10420 Degree  Polinomies .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "824e8c78-54c1-46af-8cc2-c57258f10a1d",
   "metadata": {},
   "source": [
    "* solvecomparecoef(MyEqEq,main var,var2solve1,var2solve2,..... )\n",
    "* solvecomparecoef(exp1,exp2,main ,var,var2solve1,var2solve2,..... )\n",
    "    * exp1 and exp2 = MyEq, math expr, [coeff list]..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "03a45614-1de8-4ebe-8e6d-7747a693e5cd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "481cec55-af44-4dc0-8abe-da357e6eebca",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "c4ae9f2c-d86a-4f59-a6b5-a77643485227",
   "metadata": {},
   "source": [
    "![image.png](attachment:46908ade-131b-4e1b-baf3-be6287fb119e.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6d9a92bc-b81e-4225-aeb7-544506c79ea7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 a + 3 b - 2 = 17$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b = 2 a - 2$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(2*(a-1)+3*b,17)\n",
    "Q2=MQ(a+b,2*(a-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "407100a5-d1cc-4f08-887c-fe8dfe159752",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a =5$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b =3$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,b=simplesolve(Q1,Q2,'eQ')"
   ]
  },
  {
   "attachments": {
    "7b428bb1-4d3b-438c-af57-447beed34dad.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "efe070ff-467d-4a87-908c-594e21aab3e7",
   "metadata": {},
   "source": [
    "![image.png](attachment:7b428bb1-4d3b-438c-af57-447beed34dad.png)"
   ]
  },
  {
   "attachments": {
    "22df2820-ec12-4caf-b0f4-c759d0c31824.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d2348ef8-29c3-4766-8d5f-3f739eba9b4a",
   "metadata": {},
   "source": [
    "![image.png](attachment:22df2820-ec12-4caf-b0f4-c759d0c31824.png)"
   ]
  },
  {
   "attachments": {
    "7b428bb1-4d3b-438c-af57-447beed34dad.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "1ad885e8-0780-4fa9-89c1-94c23ca25bc3",
   "metadata": {},
   "source": [
    "![image.png](attachment:7b428bb1-4d3b-438c-af57-447beed34dad.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9977556f-e730-46f5-8eec-9434621aec4d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "f12d2bd2-d643-4926-846d-476e5a0e7d5e",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
    "c25c3d44-0f91-48c3-b578-7af4b21c3dd7.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "6ac8a218-b1ca-4a65-868f-c51dd36e1635",
   "metadata": {},
   "source": [
    "![image.png](attachment:c25c3d44-0f91-48c3-b578-7af4b21c3dd7.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f3d60831-17a1-489d-b276-37c0699e3db9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} \\cdot \\left(2 a + b\\right) - 6 x + 1 = 6 x^{2} - x \\left(4 a - b\\right) + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ((2*a+b)*x**2-6*x+1,6*x*x-(4*a-b)*x+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ce7cc67e-de00-44ec-9fa2-ef0ea7e3751f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ 2 a + b - 6, \\  4 a - b - 6, \\  0\\right]$"
      ],
      "text/plain": [
       "[2⋅a + b - 6, 4⋅a - b - 6, 0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "veccoef=coef_list(Q.L-Q.R,'noncero')\n",
    "veccoef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "89d62904-9bee-4cf9-8c2e-2f44ce168a1b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "a,b=simplesolve(*veccoef)"
   ]
  },
  {
   "attachments": {
    "7b428bb1-4d3b-438c-af57-447beed34dad.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "86ee8cf0-8a2e-43c2-b019-c3f0faa5f621",
   "metadata": {},
   "source": [
    "![image.png](attachment:7b428bb1-4d3b-438c-af57-447beed34dad.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8ecb51d4-6db8-41a0-a449-dd28f5797a0b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "7e14ca55-da41-4e3f-ac99-9cf374c0233b",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
    "a363fbd1-f4c3-4330-8120-b2a3c2781a70.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "e7cdf1b9-c8ff-4e1d-a596-7e75d04eee67",
   "metadata": {},
   "source": [
    "![image.png](attachment:a363fbd1-f4c3-4330-8120-b2a3c2781a70.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a304e62a-7407-4d33-982c-4ce4f089956c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y = \\frac{a x + b}{a x - b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(y,(a*x+b)/(a*x-b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f7a5949a-0601-43db-97c8-4b05cd82cd94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{b \\left(y + 1\\right)}{a \\left(y - 1\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1.alone(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ec51c3d2-7947-4b17-8d9e-9fb07702617d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle fy =\\frac{b \\left(y + 1\\right)}{a \\left(y - 1\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fy=MyEq(Q1.R,'fy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "858fec92-aa20-4c23-be37-02e34d7377bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle fy =\\frac{y + 1}{y - 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fy.Mul(a/b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "edd58d8d-9622-4f88-b5d1-1d4ce78adb09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle fx =\\frac{y + 1}{y - 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fx=MyEq(fy,'fx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3ce226a5-c522-466c-91a8-9368eb4872d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle fx =\\frac{x + 1}{x - 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fx.set(y=x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0361f461-a107-4f26-96ba-f375c57c07a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{a x}{b}$"
      ],
      "text/plain": [
       "a⋅x\n",
       "───\n",
       " b "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test\n",
    "simplify(fx((a*x+b)/(a*x-b)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f21605d3-1228-4ac7-a5c8-84c671954f4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "kres=1\n",
    "for i in range(2,11):\n",
    "    kres=kres*fx(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c0c75906-07ee-4839-9db7-e1a51c555a24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAPCAYAAAAGRPQsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVQ4Ea1T0Q2CQAw9iQMQ3QA3AEdwBVdwBPmEPxM3wBHUDdARcAMdwbABvifXS2NCMcYmj3tXXnttD1zXda4oipSrBnwxkHz4TN3U9XYtyzIGvfk9OS3rl/A0dZGXPbG2QAow0RnIcAB92mydb/Ok2xniaNvUSWX69J/5X5PJBTjMZ4OSOK85kAA7+ORCsO3N0kllTHKEcA/k4EQDvupThKetM4ZdY+D3offihybopLJwtCIP8ATVsWXLgi6CuAYaQ83W3Dc6VrYE3gEMUjYjRxK5hFEdkx0QsFBJhHL4F9lgHdUxWYVklQpiNVu/Xyv/qG7CW0Ewh8zPgcb2+A/m8Ld0iI3pXhvL/Axf6zhbAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle 55$"
      ],
      "text/plain": [
       "55"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kres"
   ]
  },
  {
   "attachments": {
    "7b428bb1-4d3b-438c-af57-447beed34dad.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "9f88d1bd-d020-4618-b8e6-f9085fabc42d",
   "metadata": {},
   "source": [
    "![image.png](attachment:7b428bb1-4d3b-438c-af57-447beed34dad.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "59f84326-c7d1-4fb1-a48a-4a5bd1967e2c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "ededb380-9873-42fb-ba95-91454e017b7e",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
    "076e049a-1946-4b11-a57a-a5d82e9026e7.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "0a68b699-919e-4597-9bfc-3cc76a30289c",
   "metadata": {},
   "source": [
    "![image.png](attachment:076e049a-1946-4b11-a57a-a5d82e9026e7.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3531c5e4-4fdd-4885-a0e6-9410c762c430",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{n} x^{- n} = P x^{n}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQ(P**n/x**n,x**n*P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "464850a6-5e35-462a-8a55-3bcfaab82c78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{P^{n} x^{- n}}{P} = x^{n}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d06c7650-084e-4364-baaf-65bbd02fb396",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{P^{n}}{P} = x^{2 n}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Mul(x**n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "05f53f10-5a85-44b7-ac83-cf9b8e98c821",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P^{n - 1} = x^{2 n}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0e2b22bc-dd11-491a-9ecd-373139bfccb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(P^{n - 1}\\right)^{\\frac{1}{n - 1}} = \\left(x^{2 n}\\right)^{\\frac{1}{n - 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Rpow(n-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bb920f23-0634-4707-9ce0-6e8cd60acbd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P = x^{\\frac{2 n}{n - 1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.mulexpo()"
   ]
  },
  {
   "attachments": {
    "7b428bb1-4d3b-438c-af57-447beed34dad.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "46a8ae32-04e8-4f32-bc15-7bd05c902712",
   "metadata": {},
   "source": [
    "![image.png](attachment:7b428bb1-4d3b-438c-af57-447beed34dad.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "adcaeeb8-e03e-462c-8107-fd4328288e89",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "7c69e44f-30e4-4337-b587-08a199e4be09",
   "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"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "b6e93dbb-4d9b-44a4-b56f-2b1ad1bad0e0",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "03fd1a3a-c282-4f98-875b-415f9259a84b",
   "metadata": {},
   "source": [
    "![image.png](attachment:2bc6ec1a-0b27-47bd-901d-5d48a8df90bb.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "1fad02f2-4dbc-442b-9442-83bfb2d848f5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\frac{a^{m} + x^{m}}{x^{m} + \\left(a b^{2}\\right)^{m}}\\right)^{\\frac{1}{m}} = \\frac{1}{b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1=x**m+a**m\n",
    "P2=(b**2*a)**m+x**m\n",
    "Q=MQ(rpow(P1/P2,m),1/b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "dd4d74ce-dddb-485c-b506-d8e0f298239b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\left(\\frac{a^{m} + x^{m}}{x^{m} + \\left(a b^{2}\\right)^{m}}\\right)^{\\frac{1}{m}}\\right)^{m} = \\left(\\frac{1}{b}\\right)^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Pow(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "0a1bc981-6ed8-4645-8e35-d12baf6824ed",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a^{m} + x^{m}}{x^{m} + \\left(a b^{2}\\right)^{m}} = b^{- m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "a22d1fb8-0a5b-4d0d-ada7-88acfb58045b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b^{m} \\left(a^{m} + x^{m}\\right) = x^{m} + \\left(a b^{2}\\right)^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.crossMul()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "bdf0f2ff-6aef-4abd-afbf-b3bcd062340b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b^{m} \\left(a^{m} + x^{m}\\right) = a^{m} b^{2 m} + x^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "fcaeb319-6e94-47a8-9d64-ed1ffc95caf0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - a^{m} b^{m} + b^{m} \\left(a^{m} + x^{m}\\right) - x^{m} = a^{m} b^{2 m} - a^{m} b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Substrac(a**m*b**m+x**m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "6dca8321-e974-477a-af11-31d18a46d54f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{m} \\left(b^{m} - 1\\right) = a^{m} b^{m} \\left(b^{m} - 1\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "76337395-6175-4b70-9d28-9cb9477a6b54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{m} = a^{m} b^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "08bb511a-2ef0-4cac-90d7-9dc905a60ca7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{m} = \\left(a b\\right)^{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.joinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "b83f436f-b340-4423-a6df-450313c38492",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = a b$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "aae4ae0d-ae2f-4d64-84fd-b33b3fd066d6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d17e65f7-430e-4080-a446-5e866de664f4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('Libaldo')\n",
    "from  libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "bde34581-bfd4-4ed4-aca6-8a75cb734d84",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
    "e2b401a8-e5d6-4684-a4af-e30502166fcf.png": {
     "image/png": 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GDG+l4tZOtrAiY9o5UvU7LtW5rHU1YcscNc9lZeOxaZcC+36opVsP63qeMqr6ZmG59ZmgrmUzKe7n5Ro5OUTbvz6kKMt+jHQvFVHF+l01bHwHFX8c/uOOaW7blgotOVerR1ZKfBuMs1TTTjVwlukyDgQQQOC+AMGadYAAAmlSwHx5k4a38NXPHkFa7PsvvZRwFvGn9O0usypUfUXpY87r6A8/6ucTlxT/Un6VqFxJJXIbsjHZ0qNJUYf26VyOUipbKJvxF8n8qTK3dXhGF/XcWEkzl/uqvIO+cJnsxWK3GiR7RDyIAAIIpLoAwTrViekAAQRSSyD2zFqN6hmg802maWqfCrL2wji1xpH67d7ST4t95bMipwbMHaeGBVKwfyX1B0sPCCCAwHMrQLB+bkvPxBFwDQGz5frxkCkTteJifU2a3VkJtlO7xgQVq0PTu2j0sZoa4t9TlaydxuEis2YaCCCAQFoUIFinxaoxZgQQeEog5ka0XvxbdgOu93Y+XFN0tJQ9u0EngDjf/BgRAggg4CoCBGtXqSTzQAABBBBAAAEEEHCoAMHaofx0jgACCCCAAAIIIOAqAgRrV6kk80AAAQQQQAABBBBwqADB2qH8dI4AAggggAACCCDgKgIEa1epJPNAAAEEEEAAAQQQcKgAwdqh/HSOAAIIIIAAAggg4CoCBGtXqSTzQAABBBBAAAEEEHCoAMHaofx0jgACCCCAAAIIIOAqAgRrV6kk80AAAQQQQAABBBBwqADB2qH8dI4AAggggAACCCDgKgIEa1epJPNAAAEEEEAAAQQQcKgAwdqh/HSOAAIIIIAAAggg4CoC/wO+H/WVZjEuwAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "a1cbb4a9-35fb-4a70-a42a-8f9780a159b5",
   "metadata": {},
   "source": [
    "![image.png](attachment:e2b401a8-e5d6-4684-a4af-e30502166fcf.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "80e2b5b7-97fb-4798-8767-006247348b28",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(b^{b} x\\right)^{x} = b^{b^{1 - b}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1=(b**b*x)**x\n",
    "P2=b**(b**(1-b))\n",
    "Q=MQ(P1,P2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "59e2d3cd-d4b5-4f8b-930c-5aeb88ee6278",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\left(b^{b} x\\right)^{x}\\right)^{b^{b}} = \\left(b^{b^{1 - b}}\\right)^{b^{b}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Pow(b**b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "416e0011-2682-428b-8217-97da2635c219",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(b^{b} x\\right)^{x} = b^{b^{1 - b}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify('R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "dbea4514-2968-4aed-831f-18c19645ff37",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b^{b} x = b$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2=MQ(b**b*x,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "cd383a28-62c1-48d0-999c-ed6fb01c86d6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x=b^{1 - b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=Q2.solve(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "9f336135-a57e-492e-8d22-532242064ede",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle b^{1 - b} = b^{1 - b}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MQ(x,b**(1-b))"
   ]
  },
  {
   "attachments": {
    "7b428bb1-4d3b-438c-af57-447beed34dad.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "3ab31c98-705d-4104-8c3b-089e7c75d0d8",
   "metadata": {},
   "source": [
    "![image.png](attachment:7b428bb1-4d3b-438c-af57-447beed34dad.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "7233418f-a1ea-41e4-a0be-e342ab9ea2cf",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ac2914e2-ba7a-4867-a9d2-3194ebfdf7ef",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('Libaldo')\n",
    "from  libaldomath  import *\n",
    "# this cell will be initializing your variables"
   ]
  },
  {
   "attachments": {
    "20e0cd2a-95b2-4f69-8c93-5299e944d921.png": {
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   },
   "cell_type": "markdown",
   "id": "bdb6cbbd-a3ef-4dcc-8294-8d641def5530",
   "metadata": {},
   "source": [
    "![image.png](attachment:20e0cd2a-95b2-4f69-8c93-5299e944d921.png)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "7b7e5344-a9ba-4e6e-9c8c-72b90f3cbcdb",
   "metadata": {},
   "source": [
    "![image.png](attachment:cca4c9ab-6cb9-48a0-8d91-38758c4ff733.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "02a69acc-5691-4b96-9755-de90da565a92",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 3^{x - \\frac{1}{2}} + 4^{x} = - 2^{2 x - 1} + 3^{x + \\frac{1}{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1=(4**x-3**(x-cfrac(1,2)))\n",
    "P2=3**(x+cfrac(1,2))-2**(2*x-1)\n",
    "Q=MQ(P1,P2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "603cce0d-cec5-40ee-b8b6-9059c60994a0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{\\sqrt{3} \\cdot 3^{x}}{3} + 4^{x} = - \\frac{2^{2 x}}{2} + \\sqrt{3} \\cdot 3^{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.sum2mulexpo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "4743c3e1-4935-4226-b029-9b7d46486c67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2^{2 x} + \\frac{- \\sqrt{3} \\cdot 3^{x}}{3} = \\frac{\\left(-1\\right) 2^{2 x}}{2} + \\sqrt{3} \\cdot 3^{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.primefactor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "20dd2721-cd3f-4cfd-a0f0-172367ecbf2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 6 \\cdot 2^{2 x} + \\frac{6 \\left(- \\sqrt{3}\\right) 3^{x}}{3} = \\frac{6 \\left(- 2^{2 x}\\right)}{2} + 6 \\sqrt{3} \\cdot 3^{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Mul(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "07ccb72e-b211-4f86-97b5-e0244ce94aef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 2 \\cdot 3^{x + \\frac{1}{2}} + 6 \\cdot 4^{x} = 6 \\cdot 3^{x + \\frac{1}{2}} - 3 \\cdot 4^{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "d1a0ab4a-7a5a-433b-866e-20c9ae6e0c5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 9 \\cdot 4^{x} = 8 \\cdot 3^{x + \\frac{1}{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Add(3*4**x+2*3**(x+cfrac(1,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "f2913248-f4c2-4a4d-9c2c-dd3b8eeac710",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{9}{8} = 3^{x + \\frac{1}{2}} \\cdot 4^{- x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(4**x*8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "c9daf742-3da1-4ca8-bfec-5f9d6268e284",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{9}{8} = \\sqrt{3} \\cdot 3^{x} 4^{- x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.disjoinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "58b61b17-90b0-4e52-a304-bc395d1f194c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 \\sqrt{3}}{8} = 3^{x} 4^{- x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(sqrt(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "1eb74c65-c834-49c4-af83-417446557758",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 \\sqrt{3}}{8} = \\left(\\frac{4}{3}\\right)^{- x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.joinbase()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "83c006cc-ea00-4f6d-a51a-6dc592f6ec78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{8 \\sqrt{3}}{9} = \\left(\\frac{4}{3}\\right)^{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Rpow(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "4252e7b3-9030-4358-ab68-c5ccac8c9551",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\log{\\left(\\frac{8 \\sqrt{3}}{9} \\right)} = \\log{\\left(\\left(\\frac{4}{3}\\right)^{x} \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.log()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "484505dc-e2e0-4ccc-bd37-76a3a7eff408",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{3 \\log{\\left(3 \\right)}}{2} + 3 \\log{\\left(2 \\right)} = x \\left(- \\log{\\left(3 \\right)} + 2 \\log{\\left(2 \\right)}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.lexpand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "efb263b8-4e36-49a2-9d85-6162740d26f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{- \\frac{3 \\log{\\left(3 \\right)}}{2} + 3 \\log{\\left(2 \\right)}}{- \\log{\\left(3 \\right)} + 2 \\log{\\left(2 \\right)}} = x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.Div(Q.args(1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "90410df2-77a3-469b-b24a-1a2f087c6fce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{- \\frac{3 \\log{\\left(3 \\right)}}{2} + 3 \\log{\\left(2 \\right)}}{- \\log{\\left(3 \\right)} + 2 \\log{\\left(2 \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.swap()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "3204555e-6f7c-40ee-818e-0204902c1eff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{3}{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.simplify()"
   ]
  }
 ],
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