10430 Polynomial_Functions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a7e8c9ba-52b5-413e-b481-b16e04c564fc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57b9de1f-e246-484b-ac01-19c9f49f573f",
   "metadata": {
    "id": "57b9de1f-e246-484b-ac01-19c9f49f573f"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "attachments": {
    "639f001d-e725-4d76-8f10-4b06de5d0211.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "8a607297-ba59-47cb-8b12-afa8d5e1be79",
   "metadata": {
    "id": "cffc6021-bd72-4a64-9dcb-ff1d23f4d66e"
   },
   "source": [
    "![image.png](attachment:639f001d-e725-4d76-8f10-4b06de5d0211.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "efffb03a-104f-469c-a45d-8426da4f23cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABgAAAAOCAYAAAA1+Nx+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAj0lEQVQ4EWP8//8/A7VAQ0ODEdCs1UBsDGR/AJnLAiIoAUCDBID6ZwPxOyA2AWIlIIYDalgAcmkoyESgZWVACuQLOGCCs2jEGLWAYMDSPIhYoMlsL9ApoORGLAgF6jtHjGKQBaBkZkyMYnLU0DyIhpwFwtBgFIIFJyM1CjtgPIIKOBBwAWJQYgElgHtAvBsAO3sgJ/LwrLIAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(cos(pi))**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "fa41f86b-6a5c-4373-9ec0-e3bd189c3761",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{3} - x^{2} = -1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1=MQ(x**3-x**2,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "bc639cc5-31d4-4931-90fd-92aaaec8ec27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{3} = x^{2} - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1.Add(x*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "395fa580-bade-42c0-8655-499dbc1a901c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{3} + 1 = x^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q1.Add(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "c81a5689-9b23-4a4a-a821-f44f236f86fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{7} + x^{6} + x^{5} + x^{3} + 2 x^{2} + 2 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MyEq(x**7+x**6+x**5+x**3+2*x*x+2*x ,'P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "84c12d5f-1700-49e5-9b30-2774373194b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{7} + x^{5} + x^{4} + x^{3} + 2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**6,x**4-2*x*x+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "8ba13bf6-d780-4a03-b283-9bbca56de3c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{5} + x^{4} \\left(x^{3} + 1\\right) + x^{3} + 2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.efactor(x**7+x**4,x**4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "f8c40966-9535-4acf-b0a8-a7b9c0ac68f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{6} + x^{5} + x^{2} + 2 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**3+1,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c0ec90f2-d75c-439d-bd1c-6b5020f2fe38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{6} + x^{2} \\left(x^{3} + 1\\right) + 2 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.efactor(x**5+x**2,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "f32033c8-a27c-454c-a0ad-f97fa68c1528",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =x^{6} + x^{4} + 2 x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**3+1,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "fcf017ba-4789-4fd2-916e-0842fca9ef89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2 x^{4} - 2 x^{2} + 2 x + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**6,x**4-2*x*x+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "06155016-d1b0-4f52-b781-ff9ccf13961a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =- 2 x^{2} + 2 x \\left(x^{3} + 1\\right) + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.efactor(2*x**4+2*x,2*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "e57e6750-9458-4624-abe9-112e54a5c0c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2 x^{3} - 2 x^{2} + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**3+1,x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "30eee51c-3111-4ef5-b1e4-af2d2e226642",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =2 \\left(x^{3} - x^{2}\\right) + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.efactor(2*x**3-2*x**2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e5c520b5-169a-4bb2-98f5-f7bbe0a025ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P =-1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.subs(x**3-x**2,-1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b85efeea-a2d7-483d-acd4-1029f689f29c",
   "metadata": {
    "id": "57b9de1f-e246-484b-ac01-19c9f49f573f"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "c06d20d5-9403-4b5c-ada6-d0aae9fdc833",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c9f27b7-ccfe-411f-8e6e-6b4fc4c602b0",
   "metadata": {
    "id": "7c9f27b7-ccfe-411f-8e6e-6b4fc4c602b0"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p38.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b139b0ac-dc75-4fad-b5d2-b27d2c77ef66",
   "metadata": {
    "id": "b139b0ac-dc75-4fad-b5d2-b27d2c77ef66"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/lines.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "46486d04-e4dc-46a8-bdbc-48355698e0a4",
   "metadata": {
    "id": "46486d04-e4dc-46a8-bdbc-48355698e0a4",
    "outputId": "ad8595fe-ad8c-4276-ee44-23c579240061",
    "tags": []
   },
   "outputs": [],
   "source": [
    "xx=symbols('f(x)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "e59ed225-8946-4ca1-9571-121b81a0bf8e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x1=symbols('f(x+1)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "c282fc2d-1b8d-46dc-b07b-9825dfe86930",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x2=symbols('f(x+2)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "d3cb3025-254f-417a-b29a-b0e2a4079674",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(x+2) = f(x) + f(x+1) + x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=MQ(x2,x+xx+x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "cf470617-ba67-41aa-80dc-50b8ee6f7e22",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 f(x+1) = f(x) + f(x+1) + x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.setL(2*x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "dc91bab8-e6d1-428a-b376-005876a9fc15",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(x+1) = f(x) + x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Substrac(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "f0fa0caa-ed46-4892-a446-844b8ead3ddb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 f(x) = f(x) + x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.setL(2*xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "bced081b-0349-4064-8db6-489c8e4af19f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(x) = x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P.Substrac(xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "6b0679c6-096a-47c4-b505-220b250e8e4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f =x$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f=MyEq(x,'f')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "fdb9595a-a06e-4e13-ac2a-5d0851943101",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAOCAYAAAASVl2WAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAZElEQVQYGWP8//8/Aww0NDQYAdmrgdgYyP4AEmcBMgSA9GwgfgfEJkCsBMRwAFIAUhkKEgGyy4AUyBQ4YIKzcDBGFUACBj0chKHhJQQLN0ZQZAGDGBRBIOACxKC4OQfE94B4NwDm+hiAOyllRAAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(-3)+f(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d113d71-7eba-484a-ac4d-770fc9611335",
   "metadata": {
    "id": "ef255d21-01ae-4515-b20e-3a69e78e923e"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28b89ec1-c7c1-4bf9-826b-ba8a06f5d4f1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "279d9e76-2677-47cd-80bd-7703d4d289b7",
   "metadata": {
    "id": "279d9e76-2677-47cd-80bd-7703d4d289b7"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p39.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55c71b60-75a5-4b96-8866-78231e34e92e",
   "metadata": {
    "id": "b5e02550-1461-43b0-a8e0-b9845a4b8a2b"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/lines.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6628371f-6e01-405a-8cca-fbc5ff3cedc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f =\\pi^{x} + e^{x}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f=MyEq(exp(x)+pi**x,'f')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "63e71181-0086-4650-9395-0629cea416ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC8AAAAOCAYAAAC/10U/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABkUlEQVRIDcWW300DMQzGr4gBKtigbFDBBnQDugLdgIq3e4UN2g1A3aDdoNJt0G6AxAbH7wvJybl/D+VyWHJtf0ns7xIn6qQsy2xoyfP8kZwz7Hbo3DbflQ0G9KfkkiaVVOSTkg7Jr4MjyzFrt17RL8XIHboG/3bRSD/Ue6PUM9p3etuKPAvUpxt0iV9gM+wco49ZKx5DqCnikiUq8g/oB3rv4wNW3ApHHmdGvEdXAjXoRR8kfBShtjbriN2pIPYFs8GeUXE5YCt+jrwmoJKpXyD/Ft0Tuy8VUBfGtE5J63IjgPFVfYC4ANeuNgRcxCpy+Auwdz9RJxC9XoG8COzMRD+/3zC/jVwG/sRKPZWhcH+illHW6hTsXZuD2Tizr82xJcd/QtoY27Jq7UgC+TOo2qQhfhcbeEqAmrqoem0+bR3wqEVD2+iGRy3gEwgPt9/mSe2LuC5p1CZgC7S6g448k7Yii4roCZUojj7oFx7lVyTrz7N7gWz1SaL/Nn++sJZklx96vmv8UlzHXT/yS3N1rvsB8UJ4XORSt+YAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle e + \\pi$"
      ],
      "text/plain": [
       "ℯ + π"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bc07df6b-ee78-4f36-8661-32328c18fb53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle e^{3} + \\pi^{3}$"
      ],
      "text/plain": [
       " 3    3\n",
       "ℯ  + π "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(3)  # and equal 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "eedb4768-3ceb-4504-84f9-8c3ce1e5b467",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =- \\pi^{7} - e^{7} + e^{4} + \\pi^{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1=MyEq(f(4)-f(7),'F1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ddbfe4ed-0567-4e61-98f5-0aa01de924ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =\\pi^{4} \\cdot \\left(1 - \\pi^{3}\\right) - e^{7} + e^{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1.efactor(pi**4-pi**7,pi**4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4f1d34bf-27d3-46c5-abd2-0418b1ebda96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =\\pi^{4} \\cdot \\left(1 - \\pi^{3}\\right) + \\left(1 - e^{3}\\right) e^{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1.efactor(exp(4)-exp(7),exp(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6350bbe4-ca9e-46a0-95e0-d0f13719ec94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =\\left(1 - e^{3}\\right) e^{4} + \\pi^{4} e^{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1.subs(1-pi**3,exp(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "68436641-30fa-4bc6-ad3f-40ea47155c6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =\\pi^{3} e^{4} + \\pi^{4} e^{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1.subs(1-exp(3),pi**3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "824fcc48-2401-4324-b82e-6e7a4a302b47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =\\pi^{3} \\left(e + \\pi\\right) e^{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "b750267c-47fe-4e31-8df5-326e2bdc5683",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F1 =\\pi^{3} e^{3}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1.subs(exp(1)+pi,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "16cf5845-7ba2-450f-abbd-ec05008c9661",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F2 =\\frac{1}{\\pi^{3} e^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F2=MyEq(1/F1,'F2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2e11f570-1f50-4259-8168-f13a0e9bcff4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F2 =\\frac{1}{e \\pi}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F2.Rpow(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d38b457a-6ce5-4c90-8dd3-c13f68f58040",
   "metadata": {
    "id": "d38b457a-6ce5-4c90-8dd3-c13f68f58040"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "6d07dceb-531e-42c2-8e5c-b75efd774028",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9fa6896-2e2c-40b9-b32c-a092bf7a3d74",
   "metadata": {
    "id": "f9fa6896-2e2c-40b9-b32c-a092bf7a3d74"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p45.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e297d6bf-07e7-4aad-a2f6-58d8c0908160",
   "metadata": {
    "id": "e297d6bf-07e7-4aad-a2f6-58d8c0908160"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/lines.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09401fc8-0dd8-461a-b89d-992a8dd754d8",
   "metadata": {
    "id": "09401fc8-0dd8-461a-b89d-992a8dd754d8"
   },
   "outputs": [],
   "source": [
    "def fx(x):\n",
    "    return((x+1)/(x-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43dbb900-75b4-47ce-8b1e-4d680dd70577",
   "metadata": {
    "id": "43dbb900-75b4-47ce-8b1e-4d680dd70577",
    "outputId": "756b6d03-c52e-411d-e7c8-d89e3bd272a5"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle From\\;data\\;f(1/2)=\\;-3\\;.f(\\;-3\\;)+3\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE(['From','data','f(1/2)=',fx(frs(1,2)),'.f(',fx(frs(1,2)),')+3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "398227a5-81d9-4a95-957a-478c4617be64",
   "metadata": {
    "id": "398227a5-81d9-4a95-957a-478c4617be64",
    "outputId": "97bfebc8-f7b9-41b3-9e66-ffefbeee6632"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Also..\\;f(-3)=\\;0.5\\;.f(\\;0.5\\;)+3\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE(['Also..','f(-3)=',fx(-3),'.f(',fx(-3),')+3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c3590c3-09aa-4434-abc0-d586216a1f88",
   "metadata": {
    "id": "7c3590c3-09aa-4434-abc0-d586216a1f88",
    "outputId": "c5b20c70-5dff-40b3-9c8f-1f099e2f2481"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x}{2} + 3$"
      ],
      "text/plain": [
       "x    \n",
       "─ + 3\n",
       "2    "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# f(-3)  = y\n",
    "# f(1/2) = x then\n",
    "x,y = symbols('x y')\n",
    "csolve(y-x/2-3,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "afd26738-6d3c-44a7-a386-7eb72b4f545a",
   "metadata": {
    "id": "afd26738-6d3c-44a7-a386-7eb72b4f545a",
    "outputId": "d76f1474-424c-4aa6-d8f3-c70057616b29"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{12}{5}$"
      ],
      "text/plain": [
       "-12/5"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csolve(x -(-3*(x/2+3)+3),x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e092ee94-3762-4f1f-a23c-f8841c23fb70",
   "metadata": {
    "id": "e092ee94-3762-4f1f-a23c-f8841c23fb70"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4881de6-7ecc-4f62-864f-5c12fa3c0baa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "916c1537-102e-4f35-bcb4-8a9dcabefb6a",
   "metadata": {
    "id": "916c1537-102e-4f35-bcb4-8a9dcabefb6a"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p47.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20246984-bc28-4f0d-a654-4bd522f52caf",
   "metadata": {
    "id": "20246984-bc28-4f0d-a654-4bd522f52caf"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/lines.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08e18b62-6af8-4af4-b3d3-4e2b66f50e0e",
   "metadata": {
    "id": "08e18b62-6af8-4af4-b3d3-4e2b66f50e0e"
   },
   "outputs": [],
   "source": [
    "a,b,c,x=symbols('a b c x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8819a0fc-fa09-4297-8af0-7d69d76f09c6",
   "metadata": {
    "id": "8819a0fc-fa09-4297-8af0-7d69d76f09c6"
   },
   "outputs": [],
   "source": [
    "def P(x):\n",
    "    return(opemat(x*x+a,'esfs'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0251885b-2972-4c93-a715-3c93c2bcc202",
   "metadata": {
    "id": "0251885b-2972-4c93-a715-3c93c2bcc202",
    "outputId": "29a97b09-20f1-445d-d6ec-f77df964c129"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle a^{4} + 4 a^{3} x^{2} + 2 a^{3} + 6 a^{2} x^{4} + 4 a^{2} x^{2} + a^{2} + 4 a x^{6} + 2 a x^{4} + a + x^{8}$"
      ],
      "text/plain": [
       " 4      3  2      3      2  4      2  2    2        6        4        8\n",
       "a  + 4⋅a ⋅x  + 2⋅a  + 6⋅a ⋅x  + 4⋅a ⋅x  + a  + 4⋅a⋅x  + 2⋅a⋅x  + a + x "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1=P(P(P(x)));a1 # n=3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2580920-e176-448e-926b-ad9ae729a9b7",
   "metadata": {
    "id": "c2580920-e176-448e-926b-ad9ae729a9b7"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p47a.png?raw=1\" alt=\"ml\" style=\"width : 80%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b8e8db2-2bcf-44c8-b89e-ea9a8831bdd1",
   "metadata": {
    "id": "4b8e8db2-2bcf-44c8-b89e-ea9a8831bdd1",
    "outputId": "28681109-5268-48cb-e865-d5d189f9288f"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle a^{4} + 2 a^{3} + a^{2} + a$"
      ],
      "text/plain": [
       " 4      3    2    \n",
       "a  + 2⋅a  + a  + a"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(a1,'unfilt',x) # return al monom if dont have x..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4bd2d171-e4f7-4eeb-bda8-f68be9028013",
   "metadata": {
    "id": "4bd2d171-e4f7-4eeb-bda8-f68be9028013",
    "outputId": "c63fb2fa-b167-43a3-8e8f-3282a91a8707"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle if\\;a^{4} + 2 a^{3} + a^{2} + a\\;=\\;5\\;then\\;a\\;=\\;1\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['if',fpoly(a1,'unfilt',x),'=',5,'then',a,'=',1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8874aef5-c00f-4cb1-b950-07ac0c194ffc",
   "metadata": {
    "id": "8874aef5-c00f-4cb1-b950-07ac0c194ffc"
   },
   "outputs": [],
   "source": [
    "def P(x):\n",
    "    return(opemat(x*x+1,'esfs'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40d54979-5d6f-40b9-b095-8674c509e904",
   "metadata": {
    "id": "40d54979-5d6f-40b9-b095-8674c509e904",
    "outputId": "d38fda2e-0d0e-48fc-d336-bfb2f74c90cd"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAAVCAYAAAC0RVlIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGJklEQVR4Ae2a7XEUORCGB8oB+HwRgDPgIwOTwVFEAGQAxT//oyADzhHcQQYHERicAWRwxhn4nkduqWa9e7ZHuzM7M6arZH1YH/2q1a1Wz945Pz9vaujw8PAF43ZJZ6R90gfafpDPisD0DkD/Bqgz6n/OCmCAAdc30sM5YQOP5/NNYLof+XPaPbOjo50ajgDzinGfyJPyBeiPtD2pmW+sY8D1Dd4U3gnpAWXrs1NGsClP8c2N3oHtZQZF+QNlZejlMTq6W8mRSpctTQNILc1e5VyjHAYmb8Sv5CcyGPmsjE3gOiCfnUcjNugFchNfJmV6n7ZRGp6qmxFA/5gA9Z70mqTLqtWZE4npaQhOw/OZ8uc5AQSPbpwHc3a3fcjJW/FrlEefVd2MCPE9yF6TXlH20blPPhuBxiH1oOabUCXU5VFB50TeHMpyluSZJLXfhyrnD9qStzM0aNZdupFp2yUlL7PqZoxJHwPGB78PZJXSSYt/PjTQ9nrB38s1+Mku93fmyG6qxucndW/IQd061tMwuM8Gkn4nWf8oL+RVxNg/GPipanAPg/rA2GaT+VUEMW8zSPUlcGZjoBylxFOVMjL4iEkzKF05/XIPhxHVvJCLbIsMJlXzAQatp7wXpaNuJNU2sQ7tBSwEImQCXtxvDWBnhWKMlniPvOBzzi3TRjG2sQRe34sPKbdvyna3IcqnLGLSMLj3yu5t5mmHSicKYE5YiDZvCw+oQu6sBIz1gPuwXvuQM4eRwU2Qm5Xch0uTVR3gWoyM0zU2AniZntPwhdRZGRmjRfZp4QGVkoWO+jF5zZwN46rkyLg+MCZgzK0MVfT05CBXETSsg8oxMYNusO7TKC9lNcroraFV1Sq3rYyg3y6tcLMGD0M6EDfrvroX/KSN5r9tvlZ3vr7Vg6oAk4GIucVe6xrWYjQML661DRVzJAKDBrMYTerKToUoVjp17P5nNBhlPXAZWDTI6B5KPqV8ctRSLcZr1+usjDGj2q21+R513zEC3oQSxJRV2TN4kI+1367M4eNfg6NS+lZTKbJrXsVc5SAj177JzX0S5D2Wr7Uj2MynEmZr7fPjL1LVzcg8tdQXRj0KlWfBswDf2uejFuhV44oywqBMKxjJ4IxukBbzGUkq7gt9veJHBQiedE+vPJxdMAqY/luPNMKDTwCVw+CDASStuobBT0sLSkP9xjJkfCLGeONu7NaNaTtl8NALRub9rRMjA3SGJ3VMOUnKscRZ7qamiz/edH439AAek45IB9QVvoPz+4LiuAgeNRo3eQdMEiP4vLmyYVAOj0jFzaScaZL4ZP42YASmevQ3WLOeKUt/huhbu0nKSEVtvaxs7dD33or/O34s5GeMK637lDHCu7KQtKS+WX3/+NklCZFyM2V8wf9twPgEOZ2JV6Ksh6k8k0d3xx+K0/iAVCwtZX14gzQbfSMxn4uWA0Q5k8ounV5kC3+vjEAxp4Zk4dsfbb4RDLbkt1BDeZIY4Vt8huTLs4CyB9fPNwr2HnW9gkHwsV7DWhuVI/PNHqP7topiL8W/n96MNBRFjAEqzDoRp1XrNqxTDlS7A+0eLj9tZFes/e//LdNf99Qgy7VhavpMEiP49FjutTcBLP5I31vSAJqysj4IPvlgrY3KkSlnj5E9u+6C203K6AZnYpDClUpwgDZ93Ya8XLHWR0Aq42P48pZok26cym27N+SCYaE+CYzw6b5rbJb2nTZxKaPsVVC8INongU9u4XX2GEMsj8hXeX5JfuzDyU5shofWx7/+a7J6lNu3zRvqCwc6FthqFvwuffej/SeM6bomN5VcgU8OI3zrfpo0LG155H0XlzgniU8Q8D57jCEsP5Wt0iENZzrDBnCsmE5DqGrvGSkRbf7vOKpTyTycpkxTxqhBST99y2DMkYvvDD9vqKRTxiec24DRTxgLn96o51+LpUtjh41QK41EKtCGDkYmFbIDDYSopMVltc9YKXjWHZAOxEFuyt/SJocRDN58fvM9Im+7OSpo9gomLcNbgtFnhd5nVkjdU+WZAnDkTYqmWtgmwWBVAGebPHdd+xfGrjs2zv59ylE3dQykW1xc4zEw1AMPvzD2sKlbmLI3Of4HrT6d3OPCDpIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{2} + 5$"
      ],
      "text/plain": [
       " 8      6      4      2    \n",
       "x  + 4⋅x  + 8⋅x  + 8⋅x  + 5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(P(P(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1dfdac16-5102-4bbe-a24e-dfbdeecd5072",
   "metadata": {
    "id": "1dfdac16-5102-4bbe-a24e-dfbdeecd5072",
    "outputId": "60f98755-c5ef-4032-fe5c-5b693f289acb"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAOCAYAAACsAAXLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAB/ElEQVRIDZ2V7VECMRCGD4cC0BKgA8UK1A5krEDpQMd//NUO1ApQO5AOHCgBK/CjA3yeTMKE49DAzuztZvPum718thaLRZVkNBod4r+gR/g/KZ4ssS7+TWz3sV+2ic9iLJhSXMoBf5f8aMdytvl0CDyhDuSAFrAmccA77CB14ks6xZ6hE+NY8//FZdg3/GGW7+SovT2CP+gAHRIYo5vEQi7zTnKcRWdYsiSlOPHmTeAJPxYJnKy5/l4MlJhTQN8QmZyLxB3iacaLcODPyXMbpW0SOIm7Cmc2tinOIuYkOlNNkoouxd1C4qpt4qvaTaM0xSBZ7rVav39f0R8ORSmOFPNm4LUX6CfaQ1+IhWUuLo6kNYnELufK0tSBdRztNMtC+7SX+fhunUv0dZtlrY9p2w39CNF9U2cW24Q7JPcxw+k+o0/EOzsXR/IDJJ40T/lGacIRS/ssnMpa8pS2M9vfqTjIryTE/lfYXzgLS0VKV5fu1sVRkFdALy8Mv6vm7AU4i8v3Xp6uP9+qOAb0ZB1jlxs4MlqwL0yQQpyX9coPxfQjrFfMpFV7W6/pMGmfzpUppy2RT0045tgkBzhubK+BqhQXsfJ5nYSfxTqTH2g4reEqIehpssO3VfG99N56x6aTKMYCwz7C5hLuuBgoxVVw+xr4Dnu4FH/0hHbg+wUwKfvv96C/SwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 1226$"
      ],
      "text/plain": [
       "1226"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(35)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08a14fcd-8233-4e84-a1ef-18199ebc1d7e",
   "metadata": {
    "id": "08a14fcd-8233-4e84-a1ef-18199ebc1d7e"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "37494022-78a3-4a67-9a68-fd41a82d8b1a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc22dd6a-d1b9-465d-8e7c-2cd2b9504be4",
   "metadata": {
    "id": "cc22dd6a-d1b9-465d-8e7c-2cd2b9504be4"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p48.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69b2d40e-60de-4384-b62f-887acc214879",
   "metadata": {
    "id": "69b2d40e-60de-4384-b62f-887acc214879"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/lines.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aab24d18-7a58-4418-9147-13271305b42c",
   "metadata": {
    "id": "aab24d18-7a58-4418-9147-13271305b42c"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p48a.png?raw=1\" alt=\"ml\" style=\"width : 50%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f15992d9-c7ca-44e8-92f3-e13349e51db7",
   "metadata": {
    "id": "f15992d9-c7ca-44e8-92f3-e13349e51db7"
   },
   "outputs": [],
   "source": [
    "a=rpow(3*x);b=rpow(x+2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af6990c9-9607-4830-8af4-5863f61a1bc1",
   "metadata": {
    "id": "af6990c9-9607-4830-8af4-5863f61a1bc1",
    "outputId": "b0bc2e08-6be5-45c1-d264-713d9f2c9b7e"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2 \\sqrt{3} \\sqrt{x} \\sqrt{x + 2} + 4 x + 2$"
      ],
      "text/plain": [
       "          _______          \n",
       "2⋅√3⋅√x⋅╲╱ x + 2  + 4⋅x + 2"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1=expand(kpow(a+b,2));e1 #pow a+b to 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3e9f4ebb-c452-4053-8486-fe88cd4636cb",
   "metadata": {
    "id": "3e9f4ebb-c452-4053-8486-fe88cd4636cb",
    "outputId": "1e40e4a2-0b46-4351-8f86-704b1eca7bde"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{3} \\sqrt{x} \\sqrt{x + 2} + 2 x + 1$"
      ],
      "text/plain": [
       "        _______          \n",
       "√3⋅√x⋅╲╱ x + 2  + 2⋅x + 1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2=e1/2;e2 #divide by 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f7fec41-b9b5-4d21-acda-f27b40c61cd4",
   "metadata": {
    "id": "7f7fec41-b9b5-4d21-acda-f27b40c61cd4",
    "outputId": "96e92fb6-4341-43d7-8864-20fb746072ae"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{3} \\sqrt{x} \\sqrt{x + 2} + 2 x$"
      ],
      "text/plain": [
       "        _______      \n",
       "√3⋅√x⋅╲╱ x + 2  + 2⋅x"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e3=e2-1;e3 #Add -1 and get tha same eq from question "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69671396-0fc4-4164-b129-b5332b75ffdd",
   "metadata": {
    "id": "69671396-0fc4-4164-b129-b5332b75ffdd"
   },
   "outputs": [],
   "source": [
    "# creatinf func whit the same step\n",
    "def f(y):\n",
    "    return(kpow(y,2)/2-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8dec6e5b-a45e-46bf-89c3-58dac633c905",
   "metadata": {
    "id": "8dec6e5b-a45e-46bf-89c3-58dac633c905",
    "outputId": "24ead491-3b2a-450b-d32f-db89115247e4"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2}}{2} - 1$"
      ],
      "text/plain": [
       " 2    \n",
       "x     \n",
       "── - 1\n",
       "2     "
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) # whi x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7357d837-62f5-4446-a12b-6f60d1326f95",
   "metadata": {
    "id": "7357d837-62f5-4446-a12b-6f60d1326f95",
    "outputId": "aec9464f-627a-4f86-cabc-5c5bfd90d9fb"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{3} \\sqrt{x} + \\sqrt{x + 2}$"
      ],
      "text/plain": [
       "          _______\n",
       "√3⋅√x + ╲╱ x + 2 "
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+b # a+b ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58b6074d-8094-4d3a-bf4f-992d9ad7c59b",
   "metadata": {
    "id": "58b6074d-8094-4d3a-bf4f-992d9ad7c59b",
    "outputId": "09b9bf66-4b74-4ed5-ed53-9486d098d8ae"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{3} \\sqrt{x} \\sqrt{x + 2} + 2 x$"
      ],
      "text/plain": [
       "        _______      \n",
       "√3⋅√x⋅╲╱ x + 2  + 2⋅x"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(expand(f(a+b))) # test the func ok"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4c3cb04-6ef6-402b-9abe-002311fe6d94",
   "metadata": {
    "id": "b4c3cb04-6ef6-402b-9abe-002311fe6d94"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p48b.png?raw=1\" alt=\"ml\" style=\"width : 50%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b088f73-790f-4ca9-81e5-2eef55a5a227",
   "metadata": {
    "id": "9b088f73-790f-4ca9-81e5-2eef55a5a227",
    "outputId": "60d6e383-c2da-4533-a4e7-36228068820d"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2} + 4 x - 2}{2}$"
      ],
      "text/plain": [
       " 2          \n",
       "x  + 4⋅x - 2\n",
       "────────────\n",
       "     2      "
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq3=factor(expand(f(x)-f(x-1)+f(x+1)));eq3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b382abf-a88c-4d46-8f32-e86bfb6d33fe",
   "metadata": {
    "id": "4b382abf-a88c-4d46-8f32-e86bfb6d33fe"
   },
   "outputs": [],
   "source": [
    "g,G=symbols('g G')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c5bc181-a42f-43bd-8c44-c0914f78a355",
   "metadata": {
    "id": "9c5bc181-a42f-43bd-8c44-c0914f78a355"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p48b.png?raw=1\" alt=\"ml\" style=\"width : 50%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b9d79d44-12ea-44fd-b444-39d7c57c1be0",
   "metadata": {
    "id": "b9d79d44-12ea-44fd-b444-39d7c57c1be0",
    "outputId": "c1df7834-d298-4145-d688-5ff6b667df8f"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2} + 4 x - 2}{2 \\left(x + 2\\right)^{2}}=\\frac{G - 6}{2 G}$"
      ],
      "text/plain": [
       "(x**2 + 4*x - 2)/(2*(x + 2)**2)=(G - 6)/(2*G)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P=polyclass(eq3/kpow(x+2,2),(G-6)/(2*G));P.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aac46645-f754-4c5c-8f71-9ddaff3c780c",
   "metadata": {
    "id": "aac46645-f754-4c5c-8f71-9ddaff3c780c",
    "outputId": "31419b8e-5473-45a7-d02c-ad458f94e445"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2 G x^{2} + 8 G x - 4 G$"
      ],
      "text/plain": [
       "     2              \n",
       "2⋅G⋅x  + 8⋅G⋅x - 4⋅G"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq4=expand(numer(P.q1)*denom(P.q2));eq4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17dd48d3-875f-4b88-aab8-24f0a2f3b327",
   "metadata": {
    "id": "17dd48d3-875f-4b88-aab8-24f0a2f3b327",
    "outputId": "215cb574-9d73-400c-c046-245ccf57da9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2 G x^{2} + 8 G x + 8 G - 12 x^{2} - 48 x - 48$"
      ],
      "text/plain": [
       "     2                     2            \n",
       "2⋅G⋅x  + 8⋅G⋅x + 8⋅G - 12⋅x  - 48⋅x - 48"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq5=expand(numer(P.q2)*denom(P.q1));eq5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f62a7b72-5f3d-42c1-a3f4-b63f4a15fffb",
   "metadata": {
    "id": "f62a7b72-5f3d-42c1-a3f4-b63f4a15fffb",
    "outputId": "0efc4f04-3a90-4232-f863-b220a8963783"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(x + 2\\right)^{2}$"
      ],
      "text/plain": [
       "       2\n",
       "(x + 2) "
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor(csolve((eq4-eq5)/12,G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0bca8b59-bc03-4e51-b3ba-c07e1dd5cfa1",
   "metadata": {
    "id": "0bca8b59-bc03-4e51-b3ba-c07e1dd5cfa1"
   },
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    return(kpow(x+2,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627afd73-3896-4a13-a45c-0165b2f386fc",
   "metadata": {
    "id": "627afd73-3896-4a13-a45c-0165b2f386fc"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p48c.png?raw=1\" alt=\"ml\" style=\"width : 50%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a91180c-75a5-434b-9b36-3f5a53ad8a75",
   "metadata": {
    "id": "8a91180c-75a5-434b-9b36-3f5a53ad8a75"
   },
   "outputs": [],
   "source": [
    "def M(x):\n",
    "    return( 2*( simple_m(rpow(x)  ,'O') )-1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3b6f729-58df-4039-801b-f5846f873b39",
   "metadata": {
    "id": "e3b6f729-58df-4039-801b-f5846f873b39",
    "outputId": "27730f11-21b6-43c6-fa38-1f5c0565141f"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2 x + 3$"
      ],
      "text/plain": [
       "2⋅x + 3"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M(g(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b82ca90c-9b50-4d89-a94e-d69dcdc2f9d2",
   "metadata": {
    "id": "b82ca90c-9b50-4d89-a94e-d69dcdc2f9d2",
    "outputId": "123e6031-03c8-44f9-9158-817faaf6a9a9"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle M(x)=\\;2 \\sqrt{x} - 1\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sE(['M(x)=',M(x)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0c61f9f-af8a-458f-a4e7-3d7ec0e7c3a4",
   "metadata": {
    "id": "a0c61f9f-af8a-458f-a4e7-3d7ec0e7c3a4"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/linep.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b7ea0f6-3b67-4a95-ba37-225315759618",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from  Libaldomath  import *\n",
    "# this cell will be initializing your variables,get help run helplib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fde1f19-c623-445c-936b-ca2c9badd90c",
   "metadata": {
    "id": "3fde1f19-c623-445c-936b-ca2c9badd90c"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p49.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8111a399-1aba-4e19-98e3-945c6efaaf28",
   "metadata": {
    "id": "8111a399-1aba-4e19-98e3-945c6efaaf28"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/lines.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af80b428-0b29-452f-ac3f-d820eb636bd9",
   "metadata": {
    "id": "af80b428-0b29-452f-ac3f-d820eb636bd9",
    "tags": []
   },
   "outputs": [],
   "source": [
    "x,B,a,b,n=symbols('x B a b n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5c4c418e-470a-4aaf-a84f-5ed53752b26e",
   "metadata": {
    "id": "5c4c418e-470a-4aaf-a84f-5ed53752b26e"
   },
   "outputs": [],
   "source": [
    "def P(x):\n",
    "    return(simplify(factor(a*x+b)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b08ca69a-a200-4851-8b47-263156da6fa9",
   "metadata": {
    "id": "b08ca69a-a200-4851-8b47-263156da6fa9"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p49.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ede84a25-010a-4468-862b-52a3f0a5c9ea",
   "metadata": {
    "id": "ede84a25-010a-4468-862b-52a3f0a5c9ea",
    "outputId": "4208ee43-d116-47d0-f6a3-783b2b54a20c"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{a^{- n} b \\left(a^{n} - 1\\right)}{a - 1}$"
      ],
      "text/plain": [
       "  -n   ⎛ n    ⎞ \n",
       "-a  ⋅b⋅⎝a  - 1⎠ \n",
       "────────────────\n",
       "     a - 1      "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B1= (-b*(kpow(a,n)-1))/(kpow(a,n)*(a-1));B1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bae39746-f8ec-4490-8e42-246b54de925e",
   "metadata": {
    "id": "bae39746-f8ec-4490-8e42-246b54de925e"
   },
   "source": [
    " <img src=\"https://github.com/aldotb/Solve-Academic-Algebra-Math-Problems-whit-Python-and-Sympy/blob/main/images/p49.png?raw=1\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "711e15d5-a322-4f0a-98c8-32ea0b8251de",
   "metadata": {
    "id": "711e15d5-a322-4f0a-98c8-32ea0b8251de",
    "outputId": "7916b510-39e7-402b-d4d4-1bd9d1b0afe9"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{- n} b \\left(a - a^{n}\\right)}{a - 1}$"
      ],
      "text/plain": [
       " -n   ⎛     n⎞\n",
       "a  ⋅b⋅⎝a - a ⎠\n",
       "──────────────\n",
       "    a - 1     "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(B1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f0282b53-6065-488d-93b7-c67d1aebce0a",
   "metadata": {
    "id": "f0282b53-6065-488d-93b7-c67d1aebce0a",
    "outputId": "3012a727-ec1c-4edc-85c5-27ba1c7e5fd3"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{- n} b \\left(a^{2} - a^{n}\\right)}{a - 1}$"
      ],
      "text/plain": [
       " -n   ⎛ 2    n⎞\n",
       "a  ⋅b⋅⎝a  - a ⎠\n",
       "───────────────\n",
       "     a - 1     "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(P(B1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "860bdcc3-838f-4848-b6ef-a19d17c92ec6",
   "metadata": {
    "id": "860bdcc3-838f-4848-b6ef-a19d17c92ec6",
    "outputId": "00d60390-5c72-4c2c-f6ad-202f0e147a98"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{- n} b \\left(a^{3} - a^{n}\\right)}{a - 1}$"
      ],
      "text/plain": [
       " -n   ⎛ 3    n⎞\n",
       "a  ⋅b⋅⎝a  - a ⎠\n",
       "───────────────\n",
       "     a - 1     "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(P(P(B1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e419f1aa-9f88-42c6-bc38-850fe9029a2d",
   "metadata": {
    "id": "e419f1aa-9f88-42c6-bc38-850fe9029a2d"
   },
   "outputs": [],
   "source": [
    "def Pn(x):\n",
    "    return(a**-n*b*(a**x-a**n)/(a-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "32641529-9051-403c-a9c5-f6bd56fc1090",
   "metadata": {
    "id": "32641529-9051-403c-a9c5-f6bd56fc1090",
    "outputId": "ff10d721-1bea-4885-9ee4-9524c3691845"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{- n} b \\left(- a^{n} + a^{x}\\right)}{a - 1}$"
      ],
      "text/plain": [
       " -n   ⎛   n    x⎞\n",
       "a  ⋅b⋅⎝- a  + a ⎠\n",
       "─────────────────\n",
       "      a - 1      "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pn(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6fae425b-9a50-456a-ba0f-61a814003cc0",
   "metadata": {
    "id": "6fae425b-9a50-456a-ba0f-61a814003cc0",
    "outputId": "b89732b1-e9db-41f5-99e8-8e3519b7334e"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P(P(P....P(B)...)) =0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_res(Pn(n),'P(P(P....P(B)...))')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}