10126 Hard  Expotencial Law Examples.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f656adec-8517-459f-854c-923d83d3fcba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# These examples was solved  by Mathematician Professor  ROBERTO CARLOS ALCANTARA CONDORI\n",
    "# Link\n",
    "# https://www.youtube.com/watch?v=K9Jms_whis8&list=PLGbSw9USRLuSK4bwHlp_ZCngyyJa58zxB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e754801f-b3ed-4b2f-8ea5-e9c387289b9a",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from libaldomath import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "d58c30a0-7ba1-499a-b0d7-f71114fdd34f",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
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     "image/png": 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4VhaPu/70w1oDWzJyWCw0724vOXhs85Uj5JpyfTHXlvsIsUqU43fssccumZHyPY6W+abeXyaPQ2UtirkwmC0at499fV5JnKi6to5i+m8sMZChkunhoBHKXlLVFcajHG+SnzGW+metg0yOl2v54cCa265Nfxd04DBzPvfaa6/qMJvzzPNEhsMckhmblnGbJLccOwRCYPURmHqBb0hEa4gSD1KlJ8SWHRwGjRgXtRZB2xgjmjzwRAtbZFAEkZjzgOkrWkjENtHRhId2d/8tKtiin6P0iZAjiInj7sLkxb5LUI4bwbJYlaDjFMhqMP0Q4Sa2RJL7MA4KkagcQ7TQ2gbCRSlKEyOEtCj1UoLd34lYQsWOH9qq/aOWJRHBBIEoph9im8g0ThwOYoIRsZwxmZE1a9YsigBzIsSiRo5pM6VMRH4TVKLi2k6stz3TbU0q4tqcN6KU2CfIm7NAzBobQtri7+584ow4ntIFbSSMXE8cM04UIW3dxmILQjnZyk8Iv2acDo4NodXMuhCCS9SdEeb4qOUW8R7XRGA5CPqlDxxfY+5a33PPPZccS583hhw91zFzbch84OvfxB6HsdWYL9Y+851TwFFxXVqL4j7BQVpqzMft78Z83n1F9sZYjWKyD5xNW3rKzCgrMsfMdeMlqzMt5j7g3mwNVjPjKhNmzYH7AeeT48VRZeabiL5xc68zj1wjxqtlKKalf2lHCIRACPRFYCYEfutsSz0TIUTJwx72sPUcRCPttkNEeEiNIm4Xgth24fE36dtmyg3UEtuxZlRh2NcgjXocaWdRKxH8SbaRE2UL07Y1qPbhRjhacMkJm2bjKBC0o0bxiRxc1fsqfSAOiHRRakK/ZT+U/4ggckqGGacVx5133rkKdMe3K5Lyg8FsBIdTVkcpAkFrbndr0Akw717ww7SN6OQEDdaqc24IoT322KP2/5RTTqlCkEAdXLsy+KI2UV0CSxu7Ti6BL9vgb6Lq1oBgTDxzWPDSV1FuZVqycOOYuSUazWk175pDSmwT6a3kaJxjjvtZY6ukgzPRXYMj6MBpaOJy3OP28XnOlY0IRLQ5hbI41mvI7JjnnGIMvT13cD2ASDjBa/xEux2jmUXqnHX31Wkw939ReM6sUjVlf+aC8RB4cd+zLsv8lGGR6eKo+F0sBEIgBFYbgakV+CKLSldEzbvmRq4sQETVjbyJGpFrUX41821LxuUMJjGn1ESN+XbbbVcPIQLkwS7qS5D1aQRWNwWuf9066lHPRWiKUHV3Fhr1u+N+jsgU9evuDGJMPFCd3/aU02yi7haEcgRHMQJKaYrorrIFEW6iWxS3ayL5IoXKHIYtslXShB9xT6gQxCLIg2VVyl7U+hPXHE5OnPlhPjILXDkYxG+L2HJ+9a9F5rttNJcJYmsHWjTdOWTEttxyyyVxOIeSMmK3WxJjzO2OpGzLNaIvSnOUQ+HFURB1Xa5pp4yHqK2MQHNecbYWYthC8uWet/s9EXGOCyHfjfoKMhg3Y7SpzC5enE33PQ62few5fVe72tWq40bot5pzor1rnJZ2H3VddLdZFdVXnthXRm5j+QiyKK+T+ZKd4nC3KLznRNvNR1aLAyuCL1PlWZFI/cbSz/dDIARmjcDUCnwiQSRUDfJCJjJJTCgraKbeWERtoRe1jDIwIvRKGkQbuwt6PTTV3XoQ9lmP6kFFNKot5syIshERdrUhtjxslUq0GtnF+qDGWXSXoJv0C6SUiHhgeti28gvt8jsRWg/XvkxUm+MiCocNoajcxI9/i2QTe0TMqFteEsrmDpHbzQAt1WZ9NQdaKc5in1WaI2Lqs8MEvmNwGkRciTNiRXTbrkPNCG9j6sVtbRcpEVgLqNsiWI6wOdsWHzbn0NzCbdDZ0heZFwuizRnRWe3mGA8Tyj6nNMc12S2RcH78iSpGjBPlap/7qG+2G43MiXNo57j7ySs1cV3JmohYszZ3zB8//l8keKF1K9gqf5Lh6C5wdhzRZNHi1ve+5v7GHEeZnLnDyRpmMp7uQbJu3bHiqOLmv6PM5WHn6ePv2ioa371GFjuue4QgBIfUc8J1wgGalr70wSPHCIEQCIGlCEytwPeAErG0gHMwsugBJmooJStqzAhkD2hCfLnbZBISxKK62pbWVW8u0qucgdgaJoLGmW4eoMoylE20n+73W20w0bFUBEpNtMhs9y2eSjoIEwsnFzMPPf1T373Q3tcLfY/A8h0CskX7HIfgFDFbaG3EOEy6nxU51w/i3k+zJvCbOOPUtEzOsHMReUo7RDhbXfuw74jeYuyHKO4a56qxU4Musm5npVGEhBIaApGTyvHgHDSzBSmeorDmn9IfpWlKE3zHPGUi5DI3SlWUYBhv0VqC07zxo2ymGTHOSeNctDI2GQRMfH+YOZdSCdcI42jJeFmsKLrtmOqh9YnAHGSsxMbuQaOaPlsg6boTtVWiMfgyL/cBZU2L1ZyLYLtnKKVxn2Dmjrb7afNIFHih+esatasMJ6u7+Njv3W9s/brYuyBG7Wefn5PZ4GAN277SPcO4E77duWeem8d+P2yhfp/tHnYsgp2jJrDgv10zT9q9uWVFlaqZ564ZTr0x7MPhHNbO/D0EQiAEpoHA1Ap8cLbddtsqEtT7irgSUrZqUwevHIdYafW4IqGEi8iiCP5g/fAosAkAkULlJqKPFp0RF9LYHA2RIA/E5Rx7lPOP+xm1syKqxC/xQRS2CLeHNMFJ3CxmhImILtHjQTjMiDOiu21LSlR5mIree4AuN3My7LzL+TvhbT6oKW6lVo6jlMuiSwtAR63B5ygZe0KZYynTo0yHyFUiINvEzBlZJ8Jo1DlCGGsLcdzdOlQphYi5BYPGUfmLOmnznzPVXmDmd9okcs/58l4GRgApZ1Be0Rw/DoVyHhmhtgCRs2b3Hw6CxcPDTDmITI16+2Y4u/6UlxHI6u5lDgjx5mwQYESn+ThYJrLUOZvzqB8LOasyPMpj7CDUXTMzrB/j/J2zhJ32mwMWsXI8jZvzW4MwTaY8y+5Ywzjrh0XhAhfdF/O5xl0j1lBwMKfFOOfabE2HNSaubRkZzrE1GjJynhG2lXUttBJC14/5yVHmiPmueajMzA5TsRAIgRCYRwJTLfAJ0BZ5Iyw8XEW6Rei7i8XsouDmrnzGzV9Uv1tCMM7AKV8g5kQKiVepeQJaeYaaa8JlkgtYx2krES+SjonIqQeZWue2xeYotcHtxWAiwcPMVpPEDPHq2NYpcA4IrL7XJgxry7C/aysRSxTY9o8AJMaUEIk4j7vVqfpk3xFFVPpiDnCw1J43I7TNGdF2DugoTDgJ5pxx7Bph7FwEvJIfc57zYPtW5TWcXwKGE8C5kzVwXqKzmR16ZCoIfNFM7yQwP3Cx173rhsPKueME2elm2IJE0XuOnOMQ8HY0Inw52n6vfMK1quxMxB1/UX9OhCyUko9xytx8V0S67XrDeRBFNw85ceav2uvuHvzD5sa4f3dP4RS1aL9xl8khhI2/n2kSwsaIwFfatZQJCBgzQYz2wjq8jSnxu9xM6Lh8x/m8seDsuvdxcgVjzG9lY0o0OV7uR+5L7eVcrgGZlrb4nbhXhmkemvOxEAiBEJhHAlMt8LvARV6JHg/ShVL8Ijst/dpN1y5n0IjAUcoVlnPsSX2HqFIOMWrZSWuHCC6Rp1xoVLOw03ksYBN1Hlcsj3qejf2ciLIyClkNCz7NESJYrftyTVkDcaEcQGapRdIdj+DExPmI7lEXS/tOdz2DYzmG+U6scdg4FDgTu8SL48ugNGEvui2z0F2T4jg+77tEsIW9g2+7tfsKEc4IpMHyl4U4WWTrO45LNMlwmEecBM4Cp1hdtznib0SkbSo5WqNkCbrnxIaTw3HhMOBuC06CvpW1Oc9gv5c7vgt9T2bP9dG2G9WHtuaDuOfMTMsWma393fvhYixk4jh9ovgnnHBC/ZjMzKQyIX2NicyqSL05aN7JPnRLDM05P5yy5oxZU9Wd264bDu6k1yz11eccJwRCIATGJTAzAn/cjuXzwwkQXYSSko9hO6gMP1o+0ReB7r71fR2zz+MsVX5EdCtpE1Xt0/GTNWkLq/vsS45VaplLW+PCERy1vGza2emXvoy7KHva+5X2hUAIhMAoBCLwR6E0p59RqytCaqvGURaFzimGqezWNIr8eRF+UzngaVQIhEAIhEAI9EggAr9HmDlUCPRFYJoEfoR9X6Oa44RACIRACITAyhCIwF8ZzjlLCIxNYFOL/Aj7sYcsXwiBEAiBEAiBqSAQgT8Vw5BGhMBZCWwKgR9Rn5kYAiEQAiEQArNPIAJ/9scwPVgFBFZC7Efcr4KJlC6GQAiEQAisCgIR+KtimNPJeSAwKZEfYT8PsyN9CIEQCIEQCIH/EYjAz2wIgRki0LfIj7ifocFPU0MgBEIgBEJgRAIR+COCysdCYFoIjCLyvYzMi7d22mmnRZsdcT8tI5p2hEAIhEAIhEC/BCLw++WZo4XAihAYJvK9pXPdunVln332Kdtvv/1Z2hRxvyLDlJOEQAiEQAiEwCYhEIG/SbDnpCHQD4GlhP6hhx5aTjvttLJ27dqyyy67rD9hxH0/7HOUEAiBEAiBEJhWAhH40zoyaVcIjEFgIaF/xhlnlEMOOaQcccQRZb/99is77rhjibgfA2o+GgIhEAIhEAIzSiACf0YHLs0OgS6BpSL5xxxzTNlmm23KVlttFYGfaRMCIRACIRACq4BABP4qGOR0cfUQWEzoJ3K/euZAehoCIRACIRACEfiZAyEQAiEQAiEQAiEQAiEwRwQi8OdoMNOVEAiBEAiBEAiBEAiBEIjAzxwIgRAIgRAIgRAIgRAIgTkiEIE/R4OZroRACIRACIRACIRACIRABH7mQAiEQAiEQAiEQAiEQAjMEYEI/DkazHQlBEIgBEIgBEIgBEIgBCLwMwdCIARCIARCIARCIARCYI4IRODP0WCmKyEwCoFTTz21HHbYYWXfffctm2+++ShfyWdCIARCIARCIARmiEAE/gwNVpoaAn0QOO6448puu+1WBf66dev6OGSOEQIhEAIhEAIhMEUE/g+zWewKchvvUQAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "c7308d38-2726-4aca-8e98-d03a649666ed",
   "metadata": {},
   "source": [
    "![image.png](attachment:dbb46bca-7a6e-4049-b656-defbb113f52b.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "733ab78f-d806-4653-b5eb-1e59dd19fb6c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =a^{b^{a + 1}} + b^{a^{b + 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(a**(b**(a+1))+b**(a**(b+1)),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "42d596b8-0694-4776-9aa2-a46de4233492",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =b^{a + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =a^{b + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =a^{b^{a + 1}} + b^{a^{b + 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyEq(b**(a+1),'e1')\n",
    "e2=MyEq(a**(b+1),'e2')\n",
    "P=MyEq(a**e1()+b**e2(),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25d8e549-9e26-4428-845f-1901ae1083a9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1 =b b^{a}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2 =a a^{b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1.disjoinbase()\n",
    "e2.disjoinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f548a0b1-10cc-4939-8d26-542e8cb6d96c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =a^{b b^{a}} + b^{a a^{b}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(a**e1()+b**e2(),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0f1350e5-0de0-4313-98b4-09dc64ffb139",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(a^{b}\\right)^{b^{a}} + \\left(b^{a}\\right)^{a^{b}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.pow2powpow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5c4a4b68-9790-4daa-af09-63fef2cfe2d9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2^{b^{a}} + b^{2 a}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.set(a**b,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "784624a8-b3f3-439e-85c4-4724baa9a7e2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =17$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.set(b**a,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "eb963196-91d2-45a7-bf34-bbef03fc730c",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from libaldomath import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "b777f144-0aa9-433d-aba5-7b8e4509428a",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
    "881b9ae1-d39c-4e90-9b83-745418b9be50.png": {
     "image/png": 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DiloMIWIJ0YO4RnQwpsOGDbPCI9vqNZghTJgHtMG1kXFnbhHy5Vk8p1atWnYucA3Ppv2IEkJkPD/fggBjbr/99tu2L4hO5iZfHDgzLagcfPDBVqzSJ94hzlDDe0JbnVji71tuucUcdNBBOatjDtNP6uMP+Xl4lvDchVl5mati5hdtc54kPGU8i/mQVCGMj5jDI+fGm9V2PJuQJv1gTvJ5M2nSpMxjEbsIbvde4gXNp69J9Uf1iIAIVD4CsYUS31hvv/12a4zwLLDSC68ORtpf+LDlw4+VQf4VSWGQvvnmm/ZwTsJ5PBdvh9ebEaYO/zWsvOPbPIYNA9eyZUvrzeAbOgUDheH+7rvvbF6GM/S5nuXPUXLGLpdQiiqSEHUIAwwqnGk7dSxbtsyKEzwrnDWHwcDAhMlRQkxQJ2E6Ny54fcj1IinfFTx0rOpzxhohxViMHz/enmlHYXsEhKxb9YYQw6tH3hCeIlcQFhdeeKHdugHvFNy5xyXfI/qCSteuXW3iNDlvbqz4G08OApG+4LGCE8v2yZsjtAMzFhUQorv66quDHhP4exKbCScS/sGzhyHHy0r/wvSDFXK///679XrRXsKTCFd/YVVpGO8oYUi8eIiOfAtfbHjnmPd44fBWIZARssyXpApCmneauUD+IgKJLzFs2goPcs4Qk3hJee+Zl7yvKiIgAiJQLAKxhRINxEjzIYYRxWDyrQ8PgQupuE7wocs1fPDyjTdOIaSD2Bo9enSc23PeQ5I5BWMUVLzGCvGGsMJITp061RppxAGeCrwCGEC+7XIPv0dsrLvuuplHRBVKtBPhgRDAIJKvgSjCk0JdeFLw+vBvvBsYlTCr3qgHjwXf6ikk6FPHiSeemGkrS+DpC+ONkEQMkP+CJ8gl1iI8+/bta7eMoGD8CNXhEXBiylX4xRdfmDlz5lh+CLy5c+caxA/iqXPnzqUOA31DTGy22WaZpevcQD8INSHgEEok8yOGEGlcS+iNfvFMwjf5hqMmT55sGdAWr3CAAWE0xEWxC+2gv/6k8jjtYA7zbjN2bJzKeMKO+c2CiaQK7wZnIzLuhAz5QsCXC+avt+BlZGwRuXjsvOI7qbaoHhEQARHIRiAvoeStkG/FhEsQC+QQYLRdwUARviLXIm5SN9+4MbCLFi0q2EiGFS+IH7wrfKjjsaDvGCfahmHBO4I3ikRrhAWJ5nh48DKEfYa/k4Q5MVZ808aLl6u4UBqiKqzBJOxGGImdxck5I7TlzqlzogdvDG2gXxzVQv6QVwAhhMlFckvhEcesBCPXyIXnXJsJ3xCOwwuDF8z1DSHmvES5+of3Ca8DnijEpysYUvcHUYdQwuNVqJwVxv6tt96yIWf/F4OwExSxzXwgCRvvF/OKEDNhO8SI27jSm6xfWt3kRTHXsnl1w7ap2NchfuCAWGLPsdIK7z9iGCHFog3mAKJXRQREQAQKSSAxoUQjSfImVIWRxJvBh78reJvImcAQxykk/Lr8ljj3Z7uHHBrCJ+w5ROiIb9HsQcQ3aIwxYQwKK5j8ibkkluKFwnPARnzso9OgQQPrdcHLgtEjtELuTq78rSj9ID+EZyIAStv9mhVjhJrw3uHlChOy4dgXQll4q2DiHTfaiOcE75ATuYgiPDSELV3Bo0Xe0K233mp/xKaX3IenyC9WqIv5wbXkRzFvCO0gOhHUQYVn4X3y5sqQ8AsXwn+MBX0isR/hUFp+T9Czcv0ew06+GJ64bFtRPP7449ZrxZeDXAXPCL8nNwnBhAAmVwtxzZxjbrrcqtJCeaxEpP8IXcaQ3LNCCcS4vHLdx9jTZkQvf7vCXMI7h9jGs+U8vgh25kqvXr1szp4/4T/p9qk+ERABEYgslPhQJuRCbovfs8GHGAaKPAZCbO7DnWRXjCvJtuQaRCl8cyexGAFGUidJyy7xOEo9/msJH5GPQ/iKb6gIHMQQXhL+xjODwUIskXyMESqtFHqvJEQcBpDwiv+bNyu+MBp49Aj5ISDI5WjVqlUooUTdhL8IwZF3xkojVzBUeHwIebll/TwHrw0C0xW8UOQBYfQphAR79+5tjT3hPG/B0wN/5hEJuAhKRBjCiVyVoELOGO2iDS70h/cFw4oAo/14ZjDCeKzg4AreLJaVs7AgbvgGzwbzmfwdlqT7jTVzibAfgrO0LwaIAeYebfIW/1zCu1fauYG8X4hSBDKinGciOhDpiMbyXJgLhJV5v+ij+0zBO4noRYgidJkv3gR8PMyDBg2y7PG0ItwLtX1BeeantomACBSeQGShRJNYZk1ujn+HbQweHgQ+0NjHyBUMAh/kfAi6fV6CukZdGBC8Bwgvvn2TtEwIC0PEBynu90IXPDR8gAd5Zvy/d8ndLqk7V8gNY0aCMQINEVnaZnoIDkJbGA4EAXUjRBAurAAilIXwI5kXQekS3oPajpFBXDE2eEK8q4cYY56HKEEoEeqgvXgwSFp2ho1wK4KN5G1X2GqAnBLa447CoH38G2+XE82IHIQSXpQw2zogAgl70R7mImwJO1WrVs1um8DPnScHQ4ywwbvDsnP6yvMR9HELeTV405wnjhwo5jfCizASAg0PKOLRGx6M+7xs9yFuEZoIerygiEPeC0QSY8WqMMRvkMBPsk1x62Ls2PKDsC4CiHcB8USeHPML8Uc4ElFKPxHkXM8XKDxn5C+yISbhXN6LMPmGcduq+0RABNJHIJZQ4gOKlVF8OGEIWK3iEooxRBhLjAfFhbMwhHyAkd8SZLjxTGFIMaAkeZK3gmeHf+NVYmsAvA9JhLTCDnlQblGQUOI52erAsONpQ4wgkmCba/8dVozBghAkISuMJNciRAj7wQjvAsv0EUl4TcgVC+KNIEX44M1BAHsLvFmZhBEmjEVCPQIJgYb4wGuE+MFIkatDXzDcrowZM8aKGbxyeE/whuElIHxCQcRQByKL9rOEP8i4swUC1yPGESckhLNlAvMG8YyxdN4H+GJwmUvMPYRfPismEYQILvLQCIe6Y3xoE2FYhBKhIgqh0kIV5gD9dNs2uHHjywQrUPEOVpSC95FQN/MMkcv4k9fmwod4fin0EZHMvMNj537P3KTPCCyEFKvlVERABEQgKQKxhBLGkgRTVhrxoYTHBWOL4Sas4V2xgmeIQ2op3INxC8qfwNDgSSL3w3tkAvkzfItGLIQ5oiQpSK6e0sRSkFAKElqwI0zEqrGgD3q+TSNASGwl/OMKK7HwtBEWxTNEGI7cMEqQWCqNFYaKVWpubyBCHSSuk1juCh4AnpHr2zz3I1q8Iirp8clVHwKKuedPKi/W8/Wc5AgQgg/6/EjuaapJBERABFbYzxUG/L+oILglH8Mb9Xnl5fooqODjOAXdh8gkVILwQPw4YUOOlHcfJv4fl3vc+8oLe7VDBERABERABMqCQCyhVBYNLQ/PdILHKzrcz/CCkVBNeIDQjtfTQ9jHu9uyvy+EMUk+JpHaeeO43gmlsIIriJHEUhAh/V4EREAEREAEShKQUIowI7IJJW4nd4pQlDuTi2RTNh3k5+QdkYNBIfyTSzB5vU7e53h/7rxUzuMUoekZL1XUe3S9CIiACIiACKSZgIRShNHPJpRIqiVpmqX7JFTjPWJVFEmnJNuSI0T+ESLHnTmWaysBJ4TwJFGPy/0i/MbPSNx2R6w40UXzg0J7rovyKEUYbF0qAiIgAiIgAisIVCihRMIwicT5rFrKZ9SzCSX2NWI1GHsKIV5cHhFJ7Cx7ZiWU28vG7bActOcSz2ElGSupOPYEocTPWBWGeGJfndIO283VRwmlfEY//r2IXnagZkWemwMcQ8O2F0owj89Vd4qACIhAMQhUKKG0ePFiu0w9zsG6ScJ0ggkxw9J3VqoRbnNnufF7lomzMSYeJZbOe4vbY4mfOfHiF2HUTd4ThhTjyu/Zc4m9glgVF0f0xLknSW5prQuhNHDgQLvXldv6gaXwrAD0n2mWVkbqtwiIgAiUVwIVSiiVF4hO6LCpIPsPsVs5R1q489EQOXi/2G+Hs8kQU40aNco0H6+TXxh5N6bk9+Q1UR9hOxd6I3TnEsPjhN68wqy8sFQ7REAEREAERKA8E5BQijE6Xo8QgoZjO9j80oUE2b+IjTdZycbf/fv3t54gV1yeUS7h4kSUE0juvnyTuSWUYgy2bhEBERABEUg1AQmlGMPvTZ5mh/BRo0bZYz28Z6RRLeejcS2r31yJknid9PYAEkoxBlu3iIAIiIAIpJqAhFKM4feKHTxK5CFxpAabRbJppNsDiTyUJk2a2CNF4gglwmwu+Zf789lw0uuVitFl3SICIiACIiACqSQgoRRj2P1eIYQRh6JypIvLNSJ3iYRujlzxnnoe1qMUo1mhblFCdyhMukgEREAEREAELAEJpRgTIZtQ8lbDuWac4t6iRQt7QLDXKyShFAO4bhEBERABERCBMiIgoZQAeK/4ITzWsWNHu7kkR5Kwcq2sxZG3i/IoJTDgqkIEREAERCA1BCSUEhhqJ4TmzZtnd+hGjLAtgH+PpAQelXcVEkp5I1QFIiACIiACKSIgoZTAYA8fPtwsWbLETJkyxdSpU8duB8AZb66UF4+SRFICg60qREAEREAEUkVAQimB4e7Zs6epXbu2PeuNw3ApXlFSHoSSRFICA60qREAEREAEUkdAQqkAQ14ehJG/WxJKBRhoVSkCIiACIlDpCUgoFWCIJZQKAFVVioAIiIAIiEAZEJBQKhD08iSW5E0q0CCrWhEQAREQgUpPQEKpAEMskVQAqKpSBERABERABMqAgIRSgaCXB7EkT1KBBlfVioAIiIAIpIaAhFKBh7osBJMEUoEHVdWLgAiIgAikhoCEUhGGuphiSSKpCAOqR4iACIiACKSGgIRSEYe6kIJJAqmIA6lHiYAIiIAIpIaAhFIZDHWSgkkCqQwGUI8UAREQARFIDQEJpXIy1FHEk8RRORk0NUMEREAERKDSE5BQqvRDrA6KgAiIgAiIgAjEJSChFJec7hMBERABERABEaj0BCSUKv0Qq4MiIAIiIAIiIAJxCfwfDhD210SRlpsAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "567985f6-836b-4e77-bec8-f5c66531cfae",
   "metadata": {},
   "source": [
    "![image.png](attachment:881b9ae1-d39c-4e90-9b83-745418b9be50.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3b283ffb-5246-40ea-96c1-5c864416dbfd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{- \\frac{3 x}{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x**(-3*x/2),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a5c2217a-bf24-48ae-9f36-17d614682db3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{x z}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we will set z=-3/2 then\n",
    "P=MyEq(x**(z*x),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cc916a7a-409f-460e-bae7-733969db75cf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(x^{x}\\right)^{z}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.pow2powpow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7c3bcab1-20e0-44a8-b0ef-9e62a759cef1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(\\frac{1}{9}\\right)^{z}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.set(x**x,cfrac(1,9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8a7269ce-1e42-45c6-bf77-d415f5525314",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\left(\\frac{1}{9}\\right)^{\\frac{-3}{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.set(z,cfrac(-3,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4259b93f-9e6f-4bb4-b8e1-dd72539fe7a6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =27$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "410a56b9-db65-45fd-a027-dd282b4303f0",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from libaldomath import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "de8048cf-0db2-4e3e-b17b-df59b2a2bbd9",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "attachments": {
    "4f599ed3-8998-435e-b125-1cdf02a379a9.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "2567493b-98c1-44d8-b66d-f0bbf6147527",
   "metadata": {},
   "source": [
    "![image.png](attachment:4f599ed3-8998-435e-b125-1cdf02a379a9.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "98f01e66-c1e9-42d1-bbf5-e294ffa36e26",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2^{- n - 2} \\left(- 2^{n + 1} + 2^{n + 2} + 2^{n + 3}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq((2**(n+3)+2**(n+2)-2**(n+1))/(2**(n+2)),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ef71bb8d-c649-4ac3-b3a6-d128cf28ff34",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\frac{2^{- n} \\left(- 2^{n + 1} + 2^{n + 2} + 2^{n + 3}\\right)}{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.disjoinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a5e62a7f-b868-422d-921a-6396bfd19ace",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =\\frac{5}{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.factor()"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "5701ac97-d862-4a96-bc42-4de62d8dfc41",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50ab9d2f-27d3-4a1d-bb52-6840bfced4c3",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from libaldomath import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "13178c22-b769-4ba0-91dd-23bfd45ea4f0.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "30236847-7349-457a-8c3a-21de3984c895",
   "metadata": {},
   "source": [
    "![image.png](attachment:13178c22-b769-4ba0-91dd-23bfd45ea4f0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9f3338ab-15ba-44bf-b07c-63132630bca2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{x^{1 + \\frac{1}{x}} + \\frac{2}{x}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x**(x**(1+x**-1)+2*x**-1),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ca15a284-9a0c-41b0-9ed6-b6bcf6396d3e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# we will z= (x**(1+x**-1)+2*x**-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ef864a7d-b879-4454-a1df-60c1d0672e4c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =x^{1 + \\frac{1}{x}} + \\frac{2}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MyEq((x**(1+x**-1)+2*x**-1),'Q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a439eb5c-6185-4b07-9ced-05d1d7ba15a4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =2 + \\frac{2}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.set(x**(1+x**-1),2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "16f06914-df78-4f89-bfa7-bd88d14b3912",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\frac{2 \\left(x + 1\\right)}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7a9968da-2ea1-4a1c-91f0-52354a39a324",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Q =\\frac{x + 1}{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(2,'simplify')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "289cfe2e-4234-48eb-820d-24e22eedc168",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{\\frac{x + 1}{x}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x**Q(),'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3dc45ad1-c92a-4599-ac86-6735da0770f1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.set(P(),2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fa697999-ea06-4649-9a81-4b65218f4af2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Pow(2)"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "2474d984-4151-4087-9288-452684574611",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "aca6e409-a9aa-423b-90a3-d29e4f1757c3",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from libaldomath import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "0dbb83cc-1af3-4b9b-8003-70d3e6eea625.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "6a0b1c3c-e5bb-4501-aa22-00a7fe03cb47",
   "metadata": {},
   "source": [
    "![image.png](attachment:0dbb83cc-1af3-4b9b-8003-70d3e6eea625.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "84c27426-abba-4995-87e2-ec36914e85f5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def pp(v1,v2):\n",
    "    return (v1**v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "28489d81-f223-4bf0-9512-850ed1205ddd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle M =\\frac{\\frac{1}{b} + \\frac{1}{a}}{- \\frac{1}{b^{2}} + \\frac{1}{a^{2}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M=MyEq(((a**-2-b**-2)/(a**-1+b**-1))**-1,'M') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f4b1c97f-cbb1-4d95-a53b-60a016a8311e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle M =- \\frac{a b}{a - b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "26355c3d-7bd3-42d7-9a26-e95345faf39e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N =\\frac{1}{a^{2} b^{2} \\left(- \\frac{1}{b} + \\frac{1}{a}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=MyEq(((a**-1-b**-1)/(a**-2*b**-2))**-1,'N') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a90e3904-87a6-4dce-970f-e1e95e6412ee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle N =- \\frac{1}{a b \\left(a - b\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d70d9521-ac62-4425-ad9f-bf6dce27afe4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle MN =\\frac{1}{\\left(a - b\\right)^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MN=MyEq(M*N,'MN')"
   ]
  },
  {
   "attachments": {
    "5cdba332-20d4-417d-b947-9be92022f0fe.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "1acfc64d-dfca-4a4f-a530-6c10c3215118",
   "metadata": {},
   "source": [
    "![image.png](attachment:5cdba332-20d4-417d-b947-9be92022f0fe.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "85f55979-5c2b-408a-a993-408e8a4d0696",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "from libaldomath import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "8f555282-bb65-4f5d-a57f-570483a59e53.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "c9d9e68c-2d86-4c45-a417-290848068b47",
   "metadata": {},
   "source": [
    "![image.png](attachment:8f555282-bb65-4f5d-a57f-570483a59e53.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "2ef01778-ed58-4d72-8875-ce8fa6db5289",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b + c = 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a b + a c + b c = 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a b c = 3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = \\frac{a}{a + b c} + \\frac{b}{a c + b} + \\frac{c}{a b + c}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=MQ(a+b+c,1)\n",
    "B=MQ(a*b+a*c+b*c,2)\n",
    "C=MQ(a*b*c,3)\n",
    "F=MQ(P,a/(a+b*c)+b/(b+a*c)+c/(c+a*b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "12583994-c232-43d2-9885-1d4885e70f1c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = a^{3} b c + 2 a^{2} b^{2} + 2 a^{2} c^{2} + a b^{3} c + a b c^{3} + 3 a b c + 2 b^{2} c^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.crossmul()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "8b3cbc33-fc9a-484b-98f0-d3e498c48aed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = 2 a^{2} b^{2} + 2 a^{2} c^{2} + 2 b^{2} c^{2} + a b c \\left(a^{2} + b^{2} + c^{2} + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.factors(a*b*c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "fe4e209a-7fb5-47ba-bce5-3140f058cfa8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(a + b + c\\right)^{2} = 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.Pow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "c96fefb9-b1ca-4150-97ae-d0e6d9b5581e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + 2 a b + 2 a c + b^{2} + 2 b c + c^{2} = 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "380fb583-6b8b-4d20-8124-a41072247f50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + b^{2} + c^{2} = - 2 a b - 2 a c - 2 b c + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.Substrac(2*B.L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "2fe06496-4522-4ce7-891a-f7bc98f65185",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + b^{2} + c^{2} = 1 - 2 \\left(a b + a c + b c\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.factors(-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "19d1a15b-18b7-4ce2-9bc9-facd89c87d66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} + b^{2} + c^{2} = -3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A.subs(B.L,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "2cac2c0b-6bfa-45ac-922d-6cbc30d4ba69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = 2 a^{2} b^{2} + 2 a^{2} c^{2} + 2 b^{2} c^{2} + a b c \\left(a^{2} + b^{2} + c^{2} + 3\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.s()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "c1d57c7f-5018-4ac1-b0c0-48870b94d06c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = 2 a^{2} b^{2} + 2 a^{2} c^{2} + 2 b^{2} c^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.subs(A.L,A.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "781dc206-637e-4465-93ba-9510b8cc1015",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = 2 \\left(a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.factors(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "209291a2-c015-4378-9860-36898a6a65b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(a b + a c + b c\\right)^{2} = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.Pow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "56eb730c-9a56-420b-b742-75b9587722c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} b^{2} + 2 a^{2} b c + a^{2} c^{2} + 2 a b^{2} c + 2 a b c^{2} + b^{2} c^{2} = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "f274e570-fc7f-490c-bec2-310d07499428",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} + a b c \\left(2 a + 2 b + 2 c\\right) = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.factors(a*b*c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "cfba29ea-28a7-4c99-b788-1885c6ca19f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} b^{2} + a^{2} c^{2} + 6 a + b^{2} c^{2} + 6 b + 6 c = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.subs(a*b*c,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "663dc9c5-9506-4ac8-8387-f684e209887f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} + 6 \\left(a + b + c\\right) = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.factors(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "434e7249-9200-4c48-8575-71f183bd4c0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} + 6 = 4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.subs(a+b+c,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "aa3149e3-2039-495c-9263-b4984b17742e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} = -2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B.Substrac(6) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "963a6c95-ef7b-4476-b4cc-4821757a0c68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = 2 \\left(a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.s()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "0be53ace-3553-4d6b-86f6-ed5447ccf796",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = 2 \\left(a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.factors(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "4ddebf07-e2e1-429a-a7ec-0f11cf9786c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P \\left(a + b c\\right) \\left(a b + c\\right) \\left(a c + b\\right) = -4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.subs(B.L,B.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "29a17e43-9702-481f-a073-da6a3b9fdaa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = - \\frac{4}{a^{3} b c + a^{2} b^{2} c^{2} + a^{2} b^{2} + a^{2} c^{2} + a b^{3} c + a b c^{3} + a b c + b^{2} c^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.alone(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "62d50cf7-9567-4b88-85b7-9da50d86c36c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = - \\frac{4}{a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} + a b c \\left(a^{2} + a b c + b^{2} + c^{2} + 1\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.factors(a*b*c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "6a5ad21d-5992-4877-ac5b-df57f7011281",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = - \\frac{4}{a^{2} b^{2} + a^{2} c^{2} + 3 a^{2} + b^{2} c^{2} + 3 b^{2} + 3 c^{2} + 12}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.subs(a*b*c,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "04fa4db4-d193-4f98-8065-d75259a82a1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = - \\frac{4}{a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} + 3 \\left(a^{2} + b^{2} + c^{2} + 4\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.factors(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "500eb1c4-73f2-4cd0-9247-320a8d5e69aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = - \\frac{4}{a^{2} b^{2} + a^{2} c^{2} + b^{2} c^{2} + 3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.subs(a*a+b*b+c*c+4,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "e2359bbd-480e-494e-b829-5ba75996e9bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = -4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F.subs(B.L,B.R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6c6eb89-f030-49c4-8470-4f3a7fc32545",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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