5-35e98d0f54df",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "964b68e1-d9bb-4522-929d-09e531126dd0.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "30b712e8-3d48-41f2-92c6-ffe898e18c52",
   "metadata": {},
   "source": [
    "![image.png](attachment:964b68e1-d9bb-4522-929d-09e531126dd0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "bae68ff2-719c-4908-9446-21908a9f9da7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{2} - 2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq( x*x-2*x+1,'P',var=x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "654fe07a-f9bc-4234-a33a-24b8c1fd90b6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle q =a x + b + 2 x^{5} + x^{3} + 2 x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q=MyEq(2*x**5+x**3+2*x*x+a*x+b,'q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "3f7c37e3-49d5-47e0-b2ba-eee22c1d5c92",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =m x^{3} + n x^{2} + p x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MyEq(m*x**3+n*x*x+p*x+1,'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ff372608-140d-4d70-9e88-340a4f82eca0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x^{2} - 2 x + 1\\right) \\left(m x^{3} + n x^{2} + p x + 1\\right) = a x + b + 2 x^{5} + x^{3} + 2 x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(P*Q,q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "a0f24015-b192-44e0-b84c-e052e69c2c10",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m x^{5} - 2 m x^{4} + m x^{3} + n x^{4} - 2 n x^{3} + n x^{2} + p x^{3} - 2 p x^{2} + p x + x^{2} - 2 x + 1 = a x + b + 2 x^{5} + x^{3} + 2 x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "03746c1b-c683-4fc1-b6c2-2067dde067b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ -14, \\  8, \\  2, \\  5, \\  10\\right]$"
      ],
      "text/plain": [
       "[-14, 8, 2, 5, 10]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_coefcompare(A,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "42597e0a-2656-43f5-bb03-ce3e57e4c016",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAOCAYAAAAi2ky3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfElEQVQoFWP8//8/Aww0NDQYAdmrgdgYyP4AE0ensaljAQoKABXOBuJ3QGwCxEpAjAEIqQMZBLI5FKQTyC4DUiBXYQBC6pgwdJApMGoQ4YAbDSPSw0gYqkWIgFYMdYygTAtM/qCMCgIuQAzKe+eA+B4Q7wbKzQLSYIBPHQB5ZC0BptgXqwAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle 11$"
      ],
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L=solve_coefcompare(A,x)\n",
    "sum(L)"
   ]
  },
  {
   "attachments": {
    "9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "05769d99-9d4f-4cb4-9a45-4ee84945d122",
   "metadata": {},
   "source": [
    "![image.png](attachment:9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "92322550-5480-4776-a7aa-6d13ba03dfa9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "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": "9600c7f5-a1c8-4ba4-b374-b18ee26dbbb7",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "554e0426-3b9c-472b-ba88-23b1f8c9a550.png": {
     "image/png": 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mDVlvCIJATEwMRowYQcbR1NTEiBEjsGnTJsTGxqold9QlKysLWVlZSuMIBALk5uZizpw5YLPZZF7Ly8sRERGBBw8eyExVEwQBPT09cDgcdO/evUqdWFJSEj58+ABTU1PEx8dj4sSJ5LWwsDC8ffsWjo6OaNSokdpp3rt3D1euXMG+ffsojRQ5OTkICwsDUGFsaN26NTIyMhAYGIhDhw6RdbWywiESiZCfn69wdovFYmHIkCFYu3YtLC0t1bK+qUvlNsTj8RAQEAAzMzN06NCB7GM+ffqEjh07kv7gkm+hqalJKkNVNQaIRCKUl5erFffdu3cICAiAq6srgIp+i8fjka420pSUlMDDwwO6urpo3749bG1tkZaWhnv37qFbt26wtbWFqakppk6dCm9vbwiFQjg6OsLIyKhKcpcgCEp3DiqYTCZMTU2RnZ2tMC3puOPGjcOKFSvk4jk5OaF169aIi4vDzp07oauriz/++AM9e/bEP//8A6DCCOLm5gaCIFBWVgYjIyOUlpYqdX2rLHs8PDyQl5entrx/+vQpfvnlFxgbG4MgCDCZTIUL23NyckgjStOmTbFs2TJ8+PAB2dnZePToEU6dOkW2r4KCAmzbto1cRBocHIxmzZqpnHkHoLZ869KlC3bu3AmRSCSzLkLSLnr16gUrKyuIxWJkZGTg4MGD0NPTw969e9VKXx2Cg4OhoaGB5cuXA6hoh/Hx8Rg+fDh8fHzIevnrr7/CxsYGNjY2CA4Oxv379zFs2LAay0eNaB0ikQhlZWWYOnWqzDTUokWLyIopTU0p1ADQsWNHjB07Fh06dFA5JfzgwQM8evQIs2fPRlpaGjgcDqUQDgsLg76+PgYMGID09HSVSrWrqyuys7PlRsRARaXU09NDRkYGOYVMBY/Hg5+fH06fPk0K22bNmmHSpEkQCoWIjY3FsmXLYG1trTQdCeqUXV5eHjQ1NaGvr68y7tfg6ekJY2NjtGzZEgBgZGQELpcLIyMjlJWVke/75csXPHr0CC4uLtUawWpqamLKlClYsGAB0tPTq6T4fStcXV0RGxuLTZs24fjx47Cxsamyq839+/chEAhkLHdUCIVCuLm5YevWrWT55eXlYdSoUbCyspKLn56ejsaNG8soN6WlpdDU1ASLxUJBQQHOnDmDz58/Q09PDwRBICwsrMqHPKhrESgvL4ezszPlCnIej4cvX76QFh8ulyt3cpuiOv/8+XMEBwer7LypOpDp06fjr7/+kglr2rQpbGxs8PLlS8p7Dh48iMmTJ5OGBJFIhLt376Jz587o0KED5bM5HA48PDwoBxPS6OrqYu/evXKubm3btkWnTp3A5XJlwiUuEkKhEP369atSu/r06RMCAgLA5XLlLFD//vsvtLW1YWtrSyrVqgZoSUlJ8PLywuzZsym3jyMIAkZGRhg/fjy0tLRIucTj8dCnTx90795d4Td++PAhzp07hyNHjqBly5Y4d+4cnj17hn/++Yfc/7lnz55o0aIF8vLyFOYxNTUVjx8/hr29PUJCQlBeXo78/HwMHjwY6enpePXqFTp37oxRo0bJ5V3y7hwOBzdu3ACPx0OvXr0wb948uLm5ITo6GgwGA87OznLPre5JfWKxWC2lVCwWIyAgAFZWVrh9+zb69++PgoICODk5YefOnXJrL/Ly8vDs2TMUFBRAW1sbrq6uWLBgAbS1tZGamgpbW1vo6OhgxowZpLGKSsaoQldXV2bQqgyRSAShUChn1ZauE2VlZbh48SLEYjG6detGebrjxo0bERUVhevXr+POnTto2bIlevfujTlz5pBx2Gx2td5HmmnTpoHNZpOyE/if3KrcTvz8/JCamkrK+JCQEISFheGPP/6gTLtp06aYMGEC/vrrL2zcuBEMBgPr169HZGQkUlJSEBQUBFtbWwAV/e327dvJ775y5Uro6uqqzP/EiRPl3FZ4PJ7Ce9esWSM3WJVuF5K02rVrh+PHjyMyMhLv379Hz549VeZFHcRiMXx8fGBpaQlfX19wOBzEx8ejbdu2ZB5sbGxw8uRJODg4wMTEBFZWVl/9nStTI86RYrEY9+/fx+fPn1FWViZz7dixY7h27ZrcPXFxcSgqKlKYpnRDSUpKgru7O96/f08Zl81mqzX9ZWpqisOHD0MoFKJhw4bkqFSa6OhonD9/Hv3798ft27dJRVARe/fuhba2Nuzt7UkfocqC39DQED179lTq862jowNzc3N4eHhQvl+rVq1QXFyMVatWITQ0VOW7KiI4OBinT59GQEAAMjIy0K9fPzRt2lQmz0KhEHfv3sX169cRFxdX7WcBFRaPCRMmwNjYWCbc1NQUixcvJlecC4VCHD16FOPGjaPs+AUCAQoLC5GVlYXPnz+T4c+fP8fNmzdl4s6ePRtHjx79qnyrQ35+Pq5cuYLr16+Dy+WipKQEd+/eRVBQEBmnW7du0NXVxYULF2BnZ4cBAwZU2YfL0NBQZrpSkWKxdu1a8Pl87Ny5EwKBAPn5+Thz5gzlwq6CggJMmDABq1evJi1dnz9/xqlTp/DgwQMAgJ6eHmxsbDB37lw4ODhg7ty5ePToUZVPTePz+WptJXjmzBlkZWVRTs2ePXuWtDQkJydj+vTpmDdvHjmQVTaI1NfXR69evdCuXTu18isWi/Hw4UP8888/6NChA+UM0+TJk5Gfnw8XFxe5a61bt8ayZctw584dvHr1Cvfu3cP169cRHR2t8JmGhoZYtWqVWpYhKjmSkpKC8PBwGBoaypUFk8nElStXcO/ePbmDYAAo9Kl1dHTEjh07oK2tLWOhIwgC5eXlWL9+fZVctMLCwtC6dWsUFBQoNAy4u7tDLBbj0qVL4PP5KC8vx/bt2+Xeq/Kph5J3KC8vR0JCAn7++WfY2dnJGVo6deqEkydPKsxjREQErl+/jsDAQBw5cgS5ubkoLS3Fly9fYG5ujvz8fJXHcJuYmMDNzQ3btm3DixcvwOFw0LNnT0yePFnloKmqMBgMxMbGorS0FAAQFBREueUcg8FAgwYNSPfHHj16YODAgXB0dMT+/fvh4+MjE9/U1BSenp6kRRGoGEjduHED27dvl4lblWPJBQIBrly5gvT0dHh5eeHq1aswNTVFTEwMPn78iLi4ONy9e5dSXkjav3T/V7mus9lstG3bFm/evEF0dDQ2b94MHo8nl9+SkhIMGzYMlpaW6NixI1auXPnVayScnJxw4MABuLu7IyMjAzdv3sTLly+RlZWF1atXw9nZGQsWLEBYWJjc6Z0///wzli5dSlqPmzdvjjZt2ijdTSM2NhaLFi2SmZnS0NDA06dP8fLlS5m4FhYWSExMREREhEKl+MmTJ1i+fDnWrFmDtWvX4vr16zh//jzCw8Oxfv16rF+/HsuXL8eXL18o779//z7lGQyKZPPjx4/h6ekJgUCg8B2rwuDBg7Fr1y507doV5ubm6NSpE/bs2QNnZ2dyBqhPnz5o0qQJli5disDAwLrt/vHx40eMGDECLi4umD9/Plk5bGxsZASvp6cngoKCQBAErK2tMWHCBIXpvn79GsnJyRAIBHj//j1u376NPn36YM6cOTJ+W+ruWTplyhS4ublhypQpyM7Oxvnz5+XinDlzBn///TeKi4sxbNgwhIaGKrVUW1lZoUGDBnLCW3qEpquri99++01p3mxsbJCdnS23AEOCpqYmHB0dsWDBAvj7+6NLly4KpwoVVeLAwECcPXsWgwYNgp2dHf755x/ExcXByMgI7dq1A4PBQFBQEBo3bgwvLy8IhULcvHkTVlZWWLt2rdL8K+LixYsQiUQyilhJSQnGjRuHkJAQ2NnZAahQULW0tGT8n6TJyclBSEgIHj9+DD09PbKTv3fvnpxFWjJaVjQKfvToEfz8/ABUCNhRo0bh1q1bMDc3R4MGDZCRkYGcnBzMmjVLZpFDZby8vPDkyRPSqlFUVAQ/Pz+YmZmRfr+9evVCz549UVJSUq2FGUVFRcjOzoa1tbXKuLa2tmCxWPD398fbt29x/fp1zJs3j3J618jICJs2bYKzszNevHiBAQMG4PLly+jatStpedTU1MSAAQOqnOfKNG3aVK0pYQ6Hg1mzZlHmt1GjRujatSs0NDRgamqKHTt2QFdXF/n5+QgKCpJR+gQCAdhsNgQCATQ1NcHhcEAQBLhcLho0aAAulwtNTU2F05/FxcXYsWMH5s+fjx07dmDlypUybkpARedtampKOdCXWFrDwsKwaNEiGBgYULb/oqIi6OjogMvlgsFgoLS0FOnp6QAqfE0JgoCOjo5ai5wePXqEIUOGyFlQgQqlesqUKXByclKZTmWMjIzQr18/PHjwAL/++isAIC0tDWZmZlXaoUIoFKJr166IjIyk9LmVyKzOnTsjMzMTlpaWpKX///7v/1T63P7f//0fuFwuDh06BDs7O0ycOJFyRnTkyJGUC6kkDB06lHSxo/Jt37Nnj9J8SGNoaAhra2tERUXB3t5e7fsUUVBQgM2bN6Nz587kvtLDhw9HQkICLl++DAMDAzg5OaFTp05YsWKFjEImFAqxf/9+2NvbY+nSpQAq2vfixYthYmKCnTt3UtadLl26kAp25Rmb6pCVlQVnZ2fEx8cjMDAQJSUl4PF4iI2NRXR0NHR1dcFmszFkyBA59yA+n09algHqfk5y75AhQxAVFYUJEyaAy+Vi165dMsYaOzs7pKSkwN/fv0beC6goT19fXwDApUuXwGQywWKx8Pz5c+jp6cHPzw8sFkvOv/rGjRswNzdHeHg4+vfvDxaLhezsbNjb24PNZuPixYv4448/5OQAn89Hr169ZMIki/Aqr/eIjIxEfn6+0kFw//79YWNjQw6SfHx8cO3aNbRv3x67du0CUCGXFA0+2rVrp1Bhp5rFYrFYCA8PR35+PtnWq0tycjKmTp2KNWvWwNLSEtOmTVMYd+fOnXBxccGuXbswdepUtGvXTu2FtepQI0q1lpYW9uzZg6KiIpSUlGDHjh1wcHAgFSbpStSyZUvcuHEDmZmZKi1ed+/eBYvFwpYtWzBt2jTExMQgPDwcu3fvJn1xquqHduTIEfz+++9wdXUFh8PBs2fPSMWBz+cjJycHIpEIr169QmJiIrlASRHl5eW4ePEijhw5InetKotYYmJicOrUKbRp04ayM9DS0oKdnR18fHzg7++vUPlWREpKCk6cOIGtW7eSSsu+ffuwf/9+zJo1C0wmE8nJyTh37hwOHDgANzc3ABUuGSdOnEBGRkaVF0oCwG+//QZXV1f4+Phg+PDh8PT0RFpaGrS1tWXKJikpCQwGQ+H0tImJCUxMTHDjxg2MHj2a/I5r1qyR8+nU1dVFcXExPn/+TKlUN2nShFQI9PX10bhxY7Ru3Ro5OTnIzs4Gg8GAqampSgvM3Llz0bdvX5w8eZI8GY1K+ZVYidSltLQUJSUlpD9rnz59YGhoiIcPH6JFixbg8XgwMTGhXPH/yy+/wNvbGx4eHpg9ezbat2+v8KS27t27Y/369di2bRsiIiJqzL/tzZs3yM3NBVBhqZ8wYQI+fPgANpuNnj17oqCgAMXFxXL1nCAISv/coKAgREVF4dChQ2T9kFghPn78CDs7Oxml+ujRo9DR0UFQUBAmTZqEkpISDBo0CPr6+rh16xbOnTtH+gBSKft6enpYu3Ythg8fDnNzc7x69QoJCQkyPu0EQSA+Pp7SypKeno78/HzweDxwOBzKTigpKQkLFixA8+bNERUVBQMDA2zcuBGBgYF4+PAhnJ2dkZeXh0GDBmHHjh0KyzonJweRkZHQ0NCQOQFO2pLLZDJx6dIlCIVC0gJYlcV1gwcPRrt27XDlyhVMnDgRsbGxmDhxIuW3UiTzsrKycOXKFXC5XJm926URiUSIjIzEu3fvSAUeqHAf8vb2xvTp05Xmk81mo3PnzjK+35Vxd3dHXFxcjQwWVSEUClFYWKi2z7MqNDU1YWZmhsLCQrRp04Zco2BpaYmBAweCw+HA2dkZXLJM38wAACAASURBVC5Xrs6x2Wxs3LiRcqq7efPmcm5D0ujq6qKkpKRG3qFVq1Y4efIktLS08O+//6K4uBjjx4/HmDFjYG5ujoSEBIUGBC0tLcyaNYs0iKiiU6dOuHz5MnJycuQWN7LZbGhoaCj0z64OK1askPPh3rRpE8aOHat08ebJkyfB5XLBZDLRvXt36Ojo4MOHDygqKkKHDh3g5OQES0tLmW8nMQpWtmQ7ODjg6dOnMnJNYsA8ffo0+Hy+wj5WQ0NDxtBgYGCAKVOmyCjzyqz5CQkJVVqkymQyyU0jvhZTU1OcPHkS7dq1g1gslvne9+/fx9ChQ8kwHR0dLFmyBL/++itmzZqF3377re4p1ZJFAbm5uUhOTsaWLVvQq1cv+Pj4yI1++/bti+3bt2PUqFEKF+5J6Ny5M5o0aQKCIPD27VuUlpaCz+fj06dPiIyMJLcl++uvvxAcHKyWb46ksk2ZMgV5eXky1panT5+iffv2cHBwgLW1NUaPHo3y8nKlCtGsWbOwfv16hdOZ6irW3bp1w+PHj8lFXVSKkLa2Nt68eYPevXtXecW5l5cXdHR0ZKyAUVFR8PX1xejRo9G1a1eUlJSAzWajqKgIYWFh0NHRQVFRET5+/Ii7d+9i3rx5VXomUNGZhoSEoH///mAwGDAyMsKMGTOwYcMGmXjv379HXl6eygHSiBEj4O/vDwsLC6WuOc2bN1dYRt27d5drRNV5N6Cijg4bNgzv379H//79le4Qow7BwcGYOHEiZs6cicePH2PlypXYsmULpk6dCn9/fyxZsgSurq6wsbHBggULZO4tKSnB9u3bYWZmBicnJ9y5cweDBg0ilcjKNG3aFImJiZg2bRrloRvVoby8HPv27UNOTg6ACkvaixcvUFRUBJFIBEtLSxgbGyM5ORkXLlyQuVeRi4i2tjY4HI6c7+iYMWPQvHlzuW3SJP644eHh2LdvH8aMGYNt27YhKysLN27cwLp16xAdHY3IyEjS31YaNptNWkb19fVx6dIlmJqayijVxcXF8PPzo/SFbdmyJWbMmIHs7Gw5tycJZmZm2LlzJ8rLyyEWi9GqVSuEhITAzMwMDg4OMDAwQEREBDIyMijvl5CcnIxbt25h7dq1Cp8FVOwJu379+mrtkd6iRQscO3YMBgYGEIlE8Pf3r/LCHj09PUyZMgXu7u4K47i7u+Pdu3c4ceKETMdvYGCgUi6UlZUhPT1d5S4LixYtQnFxscLrAQEBKC4uJn3R2Ww2mEwm2SETBIEXL17gjz/+kPEfpZI1iYmJ0NbWrrEpZj09PTml7fbt28jJyYGurq5S9yaxWIxPnz7h+fPnpMFEQk5ODmWd8PHxwZs3b8BgMKq0GFUV0m2Oz+cjLy+PbEeqniOx/gL/27dcGRcuXICmpqbMQK6srAyhoaHIz8/H69evq/saaqHOWo4nT55Qhr99+xbW1taUp12WlpbKDRQyMzMxb948zJ07V6b9uLu7Q1dXFwwGA+fPnyetzqogCAKPHz/Gr7/+qpbMaNy4sdouNIWFhUhKSiINrzWBtrY2Bg8ejN9//x2bNm0iwyUzNBwOBzt27MCMGTNgaWmJzp07Y9WqVV/t4lqZGt0eoUmTJmAymViyZAlMTEzw119/QV9fHxYWFuTiLCaTienTp0NXV1dpgwgKCoK7uztGjx4Ne3t76OjokJvjr169mhxREQQBJycnOZ8wZRAEgTZt2uDKlSt4+vQprl+/TvoiSaYNrly5gtzcXJW+oB4eHuByuQgODlbo8F7Z94+K4OBgHD9+HFOnTqVUqMvKynD79m3o6OhUa7s4Foslp/gbGxtj2LBhZGcsGbVLrP8sFguWlpa4dOlSlUagElJSUrB8+XJcunSJHLyMHj2aMu7UqVPBZrNVLqAYO3YsOnbsiMzMTKXxpLckqkxBQQEaNmxYY9vuDRs2DOHh4TWyh6iVlRX279+PoUOHYsqUKdDX18fixYsxefJkjBs3Ds2aNcOAAQMon7V161YEBweTU9QjR45EgwYNcO7cOUyaNEnOAsRgMHDx4kUIBIIa22ZMS0tLzsf97t275O4vqqDy18vPz0fLli3lvpePjw8+f/5MWjAlZSKZ+pS05YcPH2LJkiWYO3dulbbyBCpcSSS7GUnTsGFDjB07ltIwEBQUhOTkZPj5+WHVqlUKlZ3KlvpPnz6RFsHevXurtXjN2toabdq0Ubl4+e7duxgyZEi1d8T5+++/MXbsWJiZmZGzZlQoanMMBkOp+0lubi6ePHki51Ii2XdW1aDvzp07EAqFYLFY8Pb2Vrgf9d69exEVFYUXL15QXg8JCUFAQADmz58PFouF4OBgcDgccu9vgiDIfk7ZOz948ADPnj1D3759v+lBLkCFhVGV7GGxWBg1ahT27duHjx8/ytS9U6dOUSr+fD4fdnZ26Ny5M06fPo3MzMxvcuqjskFOZZhMpowcUaZYh4aG4sGDB9i4caNMOIPBgK6uLmbOnIn9+/cDqLCyhoaGKuyfqos6a0moePLkCRYuXIiYmBjK64cPH8agQYNkDIkSQ+OIESNQVFSE1NRUPHz4EMXFxdi0aRO8vLxU9puVefHiBcrKylRuZhAXF0ceRGVtbS1jvHNxccGDBw/w999/o0OHDsjLy8OVK1fQpUsXlW6xVcHKygqnTp3CpEmTkJSUBA0NDQwbNgyenp5gs9lISEjAu3fvMGfOHJSWliI6OhrPnj3D5MmTaywPwDc4UbFRo0ZwcHAAQRCYOHEinj17htOnT+Pq1asAKjq+lJQUtG7dGvn5+QrTEYlEsLa2xsSJE5WuxGUwGOjXrx8iIyPVOtJT2v+6X79+iI2NhVgsRmJiIlatWkWOlLOzszFu3DikpaUptQCdPHkSbdu2VftQAUX7W1pYWGDKlCkKfYol5VZaWorp06crPRyAStA4ODjILYISiUQyi8iOHj2K+fPno0GDBjJTydWlrKwMPXr0UOsggyNHjiA/Px+rV69WuovL6tWrkZeXJ3OqHtVsQGFhoUIF/enTp3j79i369OkDDw8PODg44MaNGxg2bBhev36NnJwcNGnSBAsWLJCZhqYiOjoaiYmJeP36NebOnavyPdVBshpe4m6TmZkJd3d3melvqm8cHR2N9evXy8QZOHAgHj9+jLS0NBmlWlJeS5curdF9e6mQWGNVwWAwcPv2bSxZsoTsvPl8Pi5cuIA1a9bILNCT7O4gveOOon1deTweEhMTq3VoTWZmJng8ntw0a1ZWFm7evIkzZ87I3bN7926MGDECDg4OVdrpRSwWq+0qkJeXBzabDQMDA4UKtXSbGDZsGDZt2oTffvtNoTuQMoyNjeHm5oa5c+eSsrwqGBgYYMiQIUhMTER6errcAOvVq1do3rw5tm3bJmNl09LSwtixYxEZGak0fQ6HgylTpiArK0vhDitlZWWYNm0auSsCFUuXLsXixYvJAZwyZV7RAOLUqVNITU3Fpk2byBMiL126hE+fPsHW1lbtBbPqoqmpqdZgaciQIWjVqhU4HA45Y5GamopVq1aR/WtGRgaOHj0KR0dHtGrVCjY2NvDz88OTJ0/Qp0+fGj88hyAItReq8Xg8HDp0iFJJTkhIwKJFi3DkyBEUFhaiQYMGuH79OjZv3kyuh/j999/x559/IiwsjHQ9LSgowOrVq7FmzZoqu1Sqg6mpqdoHv0gjEomUzkZv27YNwcHBeP36Ne7evQuRSITdu3djwIABYDKZuHv3Ll69egWgYjYdqDCyPHnyBDNmzMC5c+dUGpX69++Ply9fqrX13r59+9CzZ0/weDwsXLgQ58+fJ906hEIhRo8ejTt37iAkJAQGBgbQ0tIit76rSWxtbREbG0v660u2KAQqjBgSBXvevHkoLCzEhg0b5PzSv5YaOVHRyckJLVq0kJm6kT5S1srKSmaq7NmzZxAKhZgwYYLCjo7D4eDNmzfkYjZFFeDq1asoKirCkiVL1Oo0GzVqhG7duoHFYuGnn35CRkYGHj16BHd3dwwYMIDsoAwMDKCpqYnTp08r3NYGqHAz+PDhA3JyctCuXbtqdVhAhaV66dKl+Pnnn2V8lyUNS0NDA0ZGRujTp49ai9Ykq+Elv0OHDuHMmTPo2rUr2dGnp6cjOzubXJFuYGCAsrIymJmZyXRsIpEInp6eag1aJMTHx+PgwYPkkbuqGuaAAQPIPVMV+TIHBwfj8+fPWLVqFa5evQoLCwsZ1xxpIfT+/XuZBY3SdO7cGXl5eYiLi4OdnR0GDRqEtm3bYvTo0dDV1cWCBQtgbGwMKysrpdPJIpEIFy5cwNSpU3H69GnY29sjPT0dBgYGNbpHdmBgIAoLC+UGXJWFroaGBszNzeWULF9fX7Rs2RJdu3YFg8EAn89HTEwMmjZtioYNG6KsrAwdO3aEjo4O8vPzv9qFpTJHjx7F5MmTVU4NikQivH//HpMmTSIHRCwWC5qamnj48CE50PP398erV69w8uRJhSdFSu9okZCQAE9PT/Tv31+p/15ZWRn4fL5MXQ0ODoahoaHc0ehbt24l/eilrXdnzpyBlZUVJk+ejBcvXiAtLU2tPZGLi4uxYcMGNGvWDIMGDVIaVyQS4erVq7h37x4iIiJQWFiIqKgoiEQi3LhxAxYWFjL17+3btzhw4AB69eoFc3Pzan/fp0+f4sOHD0oXdilTBDp06ICQkBCEh4ejd+/eEIlESE5Oxu7du+Hl5QUXFxdK+dm+fXt4eHjA0tJSpo959uwZLl68iBYtWsDBwQE6Ojrw8fGBl5cXQkJC0KtXL5k+wcPDA8uXL8ewYcMU7sQkcftQReX3FAqFmDNnDjw8PKCtrY1///0XOjo60NbWxtOnTxEdHY0NGzbUqBsFUKFQf/r0Cf369VN5oAmDwcCnT5/g4eGB169f4+PHj7h16xZKS0thbW0NHR0dZGZmwsnJCdra2mjYsCE6dOiA9u3b4+7du3j58qVKv/aqIilrZQMdCXfv3oWJiQnOnj2Ljh07ygzMWCwWwsLC4ObmhoCAANja2kJfXx9jx44ln9GgQQMwmUwMHDgQrVu3BoPBQKtWrdC6dWu0bt26WicvqsLBwUGt7esq07ZtW3Tp0oXybIKAgAAcO3YMenp6EIlE6N27N6ZPny4j87p06YIRI0ZgxIgRpD7BZrMxYsQIjBw5Uq3+qSrr1RwcHNCrVy+MGDECf/zxB1kXGQwGevbsSZ6aOnbsWDg6OmLMmDFV2jWmKrBYLJiamsLc3FzGws5gMGBgYIAGDRpg5MiRcHR0pFwU/7XUSM+flpaGO3fu4O+//5YJb9KkCQoKCmRcByRW2XPnzsHGxkZuf0wJJSUl0NLSQmFhodzuHm/fvoVAIEC/fv0QFhYmc2CDKjp16iRTUQYPHow5c+bg1q1bMspIREQEHj58iPbt28vcn5SUhKZNm5IVws7ODmw2G2vXrsWwYcMoFQcul4udO3di8ODBpOUzPj4eJiYmZAf3888/k8fHikQiMo8EQSA7Oxs+Pj54/PgxJk6cKGOJS0xMRGRkJIYMGaJUoS8uLsaAAQPQsWNHsuG1a9cOzZs3R3R0NJo3b47hw4fj7NmzWLBgAU6fPg19fX1wOBwEBQUhKCgIU6ZMUauMgYqOcNy4caT/syof8NTUVOzevRuenp6Uis+HDx9QWlqKHTt2oLCwEOnp6SgvL0dqaioaNWpE7gUqeQ6LxVLayVRezCTZ5UOy4l/ZQSvPnz/Hu3fvkJqaipEjR4LBYMDY2Bjbt29Hnz59yCnymiAmJgaXLl1SeHqftHU2MjIS58+fx549e9C1a1cQBAEvLy94e3uTOxp8+PABrq6uiI6OhqurK0xNTdGpUydMmTIF69atw5MnT1AD42wZhEKhWq4xQ4YMwd69e1FcXCyj9BAEgczMTBQWFiIsLAx+fn5q77XKYDBQUFAALS0tucWxlVm3bh1SUlIwd+5cxMTEICUlBQKBALt375aLGxkZCScnJ9LCd/LkSVy5cgWzZs3ChAkTwGAwYG5ujmPHjiEhIUHl7jkCgQA//fQT5TaflTlx4gS4XC5YLBZycnKQn58PQ0NDaGlpkUdeS2SBQCDAxYsX0bVrVzx+/Bh+fn5wdXWt1t70DAZDZi9fquvKYLFYmDdvHs6fP48tW7YgISEBQqEQmzdvxpo1a2T285VGcipt5cV00dHRCA0NxaBBg0jr9MCBA5Gamopp06bJKQRdunTBoUOH0KlTJ3VfWe13ZLPZmDFjBvLz8zF06FBSrnfs2BF79uxR+4CTqtK2bVulfuqVGTp0KAYPHkwesrRw4UKZPsvc3BxPnz6Ftra2jAy7cOFCtV0ZlKGtra22S5a9vT20tLQwffp0uXVODRs2xKFDhxAaGkr6l1euS5XXAbDZbKW7RNQE1TWuMBgMDBkyhPJa586d0bx5c0ydOlXh/cqU4W9xKJqkrkgfSEXVVr6VIl1VpA9Iq3GIGiAtLY3YuXMnweVyibS0NILL5RICgYA4cOAAMX/+fOLAgQNk3OLiYmLXrl1EYGAgkZaWpjTdoKAgIiIigsjOziaysrKIO3fuEFu3biXOnDlDiMViQiwWE1wul4iJiSG8vb3JMGW/Dh06EBwOh/w7LS2NGDJkiFw8V1dX4tdffyXu379PhuXm5hIDBgwgTp8+LRP32bNnxKlTp4jCwkIyrLCwkMjOziauXbtGzJgxg9iwYQMRExNDiMViIjk5mejXrx9x+fJlQiwWEyKRiLh69Srx4cMHwsbGhrhy5QqRlZVFzJ49m5gzZw4xb948wtXVlYiPj5d5bnZ2NrFw4ULC3t6eiI2NVVqWycnJxKlTpwh3d3fC39+fuHDhAhEVFUWsXLmSmDhxIrF7926CIAgiMDCQWL16NbFv3z7CxcWFWLt2LXH16lWitLS0SnXi+fPnxJQpU4i+ffsSKSkpat3z7NkzIi8vTyYsKSmJWLp0KTF37lziwoULBEEQxOXLlwk7Ozti06ZNhL+/P/HlyxeZcrl37x4xd+5cQigUVinP6jJv3jyiW7duhLe3Nxn25s0bYuLEiTX+rJycHOLAgQMEn89XGTczM5OYPXs2cf36dWLevHmEt7c34e7uTly7do0Qi8UEQRDEtm3biEmTJhH3798n74uMjCSGDRtGREdHE1wut8bfYcOGDURhYaHacTdv3iwTFhcXR7i5uRHx8fHEp0+f1E5LgkAgIDgcjsp4X758ITZs2EBMnDiRmD59OvHixQvKeIWFhcSIESOIT58+kWGlpaWEj4+PWjLoa388Hq9a9+Xn5xPZ2dnVfu6FCxeIwMBAymvqUlJSQrx8+ZJISkoicnNz5b5LQkICcefOHbn0CwsLiW3bthFFRUXVfneJvK3uj6b+8j3a5ff4cblc4vbt28S5c+eI0tLSWs8P3U7kYRDE16+u2r17NzIyMtCzZ0+4ubmhf//+aNy4MYKCgrB9+3aZrb+cnZ2RkpKC0NBQsNlsXL58WeHuGgRBYPv27eQJWOXl5fjzzz/Rvn170u/24sWLePXqFUpKSrBkyRKFi3tCQ0Ph4eGBz58/w8LCAo6OjrC1tYVQKERGRobMfsRbtmxBcnIyhg4dimvXrmHr1q2wsLAAl8vFsWPHsGzZMpVTqLt27UJiYiJWrFiBlJQUODg4kCO3goICuLq6YvHixdDS0oJQKMTChQtJq31CQgI2btyIV69egc1mw9zcnNLPuLy8HOfPnwefz8f8+fOhqamp0JJSXl6OjIwMREZGwsPDA46Ojhg2bBhyc3PRtGlTiEQi8jvw+Xzs2bMHXbp0waBBg6o1ZZmXl4fU1FQUFBSgX79+ao+O//33X8yfP5/8HjweD2/evEGvXr3I/AkEAly/fh3NmjWTO0yhoKCA3MVEusyquluKMjIyMlBWViZjzebxeIiIiFDLNedbIxKJ4OPjgy5duqBjx461nZ0qkZiYiKVLl+LEiRPffIFXdUhKSsL69evh5OQEY2Njtdy9akDE1hpZWVnQ0dFBeHg4vL29sXXrVkrZp077io2NhZOTEwwMDJCRkYGRI0ciPDwcFhYWEIvFyMnJwZ07d7Bp0ya5Le8IgsC5c+cQEhKCnTt3VmmLyuLiYjg7O8Pa2rpa+0XXpOygqTvUZLusTh2pzvO/fPlC6kTHjx9XeqBcbfFfby81olQXFBSgrKwMDRs2REFBAbk1XdeuXeWEX3FxMXnABkEQKncEkM5eSUnJNz9Su6bgcDgoLy+vkT0Yq0J9r9CbNm2CgYGBWlOClatuZmYmdu3ahcGDB8sd1iFNfS+jH53bt2/D09MTzs7Oda7T2LZtG7hcbpUOAZFQH5Xr+fPng8/nw9TUFA4ODpS+r+q2p1OnTiE/Px9Lly7F7du3ER8fD3t7e4SHhyMzMxPBwcFYvHixjEJducxcXV3Rrl27Ku0zHRISAoFAQLn/vypoWUHzramPckERdHupIaX6W1LHs1fnqO+Vms/nY9++fbCzs1N4SISEynVj3bp15JZCqrYYk6a+l9mPyIsXL9CjR49qLfL5lgQEBKBPnz7VXpAsob7INV9fX4SHh2PJkiXVtlDXBN+7vGiZQPM9qS/yQBV0u6GV6h+OH6FSCwQCeHt7K911Bfh2deNHKEOa+kF9lW+10Ua+dVnR7Z6mtqivckAauv1UUOeVauDHqHDfi/9Sxf6e9eK/VK40tUN9kXO13RZqupxq+31oaID60/4VQbejCuqFUg3U/wr3vfivVezarBf/tbKm+X7URXlXF+v715RTXXwfmv8udbHNqwvdlv5HzW9YSEPzH0GVEKQFDU11ka479MBRMZXzR7dJmvqKsiPXaeoP9UappiscTX2Dqr7SnTpNVaGqM99SFtbnOlqf805DQ1P/qTfuHxLqWXa/O/+1TqU+14f/2rei+bZUpy3QdZCGpm5R3/o0WobIUm8s1RJoizXNjwIhdaw6Dc3XQtclGhoamtql3lmqgfo3kqttfvTO9keoDz/6N6KhoaGhUY/61KfRfZcszNrOQHWgP2LVqE8NtDowGAy6TtDQ0NDQ0NDUKvVSqQZoxVodpJXpmlCsCYIgf3WR6ijXkntquz7V1TKloaGhoaGhorb7zbpIvVWqaWhoaGhoaGhoaOoK9W6hojT0okXlqLOHK0EQYDLVH1uJxWKZtKW/gfTzanMEK3k2vWctDU3VoBfP0tDUPt9Ct1HWtul2XzMQBFF3lOrg4GDw+Xz07NmzSvepq0D9l6BqHGKxmHRzkJSVtDuHOg1K2vVDWpGWTrvy8+uCcl1TaX3rOkYLNpraRLp919V6WNfzR0OjDlT1WCL/K18Ti8Wk4Uu6j6gcLt0/SffHld02Fe17ryot6WfXB1nxvSF1qbqw+4eXlxfevn2Ld+/eYdy4cVi6dGm10qkDr1LrKBuJVlagq6r8Su4Xi8Uy6TGZTJkGxmQyFSrZknS+5l2+Fcry9b1mRWgBRVNbVO5I6xqV219dzCMNjSpU1WPpvrRym5RWvGvDCENlxKTbYQWSMql1n+qHDx8iOTkZmzdvxpo1a1BSUoLi4uJqpfVf/rjKFD7JNbFYDJFIJOPCUZVFehKFmcVigSAIiEQiCAQCMBgMiEQiiEQiGWWbyiJeFcW0ri+MpKH5EZDuoKWtUnWt3YnFYlJ2SWQNDU19Q1KPJX0olZItmQEWCoVgMBgQCoUyCrUkXFl/XtmaTNXXS/IgeYYq3aC+yIrvRWVjJYPBUKxUf/jwATweTy48Li4OGRkZCh/C5XLx8eNHuXCRSISXL1/KhVtaWmLmzJnQ19eHra0tAgICcO7cOfL6q1evyA+tjFevXiEmJkamEvB4PFy6dEnpfXw+H2/fvpULj4yMRG5urkxYYGAgSktLKdOJi4uDQCBQ+qzS0lLKsiMIAnFxcZT3eHp6Ijs7Wy68cmWv3JAkSq6k8ZaVlaG8vJyMKxKJwOPxUFJSAoFAoFbDKCsrQ1FREcrKygAATCYTTCYTXC4XIpGItFBXJiUlBSkpKXLhJSUl+Pz5s9JnSpDO28ePH/HhwweFcZOSkiAUCuXCQ0ND5ep0eXk5Zd6kcXFxkRvohYeH48mTJyrzHRQUBC6XS3mNz+fj3bt3KtMAgMuXLyMzM5Pymru7O0pKSuTCxWIxTp48SfldBQIBXr16RZleaWkp3rx5Q3nN39+fMlwgEMi175KSEpXvV1RUpDTOx48fKcsvJSUFaWlpStOOi4tDeno65bWgoCBwOBzy76SkJKSmpipMy9XVVabtl5SUwN3dnTJuYmIipSzIyMig/E4FBQXIz8+nTEeV7AsNDUVhYaFceEhICF6/fi0Xnp2dLfPe0ggEAnC5XJSWlkIkEgGQbXf379+Xk1+lpaVK2/Dz588RHx+v8HphYaFMvS4tLZX7rtKySSAQgMfjye1sVFBQQCknFckCoOIbZmVlUV5TlJ6ElJQU8Pl8ufDHjx8jJiZGJszLyws5OTkK05I878qVKzJh8fHxePDgAWX8rKwsREdHy4SFh4crzDNBEHj+/Dnltffv35MyvTIZGRnw9PRUmvcTJ05Q9otisRhPnz5VeN+7d+8orx8/flwmvaKiIpw/f54yDSrZFxYWhocPHyp8bmpqKuX75uTkoKioSOF9CQkJMn+Xl5crlRm5ubkybVO6HvP5fJSWlio1Qkn+X1RUJOd2CVTUX+m6LWm/PB6PbL8AyL6ey+XKySWJrlC5DMvKylBcXIyysjKF/UdJSQlKS0tJGSUd7/Pnz5Ry/e3btypl2suXLymfKRQKKXU1aTgcDlxdXZXGkUBVD3g8Hr58+aL0vri4OLn8SZexQqU6LCyMUvgmJiYq7cw4HA7Cw8PlwoVCIWUhN2/eHEZGRgAADQ0NtG/fHra2tuT1N2/eKBSK0piYmKB58+YA/qdgamlpwcLCQul95eXl+PTpk1x4fHy8nID6/PkzZQcGVPiES5RWRfB4PMqyIwgCISEhMqM/XKQTdQAAFe1JREFUya9Lly4wMjKSC5d8VB6PJxOek5MDgUCAsrIysoPk8/lkg9LQ0ACLxYJYLAaXy0VxcTGZby6Xi7KyMvj5+ZFKeWXFvLCwkHympqYmtLW1weVyyb9ZLJbcu6WnpyM1NVVOgBQUFMh1QFRIhI+Eli1bwsTERGH84OBgSqUmISFB7vvxeDxERkbKhBUVFeHWrVvk3927d4e2tjaA/9Wtli1bonXr1irzHhUVpVBQl5WVITg4WCZM0cBGUg+osLS0hI6Ojlw4k8lEr169KAc65eXleP/+PWV6RUVFCAoKkgsnCEKhwCsvL5cTeAUFBQgNDaV8hoS8vDxEREQovB4REYGCggK58LS0NJXCLzExUaFSHRUVJaPopKamKpVr3bt3h6amJvm3jo4OrKysFOaZSuGKj4+nlKlZWVmUg+24uDiZzpGKmJgYSoWtZcuWaNWqlVx4YmIipSLJYDDIjlIySJaESzAzM0Pjxo1l7ispKVH6/Vq2bEnKZSpyc3NlDArFxcUy/Yd0XWMymRCJROByuaSckVzPyMhAYmKiXPohISEK+4/CwkLKe4CKwYey+hAeHk6pSLZu3RotWrSQCevQoQMMDAwUpgUA+vr66NKli0yYiYkJfvrpJ8r4mZmZckpefHy8wjZBEATlIAuoKCOqwR4ANG7cGJ06dVKa9549e0JLS0suXJEhTYKpqSlMTU1Vpqerq6uwrVlZWZGyWUKrVq0o05UQGRlJaTBMTU1FXl4e5T0EQSAoKEimPvJ4PIXGMKBCRkkMc1T1mMfjgcViKZwpZjAYYLFY4HA4cvWdxWKBy+XK+ELz+XwUFxeTSrVEJ5C0GYkBTRqJ62ZxcTFYLBaZVmlpKQoLCykHHwwGQ+ZZlTcvAIAWLVqgZcuWcvd+/PhRpUx7+/YtZR/D5/MpdTVp9PX1FdaVykRFRckZbIqKihTKBAkfPnyQs+hLypjL5dYNn2oJ+fn5mDdvHm7cuFFjadbW64nFYpw9exZv3ryBo6MjXr58ia1bt0JXV/er0nVxcUFhYSHmz5+PtWvXAgC2bduGRo0aobi4GGvXroWxsTF69OiB7t27Q0tLCwwGA3p6etDQ0ABBEHINmSAI3Lx5E2/evIG2tjZsbGwwZMgQEASBDx8+4MqVK+jYsSOWLVsmc4/EnURDQ4OcjpKkrcx1Q5kQkbB//36EhYXBzMwMIpEIWlpa4HA4aN++PcaOHQt9fX3o6+t/VVlK3kMagUCAGTNmICsrC3v37sUvv/zyP18pqV1SvqVP23/ZjYnm+1N5oTEgP81b20gsakBFOxQKhWCz2VXauYiGprapSj0Wi8UQCATQ0tJCeXk5NDQ0wGQyyXBJvyuZMa7cP0kUP+kZ5Mr9lnQfzufzwWKx5PQDaQWSSibUNVnxPaHyLa9TSvXhw4cxYMAAdO/evUbT/d6vKBaLceHCBURFRWH8+PEwMDDA2LFjsXv3bvz2229flXZhYSGWL1+ONm3aoFOnThg7dizY7P9t4iIUCnH8+HF4e3tj8ODBWLNmjYyyC1CvDBYKhYiOjsa6detgb2+PmTNnko2poKAAZ8+exc6dO9VuNJJ0K0/1qFocKQnLysrCixcvMGrUKNJCGBMTQ7pcWFpaom/fvmrlRVU+peFyuRgwYAAePHiApk2bygwOpK3w0u9V04LkvyaYaGoXRYPD2lgIpQxVnTsNTX1A3Xos6XckinRlH2bpGWtFiq6ia5X/L3mGqvgSqK7/F9silVJdp4b506dPr3GFGqi5Y6wJglDqHyjhzZs38PX1xYIFC2BtbQ1zc3Ps2rUL/v7+lNPqVcHAwACHDh1CQUEBOS0kWfggFovBYrGwaNEiDB06FAYGBtDS0iLdMio3Sun7gAp3mR49esDOzk7mWoMGDZCVlVXtwYkyfzGquADQsGFDPHv2jLTGAxXTqIsWLcL48eNx8eJFpf5s0ggEAsopJ6rna2howMzMDGvXrpWZaqpcbtLhNDT1mcoD7LraSUpb4xSt36ChqetI111l9ViyMYBk6zxpJVzitiHdJiR9E5UyXfmasmeoii/Jh+T6f3lwW9klVywW175SLRaLkZ6ejr1796JBgwYQCARwdnam9MtWRFZWFu7cuaMy3td+/JycHMyaNUtlvL59++LGjRto06YNGRYZGQlra+saGTRI/DWHDx8OQL7zc3Z2Ro8ePTBu3DgyrHLjqNxgGAwGDA0NYW1tDQ6HAzabDTabjczMTBQVFaF3795yU1RCoRBCoZDcBaSyki5B2i+7cn4VKdapqakICQnBmjVrZK4VFxcjNjYWv/32m4yFXhl79+6V85uurORL/tbS0oKXlxe2b9+O5s2bIzc3F/fu3UN5eTlEIhH4fD7pr0ZPPdP8aNShiUtK6nr+aGi+FkVuk+rcJ/0v1Yy0ov62ct9MlRaNenxzrYDH48ksVoiIiMCzZ8/Ij3X9+nWMGzcOycnJWLNmDXr16oX8/Hx07dpV7WdERkaqpVRLeP36NV68eCGzsDA0NFTh6uiqoKjyCQSCr/anlhATE4O0tDSZ1eLSDYjBYCAmJgZHjhyRuY8gCOTn52PHjh1YtGgRTpw4QcaXbJXn6emJ+Ph4aGhoQFNTExoaGti7d6+cApmamgp7e3tMnToVz549w+DBg/H69WsIBAJkZ2fj+PHj2L9/PxISEjBr1iz8/fff8PLyUjjNVRkzMzNs2LABmzZtkgnX19fHy5cv4e3trbbgYTKZlKviFSnWAHDs2DGEhobi4MGDcHNzg7+/P7Zu3Yrc3FxyeyNJ2SlKg4amPiGRA3W5A/0vW8VofhyU1ePK16RnSQFZH2YqN4/KfZLkmrK2LbF8K0ur8rPruqz43kjK5JufqChR7CT+r56enigqKkK/fv3AYDAwYcIE/P7776TSJn1KkLqIxWKVO29IiIuLg6+vL9hsNp48eYJp06ahvLwcV69eBYvFQv/+/RXeW12lKT8/H0ZGRrCxsanyvVSI/7+9+4+Juv4DOP6E4wg9FO6CI0AR8MQfwcTQmbTbsjAzMxZD0rLZ5u/SpknDMVsEo2yWNEy0/hCatn64ST+kP2xNTUILDUHkh3grEClJEXAW3MHx/YMvH4HujgMBCV+PjSns8/tzn8/n9Xnf6/16W61MnDiRLVu29Mir6rJx40beffddFi5cqGxzWVkZcXFx5OXlsW3bNn7//XfWrFnDH3/8QVpaGi4uLuh0OjZt2sTMmTNRq9UATJ48meTkZHbv3q0s/6uvvqKgoIDMzEymTp0KQEREhFJXs6v6SGtrKxqNhpCQEC5fvuywR3bv/M3i4mKOHj36r4GAjh8/TkVFBfPmzXNYAaRLa2sr69at44svvuCxxx6zud7eAXJxcTH5+fnEx8eTnp4OdJaS++abb3j66af77MkvhBBCiHvPkAfVtbW1JCYmUlpaSlBQEGvWrCEgIKBH4Ny9A1jvkmzO6OoN6wyDwcDbb78NQGZmJseOHSMiIoKXX34ZPz+/Pud3VA6m91vb+fPnef3112lvb2fJkiVkZGSwefNmp4JBR6xWKxUVFTzxxBNK79+usi4dHR2o1Wr0ej1Lly5VUjGsVivNzc1K3nVoaCgff/wxxcXFyhtpdXU1mzZtIjk5mbi4OGV9eXl5GI1G5fcrV64QGBjItGnTlN7DXRVGrFYrOp0Og8GASqWiurqa1NRUpZezs2pra/n222+ZNWsW2dnZ3Lx5k9jYWHbv3s2zzz7LqlWrnFrOTz/9RGNjo1Pl76Dz/B45coR169YRFRWl/L28vJyXXnqJCRMmyMATQgghhoWthjMxcg15UP3GG2+wb98+SkpKyMrKslt3cyCuX79OTU3Nv/J4W1paKCoqYt68eXbnNZlMnDt3jrfeestmPVfoTF3JyclRCqAvWLCARYsWcfbsWaKioqipqeHw4cPMnj3bZiUKg8HA7t278fX15ejRo1y9epWMjAx27tx5R/sdHR2ttBx7e3v3uOgsFgtbtmxh2bJleHt7K/NMnTqV8+fPM3bsWOrr66moqGDHjh1s375dmXfSpEl88sknhISEKC249fX1lJaW9qhPu3btWqVOZWtrKy4uLmzYsIGgoCDc3NxwcXHht99+4/jx42RnZ+Pq6oq7u3u/WvoffPBB3nnnHRYvXkxYWBgtLS3MmjULg8GAwWBw+G3G9u3b8fDwoKOjg7i4OLy9vTl06BBGo5Hi4mIyMjLYtGkT8+fP73HsXF1dMZvNNgdZiYyMxGKxUFtbS3h4uMOvvSQPTQghxGgkzzXHhjyn2mq1kp+fz3vvvedwEABnNTU1sX79epYvX87KlSuVmtYdHR2sXLmSmJgYEhIS+PDDDx0uR6vVsnDhQq5cuWI3v6lrxCBfX1/8/Pxobm6moKCAFStWsH79eqqrqykuLsZkMtmcf8yYMUyZMgVvb28SEhJ4/vnnmTNnzh0fg8LCQl544QVWr16NSqVCq9UqP3q9Hn9/f0wmkzIypYuLC2q1Gk9PTz744AOqqqpQqVSkp6crg5x0dHTWz8zLy+PIkSOYzWbMZjMnT55k0aJFLF68uMc2VFZWUlBQQHNzM7du3eLgwYOYTCbc3d1xc3PDy8sLHx8fvLy8BnQRqtVqDh48yNatW5WXFo1GQ1hYWJ/fZjz11FOEhoYyefJkLly4QHV1NRs3bqSxsZE///yTJUuWMHHiROW8d+9BrVKpWLVqFTU1NVRWViova0ajkba2NtLS0lCr1UN2Y5EblhBCCPHfNOQt1XV1dWRkZACdo/TYGvmtPzQaDatXr0av11NUVER0dDSVlZUEBAQQFxdHYGAgJpPJYf4udHZ48/PzY8+ePfj5+RESEvKvr1n0ej1bt25Vfm9ra2Pt2rW0tbUxZ84cJk2apOSGO+P9999Hq9WSkJAwsJ3/P39/fxISEnj44YdtDoCyceNGTCYT5eXlyrb9/fff5Obm4ufnh9FoxGw2s3fvXpKSkpQW5JaWFsrLywkKClKqecydO5ddu3ZRVFREcnKyEnympqayZMkS5s6di0qlIjw8nPvvvx+VSkV7ezuRkZEUFhY6LJsH9oNInU5HbGzsgD4v0dHRPUbl/Pzzz8nKyiI9Pb3Pz0VXWRyj0UhdXR2hoaG4urrS2NhIWVkZXl5ePUbWc9TyPtLq/AohhPjvkRSQ/44hb6murq7mxIkTrFixgjNnztzx8tzc3Jg9ezZBQUHExsbi6+tLQEAAU6ZMwWg0EhoayoIFCwgLC3O4nF27dpGWlsa4cePQaDTK3x31ym1oaCA9PZ34+Pg+gzNbvLy8bA6P2uXmzZtOLcfNzY329na+++47mxdadnY2DQ0NREdHK/uTlJTE5cuXlX1VqVRERETg4+MDoHRmvHLlCo888ohSLk+j0fDqq69y48YNzGYzFouF77//noceeogXX3wRHx8ftFot06ZN65EiUlVVhcVicfpG0PuYnz59mtzc3H5VgemuezUOFxcXHn30UafnNZvNtLS04O/vr6QWXbp0iR9//JHExMQey3dmO4QQQoj/Omkk6psqJSUlZagWfuzYMbRaLQsWLECtVmM0GiksLMTV1XVQKyh0BWDOtADX19dTUlJCVFQU8fHxuLu7YzKZuHjxIj4+PkrQaSu4/ueff/jyyy+JiYlR8pVtfciam5s5e/Ys/v7+SstubW0tn332GYmJiXbTYHJycigtLcXT0xOdTmd3H7pKujU2NtrM5S4vL8fDwwMvLy8CAwMBcHd359y5c2g0Gm7duoWPjw8pKSnMmDGDMWPGoFarGTduHP7+/jzwwAOMHTsWV1dXWlpaqKqq4vHHH1em02g0TJ8+nY8++ojLly9z4sQJrl+/jslkIiwsDLPZTFNTE/n5+cTExDB27Fi7b9rdywB26RpkR6PRkJOTQ2hoqLIf9o65reV2/ezdu5fjx4/z3HPP9Tkf3D4Pt27dIjw8nNraWn7++We8vb171Mfu3hLtqDySs+SGJYQQwpaR8HwYCdsw0g16+kd9fT07duxg/PjxJCUlMWbMGH799Veys7M5c+YMy5cv79EyPFj6OtnFxcUcOHAAi8VCXFyc0pL9yiuvMHXqVCZMmICHh4fD5Xp6eqLX69m/fz+pqal211VSUsLmzZsJCwtDp9Ph5uaGxWLhzTffZObMmXbnW7ZsGbGxsRQWFrJnzx6b0+Tl5XHy5Enq6uqYP38+x44dY/78+UBnML9z505SUlLYsmULBQUFtLe3M2/ePC5evIinpyd5eXkcOnSIffv2YTabOXz4MJWVlezfv5+UlBTKysrQ6XRkZWXh5uZGZmYmPj4+jB8/ntzcXLZu3UpAQACVlZX88MMPGI1Gpk+fzoULFzhy5AgGg4GgoCB8fX3566+/OHfuHDExMcqxtJX60fvctbW1cerUKTw8PAgODqaoqOiOctGffPJJpyuudHR0sG3bNqxWKwcOHKCiooJffvkFrVbLa6+9xn333Wd3XrnhCCGEGI3k+eYcl45B/n760qVLLF26lPj4eBITE5UgJD8/nw0bNnD+/PnBXB3QOdLhqVOneOaZZxxOd/r0abRarVJbGaC0tJTw8HCn1tPa2srXX39NZGRkn+klJSUlNDU1KeXuDAYDer2+z3V8+umnzJgxw+7IixUVFTQ0NCi/BwcHExAQoASr165dQ6fTUVBQAHR2yJwxY4YyfVFREVqtluDgYK5evUpVVZUyzalTp7BYLGg0GqKiojCbzdTV1REcHExHRwfXrl3D19cX6OzEeePGDSZMmIDVasVsNnPp0iUMBkOPlInIyEilY6G9lAlbF6ujC3iwLm57H/3uwb+tAvtd8w72TUZuWkIIIRy5WymF8nxyzqAH1eLu6KvDnKPfu7cY27twbI0+2Hu0JnvrcLQ+e4Y6qLY1AqK9EaK6l2x05lgNhNywhBBCOGO4wzZ5PjlvyKt/iOHRn97Btqbt66JxtPzeQ5p26aqk0Xvo077WN9wXsLPHbajqT8sNSwghxEgkz6f+kaD6HmUrAO4KnB21Vtsrh+coSHcmkL5b+tPpsfv/R+K+CCGEGP26pyEOx3qE8ySovgc424ptL7B2Jg/aXt6xrWlHSit1Xy8Rvaft/u9gboMQQgjRX0NZv1qeTQMjOdWjSH/TGByxFVQ7ao12tExnL87Bnq4vznaalJuWEEKIkWywnlPyXLoz0lI9ijj71urMV0d9dW50NJ+t1A9nt2k43c1RquTGJYQQYrA428jlzPxi4CSovof1Jy/LXo1pe8t0NI2jeYZb7/J5w7VOIYQQYijIM+bukfSPUWggp3SwPgb9qd880At/qG8YjtJC7uQ4yY1OCCGEGL0kqB6lBnpah+PjcKfB5VAGp0OVZy0BtRBCCDG6ufY9iRBCCCGEEMIRyakepe5mJ7zeRmMrbX87hQohhBBidJOgehQbSGA9GMH4vRJI2suzvlf2XwghhBC3SVA9yg2kg50zgbUEjrfJsRBCCCGEBNX3iP7WsOxrVEQhhBBCCHHb/wDK+F4kpQqCkwAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "a58aaa5d-1291-4b9f-954a-1c274a8d4b54",
   "metadata": {},
   "source": [
    "![image.png](attachment:554e0426-3b9c-472b-ba88-23b1f8c9a550.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "dcc5f006-e8e8-4a01-8bcc-0fe6c26475ee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{3} + 8 x^{2} + x \\left(b + 3\\right) + 21$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =4 p x + x^{4} + 6 x^{3} + 13 x^{2} + 15$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq( x*x*x+8*x*x+(b+3)*x+21,'P',var=x)\n",
    "Q=MyEq( x**4+6*x**3+13*x*x+4*p*x+15 ,'Q',var=x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "9947ab8f-92cd-4564-b135-e40e1e4bf656",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle M =x^{2} + x + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M=MyEq(x*x+x+3,'M')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "12e4ffe8-2a3e-43b9-bd75-521fa81cedde",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# if M if fcator then.---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "6e542a90-1928-4652-8cdc-80588005899d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R1 =b x - 7 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R1=P.rem(M,'R1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "67dc8a9f-a570-4d5c-af0a-112dd1840b21",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R2 =4 p x - 20 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R2=Q.rem(M,'R2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "af87561c-1a41-4136-969b-78613c8d1bd1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =7$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b=R1.solve('b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "d57f2c9f-4ff3-4f85-a560-6017200aacf7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle p =5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=R2.solve('p')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "60172766-a10d-42df-9ea0-1b8d1d95dbb3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAOCAYAAADNGCeJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABJElEQVQ4EaWT7Q2CMBCG0TgA0Q10Az82wA10BR3Bv/yVDdAJjG4gK8gGOoJxA3zepm0Q1IBeUt7rfbzt3dFOURSBkziOx+hH1gT94ewOsQ3RN3Y/Be/aY89l66GE4J4lhwKUUBNLlIJz50Tfol9kY2VdPg/WkrXGcXCBb1CJivFCjm6pClRN0NWnoUTEXSFQJWXJ2ITYh23IlHQjqdZLyxz2ykd80yFZfvBraAH+vM3NalwQiEgDMxP+iwwSNf4EaQK2GoDivUCQslEPffk/3QyCFUR90P9zOqXxABQsgWABjEB/I3T1rV2ZJKnhM9A9KXFIdMC9erOBcVEC+PI/2dPV8Axd/SpLhC0xZCjmOeCNbMQR2w39DO6s7QyqHPWrKuahPwGbS2D0goaxHgAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle 12$"
      ],
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p+b"
   ]
  },
  {
   "attachments": {
    "9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "01defae6-c0df-42b5-8067-374dc1a1667b",
   "metadata": {},
   "source": [
    "![image.png](attachment:9ae86b6b-f45c-46fc-be16-7c5fdc1f36a8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "28705c11-a831-4871-87bb-90b720d41a63",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "2bc36b01-06d2-480c-8267-c1fd60ada06b",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "fe381526-5dff-403e-bff4-1a251a6a4e9d.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "2333de76-9756-46fc-b70f-242d1f443d14",
   "metadata": {},
   "source": [
    "![image.png](attachment:fe381526-5dff-403e-bff4-1a251a6a4e9d.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "fd9abe78-a3be-4da6-91ea-c38d9a6ce62b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =m x + n + x^{4} - 9 x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =\\left(x^{2} - 5 x + 6\\right) \\left(a x^{2} + b x + c\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq( x**4+m*x-9*x*x+n,'e1')\n",
    "e2=MyEq( (a*x*x+b*x+c)*(x*x-5*x+6) ,'e2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "b8f55dcc-6aa6-4eb3-8671-4f833099aba7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ 1, \\  0, \\  -9, \\  m, \\  n\\right]$"
      ],
      "text/plain": [
       "[1, 0, -9, m, n]"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L1=e1.coef_list(x)\n",
    "L1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "d9f6a69f-8033-44ac-8214-20014f48d837",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =a x^{4} - 5 a x^{3} + 6 a x^{2} + b x^{3} - 5 b x^{2} + 6 b x + c x^{2} - 5 c x + 6 c$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e2.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "bdaff2be-ca3e-4788-8a7c-879f47ea95f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ a, \\  - 5 a + b, \\  6 a - 5 b + c, \\  6 b - 5 c, \\  6 c\\right]$"
      ],
      "text/plain": [
       "[a, -5⋅a + b, 6⋅a - 5⋅b + c, 6⋅b - 5⋅c, 6⋅c]"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L2=e2.coef_list(x)\n",
    "L2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "0f86ccc4-97ac-4e1d-9958-454a112eddd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ 1 - a, \\  5 a - b, \\  - 6 a + 5 b - c - 9, \\  - 6 b + 5 c + m, \\  - 6 c + n\\right]$"
      ],
      "text/plain": [
       "[1 - a, 5⋅a - b, -6⋅a + 5⋅b - c - 9, -6⋅b + 5⋅c + m, -6⋅c + n]"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L3=[data1-data2 for data1,data2 in zip(L1,L2)]\n",
    "L3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "17731159-6806-4f70-b954-ca7744a4767f",
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c,m,n=simplesolve(L3,a,b,c,m,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "92c21376-fc4f-4553-b8ac-ab3f965a45e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{1}{3}$"
      ],
      "text/plain": [
       "-1/3"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m/n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}