10400 Polinomies Expretions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e1a23f0b-bb8b-4a72-9fa7-04d212231c78",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "62cbaf3a-82e8-4b70-a3ab-a010f40c8d9f.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "f4acc456-3b02-4360-ae64-35bb187bf3c1",
   "metadata": {},
   "source": [
    "![image.png](attachment:62cbaf3a-82e8-4b70-a3ab-a010f40c8d9f.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6885447f-f31c-4e36-b150-aff41c8b5a2d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x + 3 y + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x+4+3*y,'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e3771548-1b5b-4528-8191-dc653fdf762a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x + 3 y + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.s()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "59d19b04-028d-43bd-a7cd-5d98f08c6a93",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 3 y + 9$"
      ],
      "text/plain": [
       "3⋅y + 9"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(5) # when () is empty refer to var main var declare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9c54076c-1b10-4317-b2d3-fc67f484f614",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADkAAAAQCAYAAACsu9d7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAACKElEQVRIDc2X7U0DMQyGr4gBKpiAjsDHBrABHxMAIyB+tf8QbABMgGAD2ICPDSgTgG6D8jwhOaXHUaGKo2fJJLEdx47f+EpvMpkUXafRaLROjLfwBvOyKV7kl5l8hflhsl3OFJ2aEmCfgK7hD3gTHsDfKNo9o7hkfqEBo5fyxuiljJcUtkUcsA0fzeOffSW8Bx+z/2aGDy9iBbuQoHbMXxie4FDdVpPkEKsht0m7OB83HGCiXnK/7SQbzv47kQlEb0K6Tu9RsFm9ybghQWsLg0N4AB9E40ds7uK8EwPxCGljsdHUaTUKBnklz9lwIaN8hMW65T5h9MbO4S6SF28x6mTzkb7gSiJWME+iZC3Wr2DJm8r1QdiRPyKuIIftFA9zEzQHaZzg+oQif7wbKF+QBUPGvWD+wx/0drHqkMwswAi9HbJO+p/pt76haY0PIbuGTiSanDAViXJoSiFJlHainPZZnOWCWXP2NyVRIPeQAWPV3mf5mVeHf4sxFQOyhLzv30mUVqQPV00GWV+eN4gF7bOqD8RdLsfg/clkuR8YvREhkMP3lLUNqHNEXKLFJrnG3IoWjBbEYvnsCrurC/kjKqe+OcjUie9FUvochDdeC8TOOhUza4t2TOzhGfaGw6FZi99XuEDhZ8Tb2YH9TWjyFXRZ/5qin7nfJPsNVvKijdOgRdg9utT5C+bp/Wkj3SITlYF6bf4XwkH/0nhSMj+NwrVNKnEuL5Q+AXRIxN3I7kn0AAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle x + 19$"
      ],
      "text/plain": [
       "x + 19"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(y=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "76e60a92-3917-4187-938a-0daddd72b93e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =x + 3 y + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=P.xcopy('Q') # clone whit "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cd71b860-222a-42b4-a08a-98eb57fb35e2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =4 x + 3 y + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Add(3*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6684d0fa-e0a3-4b48-a089-ca880c40eb30",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =x y \\left(4 x + 3 y + 4\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Mul(x*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a36a2277-0071-4aeb-964a-214da18a4307",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =y \\left(4 x + 3 y + 4\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b46150d8-8de3-4627-b423-d4935d31e938",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =y^{2} \\left(4 x + 3 y + 4\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Pow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "62a5c5b3-c595-4794-ba12-c74093e24856",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\sqrt{y^{2} \\left(4 x + 3 y + 4\\right)^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Rpow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b08955e8-7c89-43c7-9f02-88e8e9c8077f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =y \\left(4 x + 3 y + 4\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.rsimplify()"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABTwAAAAaCAYAAACaXpMbAAABRUlEQVR4nO3csQ3CQAxA0QSFAbwCa7BMmkxFwzJZg5YyDR1FmAByJwgnWe/VjuT6K74+ItYOAAAAACCBQ+sFAAAAAAB+RfAEAAAAANIQPAEAAACANARPAAAAACANwRMAAAAASEPwBAAAAADSGGqG43reaw8AAAAAgG4Z56++7yNi3RoSOgEAAACAFmoD6OZJu9gJAAAAALRS2ye94QkAAAAApPExePq7EwAAAABo7TiduuN0Kpr9GDy/fSAUAAAAAOCfnLQDAAAAAGlsBk9/eQIAAAAArTzme9X8UDK0jHPxjTwAAAAAQCtO2gEAAACANIqD5/Ny23MPAAAAAIC3SvtkHxHrzrsAAAAAAPyFk3YAAAAAIA3BEwAAAABIQ/AEAAAAANIQPAEAAACANARPAAAAACANwRMAAAAASEPwBAAAAADSeAHWwBv4lUmkzwAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "899f1e7a-b750-4f80-a442-0f9991ea6aab",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a12137e0-debf-481d-9d35-cfb8a220d0e6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "af7e64a4-f0bf-49ca-94e0-766694ec82c0",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
    "38d56fa3-23ed-422b-a236-0786f0385b0a.png": {
     "image/png": 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GGGP/FNW+BoKFhUW56U1MTOTy2NnZoXv37nLhCxcuBAB88MEH+Pvvv2FkZKRy7QAnJyecPn1aciNYkXUXBEHAvHnzxMUenZycKpTHw8MDZmZmKtPp6+uLW02WfZmYmMDCwgLW1tYYP348BEGAp6cnAKBbt25y6c+ePYvw8HCFazosXrxY8mrdurVcuvv371f4XAqCIJkqMXPmTCxdulTpGgjVvT5CixYtYGhoWO7n/P3338Pa2lqSz8vLC87OzuXma9SoEX766acqbS9jjDHGGGOMvc+qfAqDs7MzoqOjAQBFRUUqt03s1q0brK2txR0BOnfuDDc3N7Ro0QKzZs2S3LCWnXffsmVLBAYG4s8//8TatWuRm5srxqmpqaFhw4ZYvnw5Bg4cCF1dXbk2Xrx4UWmb3N3dMWnSJHHBRgBo166deCOalpaGoqIiuXw6OjoYO3Ys1NTU0Lp1a6VbCwKAvb096tevL5YpG/rv6OgoTinw9vaGjY0NBgwYAADo1KkTdHV1kZOTI5aTlZWF9evXS6YOmJiYwM/PT27UxFdffYV27dohISEBxcXFAIAHDx4obaPs3MnKFgRBbkTJzJkzce/ePezZswfFxcWoX7++GOfl5YUbN26goKAAAORu5N9Wq1atcOzYMUycOBHh4eHiMcnaPmDAAEycOFEun6amJgICAvDdd99h7969kpESampq6N+/P3bv3g19ff0qbS9jjDHGGGOMvc8EqsZ96sLCwmpkW7/4+HjJk3QDAwN07Nix2ustT0xMDMLCwhAaGgonJycEBgaKnQYA0Lp1a7Gj4OzZs+JNetu2bVG3bl2l5cbFxUlu+jt27AgDAwPJmhDOzs4wMTFRWsbdu3eRlJRUofrOnz8v3phra2srnZLy9OlTxMTEyK1xkJycLO4U0bVrV2hpaSmt622EhoYiISEB586dQ7169dClSxd06NBBZb64uDhcuXIFQUFBsLGxqXA+xhhjjDHGlHnw4AGys7Mrlcfc3LzC06YZqy3V2oHAGGOMMcYYY/8URCSORH59zTaZlJQU2NvbIyUlpVJlN2nSROXC7ozVtiqfwsAYY4wxxhhj/zSXLl3C1KlTcePGDQCl03WXLl0KS0tLSTp/f38kJyejd+/eaN68OQCgfv36MDY2xsOHD5WW/8EHH1Rf4xmrItyBwBhjjDHGGGMqzJgxA9HR0fDx8cHhw4exbds2lJSUYPv27ZJ0QUFBAIBNmzahcePGtdFUVkOuXLmCcePGvVFeQ0ND/PLLL+jUqVMVt6p6cQcCY4wxxhirEbKFlatrTSTGqtO8efPQtWtXGBoaonfv3ujbt6/CRdOzsrLg4uLC6xn8C6xZswYPHjyAlpaW0ikt5ZGtS/c+4Q4ExhhjjDFWI6ZOnYrTp0/j0qVLMDc3r+3msHfYn3/+icuXL2PJkiWoU6dObTcHANC/f3/x/8+fPwcRoUmTJnLpnj17hjZt2lT5Fubs3ZOWlgYiwpEjR+Dm5lbbzakRvIgiY4wxxhh7K6tXr4afnx/U1dVx5MgRNGvWTGG6+/fvo1WrVmjVqhUOHz4MW1vbt677wIEDCAkJAQA0a9YMAwcORIMGDd66XFY11q5di8jISKXxjRs3xqBBg2BjYyMJ37x5M8aNG4fGjRsjODi42s7p1q1bxd3cnJycMGDAANSrV6/cPCEhIfjiiy8QExODU6dOoU+fPmJcYGAgevTogQMHDuCzzz4Tw+Pi4rBy5UoApSNwhgwZwjt/VYEVK1YgNDQU69atg5GRUY3WnZqaCktLSzRt2hT37t2Dhsa/5Nk8McYYY4wx9oaioqJIXV2dBEEgQRDI09Oz3PTz588nQRBo0KBBb1VvbGws9ezZU1K3IAikpaVF/v7+b1U2qzojRoyQnB9FLy0tLdq6dSsVFhaK+WJiYsjExIQEQaCvvvqKSkpKqrRdjx49IhcXF1JTU5O0xdDQkAIDA5Xm++233yTX3KxZsyTxGzduJH19fYqOjiYiouLiYlqyZAnVqVNHUo+amhr169evyo/rn+Dp06c0depUsra2Jj09PfHl6upKXl5etGPHDkpNTSWi0vMhCAKZmZlRTExMjbZz27ZtJAgCLViwoEbrrW3cgcAYY4wxxt6Yr68vARBfjRo1ovz8fKXpw8PDSVdXlzQ1NSkzM/ON6iwoKKCOHTuSmpoaderUiebMmUMzZ84kfX19AkANGzak2NjYNz0kVoWys7Np6NCh4vVhZ2dHGzdupGXLltHo0aPJwMBAjFu1apUk75UrV8je3p4A0LJly6q0Tba2tqSjo0M9evSgOXPm0OTJk0lLS4sAUMuWLZVem4GBgTRnzhwaNGgQqampkb6+PoWEhIjxvXv3JkdHR/H9hg0bxGty/PjxNGfOHOrYsaN4zJs3b66y43rfFRcXk4+PD+no6Eh+pyh6eXh4EBFRREQE1atXjwDQmDFjarRDZsyYMQSALl++rDD+yZMnFBoaSllZWTXWpprAHQiMMcYYY+yNlb0Zkr32799fbp6VK1cSAPLx8XmjOqOiohTecPr5+YltWLJkyRuVzarepEmTxPMyb948Sdy5c+eoTp06BIAcHBzk8q5du5YAkL6+PiUlJVVJey5cuEAaGhq0d+9eSficOXPEdv7vf/9TWU6nTp0IAK1bt46IiF68eEF16tShiRMnimn69u1Lrq6ulJaWJoYlJSWRiYkJAaDGjRtXyTH9E3h4eBAAqlevHn3//fd08uRJioqKEl+HDx8mR0dHAkA9evQQ8925c4eaNWtGAGjlypU10tasrCyqX78+mZqaSjpM09PTadmyZdSoUSOxQ8rCwoK8vLzo5s2bNdK26qZWTTMjGGOMMcbYP9yNGzdw7do1GBgYYN68eRAEAYIg4MKFC+Xmc3d3h66uLo4fP47U1NRK12tubo6goCBMmzZNEv7111+jSZMmEAQBubm5lS6XVQ/ZdSEIgtzOBD169ICtra0Y/7ovv/wSZmZmyMnJgZ+fX5W0x9HREZcuXYKHh4ckfPHixdDU1Kzw9TNgwABJu0+cOIHs7Gzo6OiIaRYuXIiAgADJ/Px69erBx8eHr9P/V1xcjMmTJ8Pf3x8aGhpYunQpfvrpJ7i5ucHW1lZ8DRw4EP7+/rCyssK1a9fE/K1bt8bkyZMhCAJ++umnGtnZ4OLFi4iLi8OAAQPEXWXS0tIwcuRIzJkzBy9evICpqSl0dXWRmJiI7du3w93dHc+fP6/2tlW3f8lKD4wxxt41BQUFGD58OKjMWr6pqam4ePGiJJ2BgQG6detW081TKioqCnXr1oWBgUFtN+W98P3336NNmza13QxWTY4dOwYiwqhRozBhwgT8+uuvyM3NxeHDhzFv3jyli9E1atQI/fr1w759+xAYGChZbK4idHV10bVrV6XxVDrKtlJlsurTpUsXrFu3DkDpTdbrZOdL0TkzMjJCmzZtcPr0aZUdUxVlamoKU1NTuXBZR4CitkRHR+Po0aPw9PSEqakpsrKysG7dOujo6KBFixYAILZv6NChYj5XV1eFbRAEga/T/3fq1CmsX78eADBjxgyMHTtWaVpHR0fMmzcPx48fl4R7enpi0aJFSE1NxY4dOzBjxoxqbfPdu3dBRJJOr9mzZ+Pw4cNwdXXFxo0b0apVK0RFRWH+/PnYuXMnIiMjsX79eixfvrxa21btamfgA2OMsX+7Y8eOqZzjyK/3//XTTz/V9qXGqlG7du1IQ0ODXrx4QUREU6ZMEc/96tWry807duxYAkDTpk2rsvZkZmaSpaUlAaCgoKAqK5e9nRMnTojXxcCBA8XwkpIS+u9//0uampqkoaFBBw4cUJj/999/JwCkrq5ODx48qLZ2JiYmkoaGBgGgiIgISdyaNWsIALVo0YKWLVtG3bt3JwA0Y8YMIiLKz88ne3t7EgShQnV9++23BIBGjBhR5cfxPikuLqYOHToQADIyMqKCgoIK5UtPT5cL+/DDD+WuserSp08fAkBnzpwRw5ydnWn8+PHiAo8yUVFR4lofdnZ2lJ2dXe3tq048AoExxlitkA37dHNzw5YtW2qkztDQUDg5OYnvU1JSkJOTo3B7MFna0NBQEBF0dHRga2sLbW1tMS47Oxvx8fFIT0/Hy5cvAZRuzyXbC/r69etISEioVBvNzc0hCAISEhLQqlUrlJSUiFuMAaVPznR0dPDy5Uv06NEDQUFBKCkpkZRhYWGB9u3bAyjdOuzmzZsVqlsQBJiZmSExMbFSbVZGQ0MDX375ZZWUxd49e/bswe3bt9G5c2fxZ2jGjBnik+YLFy7gm2++UZq/f//+2LJlC27cuFFlbTp9+jQSEhKgq6srty0gqz1lh/kfPXoU/fr1AwDcu3cPsbGxAIBevXopHYnyySefQF9fHzk5OcjMzKy2du7evRvFxcUwMzOTG6HQu3dvDBs2DH/99RfmzJkDKysr/PTTT5g8eTIAID09HU+ePEHHjh1V1pOeno6jR49CEATY29tXy7G8LwoKCnD9+nUIggA1NTVoampWKJ+hoaFcmLu7Oy5fvoyjR48iNjYW1tbWVd1cAEBmZibOnDkDQRDw0UcfieHKfpfZ2tqiYcOGePToEZ4+fYqEhAQ0bty4WtpWE7gDgTHGWK04duwYgNKhrdX1R/51r9dTXr2yOEVpyoaV9+Wvqo6rc+fOSuNUffm0traGi4tLlbSDsbL8/PxAREhKSsL3338PACgsLBSHZB87dgzR0dGwtbVVmJ/KGbb+JvLz8zFt2jQQEUaMGCE3157VntfP8+vDz4HSzs5z586hZ8+ecnENGzaEkZERsrOzcebMmQrdpFdWYmIifvjhBxARpkyZIlmzAACaN2+OTZs24dWrV/jll1/g4OAgzn0HSqfgERHc3d1V1uXr64unT5/C2NhY7ID4typ7bbzt74LBgwfDx8cHRUVFSE1NrbbvFrJz7erqWuEOD9lxmpubw8TEpFraVVN4EUXGGGO1QvbHtGzvPWPs/RAbG4uQkBAAQHh4OBYvXozFixdjxYoVYpq8vDzJQmfV7cCBA3j+/DksLS2xevXqGquXqVZ2lNSYMWPw6tUrvHr1ComJifj6669hYmKCBw8eYMiQIYiLiyu3rFOnTlVLG7dt24a0tDS0bt0ac+fOlcTFxsbC19cXjo6OOHv2LPz9/SWdBwDg7+8PNTU1fP755+XWk5CQgD179gAANmzY8N7fTL5LGjduDHV1dQBAcHBwtdUjK1u2cKMqERERePLkCQCgVatWMDY2rra21QQegcAYY6xWCIJQY8OMf/311/d/0aJKaN26NeLi4sSpCK1atcK9e/eUpn893sHBAU2aNMHx48fRvXt3XL16Fb169QJQ+oQ5IiICH3zwgcKy4uPj8ejRI6xfvx6ffPJJFR4Ve5csXrwYQOkCcZ06dULPnj1x9uxZAKUdCgEBAQCAffv2Kb2hKrsy/9t6/PgxxowZg7p162L//v3Q1dV96zJZ1QkLCxPPs6urK+rWrSvG+fn5oWPHjvjqq6+QkZEBd3d3BAcHizeCMrJrpV27dlXevpCQEMyePRuNGjXC7t275erevHkzFi9eLB7DqlWr0LdvX3Tp0kVMc+HCBbRt27bcv2mFhYUYO3Ysnj17hrlz52Lw4MFVfizvm7K/A6rid4GsvBMnTsDb2/uty1Nk37590NLSqvADkL1796K4uBjq6urVvrhjjajhNRcYY4wxIiL6+uuvqUGDBtVeT3FxMbVt25YEQVD6srKyIi0tLblwY2Njaty4sfiysLAQ4/T19alx48ZkZGSksEw9PT1J2nr16kniTU1NSU1NTWmbrK2tycDAoNx2v8uvUaNGVfu5ZbUjKyuLmjRpQtra2hQQECAXX1BQQI0bNyagdI/73NxcheUcPHiQAFDnzp3fqj3h4eFka2tLGhoa9L///e+tymLVo+wiips2bVKYxsjISEyTk5MjF1+/fn0CQD///HOVtu3q1atkYmJCderUofvBPNUAACAASURBVJMnTypMk5GRQU+fPqUbN26Qrq4uAaCuXbtScXExEZVeg+rq6jR9+nSl9RQXF5OXlxcBoH79+ik8xn+jnJwc8bwbGxu/dXna2toEgFauXPlG+ZOTk2nx4sXk6upKUVFRcvFpaWmkp6dHjo6OFSrv7NmzpK+vTwDou+++e6M2vWt4BAJjjLFaERgYWCPbM6akpOD27dtwcHDAvn37FKZp1KgR4uLikJ+fLwk3MzODubm5+D4zM1Pcw9nIyAgNGjRAQkICXr16JVemgYGBuNiXoaEh6tSpIy60CACWlpZISkpCcXGxwjY1bdoUKSkpSE1NrdwBvwNCQ0PRp0+f2m4GqyZBQUGIiIhAhw4d0LdvX7l4TU1NdOnSBZGRkYiMjMTNmzcVruNx+/ZtAHirJ8oRERGYMmUKYmNjsWLFCowYMUKMKykpQX5+Po9GeAfIRqQAQFFRkVy8st+DMjdv3kR8fDwAVHjOeUXcv38f3t7eyM7Oxs6dO8UFcGXtLCoqgo6ODgwMDMStexcvXozp06cjODgYq1evxrfffosNGzaguLhY6daixcXF+O2337Bt2za4uLhg//790NbWFuOzs7Ohp6dXJU/g3zdaWlpo06YN7ty5g/T0dPj5+b3xyIGy11GdOnUqnf/y5cvo378/UlJSAADTpk3Dvn37JCNSjh8/jpycHAwYMEBleUFBQRg4cCCys7OxfPly+Pj4VLpN76Ta7sFgjDH271NcXEzW1tY0ceLEaq9r586dJAgC9e/fv9rrYuyfLicnRxzRs2LFCqXpAgMDxdEoyrZpdHR0JEEQ3ni7xbCwMGrYsCEJgkBz586VxEVERJCnpyf/3L8jJk+eLF4PgwYNkovftm2bGN+9e3fxyb7Mjz/+KMbfvXu3Stp05coVMjY2JkEQaOPGjZK4O3fuUL9+/ejrr7+Wy1dcXEyjR48mQRBIU1OTLl++TJ9++ikJgkDXr1+XS19QUEBeXl4kCALZ2NhIRuRkZWXR5s2bydDQkF6+fFklx/U+2rx5s3h+HR0dKSYmptz0OTk55O/vLxd+4MABsZydO3dWuh0bN26kb775RjJqcfjw4ZI0Q4YMIUEQ6MKFC+WWVVhYSK6uriQIwj9uxAl3IDDGGKtxd+/eJUEQxP2zq5Psi2lVD3stT35+PqWlpYnvnz59KtlTvKCggMLDwyk8PJySkpKIqPRLqWy4pCwuPDycEhISiKh0f/vw8HB6/vy5WE5iYiI9ffqU8vPzKTw8nLKysig6OppiY2OpsLBQLCMxMZGISCyLsTeRnJws7rMOgLp16ya5rmVycnJo5syZYjo9PT25m7709HQyMTGhBg0aVHjf97LCw8PJxsZGrKNu3brUtGlT8VWnTh0CQF5eXm98vKxqZGZm0qBBg8Rz5erqSqdPnxZfhw8fpoYNG4rxp0+fliuje/fuBIBatWpF+fn5b92mq1evkqmpqVinhYWF5PrR0dEhADR//nyF+VNTU8nc3JwAkI2NDRkaGlK9evUoLy9Pkq6kpIRGjRol1qOlpSWpRzYtw9DQkJKTk9/6uN5XhYWFNGbMGPFz6tq1K5WUlChMm5ubSwMGDCA9PT25uG+++UYs48WLF2/cnhs3bpChoSEBIE1NTQoJCRHjHBwcCAAFBwcrzZ+QkEDt27cnAOTp6flWbXkX8RQGxhhjNe7BgwcgInTv3r3a66L/3+1B2dDSqvbs2TP06tULubm54krLEREREARB3Pe5sLAQkZGRAABTU1PUq1cPxcXFiImJga2tLZ48eSJuZ2VsbAxzc3NkZmYiLi4Oenp6aNCgAQAgKSkJGRkZaNCgAaKjo1G/fn2kpKRAQ0MD5ubmiIiIAACYmJjAzMwMiYmJkikZ1cHFxQW7du2q1jpY7bhx4wYuXbokvg8KCsLo0aMRGBgoSRcTE4OVK1eK73NycvDbb79h69atYtiMGTOQmpqKUaNGvdGQ9NOnT4vTiQAgOTkZycnJcukqsqUeq15jxozB4cOHxfeXL19WOMVJX18fP//8s7hgq0xSUpK4yOuwYcPkdj94EwcOHBCHqQOlOyMkJCRI0giCoPT6MTY2hpeXF1asWCFeh/369ZNMSwBKp0Fs375dfF9QUIBnz57JldejRw+Ympq+8fG87zQ0NLB582bcvHkTd+/eRXBwMDw9PeHh4YGCggK0bNkSFhYWOH36NHbs2IGAgACF5+bEiRMAgP79+4t/J9+Es7Mzjh8/Djc3N+Tk5GD79u348MMPERwcjMePH6Nnz56SBTTLiouLQ+/evfHw4UP07t0b27Ztk/yOS0pKwieffII1a9bgww8/fOM21ibuQGCMMVbjIiMjIQjCW/2Br6jCwkJoaGigadOm1V4XULra8vPnz2FkZCSujWBoaAgAkrUSyn5ZlIXr6+vj1atXctt6yeJleWTvBUGAkZERMjMzYWpqiry8POjp6QEA0tLS5OpQU1NTuF5DVXr48GG1ls9qT8eOHXHlyhVJmKKf4YYNG8qlMzMzE/9/+fJl/Pnnn9DQ0MAPP/zwRm1xcXHBoEGD4OTkpDSNnZ0dr8XxDujTp49k15YzZ84gLy9PfN+pUyfY29tjwIABaNasmVz+nTt3IjU1FcbGxhg6dGiVtKlnz54ICwsr9/pp1aoVWrVqpTR+3rx5OHjwIJ4+fQqgtKPkderq6hg+fDjq1asnrqHwOm1tbXh5eVXyCP55BEFAQEAApk+fjgMHDmDv3r3Yu3evwrT6+voYP368JOzevXt48eIFBEFQuZVmRXTu3Bnz58/H3LlzsXnzZlhZWUFTUxNEhPr16ytcryI4OBje3t549OgRBEGAmpqaZGvb27dv48aNG3j+/Lm4psf7SCDZIw7GGGOshixZsgTff/+9ZG/w6vL555/j2bNnuHXrVrXXBQAeHh64c+cO7t+/XyVPyhj7p/nmm2+wdu1ajBo1Ctu2bavt5rB32MOHD9GhQwdkZ2dj3rx5+Pnnn2u7SRLJycmwt7eHhoYG4uLioKamVttN+kcIDQ3F3r17cefOHZw7dw65ubmwt7eHnZ0dGjVqhOHDh8PV1VWSZ+bMmfD19UXTpk1x6dKlKhttN3XqVKxZswZA6YLLUVFRWLZsGWbNmiVJ9+DBA3To0AE5OTkVKvfChQtKRzG867gDgTHGWI3r1asXzp07h5r4E2Rqaor+/ftjx44d1V4XADRv3hza2tq4c+dOjdTH2PskJCQEXbt2Rb9+/bBv3z65Id+MyaSmpqJLly54+PAhvvjiC+zevbu2m6TQ06dPoaGhgUaNGtV2U/6RZN8Tytuh4vjx4+jfvz+0tbWxYcOGKh3RkZKSAnt7e3GKlLa2NpKTk6Gvry9Jl5iYiNGjR+Pu3bsqy/Tw8ICvr+972+HEUxgYY4zVKCJCeno6bGxsaqS+3NzcGvtid+7cOYSHh+Orr76qkfoKCgqwbds2cd5n+/btYWFhUSN1v65p06Y1sqYFe7/t3r0b/fv3x969e7nzgJVrz549ePToEVxcXLB58+babo5SiqZdsKqjamvL6OhojB49GkDpKISqng5iamqKhQsXYurUqQAALy8vuc4DADA3N8fff/9dpXW/q97LDoSoqCgcP34cw4cPh5GRUY3UefnyZWhqasLFxaVG6mO168GDB0hJSYGrqys0NN7LHxPG3lkpKSm4desW+vfvX2N11tTfivDwcACQzPetTlu3bpXsl112obKaZmNjg6ioqFqrn70fli9fDm1tbZ7ew1SysLDA+PHjMXfuXHFtF8Ze99///hdJSUnw8PB44zVVVJk4cSKio6MREREhdlb8m1XrnVFUVBT8/f0RHByMCxcuiOFqampwd3dHz5490alTp0o9Gfr666/xxx9/ID8/H82bN0ePHj2qo+miI0eOYOTIkcjMzIQgCPD398dnn31WrXX+UyQkJOD8+fNwd3d/b27Chw0bhoCAAOTk5KCwsBCnT59G7969a7tZjP2jyHZFqInpC48ePUJhYWGNzTMMDw8HEdV4fe3bt0eTJk2Qm5uLjz766K07TNLS0hASEgJ9fX20bt0a0dHRaNu2rVy648ePi+tYfPHFF29VJ/t3ULaQHGOvGzJkCIYMGVLbzWDvOBcXFyxduhTjx4+vtikBmpqa8PX1rZay30fVdld35coV9OzZU7LKalmbN2/G5s2b0bdvX3HoZUXY2dmhoKAAgiCoHNJSFbKyspCfny9+2W3RokW11/lPcPLkSfznP/9BRkYGDh48qHQV1XdNTk4OMjIyAJQOmXr58mUtt4ixf55jx44BAHR1dau9roMHD0JLS6vGhvUfO3YMRkZGcHBwqPa6ioqKcOjQIejq6uKvv/6q8mkaM2fOVJlm3LhxVVonY4wxVhmDBw+u7Sb861RLN83SpUvRs2dP5ObmwsrKChMnTsTu3bsRGhqKVatWwcvLC6ampiAiyciEivjmm29gZ2dXY0+vPD09MWHCBLG+8+fPV3ud/wSWlpYQBAFE9F4tELJv3z58/vnnNfqE9N9q9uzZsLOzw3fffVfbTWE1TNYBXBOjexITE2FgYFAjayBERkYiJiYGWlpaMDY2rvb6nj17hujoaDg7O/PiXYwxxhirEVU+AiE+Ph4///wzcnNz0bhxYzx8+BA6OjpivOwJ/t27d9G3b19kZWVVqnwNDY0anzdXdt5VTTxV+ido3bo1Tpw4gYsXL2LatGm13ZwK09LSwogRI/DXX3/VdlP+0c6ePYtVq1ahoKCgxrbWY++OkydP1kjnIhEhICCgwh2BBQUFb/X3JScnB/n5+fj444/l4kpKSlBYWAgAVbZw3K1bt0BEmDx5cpWUxxhjjDGmSpV/e1u1ahVyc3MhCAI2bNgg6Twoq3Xr1pg6deobTUOQPb2qiSkMr9dnZWVVI3X+E3Tq1AkzZsyAurp6bTelUsqe75q6xmpbTk4O7t+/X2P1bdy4EYWFhRAEAbdu3arRuv9Nzp49i7Vr1yI3N7e2myJRUFAAAPjkk0/k4u7du4d+/fqhT58+6NOnD9auXYuUlJQ3qufRo0cIDw9Hp06dVKbduXMnTE1Ncfbs2TeqCyhdDwAABg0aJIYVFxfj1q1bGDx4MHR0dKCjowNPT09xscU3VVhYiAULFkBPT0/lujzFxcXw9PREnz598PDhw7eqlzHGGGP/blU+AuHQoUMgIri7u6scnjpjxgx8+eWXkrCIiAhs2LABOTk5AEpXYF2wYIEkjarh5SdPnsTmzZtx7do1fPDBB/joo4/w9ddfQ0NDA5cvX8aVK1fw6tUrzJkzBw0aNJDkPX/+PPLy8tC5c2cYGhpK6pP9X5G9e/fi2rVr6N27NwRBUPgESpGkpCQcOHAA+/btw+PHj6Grq4u1a9eiT58+cmmDgoJgamoKJycnJCUl4caNG7Czs1O6fczp06eho6ODjz76CIWFhThz5gzMzMwkO0k8f/4c+/fvx9OnTwEA3bt3x5AhQyQ3/c+ePcPjx4/F92WPLz4+Hrdv3xbjOnXqBBMTE/F9YGAgHB0dYW5uLmmbLJ+DgwMaN26Mq1evYv/+/cjOzoahoSG+/vpryRZvGzduRGhoKKysrDB06FA0b95c6Wd669Yt7N+/H2lpaXBwcMCUKVOUpgWAU6dO4fLly7CyssLdu3dx7do18Tz36tVLLn1YWBj279+Ply9fwtzcHAsXLiy3/LL5IiMjAQA9evSQdK7l5eXh/PnzUFNTQ9++fStUXlXy9fXFsmXLEBMTA1NT02qtKyAgAEeOHBE/4/T0dKxduxa///57tdb7b5ORkYHhw4cjMTERDg4OCn+n1JZHjx6hefPmcusSTJ48GVu2bEF+fr4YdvbsWfz666+4deuW5HdLRcg6Abt27Vpuujt37mDixInIyclBcHCwwp/7ikhJSYEgCHB0dBTDfvzxR/z0009ie4DSrclCQkJw8+ZNmJmZvVFdL1++xLNnz9C7d2+Voya8vb2xZ88eAKUdNGXbxxhjjDFWKVSF0tLSyMLCggDQ7NmzK53/8OHDVK9ePQIgef3www+SdC1btiQAdO7cOUl4eno6ffXVVyQIglwZgwYNorlz50rC9uzZI+Y9ceIEqauri3l/+uknMW7OnDlinrCwMEmdN27cIEdHR0mdgiDQgAEDqLCwsNzjjY2NJUdHR7m2CoJAR48eFdO5u7uLbbOxsaEePXqQmpoaASA1NTVydnamp0+fiunj4uLIyMiIBEGg+vXr08mTJ8nGxkYsOzIykoiIwsPDycnJSa7+Jk2aUHBwsFjesGHD5Np3/vx5IiKaOHGiGK6rq0ubNm0iIiJXV1exzePHj5cc96hRo8T2t2jRglxcXOTOmaWlJW3atIlmzpxJenp6krg6derQn3/+Kfd5vnz5klq2bCl3Ljp37kx5eXly6fft20cNGjRQeL3IXtu3bxfTZ2ZmUvfu3cW2y14ODg6UlJQkprt37x4NGDCA1NXVycHBgTZs2EBOTk6SfJaWlnTr1i0KCwujKVOmkJWVldheAwMD2r17t1x7s7KyaNWqVWRtbU0ODg40aNAg8vHxoczMTDFNcHAweXt7k7m5OS1evJj8/PyoRYsWpK6uLrZHdv6JiEpKSsjT01P8DDp37kyDBg2iZcuWSep+9uwZTZkyhdTV1alHjx40aNAg2r17t8pr/HXZ2dlkYWFBlpaWdO/ePfHzWLNmTaXKYapNmjRJ/HxfP5+1TVtbm9q0aSMJ+/333wkAubi40MqVK2n37t3k7e0tXpujR4+udD27du0iALR///5y03388cfiZ+Xl5VXpemQ6d+5MGhoalJ+fT0RERUVFpK2tTdbW1rR9+3YKDQ0ld3d3sa6RI0e+cV27d+8mADRq1Khy0/n7+0t+9yj63cIYY4wxVlFV2oHw+PFjEgSBBEGgOXPmVCpvZGQkaWlp0aeffko3b96kS5cuiTeDLVq0kKR1cnKS3MQSEd26dYssLCxIEATq1q0bLVq0iDZs2EDNmzcnQRDIw8ODQkNDycHBQWzj3r17xfx37tyhIUOGiHFlOxDmzp0rhoeHh4vhz549o7p165IgCDR9+nS6efMmzZw5U0y7dOnSco955MiRJAgCNWzYkM6dO0fHjh0Tb/z/85//iOlkN9iyl56eHrVv314S5uDgQDk5OURElJKSQs2aNRPjjI2NJWnDwsLo4cOH1KBBA9LW1qYvv/ySFi1aRF5eXqSrq0uCIJCuri49ePCAiEo7GmxtbcX8GhoaYts2b94s3vQGBgaK4ePGjRPTv96B4OHhIWmPIAhkaWlJ7du3J1NTU7k4ExMTat++vXguBUEgW1tb8Us6UekX9a5du5IgCNSgQQNatGgR9erVS0x/6NAhSRv8/f1JR0dH/DxHjx5NixYtohYtWkjqLtuBMHz4cBIEgQwNDWnBggXk7u4uplu1apWYztfXV+4YKvsyMDCgmJgYscy4uDjxum/WrBm1b9+etLS0SBAEGjp0qHgjL/uZKe9lbGxMISEhRERUWFioMI2pqalYd0BAAOnr65MgCNS+fXuxw0wQBPrjjz/KvcZft2zZMhIEgZYvX045OTliObKOJ1Y17t69S3Xr1hVvGqdMmVLbTZLQ1tYmb29vSdhXX31FH3/8MWVnZ0vCu3TpIh5H2Z/5ipB1cJbXgXD48GHS1NQU61DUOVkRsbGxBID69OkjhoWFhdGHH34o6eTLyMgga2trAkBNmzal5OTkN6pvypQpBIC2bNmiNE1GRgbVr19f0uHJHQiMMcYYexvvTAdCYGAgCYJAv/32mxh25MgR8YawLEUdCNOnTydBEMjIyIhevHghhmdlZdHOnTvFL55//fWXwg4EotIv3ao6ENatWyeGyzoLbGxsxC+9hYWFZGZmJj75Lo/sKX3ZL7effvopCYJAn3/+uRj26tUrsre3F28eL168SERE0dHR1KlTJ7FtO3fulGubIAjUs2dPCggIoMePH9PVq1eJiGjw4MEkCAKtXbtW0qalS5eK+ebOnSuGZ2Rk0OjRoyU3zMnJydSiRQtq1qyZ5FwQlT7ZlnV8vN6B8OLFCzIwMBDL2rhxo/gFOzY2VuyUkeWNj48nIqKCggLq0aOHGFf2S3lKSgoJgkBqamoUFBRERCS5QS3bEXDp0iXx5tvOzo6ePHkixt26dYu6deumMJ+sI0YWVlhYSA0bNiRBECSjZBITE8nOzk4sw8XFhdavX0/x8fF048YN8VzKOkcWLFhA8fHxFB8fL44GEASBdu3aJZbp5uZGgiCQk5MT5ebmEhHRmDFjxLRnz54lIqJt27aJYWZmZrR06VKKj4+nM2fOkLW1tRj3999/i2UvWbJE7Bjy9/en+Ph4SkhIEI+lTp06JAgC+fj4iGGyY7C0tBQ7rirCxcWFxo0bR0VFRVRUVCR2Cr3Nk1gmr2znliAI1LJly9pukigkJIQEQaD58+dLwhMTExVeS7t27RKPo6CgoFJ1yX6WDxw4oDA+NTWVbGxsJJ9V2ZFplbF69WoSBIG+/fZblWm9vLzE+t60w8LKyooEQaBnz54pTSP7HdG9e/e3ro8xxhhjjIioShdRpDJrE1Alt7/r1q0bTp06hVGjRolh9erVU1jW63UQEUJCQkBE+PLLLyXrGujr62P48OHiHNHy2qgsrmyYbG5uamoq/vjjDxAR0tLS4O7ujiFDhuDLL79ERkYGiAgXL15Eamqq0mP+9ddfERkZiSFDhohhubm5ICI8ePBADKtbty4sLS1BROjSpQs+/PBDAICNjQ327t0LPT09EJFkUS5ZezU1NbFixQr07dsXdnZ26NChA+Li4sS1Kl5fP2H27NlwcnICEWHTpk3iquEGBgbYuHEjWrVqBSLC3Llz0aFDBzx69Ajbt29H9+7dJeUIggBNTU2Fn3ODBg2gra0NIsLHH3+MCRMmoE6dOgCA+vXr44MPPgARwcTEBCtXrhTnSWtqasLDw0PhOdLW1oa3tzeCgoLE+c6yOogI9+7dE9P6+/ujoKAARISzZ89KPoO2bduib9++CusYO3YsDh48iJEjRwIo3RFETU1NrnwzMzN06dJFzL9nzx54e3vDwsICzs7OGD16tBj366+/YtGiRbCwsICFhQVmzJghV3dsbCwCAwNBRPDw8EBiYiKSkpIkdci2Qx01ahSsrKxARBgwYABmz54NCwsL9OrVC1OmTBHTR0VFie0dNmwYiAg6Ojpwd3eHhYWFuGbFoUOHkJWVJa5r8vz5c/FzIiLEx8dL1scoz3fffYd79+5h06ZNUFdXR05ODkpKSkBEuHr1aoXKYKo9fvwYx48fR+vWreHt7Q0iQnZ2dm03S/T48WMQEZydnSXhZmZm0NXVlUtf9ndZZcnyvV6XzLRp0/D8+XMcP35c/L1X2b9dMleuXAER4aOPPqpQu2QvZW0rT1FREbKystCpUye5dSRkvv/+e2zduhXTpk3DpEmTeGtaxhhjjFWJKl1EsVGjRmjUqBGio6PfaIXp3r17Izc3F5cuXcLx48exf/9+hSvhC6+tkJ+ZmYnr169DEASVi1+Vzaes3NfjyobLtnGMj49HcnIyBEFAZmYmAgIC5MpSVEdZspXBw8LCcOXKFaxfvx43b96EIAiwtrYu95hlbGxs0L9/f/z11184dOgQFixYAA0NDTGtnZ2d3BdUWZy6ujq6dOki1y4nJyeEhoYiOTlZ8mVTS0sL/v7+cHFxQWZmJiIiIjB16lSxQ+N1ytpcNk7R+ZLF6ejoiAtZypibmyv8bPX09LBu3TrxfUhICP744w8xTatWrcS4ffv2QRAEdOzYUW4RTdnxy/KVXVBw5cqV4v8fPHiAjRs3Ii4uDoIgSMovewzOzs5o3LixwjgAaNmypdK6Zf/+97//FXcsWLBgARYsWAADAwNkZmaKacruYmBtbY24uDg4OTlJyv7ggw8Upg8PD1d6ntavXy+Gd+zYEQAU1t26dWu5vGUlJibCz88PRUVFYtq0tDS8ePECgiAgLi4OmZmZMDAwKLccptqSJUugqamJjRs34vHjx1i/fj3S09Px6tUr1KtXr9y8sbGxePXqFQDA0NAQGRkZYpyZmRkEQUBhYaFkgVNFli1bhpycHPz4449ycXfu3AEAWFpaVuh4yi7w+iadCN27d1fY3mPHjmH79u0YPXo0+vTpA19f30qXrYiqnwUAuHjxIgCgXbt2aNq0aaXr2LFjBzIzM9GvXz/o6+vLxT9+/Bhr1qxBw4YNMWvWLLGDkTHGGGPsbVVpB4KWlpa4v/XRo0cRFRWFRo0aVTj/o0eP0K9fP0RFRUFdXf2NttB7+fJlpfNUhqIdDxYsWIDx48crfHpmZGSktKykpCRMmDABf//9NwoLC6Gurg41NTWUlJTg0qVLCvMo2jdddpNdWFiIkpKSih4KgNIb79e1adMGu3fvVpi+WbNm0NfXR2ZmJgDg7t27laqvKr18+RL29vbi+9TUVPz222/iDVNxcbEYd/LkSXHkgKztBgYGKq+xzp07i/8vKCjAqlWrsH79eiQkJIijM2TlK9qNQV9f/433upe1X9ZeQRDQsGFD8Ua+rLJhTZo0wY0bN8o9lrJkN2iKyOrW0NCAs7OzwhsxVTeTAHDkyBEUFBSgY8eOKC4uFjswNDU1UVhYiMzMTISGhirtjGIVExQUhD179mD69Ono2LEj1NTUIAgCUlNTkZiYWG4Hwpo1azBv3jxxtIKOjg7y8vLEeNkooZKSEqxZswZjxoxRWI6Pjw/WrVuHkpISfPfdd3KdgImJidDW1q7QjgopKSnYs2cPBEGQ6xArW5+trS0mTZokCc/KysLVq1flRkcBwJMnTzBhwgQ0b94cvr6+4t8bZR1pFXH27FnY29vD1ta23HQBAQGIjIyEIAiYMGHCG/1+CA4OhqamJgYPHiwXd/DgQUybNg36+vo4c+YMLCwsJMelanckxhhjjLHyVOkUBqD0sTqPoAAAIABJREFUqToRoaioCGvXrlWZ/sCBA4iJicGFCxfQtm1bpKenY8KECbh79y4WLFhQ4SkMrw/lVuZtpzDIwk1NTWFkZAQiQrdu3VC/fn2YmJjIvZR9GU1OTkaHDh1w8OBBlJSUYNmyZbh16xbc3NxARHJPrWV1K9o3XRY3cuRIcapG48aNxSkXRUVFCtMXFRXh1KlTcuW9ePECRARdXV1J+4uLizFlyhTExcWJ0yaCg4OxY8cOlZ91dcSVnR4SHx+P9u3b48cff0R6ejpGjhyJLVu2KBz+LGv7zZs3JZ0AMhEREXJtyMvLQ5cuXTB79my8ePECn332GdatWwdzc3OFw6sregzlXYNBQUGSsBYtWiAqKgp79+6Ve02fPl0sQ9nUkXv37onhZa+virR1zpw5uHz5ssK6VQ3ZzsnJwZw5czB69GhcunQJV69eRXZ2NrKzsxEUFCTWcfny5XLLYeWLjY3FiBEjkJ+fD3d3d1y5cgW///67+PlGR0eXm5+IYGhoCCsrK1hZWcHExET8v5WVFQwMDGBgYCD+3lNkw4YN8PX1RW5uLvLz87F+/Xq5NNeuXYOhoaGk80+ZrVu3IiwsDJaWlpg9e7YkLiwsDAMHDoSvry9mzZolN5Xm2rVryM/Px9ChQyXhqampGDFiBF6+fIlZs2aJo4zK+znIz8+Hj48P1NXV4efnJxcfHByMpKQkaGhoSLbAVWTXrl0oLi6Gubk5Bg4cKBcv+71cdlpUWZmZmTh16hR0dXXRokULSdyLFy8wadIkPH/+HCtXrhQ/47LHVnb0EWOMMcZYZVV5B8LYsWPFpzm///47zp8/rzBdXl4evvjiC3h4eODp06fiE8oJEyZgw4YNcHR0VPpE6PVwAwMD9O3bF4Ig4MiRI+IQWUXK5i2vXEVTGMqGW1hYwN7eHoIgKPySrMqxY8cQHR0NQRCwYcMG+Pj4iMPXBUGQ+2JY3tMx2VSKsnEtWrSAIAh49uwZXrx4IUmvra0tPn1XVJ5sSPugQYMkN8YHDx6En58fzMzMEBISgs8++wwlJSUYN26cZHg/UPolOCMjQ+UUhreJK/sZzZ07FxERERAEAXv27MGWLVvg5eUlpu3Zs6eYtmfPnuJT2b/++kuujocPH8q1YeXKlbhx4wYEQcAvv/yCP//8E97e3mInS9nyK3MM5V2DsjJ79OgBQRAQHx9f7poaququX7++ws+uXr16EAQBxcXFSEtLk+SR1f3o0SOV9Srj5+cHIyMjLFmyRC5OVrcgCEhOTn7jOhjwxx9/ICYmBgDg7OwMV1dXbNmyRYxXdkMqM3XqVMTGxlbo9dVXXyksw9HREYsWLYKdnR0ASKYVAUBkZCRiY2PxwQcfqDyeiIgIbNy4EQCwePFiudETS5YswdGjR8U1Hv744w9JfHx8PAD5J+5Tp07FtWvXAAA///wzpk+fjkGDBuH69esASqc4LVy4EJGRkQCAhIQE9OvXDytXrkRJSQkWLFgg11bZzbmq4woODsaBAwdgZmaGkydPyk3jSE5OxoIFC9C3b1906dIFcXFxcmWEhIQgLi5OXOulrGXLlol57ty5g4ULF2LhwoWS87BgwQIsXLhQaccvY4wxxlh5qrwDoUuXLvD09ARQ+uSxb9++GDZsGBISEpCeno709HSEh4fj888/x969e2FgYCD5IvT8+XOkp6fj1q1b4s1dSUkJ0tPTxS9psqHdJ06cKD0INTVxeHpubi7c3Nxw7NgxJCQkYNeuXfDy8sLixYsBlA7FlvHz80NkZKRYn5eXlxgn+yL++v9jY2PF/8uevB46dAjr1q0Tn/TLniAperqvyLp167Br1y74+PiIeWJiYnDnzh2EhoZK0pZdbI6IsG/fPhw+fBj6+voYNmyYGCf7bADIPWU3NTUVb07nzp0rznkGgNDQUJw7dw5qamrw8PAAUPr0bfLkyfjiiy9gamqKs2fPok2bNtiz5//au/O4KKv9D+CfYVFAAUVJRAjkIhqu1wu44pYLSJomVmqueG8KJFmuqZlhJbjeNLMyS8Xcd1DMHYXcKpFAcY+rKIjIooBs398f/Oa5jAMMsojePu/X63nJnHOec87zMDMy3znLJrRu3Rp5eXmYOXOmxroXcXFxiIuLK/F6U1JSlKHRxe/tkwoLCzWmITxZvvjPxReJKygoQHp6usY3hXl5eXj06BEKCwvh5uampL/77rtYt24d0tPTERMTg5UrV2pM31Dfuyfrz8jIwJYtW3Dv3j2lXHZ2tvIcUJ/35OgPXYr/rtQ/d+jQAbVq1UJKSgqCg4N11lHaPS0+xaJ4mU6dOgEoCuo9OfVB/RzfsWMHTp06Vc6r+K+oqCgEBgaib9++sLS01MpXf6tdkvz8fGzYsAHJyclP3e5fTUZGBlasWAFjY2NMmzYNX3zxBQYPHozBgwfDzs4OKpVKZwDhSeoFLp9G9+7dMWfOHPj6+iprW5w8eVLJv3nzJnJzc3WOPsjPz0dAQACuX7+O+fPn45133tEqM3XqVFy+fBkjRoyASqXCDz/8gKysLCU/KSmpxECaev0OdYB12bJl2Lt3r5K+Y8cOBAYG4v333wdQ9H/K2bNn0b59e6hUKqSmpmpN8bpw4QJUKpXO0ThLly5FTk4O1qxZU+JaCQEBAViwYAFUKhUePnyoFRQB/ruGi7e3t1bevn37lGtbsmQJAgMDERgYiIiICCU9MjISgYGBCAkJKbOvRERERCWSapCfny+zZ8+WWrVqaew/XdKh3vJq3bp1oq+vX2bZnTt3ypgxY5THTZo0UbYPzMrKkv79+5d67uDBg0WkaCtAOzs7nf0yNTWV48ePy8mTJ6VOnTpKuoODg/zxxx8iInLlyhWpX7++kteyZUtxd3cXZ2dnAVDmNo5JSUnSsmVLnf3o0aOHiIh069ZNAIihoaGMGzdOgoKC5J///KcAEJVKJUFBQUrdCQkJ0qJFC6WOgQMHyrlz5zTav3DhglhZWQkAsbe3l/fee08+/vhjsbGxEQAyYsQIERHJzs6Wv//970pdrVq1kry8PKWe4nu0t2rVSvbs2SMiIr1791bSu3Xrpmw9mJeXJ+PGjVPyzM3N5cCBA0p9ERERYmZmpuTPmTNHaS8+Pl5cXFyUvJEjRyrbZ65evbrM+9iwYUOpX7++rF69WgoKCjT6UNbx9ttvy8OHD2Xfvn1Su3btMp8vjRs3llmzZkl8fLzUrVtXyVNvKykiUlBQIMOHD1fyZs+erXE/V6xYoeT1799fub42bdoo6dOnT5fY2FiJjY2Vr7/+Wtzd3WXfvn0iIhIeHi4GBgYCQDw9PaWwsFCpu0+fPkodzs7Oyu/k1q1bYmRkpPyuzpw5I+vXr5fjx4/L5cuXlddlgwYNZNOmTRIbGysxMTEyceJEcXd319hO88nneLt27QSATJgwocQyqampYmlpKQCkQ4cOGtv0vfXWWwJA2rZtq9wH0lZQUCBjx44VALJ+/Xqt/MDAQAEgrq6uUlBQUGo9P/30k3h4eCiHjY2NuLi4aKR5eHjIgAEDJDExscw+3bx5U3muffDBB0p6UFCQAJCxY8eWeb63t7cAkGHDhkl+fn6ZZefPn6+0FR4erqQPGjRIatWqpbGtr4hIZGSk+Pv7axxdu3YVY2NjASCWlpYyfPhwOXbsmMZ5jx8/lrZt2woAsbCwkJSUFCVvypQpoqenJ2fOnCm1nz/99JMYGBiIr69vqWXOnz8v4eHhYm9vr1zTmjVrlPz8/HzlvX3Xrl1a52/evFnjugIDA8Xf3188PT2V+vr16yf+/v4a70tENeG333576q1ZiYio5lVLAEFt//79Mnr0aKlXr57WBy53d3cJCQnR+IN2+fLlUr9+fenWrZusWrVKzp8/L82aNRMA4uLiIsnJyfLOO+9Iv379lGP79u3K+VlZWbJhwwalPSMjI+nXr59Mnz5dY3/xxYsXawQFAMi4cePks88+E1tbW7G1tZW33npLsrKyZM+ePdKvXz8xNDQUANK1a1eNPyx//fVXcXV11bq+Fi1aSERERJn3Z+/evdK+fXsBIJ06dZL169fLJ598otTRvXt3OXnypGRmZip/3JZ0vP/++xr1zpgxQ6vMmDFjtNqPiYlRPrwVP5YuXSo5OTkiIpKRkSGdO3fW+MCfmpqq1FE8UAFAhgwZIpGRkaKnp6eR3qlTJ8nJyZGEhASt9mrVqiVXrlwREZGhQ4dq5BVvb+DAgVrnqv8IzsnJkQ4dOmicN2XKFI3rs7OzU8rn5uYqH7qKHx07dtQImACQgwcPikjRBxJ1mqGhofj5+Unz5s2VtJdeekk2b96scb8ASN26deX7778XEZFt27ZptRkSEiIiIiEhIVpBtDlz5oiIyOnTpzWCVU8eoaGhsn//fq2gnfqD98qVK0WlUmnkLV68WPk99ujRQ6tOdf6CBQtKbbd+/fry8OFDrefWxYsXpVGjRko5JycnrTK5ublKgEF9eHp6Ku8J6mAWAElKSirtZfSX98MPPyj3uKQAwY4dO5T7+ODBg1LrUQcadB0GBgYSHR1dZp9yc3PFyclJgKJAmJr6Nffhhx+WeF5OTo5MnTpVDAwMpFevXvL48WON/EuXLmkFrFJTU5W+jR8/Xkk3NTUVd3f3MvtZ3KuvvioAZOPGjaWWOXPmjPIa8/PzU9Ld3NzE3Ny81PMuXLggjRs3llGjRmnlxcfHS3p6ukba+fPnpWHDhgIUBYhXr14tIiKJiYkCFAWyn7w3Zdm6datyj3766adyn0dUXU6dOiX6+vqSnJxc010hIqqUx48fy6hRo8TMzEzjsLKykuHDh5d6tG7dusz8ko6SvjyoCSqR6t8UOj8/HxcuXFAW8Wrbti2aNm1a4vzw/Px8jWkGBQUFKCwsVHYoKG976ssqbduv4mWKl1MPmX9yISz1cPKS6issLMSBAwc0Vizv1KlTubYpk/9fzFC99SJQNI3g0aNH6NChA1QqFfLz89GuXTvExcWhZ8+e8Pf3B1C0Snrv3r1L7NOT0xb09PRKXNwrMzMThw4dwp07d2BoaAhvb2+t1dHVfQSK5teX9PtRU+c9OXS/+HnJycmIjIxEnTp10LNnTwCa9//EiRNo3749rl69ijZt2ijnlTSlofh9KywsRHR0NO7cuYO+ffvCwMAA165dw4oVK+Do6IgJEyZo3AMRQVZWljJtxMXFBTY2NhARzJ8/Hw8ePICjo6MyHFtEEB8fj4sXL8LT0xNGRka4e/culi9fDjMzM/j7+6NOnTo4cuQItm7ditzcXHTv3h2mpqbo2rUrLC0t8Z///AebNm2CgYEBMjMz0bp1a3h4eMDY2Bj3799HRESExvU1a9ZM2erxwYMHmDBhAo4dO6bkGxsbY9OmTejYsSP++OMPLF26FEDR869BgwYYOHAg9PX1ERMTg2XLlinnubq6omfPnsqc7ZSUFHh5eSElJQXe3t7w9vaGi4uLcm9/+eUXBAQEaCzE5+zsjB07dpS4mr76d5yRkYGIiAi0aNECU6dO1SiTm5uLiRMnaqRZWlriiy++gEqlwsKFC7Fo0SJMmTJF61wqUlhYCGdnZ1y+fBkbN27EW2+9pVVm165deOONNwAAR44cKXFXAqBoCkvx9zCgaMqUs7MzMjMz8dtvvwEAbGxsSq2juJkzZyIoKAimpqaIj4+HlZUVunfvjhMnTmD79u0YPHiwRvn8/Hy8+eab2LVrl/LaUr/2MzMzsXLlSgQHB+P48eMa05AAYMaMGQgODkazZs0QHx+PqKgodO3aFdOmTcOCBQt09hUA+vTpg8OHD5d6H9UGDBiAsLAw6OvrIzo6Gg0bNoSTkxM8PDywadMmrfIhISGYOnUqkpKSsGXLFvTv31/J27FjByZMmIDw8HCtLXV3796t3KN69eohLCwMiYmJGDp0KN5+++1Sd8opyfbt2zF06FAARf+/PLnGTm5uLubMmYP+/fuje/fuGnnR0dFYvHgx7O3ttbblTEhIwPz58xEYGIhGjRqVuz9E7dq1g7W1NXbv3l2h7VmJiJ4XoaGhJS6KXB1MTEyQmpqqLJpfY2osdEFPRT2F4fPPP6/prhDRc+DBgwcyatQo5Ztl9fSh4rKzs+Xdd98tcyRSdfntt9+UETUrV64UERF3d3cBoDFtSe3J0UclHSYmJvLnn39qnaueCqOvry/bt29XRmVMmzatXH29ffu2MmLCy8tL7t27V2rZQ4cOKf355JNP5Oeffxbgv9O+ivvjjz+0RmM9edStW1fS0tK0zn38+LEyQg3/P6pKPUri5MmT5boukaLngHq6GwBZtmyZVpni0/+Kj0wSERk2bJgy8mTnzp1K+r1798TCwkIAiJmZmZw9e7bcfSJSj8ojInrRTZs2TUxNTSU0NFSuXr1arYeuKaTPCgMILwh1AGHbtm013RUieg4MGDBA44Oora2t1hQG9ZoD6kNPT09OnTr1zPqoXiPFxMREYmNjxcTERACUOPy++JSX0g71mjAlmTRpkgBFc/ynTJlS7gDCjRs3lOkC6sPNza3U8oWFhcp11atXT5n+o55mUJyvr6/Oaypr6sO1a9fEwcFBK4iSkJCg87pEioJMrVq10jhfX19f1q5dq1Gu+LpAPj4+GnnqAAIAZa0VkaJpGcXrLR5cICIi+quoU6eOvPbaazXdjWfqv2PR6bmVmpqK2NhYqFQqnDhxQmtfcyL669myZYvG9KGSpnlNnjwZTk5OyM3NhYWFBTp37gwjI6Nn1seAgABERkYiOzsbixYtQnZ2NqytrUucTvXpp58iLy+vxN061MoaIujt7Y3ly5fj4MGDSElJgUqlgqenp84+vvzyy/j222+Rl5eHuLg4PH78WGsYf3EqlQrTp0/HL7/8gvT0dBw/frzUXRFmzpxZZl3Hjh1TpnGVxMHBAUePHkXnzp2RmJgIAHBzc4Otra3O6wIAc3NzLFy4EBkZGRrpT24BGRERgTlz5sDc3ByTJ0/WyFu1ahXq1auHBg0aoF+/fkp6q1atsHfvXqxfvx4uLi7w8PAoV5+IiIheJHl5efjmm2/QpEkTremX586dQ3Z2Ntq1a1dDvasZz2QNBKqcYcOGKXNrDQwM4Ovri3//+9813CsiorLl5eWhWbNmGmtn9O3bFwcOHKjytjIzM/HKK68oW+3WrVsXt2/fhpmZWZW3BQBjxozB2rVrNdqvW7dutbT15ZdfIiAgAEDRtr9+fn7V0g4RERFpCgoKwowZMzB06FBs2bJFI+/QoUPo06cPZs2ahfnz51eqnatXr8LIyAg2NjaVqudZKN+qhFSjkpKS0KNHD7Ro0QKvvfYaFxwioheCoaEh/va3v2mkvfTSS9XSlqmpKYYNG6Y81tfXr7bgAQAsWLAAderUAQB07NhR+bk6+Pn5Ye3atVi5ciV8fHyqrR0iIiL6r0uXLmHmzJlQqVQlLv4fFhYGlUoFOzu7SrVz9+5duLm5wc7ODvr6+srx4YcfVqre6sIpDC+AI0eO1HQXiIgqpEuXLjh69Kjy2N3dvdramjdvHhYvXgwAqF27drW1AwBWVlYYPnw4Vq9ejdatW5f4h0VV0dfXx6hRo6qtfiIiItKUmJiI3r17l1kmLS0NJiYmGjssVcSGDRuQlpaGkSNHKl+86OvrY/To0ZWqt7owgEBERNXm/fffx9dff42UlBQARdslVhdjY2O4uLjg7Nmz1dqOWlBQEDp27Ijhw4dXe1tE/0tERNmim4joeZOdnQ0fHx8kJSVh8uTJWLJkCZ6c9f/w4UMcOHAAxsbGaNKkSaXaO3HiBOzs7LBq1SoYGxtXqq5ngVMYiIio2lhYWCgLBZY2BLCqqFQq+Pr6Qk9P75kEEOrXr49x48Y904Upif4XfPfdd2jYsCGio6NruitE9IISEWWB4ao2cOBAhIeHY/369VpTMdX+85//4M6dO+jRo0eVtGlmZobk5GSEhYVpLX78vGEAgYiIqtVnn30GQ0NDtGzZEvb29tXa1pgxY1BQUPDcDvsj+l/wwQcfoE2bNqUegwYNwkcffYRdu3aVeH6fPn2Qn5+P119/HWlpaZXqS2FhIaKiohAVFYWvvvoKH330ER48eKDzvPv37+PgwYN499130aZNG3Tp0qVc5xHR8+Hx48dwcHCAn5+fMsqxKgQHB+Pw4cPw8/ODt7e38uXHk+8P6vTi6y89KSEhAVFRUUhPTy+zTZVKhZiYGDRt2hQDBgxA8+bN0b9/f53n1RROYSAiomrVrFkz+Pr6wsrKqqa7QkRVwN7eHteuXUNWVhYAwMTEBI0aNUJSUhJyc3MRExOD3bt3Q09PD++99x4+/fRTjUVNmzZtiqCgIPj7+8PDwwP79+9H/fr1K9SXb775Br6+vhpprq6uWtutFZecnIwRI0bg0KFDGukRERF4/fXXK9QPIqq45ORkTJ06tVxlJ0+ejHbt2sHQ0BCOjo5YuXIlrl27hvDw8Crpy4oVKyAiWLNmDWJjY3Hz5k2ICA4fPgwvLy8MGTIE48aNw7lz5yAiJW7huGfPHkyfPh1//vknsrOzYWpqijZt2uDHH3+Eo6OjVvkuXbqgVq1aAIqmT4SHh2P//v345ptvMG3atCq5rqrEbRyJiIiI6KnY2tri1q1bsLKywpUrV5RtTC9evIioqCgsWrQIly5dAgA4OTlh7969cHJy0qjDysoKSUlJmD17NgIDAyvUj40bN+LcuXP49ddfcfz4cQBAaGgovLy8Six/9+5djBw5EkeOHEGfPn3QsmVLJW/WrFmwsLCoUD+IqOJSUlLg7u6uvGeUZezYsVizZg0AICQkBD4+PigsLMS6devKHA1QXj169MCdO3eUx7dv38ajR4+gp6cHR0dHDBgwAIsWLUL37t2RlZWFM2fOaEzPPHz4MN544w1kZ2ejadOmyMzMVOqzsbHB4cOHtd4Ln/T9999j/PjxsLS0RHx8fIUDrNWFAQQiIiIieiovv/wybt26BTc3N5w6dUorPzs7G3PnzsWiRYsAAL169dL6xj8wMBBz586FtbU1rly5UqnFw7Kzs/HSSy/h0aNHuH79eqnTpYYPH45NmzZhypQpCA4OrnB7RFS1bt26BUdHR+Tm5sLJyQn+/v7o27cvDh8+jOzsbFy+fBk//PADmjRpguvXryvn/fzzz/Dy8oK+vj5Onz6Ntm3bVmm/Fi5ciOnTp8PT0xNhYWFKeo8ePVC7dm0cOHBASYuIiEC/fv1gZmaGPXv2oEOHDkhPT4enp6fyPunq6orTp0+X2WZOTg6sra2RlpaGixcvonnz5lV6TZXFNRCIiIiI6KmIiHKUxNjYGB9//DEsLS0hIjhy5Ah2796tUWbs2LFo3Lgxbt++ja1bt1aqP8bGxlCpVGX2KSEhARs3boS+vj7Gjh1bqfaIqGrZ2NjA0NAQIgI7Ozv4+/vDyckJEydOxAcffIBVq1Zh9OjRWsHBvn37olmzZnj8+LESsKxKaWlpEBGkpaUhPz8fQFHA8uLFi3Bzc9Moa2lpiebNm2Pjxo3o0KEDAMDc3Bz79++HtbU1RATnzp3DzZs3lXPy8/O1Fk28fv06srKyYGNjA2tr6yq/pspiAIGIiIiIqlzdunUxbtw4AEUBh82bN2vk29jY4I033gAAfPnll9Xen23btgEAOnTogFdeeaXa2yOip9OlSxeNf5+0YMEC7NixQyvdz88PQNGUhtzc3Crrz5UrV7Bq1SoAQFRUFGbNmgUAyMvLQ3JyslYg8pVXXsH58+fRq1cvjXRzc3N4enoCKFr4tbCwUMmbN28eLC0tlffH+Ph4vPfee3j8+DGmT58OU1PTKrueqsIAAhERERE9FfUK5Lq2Zi2+ivmhQ4e0VhX38/ODSqXC77//jl9++aVa+7Rt2zaoVCq0b98eH374ISZNmoRJkybhxx9/rPRuEERUefn5+VCpVKWuRWJhYYF69epppbu7uyuv/ScDlZVhbW2NefPmYfny5Vi+fDlat24NAIiNjX3qral///33Et+j+vTpg7y8PIwePRoODg5o3749jh49ilGjRsHHx6fKrqUqcRcGIiIiInoquqYwqFlbW8PU1BQZGRm4d+8eHj58CHNzcyXf2NhYqefkyZPo1KlTtfXpxo0bEBF89dVXGt8AAkBQUBB+/vln2NraVrh9IqqcO3fuQESQmZmpkX7v3j0sXrwY169fx5YtW7TOc3Z2hrOzM2JjY3H06FGMHDmyUv3YuXMnQkJCMG/ePPj7+2vlb9u2Dfr6+tDTK9938eqFFEUEjo6OaNSokZLXrVs3REZGYtu2bTAyMoKLiwtatGjxXI+SYgCBiIiIiKpF48aN0bBhQ605vsXzHR0dcfXqVY2Vz59WQkJCmUOXs7KylPnLhYWF8PDwgJubG86cOYPw8HBcunQJwcHBWL58eYX7QESV06ZNG8TFxeGjjz7Czp07lW/qz549CxEpdXtWAwMDvP7664iNjcWVK1cq3H7xxV/Vgcjt27drlYuPj4erqyvs7OzKVW9QUBASExOhr6+Pb7/9FiYmJhr5nTp1qlTw9FnjFAYiIiIieirlncKgq3ytWrVgYmLy1MOBn5SRkYGCgoJS67l48SLu378PlUqFZcuWYd++fZg3bx52796NQYMGQaVSYdeuXUqQgYieveLvE+fOncPZs2dx9uxZjbzS1K9fHyqVCjExMRWeknTw4EFs3boVjRo1gkqlws6dO3Hs2DGNMqmpqTh69Ci6detWrjrDwsKwePFiqFQqzJkzBz179qxQ354nDCAQERER0VMp7xSGuLg4XL9+HSKCpk2bokGDBhWu62n6VVYbr776qvJBpFatWli4cCFEBLdu3SpxS0oiejbUr9Hx48criw0WFhbizz//hJeXV5nvEepzHz58qLHLwdMYOHAgbty4gYMHDyo7QixZskSjTExMDLKysuDq6qqzvtzcXEyZMgU5OTkYOXIk5s6dW6F+PW8YQCAiIiK5i0f7AAAGn0lEQVSiarFnzx7l5759+6J27doa+Xfu3MHVq1cBAC1atKhwO/fv3y9z9EDLli3RsGHDEvMcHBzwj3/8AwCQlJRU4T4QUdVQL1aoZmtri2+//RbDhw/Xea6FhQXatWtXqfZbtWql7Axz4MABrSCCkZGR1haOJZk7dy4uXboEFxcXfPLJJ5Xq0/OEAQQiIiIieirlmcKQm5uL9evXQ6VSoV69eggMDNQqk5eXh5ycHKhUKjg5OVVJf0rqk7GxMQwNDaFSqRAdHa2RV1hYiOzsbKhUKvTt27fCfSCiyhGRUl/DjRs3hre3d6nn3r17t9JToYrz8fGBh4cH8vLyMGPGDFy8eBFAUUDByMhI54Kr3333HRYtWoTOnTsjKioKTZs2rZJ+PQ8YQCAiIiKip6IeLpyTk6O1owFQtH/6wIEDERcXBxHB8uXLSxwBcOTIEYgInJ2d0aNHj0r3R0Rw48aNEsv07NkTIoKQkBCNPsfFxSEuLg62trZai5sR0bMTFhamczrTggULsGDBAo203Nxc7NmzByICe3v7KumLgYEBgoKCICLIy8tDcHAwgKIdGnS1cejQIfzrX/+Cvb09Nm7cCENDQyXvwYMHGDx4ME6ePFkl/awJDCAQERERUbl9//33ylD/6OhoBAQEYNWqVThx4gRmz56NN998E506dcKBAwdQp04dfPzxx3jnnXdKrGvVqlUAAD8/vwr3JycnB0uXLlUeR0RElFhu4sSJAIDw8HBlSHJ6erqS7uPjA319/Qr3g4gqLj09XQnspaamlljm0qVLmDlzJkJDQzXSExMTlalQ5V3csDzatGmDQYMGAQA2bNiAJUuW4N69e2jZsmWp52zevFnZRtLa2hpXr17FiRMnsHv3bkyfPh2jR49+4RdsVUlVrFhDRERERP/zUlNT0bhxY+Tl5ZVZzsTEBA4ODlizZg1cXFxKLPP111/Dz88Penp6iI6OLvOP8tLk5eWhefPmGoumGRgYYNy4cUpwQk29DVxoaCgKCwthZmaGgoICPHr0SAl41K1b96n7QESVt27dOowZMwYAYGVlhYCAAMTExCj5aWlpOHjwIPLy8vD5559jxowZSt769esxevRoAMC1a9eqdLpAeno62rdvrzGyaenSpQgICNAqO2nSJKxcubLEUVnFtWrVCufPn4ee3ov5Xb5BTXeAiIiIiF4MFhYWOHXqFDIyMpS0u3fv4ty5c8pjBwcHjBkzBsbGxqXWk5OTg48//hgighEjRlQoeAAUrX0wZMgQHDt2DE5OTjAzM9Padq142V27diEkJAQLFy5Ebm4uAGD8+PEYP348gwdENeTEiROYOHGiMnXhzp07GgGC4gwNDTFkyBCNtK+++goiAldX1yqbwqBmbm6OWbNmwcfHR0kr/nNxkZGRKCgoUB43bdoUCQkJGmkA0K9fvxc2eABwBAIRERERPWP79+9H//79YWxsjLNnz1Y4gEBEL77ExERs3bq1XGUdHR3h5eWlPD59+jS6deumrIMwYMCAKu9fTk4OevfujcjISABAZmZmiQHHjIwMJCcnK49ffvll3L59WyuAYG9vDwODF/d7fAYQiIiIiOiZiYmJQa9evfDw4UPs3LkTHh4eNd0lInoBpaamom3btrh9+zZ8fX0RHBxcbQuh7tq1C+PHj0eDBg1w4cIFrS1p/0oYQCAiIiKiZ2bMmDFYu3Ytdu/ejYEDB9Z0d4joBSQi8PLywv79+9GtWzeEhobC1NS0prv1l8AAAhERERE9M7/++ivS0tLQs2fPF3oeMBHVnOzsbJiYmMDJyQlhYWFwdHSs6S79ZTCAQERERERERC+MwsJChIaGomfPnhx58Iwx7EtEREREREREOnEEAhERERERERHpxBEIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpBMDCERERERERESkEwMIRERERERERKQTAwhEREREREREpNP/AbfpyqwYlbHYAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "d3096c77-6067-47ea-aae7-fd8162d5159e",
   "metadata": {},
   "source": [
    "![image.png](attachment:38d56fa3-23ed-422b-a236-0786f0385b0a.png)"
   ]
  },
  {
   "attachments": {
    "8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "db2b7539-767f-4a22-b86b-95bf32dcd431",
   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5a600271-2a44-43ce-b06d-b0559c5b384a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A = 2 \\sqrt[4]{A}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(A,rpow(2*rpow(4*A,2),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fa6b239b-3d55-4bde-9353-581026c89fb6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A^{4} = 16 A$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Pow(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "21bd03db-1849-4bcc-90aa-f80a651e1f46",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A^{3} = 16$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f8d10e32-574a-4068-9fe6-7b92bc71eccb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A^{3} = 2^{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.primefactor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "43f82ad5-1caf-47b6-9510-a17224e7441e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt[3]{A^{3}} = 2 \\cdot \\sqrt[3]{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Rpow(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "43785b2e-7646-4c8d-ab7a-4219fc40ffb0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A = 2 \\cdot \\sqrt[3]{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ee6b2716-5523-4a6e-9add-47d28dbd4d91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A = 2 \\cdot \\sqrt[3]{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "3be5efc1-7652-45e4-9477-d5c9dfcee76c",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "21e3ab7c-58ca-4c10-bf5a-3b5e05922ad1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "4d5fe3a3-151c-464e-8946-c4dadd4a89dd",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "94a3eb4e-f102-4746-92dd-32d7ebcca9ee",
   "metadata": {},
   "source": [
    "![image.png](attachment:9c45fd55-f23b-4b05-ba86-8da17250dff7.png)"
   ]
  },
  {
   "attachments": {
    "8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png": {
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    }
   },
   "cell_type": "markdown",
   "id": "12acaf16-0c64-4c93-98b5-5fcab260448d",
   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "06060309-a0fa-435e-a703-b43df67ac4e2",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def fx(a,b,c):\n",
    "    m1=kpow(b,c)\n",
    "    return kpow(a,m1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2b5eebe3-4fae-4460-ba72-912ff9798ee9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =a^{b^{1 - a}} + b^{a^{1 - b}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =a^{b^{a + 1}} + b^{a^{b + 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e3 =a^{b} b^{a} + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq(fx(a,b,1-a)+fx(b,a,1-b),'e1')\n",
    "e2=MyEq(fx(a,b,1+a)+fx(b,a,1+b),'e2')\n",
    "e3=MyEq(1+kpow(a,b)*kpow(b,a),'e3') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c3c8b5de-8e39-41f1-bf3a-33f1a9fb73ef",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{a^{b^{1 - a}} + b^{a^{1 - b}}}{a^{b^{a + 1}} + b^{a^{b + 1}}}\\right)^{a^{b} b^{a} + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4=MyEq(kpow((e1/e2),e3*1),'e4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8b0cc2f7-2bf4-4319-a908-43d1e0029cc6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{a^{b^{1 - a}}}{a^{b^{a + 1}} + b^{a^{b + 1}}} + \\frac{b^{a^{1 - b}}}{a^{b^{a + 1}} + b^{a^{b + 1}}}\\right)^{a^{b} b^{a} + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6f9510ad-1046-4507-ac73-9a76003491e6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{a^{b^{1 - a}}}{a^{b^{a + 1}} + b^{2 a}} + \\frac{b^{\\frac{a}{2}}}{a^{b^{a + 1}} + b^{2 a}}\\right)^{2 b^{a} + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.subs(a**b,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9dd2d84c-301d-4e9a-9bb2-986bab5f5c3c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{a^{2 b}}{a^{\\frac{b}{2}} + \\frac{1}{4}} + \\frac{b^{\\frac{a}{2}}}{a^{\\frac{b}{2}} + \\frac{1}{4}}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.subs(b**-a,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ce0e755f-0121-4774-9f15-92a3d92c8243",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{b^{\\frac{a}{2}}}{a^{\\frac{b}{2}} + \\frac{1}{4}} + \\frac{4}{a^{\\frac{b}{2}} + \\frac{1}{4}}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.subs(a**(2*b),4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "7f5d9188-1b36-4477-86e7-0dba11472786",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{b^{\\frac{a}{2}}}{\\frac{1}{4} + \\sqrt{2}} + \\frac{4}{\\frac{1}{4} + \\sqrt{2}}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.subs(a**(b/2),sqrt(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f6f4f494-5214-4672-8008-2b5c4857a08d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =\\left(\\frac{\\sqrt{2}}{2 \\cdot \\left(\\frac{1}{4} + \\sqrt{2}\\right)} + \\frac{4}{\\frac{1}{4} + \\sqrt{2}}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.subs(b**(a/2),cfrac(2)**cfrac(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7f6f5a30-407d-416c-9b65-b8f338ed4580",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e4 =8$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e4.simplify()"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABTwAAAAaCAYAAACaXpMbAAABRUlEQVR4nO3csQ3CQAxA0QSFAbwCa7BMmkxFwzJZg5YyDR1FmAByJwgnWe/VjuT6K74+ItYOAAAAACCBQ+sFAAAAAAB+RfAEAAAAANIQPAEAAACANARPAAAAACANwRMAAAAASEPwBAAAAADSGGqG43reaw8AAAAAgG4Z56++7yNi3RoSOgEAAACAFmoD6OZJu9gJAAAAALRS2ye94QkAAAAApPExePq7EwAAAABo7TiduuN0Kpr9GDy/fSAUAAAAAOCfnLQDAAAAAGlsBk9/eQIAAAAArTzme9X8UDK0jHPxjTwAAAAAQCtO2gEAAACANIqD5/Ny23MPAAAAAIC3SvtkHxHrzrsAAAAAAPyFk3YAAAAAIA3BEwAAAABIQ/AEAAAAANIQPAEAAACANARPAAAAACANwRMAAAAASEPwBAAAAADSeAHWwBv4lUmkzwAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "5a685017-acb8-4f06-98b4-9b541faaebc9",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "1666be24-1e72-4900-b89b-f512c52e2f77",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
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   },
   "cell_type": "markdown",
   "id": "90345386-1f55-4df2-b8b8-2da9db50f2a1",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
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"
    }
   },
   "cell_type": "markdown",
   "id": "bd14fb2c-a992-47d8-b5b8-f3603e8c31bf",
   "metadata": {},
   "source": [
    "![image.png](attachment:8a761dd8-b5c1-4ca5-9445-75cfbb95471f.png)"
   ]
  },
  {
   "attachments": {
    "8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "2bd53e3e-19c7-42f1-b245-2fa707e6599e",
   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "80c4a5dc-df9c-4c36-a783-20ae8b8b4818",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{x^{2 x^{x + 1} + 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x**(x**(1+2*x**(1+x))),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c0123358-5e87-4d12-ad20-e5ecf99b75c7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{16 x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a24dc422-5ea5-4eb6-88fa-3aa5e3bbd2ab",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{a x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we will set a=16\n",
    "P.subs(16*x,a*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "25eef93b-58bc-4908-a690-64c1801181c1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(x^{x}\\right)^{a}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.powexpand(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "aeb7aa79-dfa3-4a20-bc2e-ca06853de5e0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2^{a}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "64e777ff-7467-47c4-b648-43e1f1e69516",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =65536$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(a,16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ef1a6ccd-64be-47e6-8e7b-a2c93bb54bb4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2^{16}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.primefactor()"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "cc779c11-0766-4ea9-9697-e5ba65a0b4db",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "c059d38d-6430-4596-97dd-9344b94c7cbb",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "df0295ab-a8f0-4de6-b7ab-787d7367ccc6",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "516dced8-6fa9-4b99-a200-4b08298373c0",
   "metadata": {},
   "source": [
    "![image.png](attachment:1494b4f6-8275-4f7c-915a-ea865f4e0e41.png)"
   ]
  },
  {
   "attachments": {
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   },
   "cell_type": "markdown",
   "id": "756a6a6c-e5e3-4b0d-b3f0-7c8c5f84453c",
   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "attachments": {
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     "image/png": "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"
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   },
   "cell_type": "markdown",
   "id": "0a8e0b69-e8e4-4114-8dfb-f10baf1ccc62",
   "metadata": {},
   "source": [
    "![image.png](attachment:2c53e251-0f4b-4dae-ab86-1c991b37ce47.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7ba1d73e-fc6a-45ab-b384-041955d9362e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =x^{x + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq(kpow(x,1+x),'e1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "b5804aaf-4cdf-45a9-a919-ed16d380766e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =x^{x + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1.set(kpow(x,x),2)"
   ]
  },
  {
   "attachments": {
    "b842f6e5-13e6-434e-beb8-bf050c6f37f0.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "88ead5c7-2db6-4e99-b96e-9c0c962e6c4b",
   "metadata": {},
   "source": [
    "![image.png](attachment:b842f6e5-13e6-434e-beb8-bf050c6f37f0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "5486e8c2-16e8-45f5-90cf-423c5f96da78",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =x^{2 x^{x + 1} + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e2=MyEq(kpow(x,1+2*e1),'e2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "e64d4531-40c8-4d46-8638-a3c527d55b4a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =x^{2 x^{x + 1} + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e2.set(kpow(x,x),2)"
   ]
  },
  {
   "attachments": {
    "a58b5768-a48f-4dc9-8fc8-bfc2b872b8cd.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "8cdc0759-2f6c-4125-bdbc-13dbf7152b36",
   "metadata": {},
   "source": [
    "![image.png](attachment:a58b5768-a48f-4dc9-8fc8-bfc2b872b8cd.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "ca3b5292-9980-4f92-b63a-a9c6a46c252a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e3 =x^{x^{2 x^{x + 1} + 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e3=MyEq(kpow(x,e2*1),'e3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ecd64cb0-792e-4d7a-9857-10824f5c277b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e3 =65536$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e3.ksym=kpow(2,16)\n",
    "e3.s()"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "40b81955-3086-446c-81bf-b999761dd2ad",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "f4e01b39-4bd3-461c-aa8e-0ac36e7758a5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "9fe2f7f1-c738-4017-bd6f-795a9d2aa8e2",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
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"
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   "source": [
    "![image.png](attachment:fc99cb5e-1a01-4fbe-a0ea-3ed4e59b647e.png)"
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   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "3f1c1882-acb6-42b0-8b08-0c28ce11ffcc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def testx(x):\n",
    "    return (5**x+4**x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "a395f7ee-1780-410e-a7c9-d1936917cc79",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAOCAYAAADNGCeJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVQ4EaWT3Q3CMAyEKeoAFWzQEfjZgBUQG9AN4LXPbACMABvABkiMwAjQDcp3lRulpSkSWLKc+C5XO3WisiwHXZbn+YR8Rsx68BPYFE4hTtxFtJyIdx/nUML+iD/xGZ7izjrFOLRxDG9hFSyVMo6qdzZ0K1tAEkFlV6W38b79hxjkFYKHvkMhrCFmpe9D5G95J4ZQCrkgPr4dCuFODILG4Kf2avFKDJE1iZ/bc2LWXvJPe7WY5kx3NUdMQ+qbRiS1/IO49cGudQzpCiBvGPkXiSuxGtIGGNj4P6BN0dORh2xswKgmRO2HTiX6EWp9YaQz8UZ+pz2xvg7h+pjer8bp8gYE60xz/3RESwAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle 41$"
      ],
      "text/plain": [
       "41"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testx(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "d365a46d-489b-48d5-bedf-aeac0b6f8833",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{x} = 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MQ(x**x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "d13dca5a-cb25-44db-b9d7-f451467dae27",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P1 =x^{x - 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1=MyEq(x**(x-1),'P1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "1adf5419-c95a-4010-b597-8bbec9f77389",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P1 =\\frac{x^{x}}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1.disjoinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "5449eddd-3070-41be-b30b-bb8a6c742a11",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P1 =\\frac{x^{x}}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1.set(x**x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "47c16b25-128d-4eae-8663-8178b7942fbc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P2 =\\left(x^{\\frac{5}{k}} + x^{\\frac{1}{k}}\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2=MyEq((x**cfrac(5,k)+x**cfrac(1,k))**2,'P2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "c4c3cae8-d521-4ed4-8b47-890a5679d3be",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P2 =x^{\\frac{10}{k}} + 2 x^{\\frac{6}{k}} + x^{\\frac{2}{k}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "032f208e-19ec-407b-ac3c-91e9fb54fa0c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P2 =x^{\\frac{10}{k}} + 2 x^{\\frac{6}{k}} + x^{\\frac{2}{k}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "68b64038-cc7d-4a8d-8ea6-cf2f793da390",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P2 =x^{\\frac{10}{k}} + 2 x^{\\frac{6}{k}} + x^{\\frac{2}{k}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2.set(k,P1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "73472d31-0560-404c-900b-cb81e535e837",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P2 =x^{10} x^{\\frac{1}{k}} + 2 x^{6} x^{\\frac{1}{k}} + x^{2} x^{\\frac{1}{k}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2.disjoinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "91b9b006-c6e0-4f71-885a-854bcb07306e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P2 =x^{10} x^{\\frac{1}{k}} + 2 x^{6} x^{\\frac{1}{k}} + x^{2} x^{\\frac{1}{k}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P2.set(x**x,2)"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABTwAAAAaCAYAAACaXpMbAAABRUlEQVR4nO3csQ3CQAxA0QSFAbwCa7BMmkxFwzJZg5YyDR1FmAByJwgnWe/VjuT6K74+ItYOAAAAACCBQ+sFAAAAAAB+RfAEAAAAANIQPAEAAACANARPAAAAACANwRMAAAAASEPwBAAAAADSGGqG43reaw8AAAAAgG4Z56++7yNi3RoSOgEAAACAFmoD6OZJu9gJAAAAALRS2ye94QkAAAAApPExePq7EwAAAABo7TiduuN0Kpr9GDy/fSAUAAAAAOCfnLQDAAAAAGlsBk9/eQIAAAAArTzme9X8UDK0jHPxjTwAAAAAQCtO2gEAAACANIqD5/Ny23MPAAAAAIC3SvtkHxHrzrsAAAAAAPyFk3YAAAAAIA3BEwAAAABIQ/AEAAAAANIQPAEAAACANARPAAAAACANwRMAAAAASEPwBAAAAADSeAHWwBv4lUmkzwAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "d2e37cb5-9faf-45ff-852a-bbcd4a49b003",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "fd8e7fe6-2501-4182-a1ed-cbbdc5d4009d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a56abb9c-e55c-43cd-9d3d-39a292c16989",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "8f87acc9-08b3-4ae9-9b25-75cb400dd2f7",
   "metadata": {},
   "source": [
    "![image.png](attachment:c94224e5-7bb0-4d18-a02c-f0de5cfe1640.png)"
   ]
  },
  {
   "attachments": {
    "8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "7c4c4ae4-938c-4147-9e99-97c55b5af6e0",
   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "4a71514f-e2af-40d1-89a6-2415e1d6cbfd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{\\frac{1}{m + 3}} = \\left(2^{m + 2}\\right)^{m + 5}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=MQ(sqrs(x,(m+3)),ppow(ppow(2,m+2),(m+5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "6edfd4ac-17c3-44ad-847e-8e62e3caaac9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x^{\\frac{1}{m + 3}}\\right)^{m + 3} = \\left(\\left(2^{m + 2}\\right)^{m + 5}\\right)^{m + 3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X.Pow(m+3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "ab875c72-76ec-482a-b6e2-3a2924b75331",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\left(2^{m + 2}\\right)^{\\left(m + 3\\right) \\left(m + 5\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "3b0a3e6d-a635-4338-aad2-bfe9d52b84a3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = 2^{\\left(m + 2\\right) \\left(m + 3\\right) \\left(m + 5\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "d516b25e-554d-48c4-8891-53c899440790",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x=2^{m \\left(m^{2} + 10 m + 31\\right) + 30}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=X.solve(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "adc466a8-ef29-4963-8a5f-c21769b39177",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\frac{1}{y}\\right)^{\\frac{1}{m + 7}} = 2^{m \\left(m + 3\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y=MQ(sqrs(frs(1,y),(m+7)),ppow(2,m*(m+3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "a4fa247c-21c5-4e42-9727-74055354baed",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y^{- \\frac{1}{m + 7}} = 2^{m \\left(m + 3\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "3fc2a67e-b36d-432a-9a55-49eb6408deb9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(y^{- \\frac{1}{m + 7}}\\right)^{- m - 7} = \\left(2^{m \\left(m + 3\\right)}\\right)^{- m - 7}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y.Pow(-(m+7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "46d96132-41f1-4ba1-83d9-053bc6f39ee5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y^{- \\frac{- m - 7}{m + 7}} = 2^{m \\left(- m - 7\\right) \\left(m + 3\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "7ed58010-5d92-49c4-9660-b47982603dc9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 2^{m \\left(- m - 7\\right) \\left(m + 3\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "a69d866f-5f53-4303-b209-5a2f15fae650",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = 2^{- m \\left(m + 3\\right) \\left(m + 7\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "43c6b8a4-40c0-425c-8332-418bbe41c1be",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y=2^{- m \\left(m^{2} + 10 m + 21\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y=Y.solve(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "4b94a06e-66c1-458f-9fac-db7d191cbfb2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle z =2^{- 10 m - 35}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z=MyEq(ppow(2,-5*(2*m+7)),'z')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "f405daa9-b286-45a6-8b29-82b00ad2ab3a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =2^{- m \\left(m^{2} + 10 m + 21\\right)} 2^{- 10 m - 35} \\cdot 2^{m \\left(m^{2} + 10 m + 31\\right) + 30}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MyEq(x*y*z,'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "2bb689d5-3cf9-4afe-a745-818a7f2ec83c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\frac{1}{32}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "attachments": {
    "f604a6f6-5218-40f9-b526-696763e55607.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "e9819473-565f-4246-83e9-35b0654bb5ab",
   "metadata": {},
   "source": [
    "![image.png](attachment:f604a6f6-5218-40f9-b526-696763e55607.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5e3a7dd4-1ec7-4c01-830b-e15cd06d1e8c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "6e454911-5f71-4eba-b87b-00ec053a53f5",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "e7a7b703-bf92-4f5b-ae8b-8a79cbb679f8",
   "metadata": {},
   "source": [
    "![image.png](attachment:41b957b7-470e-497e-9ce2-48b15f3c5549.png)"
   ]
  },
  {
   "attachments": {
    "8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "80b57a5b-ca85-40f5-a54e-7ca9ac1f16c2",
   "metadata": {},
   "source": [
    "![image.png](attachment:8bd895b7-0cd2-4f0a-9639-485a2209d1b8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "c69a5d05-110e-4b18-88f9-3ba7583de1b0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =- x^{2} + x + 13$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq(x-x*x+13,'e1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "3035eb5f-9e50-4893-94a2-8d41464a4c45",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =- x^{2} + x + 13$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "62ec3358-ebc9-4460-aec8-d7d4879241db",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{- x^{2} + x + 13} = x^{2} - 12$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEqEq(ppow(x,x-x*x+13),x*x-12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "ba834d8b-d93e-4b1e-808c-a8de93175a06",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{- x} x^{- x^{2} + x + 13} = x^{- x} \\left(x^{2} - 12\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Div(x**x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "8c56f122-93da-476a-8ac1-a97974361674",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{- x} x^{- x^{2} + x + 13} = x^{- x} \\left(x^{2} - 12\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "70a1b5d7-e073-472f-ad49-99205f624f09",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x^{- x} x^{- x^{2} + x + 13}}{x} = \\frac{x^{- x} \\left(x^{2} - 12\\right)}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Div(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "7266b3e0-05aa-4021-a9cf-febad99acb71",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{12 - x^{2}} = x^{- x - 1} \\left(x^{2} - 12\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "0b2932d2-3812-4e16-86ed-eb6516b36542",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x^{12 - x^{2}}}{x^{2} - 12} = x^{- x - 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Div(x*x-12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "e71a6d61-6832-474e-a988-29a84f7cb25c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} - 12 = x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  then x**x-12=x\n",
    "Q=MQ(x*x-12,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "188c04b5-fad6-4b02-b2e0-bebb27f78016",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} - x - 12 = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Substrac(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "308499bd-82aa-4cab-a924-ba3c22c7ab61",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x - 4\\right) \\left(x + 3\\right) = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "328d5009-9931-4d9b-912a-27e004f0cfb9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ -3, \\  4\\right]$"
      ],
      "text/plain": [
       "[-3, 4]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(Q.L,x) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74bfd500-7d93-405d-89ef-3511586be1ce",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
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