10060 Preliminary Equations.ipynb

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    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
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    }
   },
   "cell_type": "markdown",
   "id": "2838db90-ee82-4b7f-95c3-1e5b34e45dba",
   "metadata": {},
   "source": [
    "![image.png](attachment:fe4d89c2-2fe0-4968-89ec-eacf08018c0b.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "682bb6d7-01ec-47e6-866e-98c65ae922a0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    " \n",
    "from Libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "59c620ca-3df0-4dab-845f-5ea234d58603",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "5092855c-bd35-4c3b-9e48-ee11f9ec42b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from Libaldomath  import *"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "69b625b5-c204-48b5-ab1f-775b3a33a022",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c7722bdc-1d0f-4a03-b319-2ec0a6c827ab",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ -2\\right]$"
      ],
      "text/plain": [
       "[-2]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# classic metohode\n",
    "solve(x+2,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "58be60d4-28bd-4b52-92fb-869fed50c240",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =3 x y + x + 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# usin MyEq and MyEqEq\n",
    "Q=MyEq(3*x*y+x+2,'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "622a7095-cd1c-4eff-a0de-88c5c8572582",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =- \\frac{2}{3 y + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=Q.solve(x) # solve(x) return the value of variable finding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "300d4904-33a8-4fbb-9d95-e65fca15c806",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# what is the difference of these methode... see beloww..\n",
    "# x(y=2)   this jump error..because x is a symbol variables..but... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "81a4a1da-ce36-4145-a0eb-72f935497b4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =- \\frac{2}{3 y + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=Q.solve('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7a6a5bc4-e211-4310-ab72-8051452f1c43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{1}{5}$"
      ],
      "text/plain": [
       "-1/5"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x(y=3)"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "5bae1e7a-3f4b-4c56-97ab-4104cbb3e82a",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7e2db3b8-2330-4aa7-9ec7-90e780a55a81",
   "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": "1b9bc74d-ff43-4ee7-a4b3-84370a6a8c81",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "bb60df4d-4679-42ad-9091-489bd8f21732.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "cca5afd8-4914-4615-a89a-d129b13df14a",
   "metadata": {},
   "source": [
    "![image.png](attachment:bb60df4d-4679-42ad-9091-489bd8f21732.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d9aab39d-bd65-4be4-9f57-a2975eef5686",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =c + x^{2} - 6 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x*x-6*x+c,'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e79dc1fe-9416-4438-825e-ae91e2006623",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =3 - \\sqrt{9 - c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "3 - sqrt(9 - c)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.solve(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "3c82092e-76d0-4349-951e-6f0fc84df12e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A =x + 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MyEq(x+4,'A')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "48ce4a56-caf5-4823-a996-0999808b9474",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAOCAYAAADaOrdAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVQ4EbWU7w2CMBTEq3EA4giOgCs4gsYNZAO/0jVwBRxBJzBxBFaQDfB3CY9E0w/+eX3J5Wjh3TXX0jAMQ/BGXdclaEx3HvJUi+zSpN1NYoxHEzd2NcGgRLgfYR7B1QTVPUanSX18cDMZY2reDTR2McFghVYPd9lMEK5SMZnhgpcFgysQf1o7+u76GD5AyZhMTCY6DWub+IbpVUwFnIzJtGb6K38txDf0Von+LXNa/AV07leKFs2V8gBt7mtF+zvt8V9xIfRSxKcDoH1SjKozuD0BwkfB66uFKFcAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle -4$"
      ],
      "text/plain": [
       "-4"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.simplesolve(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7fe1bed2-c029-4bab-be39-93c43ad6fc4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGIAAAAVCAYAAAC9gjt3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAADd0lEQVRoBd2Y7VHcMBCGDyYFAOmAdBBIB6QDSAdAB2Hyj38Z6ACoIAMdQCoI0AGkgsB1QJ7Hp3Vkx74hmfOhY2d0Wq1k691Pybf09PQ0ek10eHj4Hn1uFk2nN4sG+Bl4j1izgUNun7G2mCXLxSCZAZCUDaNFc4KqvypHoM8XmhmxcFSXJqJoHfT7SYMVesdHyK+SrOgu4V9v42V8kgFfg99FNs5kRbCVIwCm4Q/owxEj+G1kl/Q7tIsi0E4HcaAOsQTM6uShfQJ/rJzeg/wnvWfIvbJSKErTHoD2AKfxgyITTPeiCdwafZM+MIv3jLaGrHKCAngP8GtaniVOvTiFIwRoutoqAnTNh6zg3nPhawufQdUV9eq6hX46rxiK0mQkreaoABrZUVz0tHBqUA2bl9Uw8kO+NvG/Ur9Jn2dQx9L5ierDOt8SpbYYG2X78Kf5XIG8pbNxUwLzmCZUD+c2vU2C9fbEvMZgE28EhJXnuuEIFniY6YQPtKinsC9D4DErNeq0yN1m/l0HQi8Y6tImdZQiayajOfyCU+df0rwYVRcgeivOznK+P8Jb2jFtB/k32g18lKh86eA8+35mEw/cRrTnG6c1faVz17WsqZ0BrxOMQKnr/JjMDPerEy7Akd9CPyG7XJr2XxMPPLLIyFmFDwUY/iHkzn+n2T+XvBKbcZ3EnAbTUJYdHdL5lwXr7mhd2cAjlRPEpCPvaJakHzSjUlnnO5GPeOcQOhkw3k47bVmVJjau0pW+bRyvekaULfciwwnxzBhuI8az6AMHvTchHaFDzNKamFOpvmyo1iVs9SGuEFlkWG9GpOdmqhNbG/lX6d1CaVCUJj98LEP/EtWNFw0xSKC9LHgOGMk5+fH2PxcJg67XIPkGs+KTXbWtpamTwhFGtbXLPieveNK0w3KyYrjfiOD8q9lzqwtvjQJddN5jMkIlT7zZXb+rfmBAhn3DrtE3dmN+KxwhsIa3mFTZFZpX2M4XNN420IC9LSEGwh68eCRLVfsDrprIfsyg9nfEOTL1aZfg7LHBWLO3UV7dCSwG2kN9WCMwUvKFKlLEn34Jm4FiwOiYj8gatR/ZX5SUVB4OPEf2Ytmd4fHyIInrFPm4dkQlLvgHsJ5jBoeO8NbVe9gWrEYvtChNvQsKmrAUGUH3r80J2nhhHIHxvT5b2+d60GqkedBvDu08u+ocurUAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle 3 - \\sqrt{9 - c}$"
      ],
      "text/plain": [
       "      _______\n",
       "3 - ╲╱ 9 - c "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.simplesolve(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5169f4ee-f075-4fe7-8813-3c8b3ce03bda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x1 =3 - \\sqrt{9 - c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x2 =\\sqrt{9 - c} + 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ 3 - \\sqrt{9 - c}, \\  \\sqrt{9 - c} + 3\\right]$"
      ],
      "text/plain": [
       "⎡      _______    _______    ⎤\n",
       "⎣3 - ╲╱ 9 - c , ╲╱ 9 - c  + 3⎦"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqSolve(P.ksym,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "edc5c413-5e6a-4629-9a00-f97c320c310e",
   "metadata": {},
   "outputs": [
    {
     "ename": "UnboundLocalError",
     "evalue": "local variable 'vecname' referenced before assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mUnboundLocalError\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[22], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43msimplesolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mP\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32mD:\\Libaldo2\\Algebra-Math-Symbolic-Biblie-main\\Libaldo\\lib_MyFunctions.py:26\u001b[0m, in \u001b[0;36msimplesolve\u001b[1;34m(kshow, *args, **kwargs)\u001b[0m\n\u001b[0;32m     25\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21msimplesolve\u001b[39m(\u001b[38;5;241m*\u001b[39margs,kshow\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m,\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m---> 26\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m simplesolve2(\u001b[38;5;241m*\u001b[39margs,kshow\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m,\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
      "File \u001b[1;32mD:\\Libaldo2\\Algebra-Math-Symbolic-Biblie-main\\Libaldo\\lib_MyFunctions.py:130\u001b[0m, in \u001b[0;36msimplesolve2\u001b[1;34m(kshow, *args, **kwargs)\u001b[0m\n\u001b[0;32m    128\u001b[0m         lvalor\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mlist\u001b[39m(kres[i])\n\u001b[0;32m    129\u001b[0m         nvecval\u001b[38;5;241m.\u001b[39mappend(lvalor[i])\n\u001b[1;32m--> 130\u001b[0m         nvecname\u001b[38;5;241m.\u001b[39mappend(\u001b[43mvecname\u001b[49m[i]\u001b[38;5;241m+\u001b[39m\u001b[38;5;28mstr\u001b[39m(i\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m))\n\u001b[0;32m    131\u001b[0m sname\u001b[38;5;241m=\u001b[39mnvecname\n\u001b[0;32m    132\u001b[0m vvar\u001b[38;5;241m=\u001b[39mnvecval\n",
      "\u001b[1;31mUnboundLocalError\u001b[0m: local variable 'vecname' referenced before assignment"
     ]
    }
   ],
   "source": [
    "simplesolve(P(),x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f2c87e3-2827-445a-9c34-9d834927cceb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7b6cb2f7-f2ee-45e8-9742-3ff27292d124",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =3 - \\sqrt{9 - c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "TypeError",
     "evalue": "cannot unpack non-iterable MyEq object",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[17], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m a,b\u001b[38;5;241m=\u001b[39mP\u001b[38;5;241m.\u001b[39msolve(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mx\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "\u001b[1;31mTypeError\u001b[0m: cannot unpack non-iterable MyEq object"
     ]
    }
   ],
   "source": [
    "a,b=P.solve('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6ea2a90-c8fb-48e9-8ebd-569884c76089",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1bdd426c-32aa-4d2c-a69f-f915425ba1a2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c + x^{2} - 6 x = a b - a x - b x + x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f5464b5a-e330-449c-b602-d0a4318fa046",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( \\left[ 1, \\  -6, \\  c\\right], \\  \\left[ 1, \\  - a - b, \\  a b\\right]\\right)$"
      ],
      "text/plain": [
       "([1, -6, c], [1, -a - b, a⋅b])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.coef_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "800aff73-5e68-4a37-89c2-ed9fe15c102d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b = 6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a^{2}}{9} + \\frac{b^{2}}{9} + \\frac{2 c}{9} = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(a+b,6) #a*b=c\n",
    "P=MQ((a*a+b*b+2*c)/9,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "fa83c204-b7f0-4ab0-ac6e-d377e7340f1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(a + b\\right)^{2} = 36$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Pow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "5f0de7ff-769d-4125-a659-d41db2280f21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + 2 a b + b^{2} = 36$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "6a08637d-161b-4653-b18e-f0e65a8e8195",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + b^{2} = - 2 a b + 36$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Substrac(2*a*b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "e019beb7-a3cc-4d2a-9dc7-7b2256af3bba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + b^{2} + 2 c = 0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Mul(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "dc97adda-f884-4de2-af3b-cbbeb4866f07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + b^{2} = - 2 c$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Substrac(2*c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a25e538-f76f-4871-8086-827aed718887",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "74bdfb97-67d4-4e0f-8432-ae374c12ae52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q1 =a^{2} + 2 a b + b^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24bcea5b-39c2-4e97-ad36-cff11873302b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0b126fae-5cd2-4e17-be6d-e0cd3c25e9ad",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{a^{2}}{9} + \\frac{b^{2}}{9} + \\frac{2 c}{9}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=MyEq((a*a+b*b+2*c)/9,'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "01490d84-8061-4ca2-9c00-1a0e8a0efe2b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{a^{2}}{9} + \\frac{2 a b}{9} + \\frac{b^{2}}{9}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.set(c=a*b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "3bd3b0dd-a1b2-4a3a-b5de-6329325b27bf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{\\left(a + b\\right)^{2}}{9}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "18581bce-3c8f-4ee1-b67e-a3d51f0259d2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.subsubs(a+b,6)"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "c6bd8578-5f57-48d6-a38d-03016e2ba273",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "a5cbd846-15bb-435b-9881-15895cfa8f2a",
   "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": "f2260ede-1d7a-4668-90ad-492b90813e6f",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "d36392dc-6913-4870-bebf-bc88922efb57.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "a4fd49f5-e220-4d84-8c57-007218e85271",
   "metadata": {},
   "source": [
    "![image.png](attachment:d36392dc-6913-4870-bebf-bc88922efb57.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "9ddc9bad-5242-40a8-8b44-201ca24bc561",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 b x + 2 c + x^{2} = \\left(- p + x\\right) \\left(- q + x\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q=symbols('q')\n",
    "P=MQ(x*x+2*b*x+2*c,(x-p)*(x-q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "dbe115ff-127c-449b-a467-2d6ab1ffadc8",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 b x + 2 c + x^{2} = p q - p x - q x + x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "42d737b4-e012-4c85-8339-dec0fa1d7b61",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle p= - b - \\sqrt{b^{2} - 2 c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle q= - b + \\sqrt{b^{2} - 2 c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p,q=solvecoefflist(P,p,q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "0f9aee28-6403-4d83-9e3f-9b99cbdf951a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{1}{\\left(- b + \\sqrt{b^{2} - 2 c}\\right)^{2}} + \\frac{1}{\\left(- b - \\sqrt{b^{2} - 2 c}\\right)^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=MyEq(1/(p*p)+1/(q*q),'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "f42de4a4-d4f5-41c2-b3eb-b6e4441c17e0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{1}{2 b^{2} + 2 b \\sqrt{b^{2} - 2 c} - 2 c} + \\frac{1}{2 b^{2} - 2 b \\sqrt{b^{2} - 2 c} - 2 c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "325c23d1-92b9-4bbb-8fe8-bc61eb9c3478",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{b^{2} - c}{\\left(b^{2} - b \\sqrt{b^{2} - 2 c} - c\\right) \\left(b^{2} + b \\sqrt{b^{2} - 2 c} - c\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "e36aa842-723a-4700-b79a-0c36ed432cb5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{b^{2}}{c^{2}} - \\frac{1}{c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "66e2939b-24c1-445c-806a-80c755b1910e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{b^{2} - c}{c^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.factor()"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "ea9d116d-d885-4a38-82a4-c4476a4586f1",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "35f1b1e5-80fb-4f3d-b37b-346fda43d5f3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "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": "377d5cda-46c6-4e98-855f-52440d5d80fb",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "7848ba16-90ee-4a21-8e95-377fec840373",
   "metadata": {},
   "source": [
    "![image.png](attachment:4aa4fcc0-8f6d-4df1-baa7-df2f5d2d7bfc.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "8a7a8a0b-8904-4644-8ee7-e418de6ed7f0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "r2=(r1+2)/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "f648a82c-3a65-469b-93cb-60a81c696cbf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle n^{2} - 2 n x + x^{2} - 4 = \\left(- r_{1} + x\\right) \\left(- \\frac{r_{1}}{3} + x - \\frac{2}{3}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q=symbols('q')\n",
    "P=MQ(x*x-2*n*x+n*n-4,(x-r1)*(x-r2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "3c37ffa0-8f1b-4090-ac76-bfb44589724e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle n^{2} - 2 n x + x^{2} - 4 = \\frac{r_{1}^{2}}{3} - \\frac{4 r_{1} x}{3} + \\frac{2 r_{1}}{3} + x^{2} - \\frac{2 x}{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "60a6b690-a40a-4687-9eed-372dbd7df3ce",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 n^{2} - 6 n x + 3 x^{2} - 12 = r_{1}^{2} - 4 r_{1} x + 2 r_{1} + 3 x^{2} - 2 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Mul(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "dd745ffe-2316-4822-af16-5c7687d932e1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 n^{2} - 6 n x + 3 x^{2} - 12 = r_{1}^{2} + 2 r_{1} + 3 x^{2} + x \\left(- 4 r_{1} - 2\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.sortdegree(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "3e585f7f-01bb-4de0-84b4-7a81763ec3fc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle r1= -5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle n= -3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r1,n=solvecoefflist(P,r1,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "3b5965ce-0948-47ac-8875-00c99651b3b0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{1}{q^{2}} + \\frac{1}{p^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R=MyEq(1/(p*p)+1/(q*q),'R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "5b107a64-456d-44d5-985e-b19c85ac072f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{1}{q^{2}} + \\frac{1}{p^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ca279b3f-2a68-4101-87bf-d0cc36c0301c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{p^{2} + q^{2}}{p^{2} q^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "bba332d3-18b1-4733-bd2f-fdb23d45e11c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{1}{q^{2}} + \\frac{1}{p^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "7845dc0a-bce2-4bb6-8305-842095624cde",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R =\\frac{p^{2} + q^{2}}{p^{2} q^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R.factor()"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "85071054-8b73-467e-a619-db6406ab8780",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "67cb913f-a157-4fc3-848b-fe4f2b761839",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "b74a0778-7a14-4981-a943-e42b705207ee",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "aa0da48b-c2a4-4fe8-9154-7aaa032885a0.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "eeafe99f-8f7f-4d43-8da3-42f10a52c154",
   "metadata": {},
   "source": [
    "![image.png](attachment:aa0da48b-c2a4-4fe8-9154-7aaa032885a0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "2c6ca2c7-52d8-4cbf-b994-2723b4dbe7a6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle p x + q + x^{2} = \\left(- r + x\\right) \\left(- s + x\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q=symbols('q')\n",
    "P=MQ(x*x+p*x+q,(x-r)*(x-s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "9faba35b-06ed-48b7-a0e0-69b082823086",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle p x + q + x^{2} = r s - r x - s x + x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "5cd46a4d-0cf0-4fbe-a3ec-6e908029ed3e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle r^{2} - s^{2} = 32$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle r - s = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(r*r-s*s,32)\n",
    "Q2=MQ(r-s,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "303c37d9-ffeb-4366-bce9-bdf4a9ef87e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle r =6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle s =2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r,s=simplesolve(Q1,Q2,'eq')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "4f2c393a-6375-49ab-8e9d-8cc610767ca5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle p x + q + x^{2} = x^{2} - 8 x + 12$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.set(s,r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "bc9fa522-184a-44b1-a8bc-2001352883d7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle q= 12$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle p= -8$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q,p=solvecoefflist(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "5a34de43-0b67-4d41-8dca-267e4f8b1346",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{4}{9}$"
      ],
      "text/plain": [
       "4/9"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p*p/(q*q)"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
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   "cell_type": "markdown",
   "id": "33ab69ee-9673-4977-83ce-38c8feb9d39b",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "23ba53e3-a3f2-43fb-ab87-f61d3a1702fb",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "attachments": {
    "73517cb3-98da-4c40-8d77-21db4972fcb9.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "292fd935-cfd9-446d-bf48-3bfaad6285b3",
   "metadata": {},
   "source": [
    "![image.png](attachment:73517cb3-98da-4c40-8d77-21db4972fcb9.png)"
   ]
  },
  {
   "attachments": {
    "5b456c0a-bee8-4e7b-8d13-3587ba9d6c53.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "58df50b4-3027-4b2a-89ac-2b788b27e490",
   "metadata": {},
   "source": [
    "![image.png](attachment:5b456c0a-bee8-4e7b-8d13-3587ba9d6c53.png)"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
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   "cell_type": "markdown",
   "id": "4f75f82a-355c-40d8-81e8-d03d244ab4d6",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "86d368e8-0dd1-4cca-82be-1776ba8c9858",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A1 =\\frac{\\pi L^{2} \\alpha}{360}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A1=MyEq(pi*L*L*alpha/360,'A1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "74e77563-a971-495f-82f1-24f93a791fc3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A2 =\\frac{\\pi \\alpha \\left(L + 10\\right)^{2}}{360}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L2=L+10\n",
    "A2=MyEq(pi*L2*L2*alpha/360,'A2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "fdbca2fd-e78e-4068-ac59-c8ca9b424395",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\pi L^{2} \\alpha}{90} = \\frac{\\pi \\alpha \\left(L + 10\\right)^{2}}{360}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(4*A1,A2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "11401dc9-6e34-4423-8c5e-d97adf448d0b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 360 \\pi L^{2} \\alpha = 90 \\pi \\alpha \\left(L + 10\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.crossMul()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "36fb5dfc-c7cd-42b4-a2a4-c7db8370c458",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 L^{2} = \\left(L + 10\\right)^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(pi*90*alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "9af4fd21-0853-47e9-8f30-e5e8e61cdd55",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(4 L^{2}\\right)^{\\frac{1}{2}} = \\left(\\left(L + 10\\right)^{2}\\right)^{\\frac{1}{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Rpow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "6d029b28-e48c-4380-8c38-6235e08feb71",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(4 L^{2}\\right)^{\\frac{1}{2}} = \\left(\\left(L + 10\\right)^{2}\\right)^{\\frac{1}{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.rsimplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "4105c8f5-b837-4612-aac2-e0a93632e8ee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle L =- \\frac{10}{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L=Q.solve(L)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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   "language": "python",
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