02 Exponential Theory.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0ca73c4b-6ba3-477a-80e3-96a416e8964a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sympy import *   \n",
    "from libaldo_polyclass  import *\n",
    "from libaldo_lib import *\n",
    "from libaldo__util import *\n",
    "import lib_algebraEq as ae\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b02d5362-6892-407a-9469-00d52990f5b1",
   "metadata": {},
   "source": [
    " <img src=\"images/linep.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8640f05e-9fe9-4cc7-95c8-881cdeb75cbd",
   "metadata": {},
   "source": [
    " <img src=\"images/p2.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5293e655-2fec-4b2d-8e84-284f1f5cb69c",
   "metadata": {},
   "source": [
    " <img src=\"images/lines.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c379acba-7acc-41f5-9d2b-a0db0f86038f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Create\\;the\\;Eq\\;P\\;whit\\;policlass\\;>\\;x^{\\left(x - 1\\right)^{2}}=2 x + 1\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=symbols('x',positive=True)\n",
    "P=polyclass( x**(pow(x-1,2)),2*x+1)\n",
    "show_exp(['Create the Eq P whit policlass >',P.Q ])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d26158f7-0acb-468f-b203-85a390075c26",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/linesex.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7cc02cbf-44bb-4bba-badf-03e1f1e039e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ope4('op..',Exp(x))\n",
    "  # this function Add,Multi,Divide,Pow ..etc our Mono o Polynomie\n",
    "# P.ope4('S',3*x) , Add 3*x to P\n",
    "# P.ope4('M',3*x) , Mul 3*x to P\n",
    "# P.ope4('D',3*x) , Divide 3*x to P\n",
    "# P.ope4('P',3*x) , Pow 3*x to P"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "593513bb-034c-44b7-b736-2a2c05eb5cc5",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/linesexe.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8d075c15-e965-485e-b630-c1ce13d22ec6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle we\\;Mul\\;the\\;Eq\\;by\\;x^{2 x + 1}\\;using\\;ope4\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{\\left(x - 1\\right)^{2}} x^{2 x + 1}=x^{2 x + 1} \\left(2 x + 1\\right)$"
      ],
      "text/plain": [
       "x**((x - 1)**2)*x**(2*x + 1)=x**(2*x + 1)*(2*x + 1)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_exp(['we Mul the Eq by ',x**(2*x+1),'using ope4'])\n",
    "P.ope4('M',x**(2*x+1),1)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "55d91bea-9475-43c9-b200-d5c7488494a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{x^{2} + 2}=x^{2 x + 1} \\left(2 x + 1\\right)$"
      ],
      "text/plain": [
       "x**(x**2 + 2)=x**(2*x + 1)*(2*x + 1)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.opemat('s',1)  # simplify Eq and update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1051b986-0ed6-4975-ac28-4e7345d742a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} x^{x^{2}}=x^{2 x + 1} \\left(2 x + 1\\right)$"
      ],
      "text/plain": [
       "x**2*x**(x**2)=x**(2*x + 1)*(2*x + 1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sometimes we need to make math ope only in one side, left or right\n",
    "# expand only left side P.opemat('e','1',2), (right would been P.opemat('e','1',1))\n",
    "P.opemat('e','1',1)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b73188dd-7d06-4043-91a5-a65045f5711e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle if\\;x^{2} x^{x^{2}}=x^{2 x + 1} \\left(2 x + 1\\right)\\;then\\;x^{2}\\;=\\;2 x + 1\\;and\\;again\\;create\\;Eq\\;A\\;to\\;solve\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2}=2 x + 1$"
      ],
      "text/plain": [
       "x**2=2*x + 1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_exp(['if',P.Q,'then',x*x,'=',2*x+1,'and again create Eq A to solve'])\n",
    "A=polyclass( x**2,2*x+1);A.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f039a272-40af-40f5-b1ad-07d6a16f442d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{2} - 2 x + 1=2$"
      ],
      "text/plain": [
       "x**2 - 2*x + 1=2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.ope4('S',-2*x+1,1)   # Add -2*x+1 to both sides of  Eq and update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d5715f93-e23d-4dc8-84ac-5e3c69d00671",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(x - 1\\right)^{2}=2$"
      ],
      "text/plain": [
       "(x - 1)**2=2"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.opemat('f',1)  # factor Eq and update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "05fc008e-9c9d-465f-84d5-5aca07504f09",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle In\\;polyclass\\;exp\\;or\\;Eq.solve(x)\\;is\\;find\\;the\\;value\\;of\\;x\\;in\\;Eq\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x\\;=\\;1 + \\sqrt{2}\\;......voala....\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['In polyclass exp or Eq.solve(x) is find the  value of x in Eq '])\n",
    "show_exp(['x =',A.solve(x),'......voala....'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9c10288-6b2e-46a4-a498-d0e1a5562cfa",
   "metadata": {},
   "source": [
    " <img src=\"images/linep.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdb7b39c-1f90-40ef-abca-f7da53a5e935",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/p26.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "28126876-4b02-415b-b445-e9a8ca05ccbf",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle In\\;my\\;native\\;language\\;maybe\\;I\\;would\\;say...\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle ESTE\\;PROBLEMA\\;ES\\;UN\\;REVERENDA\\;MIERDAAAA....\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['In my native language maybe I would say... '])\n",
    "show_exp([' ESTE PROBLEMA ES UN REVERENDA MIERDAAAA.... '])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c49266d-83c0-498e-8b7c-5c05c482ff64",
   "metadata": {},
   "source": [
    " <img src=\"images/lines.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6106ca09-abcb-462b-b0c8-f541fd747755",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/26a.png\" alt=\"ml\" style=\"width :65%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "15cc6c0f-313a-4ec8-8610-01dfeb784cda",
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c,z,y,k=symbols('a b c z y k')\n",
    "# we will make z=a*b*c\n",
    "P0=lambdify(a,(a**3-z)/z) # lambdify are in sympy library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2c189394-fb2f-440e-9602-efda4fada2c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1=\\;\\frac{a^{3}}{z} + \\frac{b^{3}}{z} + \\frac{c^{3}}{z} - 3\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1= opemat(P0(a)+P0(b)+P0(c) ,'e')\n",
    "show_exp(['e1=',e1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4bbcba6a-6ad9-42bd-aaa1-266899b9cf2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e2=\\;\\frac{a + b}{c} + \\frac{a + c}{b} + \\frac{b + c}{a}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e2=((b+c)/a+(c+a)/b+(a+b)/c)\n",
    "show_exp(['e2=',e2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cfc4974-8d8e-466e-8a4f-58461d4ce5fa",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/linesex.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a845475e-41d4-41a0-b9d2-3189a3f85e6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# fpoly() is a resumme....or.. compilation from  most common \n",
    "# and relevant functions that allways you need to solve a monomial \n",
    "# or polynomial equation. and derive from sympy\n",
    "# please i clarify that my library is based on wonderful sympy...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "77cc86fb-4f19-4cb8-a39a-1763b9f68014",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle some\\;example\\;of\\;fpoly()\\;funtion.\\;If\\;we\\;have\\;W=\\;9 k y + 9 x^{2} - 6 x\\;then...;\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "W=9*x*x-6*x+9*k*y\n",
    "show_exp(['some example of fpoly() funtion. If we have W=',W,'then...;'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "daa92684-b101-4ccc-8fd8-b845c0ff9aea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVQoFXWS0Q2CQBBEgViAtGAJRjugBGkBSjD+8UsJWoJSAiWorUgHOG+5vZwkbrLuzNzsLXsxn+c5I7qu26m0RrJsqwrvpY9oOUYRDhDdiNZIuypr4aEQIBAbCSdjy8894AvVjW/hKSQ6N8JjbEAS+Y4yqovmtzM+3ph6aKwk9MpW+Mah3QggJO5VMB2VfM5TaWFbO0mrmhj9UNrWf400yfxR4elK25qRJIer8NFVIQMdLzLglXehGP39hoBT4yGQ0bc+p6dgNbEM03iiKS4jwrPUSo+fP8UX4QdVmcOnmX8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 3$"
      ],
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'n') # numbers of args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8caa8afa-efd5-449b-9491-a17bf3a2b29f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ - 6 x, \\  9 x^{2}, \\  9 k y\\right]$"
      ],
      "text/plain": [
       "⎡         2       ⎤\n",
       "⎣-6⋅x, 9⋅x , 9⋅k⋅y⎦"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'list') # all args in list form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "050feb7e-17e7-46ff-8b8f-b20bbdd1efd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACQAAAAOCAYAAABHN77IAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABpElEQVQ4Ea2U0VECQQyGF4cC1BK0A8QOsAPRCpQSGN54c44SpALFDsQKUDrQDmToAL9vvcPjUDm9y0wmmz+7yT+b7DZWq1WoS4bDYVLIdQc2L2C/us1foyWDFD1i6yPaYz31GHaCUY/1y8pe2Y079ll4mpFJ9+5j33ac2wo3qrYMEudkldAB6+VWhT8CddzQgJrLOsjIvY4ZapFnDiHtJfqOOjcTsDhPrKPg28br1D3FXqHOn+eUWaUbSgt8pgqhjd9HR2gPUEK2My9JGh8BztAx2gHrYyWbVCJEgkxaJL3NnNTeY8fgFgpYb6b4LUj4wThyiCbN9MATTjxopIR0OWebnB23f/eaXsAl0UZt3TN78/vOwMwRMWwXP0hoiT3R+aeY0Bw/iTMSqFP8IDvAtmpD6hhqCcWiG5m/nPytRBRyklGydkk4dqgOQs6Fv3RRvHVb6odpMf8qh9r2OfSBdZ7sAL9feajTAhZdDyxrCVygPmvFG1EXaWzBet1mMGO+ulD5pzaJQlIJxWvH+mJuwOLcYMWNv6Lu9WvwhTnYDr9EY/s+ALoRmfNLWKBDAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle - 6 x$"
      ],
      "text/plain": [
       "-6⋅x"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'get',0) # return first args  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2a89aa76-4db2-4ed1-864e-1a4a915822bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 9 x^{2}$"
      ],
      "text/plain": [
       "   2\n",
       "9⋅x "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'get',1) # return second args  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a6a4951a-bd12-4cc2-ba48-ad209b424644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAASCAYAAADVCrdsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACXElEQVRIDb2V0U1jQQxFA0oBCCoAOgBKgA6ADrJ0sIi//CHoAFIBYjsAKiDQwdIBbDrInuMdP+YN+SFS1pLj8bXH47H9Jmvz+XyQNB6Pb3KN3IRHYLMKG6BvoN/DB/AH+m5tX2a9ZhIl8AsBblhfGwi5h3iC91m/idUEpv8UeVbjy6zXy6YJcpOAkYAY61fEFD5XX0Am+bAA/zaUSRyz88ttwUzkRxuVBA8L9tjaltHXCWiPpY9/ovf7roaPt67pCGUG3puX2uE766GBYPc4iC1tFaC1WYmuCuy3kjuwQ3qeySG9oJUU/41et1vbBOwk2/ELwCAtZQU6WwksHvOAbgKSMU4Lq0sX5WB9LwL5/NE39mYSI21syF679qAsd92q9HlMf6QJeDPnKioEZuLPsGT72pkTC9+hHmywJdssr5AebhsMILdDG/MAbjJ+onmoQ7wPJ/mGmJzkrS9j9fnj/sAiCXE2eOveNw+Wj1d9Czere+AuPu41gR6BRRWR+lul23QA86JicYFsR9pbeaBjFdCNltnhM2F7/VKCslxIJ6CvGaN4mJjVj+QjCZRj+A/sIUGsPcyM68fKsg6wxQ1YTtUhfcV/KhvSVldSczcPKpEEUsd6+LTZijMC16XubdapUB6Sn3TiyrQFRjyrIHevbfx3aMV4pSxkRe7B8sYBo7vR/5ccuAFrbx/vAPIWfRbO5QfdWBPYZHz89I23A1sk2CWB4b8QB3vZQ2T3JWU7VpIAB1k1/22DWFsVq9D7XFeaBIfZ+zs4ybbYsq6dGlbaDg7zoXPoJWfhy5xp+AtyPun8SRzHPwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 9 k y$"
      ],
      "text/plain": [
       "9⋅k⋅y"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'get',2) # return No.... args  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2d4167c3-bea8-43d7-a55b-6ebe5acf3f43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 9 x^{2} + 9 x y - 6 x$"
      ],
      "text/plain": [
       "   2              \n",
       "9⋅x  + 9⋅x⋅y - 6⋅x"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'zubsV',[k],[x]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "92c07e5f-114a-4cac-b4e4-600de50046c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 18 x^{2} - 6 x$"
      ],
      "text/plain": [
       "    2      \n",
       "18⋅x  - 6⋅x"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(W,'zubsV',[k,y],[x,x]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "fb90bf63-a59b-4986-85bf-d2ba70e7576e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle for\\;example\\;if\\;we\\;have\\;A=\\;30 x + \\frac{9 x^{2} - 6 x + 15}{12 x}\\;then...\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=(9*x*x-6*x+15)/(12*x)+30*x\n",
    "show_exp(['for example if we have A=', A, 'then... '])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ca625b87-0726-45f0-a934-07b4a349e594",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOCAYAAAD9lDaoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVQoFW2RMRKCMBBFg3qAjEeA1orRnsIjWNupR6CEVm8gpa2tnRY0tt5AjoDeIL4fBycqf+ZPsn//bnYhcs6ZsixjY0wOhSlsYY5+kzCEMmwRllmWnWBV1/UE7cB5JW4GMsAV/IACdX3Co0SZ5vBBwkoIcOFu0WOZFDQEquyDNRq8j0VR3CEp55/7q6ZriqiF/MZ6rg8auMK8UzJSuxAk9oo5N53+1YnE+tegeNS5MSy4J2EH7prrPTiBBp1xdr9GOUGFbcSacp+hvleIMUFKYaLntImMfh7OEP4HvwBvn1+w+m4NrAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(A,'n') # numbers of args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "429b7dff-08e9-4d31-8156-9dd915449602",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 30 x, \\  \\frac{9 x^{2} - 6 x + 15}{12 x}\\right]$"
      ],
      "text/plain": [
       "⎡         2           ⎤\n",
       "⎢      9⋅x  - 6⋅x + 15⎥\n",
       "⎢30⋅x, ───────────────⎥\n",
       "⎣            12⋅x     ⎦"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(A,'list')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1874ee6b-ff84-461e-b7ef-51ad000bf81b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 30 x^{2} + \\frac{9 x^{4} - 6 x^{2} + 15}{12 x^{2}}$"
      ],
      "text/plain": [
       "           4      2     \n",
       "    2   9⋅x  - 6⋅x  + 15\n",
       "30⋅x  + ────────────────\n",
       "                 2      \n",
       "             12⋅x       "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(A,'zubsV',[x],[x*x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "9d1ee2b7-4ffa-44c9-a88d-8192f48eac40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 30 x^{x^{x}} \\left(x - 2\\right) + \\frac{x^{- x^{x}} \\left(9 x^{2 x^{x}} \\left(x - 2\\right)^{2} - 6 x^{x^{x}} \\left(x - 2\\right) + 15\\right)}{12 \\left(x - 2\\right)}$"
      ],
      "text/plain": [
       "                      x ⎛      x               ⎛ x⎞             ⎞\n",
       "    ⎛ x⎞            -x  ⎜   2⋅x         2      ⎝x ⎠             ⎟\n",
       "    ⎝x ⎠           x   ⋅⎝9⋅x    ⋅(x - 2)  - 6⋅x    ⋅(x - 2) + 15⎠\n",
       "30⋅x    ⋅(x - 2) + ──────────────────────────────────────────────\n",
       "                                     12⋅(x - 2)                  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpoly(A,'zubsV',[x],[(x-2)*kpow(x,kpow(x,x))])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e6cb7f0-8fb8-4185-ac37-70686af0c30e",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/linesexe.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7f462e00-431e-4bce-869f-1e021b528f97",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "a1,b1,c1=symbols('a1 b1 c1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "62dfff0e-fb4f-4ab9-b252-f6118e13b0cd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle we\\;will\\;make\\;a b c\\;=\\;k\\;and\\;and\\;temporaly\\;a1,a2,a3\\;if\\;not\\;esta\\;mierda\\;..\\;auto\\;canceled\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['we will make ',a*b*c,'= k and and temporaly a1,a2,a3 if not esta mierda ..  auto canceled'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5f916b10-3432-4395-98c8-1559d6673b47",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle if\\;a b c\\;=k\\;then\\;a1=\\;\\frac{z}{b_{1} c_{1}}\\;b1=\\;\\frac{z}{a_{1} c_{1}}\\;...\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['if',a*b*c,'=k then a1=',z/(b1*c1),'b1=',z/(c1*a1),'...' ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "af74eba2-2867-4905-b4cb-d721603fb438",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle in\\;e2..change\\;a\\;to\\;\\frac{z}{b_{1} c_{1}}\\;b\\;to\\;\\frac{z}{a_{1} c_{1}}\\;and\\;c\\;to\\;\\frac{z}{a_{1} b_{1}}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e3=\\;\\frac{a_{1} b_{1} \\left(\\frac{z}{b_{1} c_{1}} + \\frac{z}{a_{1} c_{1}}\\right)}{z} + \\frac{a_{1} c_{1} \\left(\\frac{z}{b_{1} c_{1}} + \\frac{z}{a_{1} b_{1}}\\right)}{z} + \\frac{b_{1} c_{1} \\left(\\frac{z}{a_{1} c_{1}} + \\frac{z}{a_{1} b_{1}}\\right)}{z}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e3=fpoly(e2,'zubsV',[a,b,c],[z/(b1*c1),z/(c1*a1),z/(a1*b1)]) \n",
    "show_exp(['in e2..change a to ',z/(b1*c1),'b to',z/(c1*a1),'and c to',z/(a1*b1)])\n",
    "show_exp(['e3=',e3]) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "316a6974-5ea0-4075-bf1b-454bc93c1406",
   "metadata": {
    "tags": []
   },
   "source": [
    " <img src=\"images/linesexe.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "9cef387f-cab9-4060-a5ab-b98c93cd60c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a_{1}}{c_{1}} + \\frac{a_{1}}{b_{1}} + \\frac{b_{1}}{c_{1}} + \\frac{c_{1}}{b_{1}} + \\frac{b_{1}}{a_{1}} + \\frac{c_{1}}{a_{1}}$"
      ],
      "text/plain": [
       "a₁   a₁   b₁   c₁   b₁   c₁\n",
       "── + ── + ── + ── + ── + ──\n",
       "c₁   b₁   c₁   b₁   a₁   a₁"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e4=opemat(e3,'s');e4 # simplifyyyyyyyyy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "79e67652-8ea5-4fb0-89a8-7f85f71d2e0b",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle returning\\;a1\\;b1,c1\\;to\\;a\\;b\\;c\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a}{c} + \\frac{a}{b} + \\frac{b}{c} + \\frac{c}{b} + \\frac{b}{a} + \\frac{c}{a}$"
      ],
      "text/plain": [
       "a   a   b   c   b   c\n",
       "─ + ─ + ─ + ─ + ─ + ─\n",
       "c   b   c   b   a   a"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_exp(['returning a1 b1,c1 to a b c'])\n",
    "e4=fpoly(e4,'zubsV',[a1,b1,c1],[a,b,c]);e4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "d515b8c1-bcc7-44bc-8ab0-05bc9ffc6b78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a}{c} + \\frac{a}{b} + \\frac{b}{c} + \\frac{c}{b} + \\frac{b}{a} + \\frac{c}{a}$"
      ],
      "text/plain": [
       "a   a   b   c   b   c\n",
       "─ + ─ + ─ + ─ + ─ + ─\n",
       "c   b   c   b   a   a"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opemat(e4,'s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "7be374c6-fc20-408d-badc-957ef2a27c83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{3} - z}{z} + \\frac{b^{3} - z}{z} + \\frac{c^{3} - z}{z} + \\frac{d^{3} - z}{z}$"
      ],
      "text/plain": [
       " 3        3        3        3    \n",
       "a  - z   b  - z   c  - z   d  - z\n",
       "────── + ────── + ────── + ──────\n",
       "  z        z        z        z   "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1=P0(a)+P0(b)+P0(c)+P0(d);e1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "ecd36f9c-2e72-44a2-ae08-4574665146ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "P1=lambdify(a,a*a/(z-1)-a*z/(z-a)+a/(z-a)+a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "cdc01e7a-5433-44af-9af5-c269e82e4e8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{2}}{z - 1} - \\frac{a z}{- a + z} + \\frac{a}{- a + z} + \\frac{b^{2}}{z - 1} - \\frac{b z}{- b + z} + \\frac{b}{- b + z} + \\frac{c^{2}}{z - 1} - \\frac{c z}{- c + z} + \\frac{c}{- c + z} + \\frac{d^{2}}{z - 1} - \\frac{d z}{- d + z} + \\frac{d}{- d + z} + z$"
      ],
      "text/plain": [
       "   2                         2                         2                      \n",
       "  a      a⋅z       a        b      b⋅z       b        c      c⋅z       c      \n",
       "───── - ────── + ────── + ───── - ────── + ────── + ───── - ────── + ────── + \n",
       "z - 1   -a + z   -a + z   z - 1   -b + z   -b + z   z - 1   -c + z   -c + z   \n",
       "\n",
       "   2                       \n",
       "  d      d⋅z       d       \n",
       "───── - ────── + ────── + z\n",
       "z - 1   -d + z   -d + z    "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2=P1(a)+P1(b)+P1(c)+P1(d)-a-b-c-d+z;e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5227c3d1-d946-4af2-82fc-64c13d11f42b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{2}}{z - 1} - \\frac{a z}{- a + z} + \\frac{a}{- a + z} + \\frac{b^{2}}{z - 1} - \\frac{b z}{- b + z} + \\frac{b}{- b + z} + \\frac{c^{2}}{z - 1} - \\frac{c z}{- c + z} + \\frac{c}{- c + z} + \\frac{d^{2}}{z - 1} - \\frac{d z}{- d + z} + \\frac{d}{- d + z} + z + 1 - \\frac{a^{3} - z}{z} - \\frac{b^{3} - z}{z} - \\frac{c^{3} - z}{z} - \\frac{d^{3} - z}{z}$"
      ],
      "text/plain": [
       "   2                         2                         2                      \n",
       "  a      a⋅z       a        b      b⋅z       b        c      c⋅z       c      \n",
       "───── - ────── + ────── + ───── - ────── + ────── + ───── - ────── + ────── + \n",
       "z - 1   -a + z   -a + z   z - 1   -b + z   -b + z   z - 1   -c + z   -c + z   \n",
       "\n",
       "   2                               3        3        3        3    \n",
       "  d      d⋅z       d              a  - z   b  - z   c  - z   d  - z\n",
       "───── - ────── + ────── + z + 1 - ────── - ────── - ────── - ──────\n",
       "z - 1   -d + z   -d + z             z        z        z        z   "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e3=e2-e1+1;e3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "003a34b7-b8c0-47f6-900c-979d88304ff5",
   "metadata": {},
   "outputs": [],
   "source": [
    "P2=lambdify(a,a*a/(z-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "f727a817-d770-484f-b126-24f234fd40f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{a z}{- a + z} + \\frac{a}{- a + z} - \\frac{b z}{- b + z} + \\frac{b}{- b + z} - \\frac{c z}{- c + z} + \\frac{c}{- c + z} - \\frac{d z}{- d + z} + \\frac{d}{- d + z} + m + z + 1 - \\frac{a^{3} - z}{z} - \\frac{b^{3} - z}{z} - \\frac{c^{3} - z}{z} - \\frac{d^{3} - z}{z}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "   a⋅z       a       b⋅z       b       c⋅z       c       d⋅z       d          \n",
       "- ────── + ────── - ────── + ────── - ────── + ────── - ────── + ────── + m + \n",
       "  -a + z   -a + z   -b + z   -b + z   -c + z   -c + z   -d + z   -d + z       \n",
       "\n",
       "         3        3        3        3    \n",
       "        a  - z   b  - z   c  - z   d  - z\n",
       "z + 1 - ────── - ────── - ────── - ──────\n",
       "          z        z        z        z   "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m=symbols('m')\n",
    "e4=e3-(P2(a)+P2(b)+P2(c)+P2(d))+m;e4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "0d388a0b-ec81-488c-8372-61377c6441df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HlioH1woFBxCAAAR2CGxl67idRhM5TEA3TK9Z9ibkNgZtOOMOE/As3Y7B0cwKzyaR8XGYjmMofhehhPKrqEUUruO4cjUEIJAvAYzlfPt2cMt00/TMqT/x7a952SDENQgcMjga2YooPNuojEuD6Sh+/iKpX+b1//mOg+sODiIQgAAECgIsw0ARznSD9Brc/8k/0HG5drm8kXpdbpkGrW8Ejhkc8PzGKcoROhoFY1mIZ5aLWWW4lkgIIQABCBwmgLF8mE02Z3RD9Ms8nim2AfxF/p38I6WX28Rd6vir0uq7X/iG6vxv5Wd3kscz2n6Jzu6x4p/k3Y4LhSmspTYfy1QuVfFLfu8VfyefHE/Jdia5UmdqMS2nXyy1ntp5V5Y3SjNrdLRA0v2PmDX/920kWw+KHTB0Hl3tjpOcEIDARgnwBb/MO143Qxt1Njr9Uk9hDCv0Olun3/HNUuGZQt9A/WJfaaT4oyTPlF43oJU0j1O9fnnujbyNJctmme8q/anCRZ1k8Mzxf/KecfdsvA2OMs0y+hF3UjwNTDIlyzTIZ8PO/Wy98w86y/xKwblCr6FPiqnkSZ3nKv/3Q78nzdYy4iAAge0QuLWdpm6vpbqZ24Czodw0em0A76xZVF4bfvaLO8lio6kwQkthlOb104sbykEeGyF2lYySzQaz07zt1ksdJ8PTQkme1JlaTBvKnpkvDGUnyP0kX86CJsM0dZ6S79j/vmfpLwu6+qPjZLhaJsmzBl0t8RFCAAIbIICxnHcn+3G2b5rNpRQ29uoGyWAKurG5fH/pz2FXVyyrOJRZZVaz2aF8t8PLSFJxXq/cNDjK9nsmfLCbgqeFSZ2p5CtmkCVqYRiXAJU++guSKmOLOrrK//016Gqpm4QQgMB2CGAs593XnpX7IGPhsmxmMBzKx91l8uAwlH1vcAFHLlTZltMfTUhlRrmU1i89fiwjIXSa3d/XwbC/U/K0RAkz3dPVYQT3r5qS6Zp4Slb/aFjF/757MWG2+0pGCgQgkDWBm1m3bsONCzdG3xybSytslPhGtLPHamqoJJ9nv/0SYjWjrGO3JwXntbNeU1l3j0MkWa6pMg392qardb7JHa+Q5yr+993RqbJNTgkRCAIQmIUAxvIsmBetpDnTaaOuMKB1Q7Ix6pmmpFy4UfqlrmK3jppwr2vHSx82l4rYEPEs+OXSgrXVnzLTGrN/j8jedmqxtJR51qCs7n/fsq+EbQ0zhxCAQO4EWIaRaQ/bAJG3UVwZw4r/EuLl7Od9pUVZuxwLo+TxrK1nk70m2C982XsdsF+cK2dvdbioM7OKq479EuVbyZvClnZ7YFbC1Oz2lvNIdq+9fbPXqAUTUucp+Vb5v+8uTZ3tgmpH1RCAwIIEMJYXhD9D1f5s9WvdgH5VaIPTRodfTvPOEk5LygiRPHZPJJtlPFNoA9mzyZ7F9axtc0mJkhdxP6vWkqH3V34l2ZL60dGgkjxT8XP/mqmN4y81+Z8rLbXZ+uR5it8a//fd7WtgW1NPDiEAgS0QYJ/lyL2sG7tnRj3T6H2NU7vJR24txUEAAhDYLgHG++32PS3fFgFmliP0twZMv5zkGdCv8t4Vof6IXlEcBCAAAQjkQIDxPodepA0Q6EdgMWNZA86FRPVLXEms8xwjj671DHKxnlbHXt7g2WUcBCAAAQhkRoDxPrMOpTkQ6EDgZoc8U2XxbKx9Ki41eVLhghwQgAAEIAABCEBgswSWNJY3C52GQwACEIAABCAAAQisg0CxDCMsQfAOBF5rW34Ewl9N81vp9+X/Vp6X8l5e8CSkl7sqlNuQKXleF+Txy3R2xSeUleY2XChMYnlHIRl/IAABCEAAAhCAAARWSaBcs/xQxuUzee9p+0r+veNukUIvT/hP4aXCz7V0b+dlQ/WO/FLOL9VZXm+L5m2nLP9dhal9Hlli4SAAAQhAYC4Cug/43uB3Y/o47++eyn7ufeQmLwQgMCGBWxoYPFtsI9POOzl8VFr9y2nfFWeujdD6bK3TF1tzLBk9g/xAoY34wunYBjOGcgmEEAIQgMBGCXAv2GjH02wITEDAM8ueLfavaRu+9v4oQN3ZmLZ7fh1Uf70M4+QSDJV76Nd9YYQfGNBO/rrXdc3PDVvucglJJWTzYCp5mvV0jUseM/9L3mFXVyw56Zp5i/ngGr/XYRqXKTzj8qQ0CEAAAlMR8MzyZSi8eFyleNMAtlFs47XMV8ri/E0DujxXhbqudaZX6f46m7eOq89iV9d1PdD1nmH2179a62mWcyif0qPI06zvVFz1muveZ35PXXfqvMq9OpVn7efVxhuH2gDXQ2QOpx/j6atgepjdoTPHmMLzELXT6ce4nr6aHBCAAAT6EfDMcun84l7b54RtFO98ylcDldM8E1qkK347DPxKms8FOX5QWM0oLyXLfK3uVpM4HDQku5VArjYCcG2jMi4NpuP4Na+G5zURcTj0VLOJrB4/+VSznpljCEBgGwTqxrIN4Pqa5DMNNjaIPXNbrmkuqXgW14OKl3D4vJdq7BjUZcapQtVredtmpv3SHy9oTAWeciEAAQisgIDuEZ2eNq6gKYgIAQgsTKAwloPBa8P4TUOenxzX+ebSDBvIZZqXQFQzu43rJ4mqPhvnrtMGuw15e++I4aUUGMqCgIMABCAAAQhAAAIQGE+gnFm28Vu86Nco0gb0zmxzOP9cobeb86ed/ahrbvdEdXst9ZlCG8ieTfYLfzbc25aS6NS0TvV6Gz3z+jHU9E+QpdijetraKR0CEIAABOYiwHg/F2nqgUAaBG5cXS3zHpgGm0VeqDuEPTV5DslJOgQgAAEIQAACEIDAfARuzlfVXk2XSrFPxaUmTypckAMCEIAABCAAAQhslsBiM8ubJU7DIQABCEAAAhCAAARWQ2DJmeXVQEJQCEAAAhCAAAQgAIFtEsBY3ma/02oIQAACEIAABCAAgQ4EMJY7QCILBCAAAQhAAAIQgMA2CZRbx22z9bR6NAHtIuI9r71tnt1jxb339bmOLxS2bTtYZOTPYQIwPcxm6BmYDiV3+DqYHmbDGQhAIC8CvOCXV3/O3hrdMP9Rpf6YjT8KY8PZH4i5q3S+niUQQxxMh1A7fg1Mj/MZchamQ6hxDQQgsEoC3mcZD4MhOvDbb7+dy9+uX6v4i3qc4366BdN+vLroF0xh2kVPyBNfT2AK01x0gJnlVf7ESU9ozTL564Uv5J/pOKX9s9OD1VEimHYE1SMbTHvA6pgVph1BkQ0CEFgtAdYsr7br0hFcN0uvUfanxll6EalbYBoJZK0YmNZgRDqEaSSQFAMBCCRNgN0wku6e9IXTzfJCUj5S+KyUVseeZcYNJADTgeCOXAbTI3AGnoLpQHBcBgEIrI4AxvLquiwdgcPN8lzhy4ZUrxtxoh0JwLQjqB7ZYNoDVsesMO0IimwQgEAWBFiGkUU3zt8I3Sy984Vnk71VnHfAsPeOGI/kH8vjehKAaU9gHbLDtAOknllg2hMY2SEAgdUTwFhefRcu1oAnumk+dO0KbSB7NvmzvNcuf1KI608Apv2ZnboCpqcI9T8P0/7MuAICEFgxgf8Dk0R1DRsGxFgAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle - \\frac{a z}{- a + z} + \\frac{a}{- a + z} - \\frac{b z}{- b + z} + \\frac{b}{- b + z} - \\frac{c z}{- c + z} + \\frac{c}{- c + z} - \\frac{d z}{- d + z} + \\frac{d}{- d + z} + m + z + 1 - \\frac{a^{3} - z}{z} - \\frac{b^{3} - z}{z} - \\frac{c^{3} - z}{z} - \\frac{d^{3} - z}{z}=1$"
      ],
      "text/plain": [
       "-a*z/(-a + z) + a/(-a + z) - b*z/(-b + z) + b/(-b + z) - c*z/(-c + z) + c/(-c + z) - d*z/(-d + z) + d/(-d + z) + m + z + 1 - (a**3 - z)/z - (b**3 - z)/z - (c**3 - z)/z - (d**3 - z)/z=1"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=polyclass(e4,1);A.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "eaf50fc7-2f4a-4a49-9f08-e76ea5b13c50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HCXh2bs/YaJ4O0yaR8WmYjmMofid1CeELmVUSruO4cjUEIAABCORPYJSh7ObpZunZUn/m2V91siGIayEgNq3GRsupMG2DMjIPPR0F0F+n9Mu7/q3vObju4SABAQhAAAKFEei99EI3Rq+3/T/5h4qHtcrhBuo1uCGvMFSjm3PI2IDpaLz7BaCn+zxGpvxPXjWbDNeRJLkcAhCAAARWReCSoawboV/a8Qyxjd9/5T/KP1Z+2AruTPHvyot3ufCN1Oe/l1/ESSbPZvuFObsnSn+Vd1tOFOawftqMLFNYouIX+j4p/VEepoIx1ImfXyS1rtp5B5ZT5Zl1VnoqeXLX0SPJ2Pz920C23NVOFzqOrgoGDgIQgAAEtkFg78t8ugnamLOx6Zd3KkNYodfUOv+Ob5IKjxT6xumX+IJx4g+OvFB+bDwraz6nuv2i3Km8DSXLZ7nvKv+ZwkWdZPCM8Q95z7Z7Jt7GRsizjH6sDdOevSRmNurcz9Y9/0N3pPCtgmOFXjefFVPJk62O1uz4/RsEDgIQgAAEIFATuBVI6CZuw81GctPgtfG7tz5R59rgs8/CSR4bTJUBGgRSntdML24k1/LYALHbySjZbCw7z1trvVEcpqbRz9lI9ox8ZSTXl/6iMMx+ZsNUMmato5Lv0O/fs/NnoWsUz4arZZI8WbMN3AghAAEIQGB9BHaGskT342vfLJvLJ2zkxYaIksOcbmgu31/wc9jVVcsoDp2scncz2XUdbouXj+TivD65aWwEBp4BH+y2ylTtrmaOBa4yigNA5Y/6OuRWeYofv/+gRIQQgAAEIACBmkBsKHsm7rMMhbNApzYawuPtkD04rMu+N7iAay5U+ZbVH0TIZSY5SOyXHL+ERB06z+6vi2DY3w0zvaSvwwjuXwVPfv/7GkEKAhCAAAS2TOCmGy/jwLOb9s3lFDZGfHxv/1Tn5eYko2e+/dLhbiZZ8TBru7S4Xivr9amxe1InsmWbK9O6X9v0NeabXXyFPPn9Z6dFCAQBCEAAAnMSqAzlqMLm7KaNucp41k3eRqhnbLNztQHiF7iqnTkiAd9F8aWjzeUhNkI8+322tGBt9efMNGL2zwHZ2w4tlpczzwgKv/8IBlEIQAACEIBAtfTChoe8DeKdIaz0b3U6zHg+UF6StcopsUsmz9Z6FtlrgP1yl73X/foluTBrq+iiztx2bBX3S5PvJW8O29ZdArMSpmZ3aRmPZPda29NLjVowI3eeko/f/4L6QdUQgAAEIJAvgXiNsj9F/U43zecKbWja2PBLaN49wnlZGR+SJ7inks9yHim0cexZZM/eera2uZRE2Yu4X1Vr4Oj9k99Ktuz+6YjIZM9U/Ny/ZmrDOGxT6Ca8Ul5us/TZ8xQ3fv/WHhwEIAABCEAgIrC3j3KUTxQCEIAABCAAAQhAAAKbJtBco7xpGDQeAhCAAAQgAAEIQAACgQCGciBBCAEIQAACEIAABCAAgYgAhnIEgygEIAABCEAAAhCAAAQCAQzlQIIQAhCAAAQgAAEIQAACEYF414somygEIAABCCxNQDu4+ENK3tXnWD58TMlfHvVOLw/k/9I5b+S9TebTOj/sVhS29lT2vK6Wx9tg2j1R2tt3ug0nCrPcFrOSlD8QgAAEGgQwlBtASEIAAtsjIOPtrVpto7SPs/E39V7tj1THC3nvD28ZPzltIRX665Q/FHo7xG9RvrfHtJF6R34p5206La+3GvU2jpb/rkIb+TgIQAACqyGAobyarkJQCEBgKgI5GnCSybPENjDt7st/UV789dGfqiMXBmg8S+t8G9GLOMnomeOHCnf7mStuYxkjeZEeoVIIQGAMAQzlmp4Gcd9Y/pTvc4OpHimO6YBSr4Vn+p6FaXqmU5c4ss88S+xZa49J9v64TuxsSNu9ugh2f7304tplFyNl21XWjKhcz2hXrq7DcodlI/URAghAAALrIFB9cESD2fk6xB0updp4Y/jVw68smS1Mh+vFVVcuwbRkHQ2cl+Aa6h4bSnZ/cfRDsw1Ke2nDfYV7n3JX+ofy/YXKePZ5rBi9r1f9nln2FzQxknvT4wIIQCAXAtWMsgayRYzIXCBMKQds09OFaVqm8KzW++a6Rtmd7Zf0vrb0utdUf4zz1ZfO8+xzla/0bfmz+Jw54rUcPyvcGclLyTJHe6kDAhAolwBLL8rtW1oGAQh0JCAjLuf1szZ+4zXIRzY6lecZ27CGObTU7fByDS/b8HEvz9gzpsOJU4Wq1/IeK2zOaPsFv6lffpyqWZQLAQhslACG8kY7nmZDAAL5E6iNXRvFpw1pf3Fax5trkW0ch7zZlz1IHhvmnkW2sW4j3t47X3j5CEayIOAgAIF1EcBQXld/IS0EILAtAjZ8q5f6Gs228bw3y1wf94t93lLuuUIvJ5nbPVXdfpnwSKGNY88i++U+G+1ty0d0CAcBCEAgXwLVy3z5iodkEIAABCAAAQhAAAIQWIbAzWWqpVYIQAACEIAABCAAAQjkTQBDOe/+QToIQAACEIAABCAAgYUIYCgvBJ5qIQABCEAAAhCAAATyJoChnHf/IB0EIAABCEAAAhCAwEIEMJQXAk+1EIAABCAAAQhAAAJ5E5h1ezhtD+Q9Nj/USJ54uyD5Y6VPFLZtdZQ3vUykg2vajoBnWp6hNLgGEoQQgAAEILAWArNuD6cb5d8C443zvQG9jWZvRn9X+Tl/FUsi5u3gmrZ/4JmWZygNroEEIQQgAAEIrIbA+fn50Rz+5cuXx/K347qUfh2niffvC7j2Z3ZIz+CZlmdgDddpuAa+hPBFB9ABdGAaHZh1Rjn896CZJX9V6rX8C8XPQj7hOAJwHceveTU8m0TSpOGahiOlQAACEIDA9ARmXaPs5ugm6TXJ/pwpyy0S9i9cE8JET9PCjEpDTyMYRCEAAQhAIHsCs+56oZvkiYg8VvgikFHcs8u4EQTgOgJey6XwbIGSIAuuCSBSBAQgAAEIzEpgNkO5vkkeK3zTaOG7RppkDwJw7QGrw6nw7ABpwClwHQCNSyAAAQhAYHECsyy90E3SO1x4FtnbwXmnC3vvfPFY/ok8bgABuA6AduASeB6AM+IQXEfA41IIQAACEFiUwCyGslr4VDfLR26pQhvHnkX+Ju+1yl8V4oYRgOswblddBc+ryIzLh+s4flwNAQhAAAILEfh/WmsI97Yv9jMAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle - \\frac{a z}{- a + z} + \\frac{a}{- a + z} - \\frac{b z}{- b + z} + \\frac{b}{- b + z} - \\frac{c z}{- c + z} + \\frac{c}{- c + z} - \\frac{d z}{- d + z} + \\frac{d}{- d + z} - \\frac{a^{3} - z}{z} - \\frac{b^{3} - z}{z} - \\frac{c^{3} - z}{z} - \\frac{d^{3} - z}{z}=- m - z$"
      ],
      "text/plain": [
       "-a*z/(-a + z) + a/(-a + z) - b*z/(-b + z) + b/(-b + z) - c*z/(-c + z) + c/(-c + z) - d*z/(-d + z) + d/(-d + z) - (a**3 - z)/z - (b**3 - z)/z - (c**3 - z)/z - (d**3 - z)/z=-m - z"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.ope4('S',-1-z-m,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "6126ae26-5b06-47f1-9571-0c9a3b4fde64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pICA2lYpGRVKYVkHpGYec9gLor1Z6o65/6zsGrjs4CEAAAhCAwMoItFpuoYei19f+V/ax/GFtcnh4es1tiFsZpt7NqVM0YNob724GyOkuj54h/4OXzSLDtSdJbocABCAAgUUR2FGS9RD0Bh3PDFvx/Vf2o+xTxYfj3q7k/664+DQLP0Sd/r3sJEZ18iy2N8fZnCv8VdZtOZM7h/XSZuQ6hWUp3rz3SeGPsjAVjK5G/Lxp1LJq45NWLhVn1rOSU9Vn7jJ6ojqWf/9Wjl3v7EQLXUdWBQMDAQhAAALbIFB8cU8PQCtyVjS9USdTguV6Da3j7/kBKfdErh+a3rAXFBN/TOSl4mPFWVHjGZXtTXGXslaSXD/X+77in8ud1KgOnin+IetZds/AW9EIca6jX2XDtGUviZkVOvezZc//zJ3IfSvnVK7Xyc+KqeozWxnN2fH7NwgMBCAAAQhAICdwx64e4FbarCCXlV0rvjvrEZXWyp7tLIzqY2UpUz5DhRTnNdKTK8h5fax82BR1VN2sKDvOx2e9kR+mptHOWEH2THymIOe3/io3zHrOhqnqOGsZVf3qfv+elb8KXSP/bLi6TqrPrNkGbrgQgAAEILA8ApmSrGr7lbUflOUlE1bwYiVEwW5GDzPn7y/z2W1qsqUTdYmVbzGDnZfhtnjJyFyM1yOXFY3AwDPfnc1Wmard2YyxwGUKcQCo+F5ffdwqT/Hj9x+ECBcCEIAABCCQEwhKsmfgPktJuApkcoUhvNIO0Z3dPO8HnTM4cqPyd139sYO5zCCHGntD45cQyF3H2fx143T7u2Gme/LajeDuXfDk978rEYQgAAEIQGDLBG5LMfCspm15CYUVkRNd3zkf1XFzM6qjZ7y9wbCYQZY/zNZOXV2vjfV61Nic54HZsp0r07xfq+Q15js7/wJ58vufnRRRIQhAAAIQGJPA7aiw8qymFblMcdYD3gqoZ2pnZ3Llw5u1shM4ogq+i/xTe8tLQqyAeNb7auqKVZU/Z6YRs39q6l51abK4OfOMoPD7j2DghQAEIAABCNyx0iFrZbhQghX+PQ+Hmc5HikuyNjklctXJs7SePfaaX2/ksvU6X2+IC7O18k5qzK1gK783SL5XfedwNN0emIUwNbu9pTuqu9fWXu41asKIufNU/fj9TygfFA0BCEAAAvMlENYk+/PS7/TAfCHXSqYVDW848ykRjpuV4qH6BPNM9XM9T+RaMfbssWdtPUtbXj6i6EnMbyo1cPT5yG9Vt9n9wxGRmT1T8XP/mqmV4nAUoZvwSnFzm52fPU9x4/dv6cFAAAIQgAAEIgLFOclRHF4IQAACEIAABCAAAQhsmkC8JnnTIGg8BCAAAQhAAAIQgAAEAgGU5ECiwtWr+zNZr8/GJCAAzwQQS1nAtARk40HkYeMCQPMhAIGkBFCS63H6qDFbTBoC8EzDMc4FpjEN/MgDMgABCEAgEQGU5EQgyQYCEIAABCAAAQhAYD0EwukW62kRLYEABCAwAwJe+qBq+PSdU9nwoSN/EdQnsjyS/Utp3sj6KMtneXw4VSgcv6nocU1eHx9VaXOusI/YdBu8/GyWR1dmNeUPBCAAgcQEUJITAyU7CEBgWQSk+L1Vja3QtjFWHI+dxf5EaV7K+vx2l/HJYRci18sifsi9kvstivcRllZQ78lOZXyUpuvr40B91KLrf1+uFXwMBCAAgc0QQEneTFfTUAhAoIrAEMqf8vTssJVLm4eyXxQXfxX0p+zKjfIZz8463gr0JEZ19IzxY7lW3jMjvxVlFOQABBcCENgMAZRkdbUeAIdmkrIH2YEHRJOZpM0IUtxQeMY00vhhmobjiLl4dthjhBVeW3/4JjZWom1e3TjFXy+3OLrUYih5UL6eyc5MXnfXOywVya/gQAACENgGgVsXFxfXa2+qBvtbXdqo+/wVv1O58QxQ46x032rZdmHal6fBw3RX/PoyXTPPQEpt7PT7D/f3cfP++VCug8L+x/yh3J3Pqyv8Q/H+cmTXMafXmBXaqvI9o+wvW6IgByi4EIDA5gjc0SA42QNk7bRhm76HYZqWKTxr3yTVwW76Jskb8r5WZOQ10Dufp1dfOM6zzlm8wndli2UPFXkMEpXX4xe5hYI8VV0GaSCZQgACEGhIgOUWDUGRDAIQWCcBKYBDrre14huvOT6xwqk4z9SGNcsBrOth5dtLNXzdSzJ2FOmQcChX5bq+VW/PvJnv2EbFoapFvhCAAAQmIYCSPAl2CoUABNZOIFd0rRBfltr6q8O6Xl57bMU4xI2+1EH1sVLu2WMr6lbgbX3ChZdwoCALAgYCENgWAZTkbfU3rYUABMYjYKU328BXKtKK887scn7dm/h8bNwLuV6zPLZ5prK9cfBErhVjzx57I58V9qolI7qEgQAEILBeAijJ6+1bWgYBCExIQIqlZ4Xvl6ug+MpNeYr30opRl1fEdVP58RrkSesS1ws/BCAAgakI3J6q4IWU600ztpg0BOCZhmOcC0xjGviRB2QAAhCAQCICt66vV3tKWSJEZAMBCEAAAhCAAAQgsDUCzCRvrcdpLwQgAAEIQAACEIDAUQIoyUcRkQACEIAABCAAAQhAYGsEUJK31uO0FwIQgAAEIAABCEDgKIHRTrfQzmmfwfkhr9G5wj6L81ThM7lVxyEdrTwJsqOa4JpQEJDThDCjrOAawcALAQhAAAKLIDDaxj09JP8WER+q78Pprdj5oPr7ih/ya1cqYt0Grmn7F55peYbc4BpI4EIAAhCAwGII+HSLoe3FxcWp7N24HIVfx2H87fsBru2Z1ckZPNPyDKzhOgzXwBcXvsgAMoAMDCMDo80kh/8aNKN0V/7Xsi/l95memAQE4JoAYpQFPCMYCb1wTQiTrCAAAQhAYFACo61Jdiv0gPQaZH/ilCUWCbsVrglhIqdpYUa5IacRDLwQgAAEIDB7AqOdbqEH5JloPJUbf/rUs8qYHgTg2gNexa3wrICSIAquCSCSBQQgAAEIjEpgFCU5f0Ceyn1Tat27UphgCwJwbQGrQVJ4NoDUIQlcO0DjFghAAAIQmJzA4Mst9ID0SRaePfaRbz7RwtYnXDyVPZfFdCAA1w7Qam6BZw2cHpfg2gMet0IAAhCAwKQEBleS1bpnelA+cSvlWjH27PE3Wa9N/ioX040AXLtxO3QXPA+R6RcP1378uBsCEIAABCYi8D8iqTQRv8vNkAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\frac{a z}{- a + z} - \\frac{a}{- a + z} + \\frac{b z}{- b + z} - \\frac{b}{- b + z} + \\frac{c z}{- c + z} - \\frac{c}{- c + z} + \\frac{d z}{- d + z} - \\frac{d}{- d + z} + \\frac{a^{3} - z}{z} + \\frac{b^{3} - z}{z} + \\frac{c^{3} - z}{z} + \\frac{d^{3} - z}{z}=m + z$"
      ],
      "text/plain": [
       "a*z/(-a + z) - a/(-a + z) + b*z/(-b + z) - b/(-b + z) + c*z/(-c + z) - c/(-c + z) + d*z/(-d + z) - d/(-d + z) + (a**3 - z)/z + (b**3 - z)/z + (c**3 - z)/z + (d**3 - z)/z=m + z"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.ope4('M',-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "4e7e022c-9ffa-40fd-9e2d-565b78bc3eed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbsAAAA0CAYAAAAT+JanAAAACXBIWXMAAA7EAAAOxAGVKw4bAAANT0lEQVR4Ae2d7bXUthaGDywKANJB0sEJVADpILlUENIBLP7xj5V0QKgAQgeQCkLo4CYVhJwOyPv4WMbj8YxlWxrL41dreWRrZHnrkUbbW19z4/Pnzxdrcs+fP/9a8n6v40rHbR33dbxQ+Ef5diMJmOdIYBHRzTQC0oQo5joBmm9pCNxqztZz8rNE/UsV/xdElv9E3u867nBtN5qAeY5GNniDmQ4imhTBXCdh800QOKmyk2L6Tc98Kf/9DPwvOvd+peu/OmG+jCdgnvGsYmOaaSypcfFWy1VtHr1QtH8/6JxeKbsTEziZsqsV3buZiu5C93e7K+nS5I3PbgIB85wAbeAWMx0ANPHrNXOV7Fc6nirrv8t/wPVEDL5tIoGTKDsVLG80dD3+OlHOvduUFt2Xj3RgKSZLd+9BKw4Ql/A2eU/Z+KTrbw5lxzwPkZkebqaz2F3q7lc6GKN/I5Y/hdTWylVyf9SBdfqnjoO/xZBP+2kJ3Mg9QUWF+1giP5WfvHCVZmjMsRirMby0eM4jNbHhx/VBftNg9OXMPPuozAsz09n8mEFH19/bdkpr5irZXyovd+X/0M6Tz/MSuJkzeRUmb2UUbJZCVfp0BdA18LPOeRO06ycAm3f9X30JNc8vLFKdmel0kmL3sL57b4x/zVwlOy+dl/IxBOxORCB3NyYN7C8q1O4426TsKR0sub910Ocd0kTh4eiqC2FVgD+q2arHGgzzTFxJXEeTAv1OqTH8wXjXudVVXtJfKV900YY2LCk8J7ZLIJtlpwLkrQVTnUJN4upK8UmJtWdf0phTWd4kecj5JdI0GN2smWeXyPxrM53PsJUCv+3Kqjs3rsoP3bK0Y55c1yrwnKc5LTsKcdTEEVUAuj1Rjiivf3RQIb5XeHs8ji7RZwrjexyLyr/V9SJvR3ouXYRMwMExtsAgNPl4KH9U/qsU0n/QYCATE3pwjJ0yxhnGQIriiYCSrXSmiImc1PFQD1kC81ph9C6YqSCMceLW/e2j5KgHTOgI7ty40tbxW2QYpv0CH/JrPyGBLBNUVHA0rDQEd3QepYQUj0YZpYHiqgpePt2ghEeno7gndZKRyR+vddDYhbGxbxR+dDLIKYSUDLf1nH910ABX051bYchY5A9MchXLlHKTfDTM1E0mXlUvDfIZm/5aPpZ0cU5yFctUsq3yt08hz+Va3z84eay4CrVCgW5lkpmG/q0KMlbR0Sij6Gg82g0w51WfvfzinGSl0auUSBBOYbylLa7oanloRHCNjJKN8Q/CWJ/YtpgJW9xJttKZwghFR/0O1jFh/9PRtkIIK8KVzFSyHfvt0yMR1YYsAToRV+rMb0qLtq/YvC7BN/Uzkys7FRjWDQ0WXQ6xDiuQSt8dd6OxbjcosentxZNcpM+2YvixruqWPBRZaTaKuU6ffCQbozz03BHhWBk7DUYtJ0lgiU52OXgijNItmqnkqyw4ibqj2BQ+e7s6pZG8jq6A6Sp/+wm5hpmmzHEo7uWTfJ6LS67sBOaZDqyHMTMjeSt+r3uuAtj6hx+6i0LwZL9O+9vJCRy5UWkj50/yS7HogrTMUP0QLmqfMNwf1960z5w8kahgpnt1dRrB/bs2ynSPpzig9Ffx26cU59RVylwHCo+2w8oOoJnczQzpYo2Ft5XB5FXQVGyOrnLkR3BRVwROi3SSj/wyiaax6HROfkpwWNmM1bRdsLijy6h98ynOS2Val2tfXT0FllnPKJHpEZ6r+O1TIIm4MoTDeC8K3i4TgaTKToVF40pjwJjGWNe1NGiUKwWodFEmxVUEyYSio5J238hejc18xvjdbkEaEqzQq4zPnJx0yUxbzP7fl8Fa9r6vFg0rmWkNZnW/feROyDUM39Ce2GUicCtxuo/q9KKtBlWY0OXZKDOF0X/NdUjnvsKSjN2lyq/kQbFjzTEmhnLnYByMiR/BetLpog5mDVed8wbJItYSlkTsgVkJU9jtdYdLdsaeXu9lauGAkplKtlX+9inSlFxrDrx8MsZe5G+TPK/dpVZ2KAAqcGNNRAJ6oHjsJvBEPgqDRoOCZ2YjYcU1IpLpkWSrppnLR8FhzZFvrKZul6yCF3E/6qmBIevr2DS7qJeGDpXimYof5QtTlNs/LflfKKxEa7l0pmv87VPsqbkytk77aZeJQNJ1dvqxs6aLNSOVEsgks5M1ARMwgbMiUL88PZF/46wyVlBmbqaSRYXEWB3HWKsulQhOxwRMwATWSqAaB1Y76nG7TCWYTNlJvjA21Dt4n0n+s02WSq/Du6InLGEzTQhTSZlnUp50Y+I225WZuz7lUHa27K4r7dzPYCnPTcf3fyFgpl9YpDgzzxQUr9MI7SZj61t1WetTSmV3ty6hUGhbLTDn2wRMwARGEZBVc1XfENrRUfc78jCBndmYAo4JzfR03Ngd/NHKuFBo11f+NAETMAETiCUQ2tHY+Fni0aWohJloyPBU2DCDXV6YgXxfxx+Kw3+VojNYckY48ZmpHJaM6fK0rpanV4ftKDuJxfR59v5j+j9Cs3aM3fFjtsHiHtyna8+fJmACJmACIwhgKIyy7NQ2016PndTC2uChtcDfKc5THegAnsFfEVVKTz4K+V/5yMtG/SGcXj0Uzex9YpXGVHdQhzXKTgKjwZvd8XmSwlB4MYqO6EW8kSCInQmYgAmskACGwqh2dET7HI1DaWKtoeRw1f66CmvvEhUUMoZQexE84aPkr56Q6EOyHNVhbWXXjLXpJgRm0WwwX2PEqQDo3quYyCGO4n8O5+fqK48H187ou0NvZoFn38vG4JvZOXM9xpM6ZKbjf0nHmJrneJ7hjmNcQ5yOHxRJJ/ikl1hrtDHogaAL2gJc1hcv2oE6pxtzsAszY306qsP2FpVLELQju0SMUXQXio/5yh6WBxt2fW8XSUAc2ZWlb9/NyBQcrUvATLtE5l2b5zx+3bvFk2Vbd+Uv2Q3YiFWXL/+1t9Om65oX9Hvyd7bN0zWbirCTUNsKbNIbOtF9Sdo8pdOrwxrLDkEUib7fS/mNotP5bR0x1lo1Vjci/lDe/b0JmIAJbI3AqDkPam8P9Qwd4zbYM1Tf/Ej+x56E0BM72w5KDsKwAqvwpfRALUevDmuUXR2pz5JgwG9oMFNRmlmYmOExypF77EzABEzABK4J0HY2XXExUNRu9w1zxNwaEwcF1h6Tu9DzUGhYTmFML6SDHChRukD5nq7OHYUYIuby9VzkPajDKmWnSAiGNYewZIKD2ZWYlTGKTtGaTXGBYWcCJmACJjCewChlNz75uDtqhUVb3t2E/9B/DaLgwnjd6GGwOKkOx4rRYcGyS7GDt625w2Xhb0zABExgiADKZVQ35lCCM75HeVUTVTppIOOOtVd/z2QVlivwLzV0rZ7aDeqwYNm1x+gwPaeYn6GQMMXtTMAETMAEIglISaBEcEUYDZIHK21v6zKF904+UfhUvVFleu6Hnj+ow27OfUjr/mB+80ZgN58Alb6Iij8/K8WkYKZpi8I80/EM7Wb7PxLTpb6OlLLWp72lB3OYSLuyZu5X+TkHTeeI6HtNwARMoDgCajOZH8HyLbZpnNKzVlyeShMopWVH3rDu7pWWSctjAiZgAoUTCJZd31T/wkVfh3iplR0FFQptHQQspQmYgAksT4DNlS9k1YXhoOUlOjMJwmzMVNliyQK7qMQuRE/13MF0JBPLK3p3w9Z3fbOLBtPcegQzTV8DzHSzTB8q52HqfnoITvEitbL7UDOl4Errd34lmZgSO+UfHeps2esQMNMOkASXZpoAYieJopnqBYfesNs63nXk9mVCAkmVnQqNRenMqGGbmWKUXV2Z5vyjQ0Lk55GUmaYvRzPdLFOMA1wxbea1OOf1mVTZ1WjeyK9W2ZeCSo1I0w+uc96gxv6jQylZKUYOM01fFGa6Wab8WwALuJt2Kj0Jp5hD2TEu9lgF91BHUX3QkofuAray8dKIRHXfTBOBbCVjpi0YiU4LZ8qyg2ZRdKIsO5kOgZud69mXqlQoON5QYvfUnP3MmAQkF10FTJ5pKpXOsfLsJhIw04ngjtxmpkfgTPyqZKaS7XGdLU+Sm1i+sbclV3b1g+kmxLorQpnUlf3QbtixrByvRcBMWzASnZppIpCtZFbAlJfvt5KTuQ52GQnk6Ma8UMGxiwoK75mOxpLKmI+DSUuOFP/ocDD9LX5hpulL3Uy3x1RlTm8TQyuM2dllJpBF2dUyo+ReqkD559ol31oGd8POzPgckzfT9KVqpttjGqw6T0xJX/Z7KSbdG7ObupTcnwp7L39R664rl69NwARMYEkCahOx6lhXd2dhY2BJDCd9dq4xu5CJH3XC2B2mup0JmIAJmMA1gbDp85K9Xpsqi6zKTkqOvTL5U7+wTdem4DqzJmACJtAloHaR9pAeLy8i78LJeJ1V2SG3CpQ/+2PBJBNW7EzABExgswTUDrKmjpnhRS3N2kKBZFd2QKwL9lJ+WFOyBbbOowmYgAk0BNT+MTOcGeoPmkCfnIzASZQduVFBM72WPyZkYNbOBEzABDZDQO0ea47ZkHpnj97NACggo/8BxYk0bzGCnaYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle z \\left(\\frac{a^{3} - z}{z} + \\frac{b^{3} - z}{z} + \\frac{c^{3} - z}{z} + \\frac{d^{3} - z}{z}\\right)=m + z$"
      ],
      "text/plain": [
       "z*((a**3 - z)/z + (b**3 - z)/z + (c**3 - z)/z + (d**3 - z)/z)=m + z"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.re_eQ(z*e1,m+z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "27169928-3173-4f40-be3a-b773c1e396d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle z=m + z$"
      ],
      "text/plain": [
       "z=m + z"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.re_eQ(z,m+z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "20bcb84c-c962-4166-9c05-98c8a2e810e0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle tanta\\;huevada\\;paque\\;salga\\;cero\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle from\\;upper\\;cell\\;we\\;solve\\;the\\;Eq\\;and\\;then\\;....\\;m=\\;0\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['tanta huevada paque salga cero'])\n",
    "show_exp(['from upper cell we solve the Eq and then .... m=',A.solve(m)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e475ac8-7ecf-4e7d-8b4c-8694ebebc628",
   "metadata": {},
   "source": [
    " <img src=\"images/linep.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1a3ecf7-a41d-4362-b382-ed759714b545",
   "metadata": {},
   "source": [
    " <img src=\"images/p5.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0858b42-6d87-41b9-aa36-81d0545d7db3",
   "metadata": {},
   "source": [
    " <img src=\"images/lines.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "540d480c-5d67-4c09-8f56-c65c9dfc552d",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sympy import *   \n",
    "from libaldo_polyclass  import *\n",
    "from libaldo_lib import *\n",
    "from libaldo__util import *\n",
    "import lib_algebraEq as ae\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "191e7199-8c4c-4828-89aa-ae971ec42500",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle we\\;now\\;create\\;Eq1>\\;x=t^{\\frac{1}{t - 1}}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Eq1=polyclass(x,sqrs(t,1/(t-1)))\n",
    "show_exp(['we now create Eq1> ',Eq1.Q])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "1d2e42c5-df1e-4dee-b0c3-4fd350fe4ce2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle also\\;create\\;Eq2>\\;y=t^{\\frac{t}{t - 1}}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Eq2=polyclass(y,pow(t,t/(t-1))) \n",
    "show_exp(['also create Eq2> ',Eq2.Q])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "02d512cd-e5b9-4a23-b6ff-6e4ca942894f",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle RESUME\\;RESUMEN..\\;RESPUTOSUMEN\\;RES....\\;etc\\;etc\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Remember\\;that\\;if\\;you\\;create\\;Eq\\;with\\;name\\;P\\;like\\;this\\;:\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle P=polyclass(2*x+1,3*y*y+2*y-10\\;..\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle to\\;see\\;all\\;Eq\\;use\\;P.Q\\;command>\\;2 x + 1=3 y^{2} + 2 y - 10\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle to\\;see\\;left\\;side\\;use\\;P.q1\\;command>\\;2 x + 1\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle to\\;see\\;left\\;side\\;use\\;P.q2\\;command>\\;3 y^{2} + 2 y - 10\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Add\\;2*x\\;to\\;Eq\\;4 x + 1=2 x + 3 y^{2} + 2 y - 10\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle to\\;see\\;all\\;Eq\\;again\\;but\\;no\\;update\\;the\\;Add\\;include\\;1>\\;2 x + 1=3 y^{2} + 2 y - 10\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Add\\;2 x\\;to\\;Eq\\;and\\;update\\;2 y \\left(2 x + 1\\right)=2 y \\left(3 y^{2} + 2 y - 10\\right)\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle solve\\;x\\;\\frac{3 y^{2}}{2} + y - \\frac{11}{2}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle solve\\;y\\;\\left[ - \\frac{\\sqrt{6 x + 34}}{3} - \\frac{1}{3}, \\  \\frac{\\sqrt{6 x + 34}}{3} - \\frac{1}{3}\\right]\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['RESUME  RESUMEN..  RESPUTOSUMEN  RES....  etc etc'])\n",
    "show_exp(['Remember that if you create Eq with name P like this :'])\n",
    "show_exp(['P=polyclass(2*x+1,3*y*y+2*y-10 ..',])\n",
    "P=polyclass(2*x+1,3*y*y+2*y-10 )\n",
    "show_exp(['to see all Eq use P.Q command>',P.Q])\n",
    "show_exp(['to see left side use P.q1 command>',P.q1])\n",
    "show_exp(['to see left side use P.q2 command>',P.q2])\n",
    "show_exp(['Add 2*x to Eq',P.ope4('S',2*x)])\n",
    "show_exp(['to see all Eq again but no update the Add include 1>',P.Q])\n",
    "show_exp(['Add', 2*x, 'to Eq and update',P.ope4('M',2*y)])\n",
    "show_exp(['solve x ',P.solve(x)])\n",
    "show_exp(['solve y ',P.solve(y)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "55552e85-6bfb-45a0-b2fd-57dd04889e50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{1}{t - 1}$"
      ],
      "text/plain": [
       "  1  \n",
       "─────\n",
       "t - 1"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get_expo_fr_mono(monom_exp,var that get exponent)\n",
    "get_exp_in_mono(Eq1.q2,t) # get exponent of t in left side of Eq1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "e21cc6d8-b201-48ac-9394-524287c0a449",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e3=\\;\\frac{1}{t - 1}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{t - 1}=\\left(t^{\\frac{1}{t - 1}}\\right)^{t - 1}$"
      ],
      "text/plain": [
       "x**(t - 1)=(t**(1/(t - 1)))**(t - 1)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e3=get_exp_in_mono(Eq1.q2,t);show_exp(['e3=',e3])\n",
    "Eq1.ope4('P',t-1,1)   # Pow Eq  t-1 and update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "def612b5-ed8c-47ea-b4dc-2311e2a985da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle all\\;letters\\;includinn\\;in\\;op1\\;will\\;be\\;ejecuted\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle monomath(f(x),SeOf...)\\;or\\;Eq.polymath(SeOf..)\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle O\\;=\\;\\left(x^{a}\\right)^{b}\\;to\\;x^{a b}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle S\\;=\\;x^{a}\\;to\\;x^{b + c}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle F\\;=\\;x^{a}\\;to\\;x^{b c}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e\\;expand,\\;f\\;factor,\\;s\\;implify,\\;1\\;only\\;left\\;Eq,\\;2\\;only\\;right\\;Eq\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Eq1.polymath()  # show help polymath , see that op 'O' is nedeed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "507c34fb-4306-4dc0-afd3-e586273f7ed6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{t - 1}=t$"
      ],
      "text/plain": [
       "x**(t - 1)=t"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq1.polymath('O',1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "902d2d9b-345c-462a-93cb-89f8d9c25891",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x x^{t - 1}=t x$"
      ],
      "text/plain": [
       "x*x**(t - 1)=t*x"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq1.ope4('M',x,1)  # Multiply Eq1 by x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "14ffb34d-84a5-424d-a6e5-366dddddb824",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle x^{t}=t x$"
      ],
      "text/plain": [
       "x**t=t*x"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq1.opemat('e',1)  # expand Eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "97b8fbc2-4dfd-44e9-979e-6a04e077148e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle take\\;note\\;to\\;more\\;advance..\\;x^{t}=t x\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['take note to more advance..',Eq1.Q])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "6e31fc6a-d284-4f2b-a90a-e4d9cc4553b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEoAAAAaCAYAAAAQXsqGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACwUlEQVRYCeWY0VEbMRCGbcYFMCnBdBBSgukgpITQQZg82W8Z6ACoIBM6gA5I6MDpIBk6cL5PSDc6G+csmzOY08zeSvJqtftrtZLcn81mvS6VyWQyxN8z+HGJ33slwm9EdoQfd6W+dAooougLAJ1CB9Q/FoHl1usSjcfj6Tr+di2i9omih6JIisKdAgqfzU8/9Z2t91m+aukaUPcCE0G6XRUk5fpdux6UgJPLdi2ict+L6oMi6RcUZruYiH9BR9R/56bQbv3WvDNAAYyJeDgPkoDR15e3WXYJqCOACMl4GSAANuS34udJri/quKDvmHp1ldilHGVENZ1UyhQ/TxJQAPOeumBLtRJOPQTc/94rDqAp7fMkFX+7ghc9ItP4TThz6vgJpH0JKFf5LreRdo+2zxNlBfOG9jV8rcLYKQMP4VVEDaKmr3SeQr5/rqAKKOqfoMZ3EWMNV50pKfeMW7oA/KbTt9GuEdzt92Tht3PoRHpSYMPOAYoNsxSuGlI7UWjb1xTyvbYMZG7LKvnJqKsiIIziE/3zIbys/ECm0T8j6i+CKUyNnm9zGo2S+b45kdab2pBsXDaZMtXzBJ8uFYS78BtH2R6KwirAnchVCRPAncTkZl8j4sq3UbDB+Y36mwb9az9Pkl79hcx17yBPzyrlDJIQ3FxhzgjAxX7Be6Dvv8eyssg8e46KNnyI+qvFYq59KLfT+TeOHHTop5Tn6GBGDpSrtlZ+UhOTbBzewaLFTy0/MY+rrDM1oBaHPW/PXqauBhIGGU1SU8hnKlqpVguITWEbwmu2tjLrnNI8ojwZvC+dwf9A3qksVcg/Nrf+1a4L7Ar/H8EXtsU2LFr6N0sEbAQ/3IYhr32OsPUAwxXzZR4KdUPcFXzpa8GjQa/gm3KUueh7Zo+380sAa7q7ZEPedjW99TxJTJoWc9NKt9Ug3ZHPP95Jwtxq3JMvAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle y=t^{\\frac{t}{t - 1}}$"
      ],
      "text/plain": [
       "y=t**(t/(t - 1))"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq2.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "bdf553bd-93fb-4282-9302-1b46feedb61d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJwAAAArCAYAAACNd+GAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAG50lEQVR4Ae2b7XEUORCGscsBcFwGJgOfMzBkAJeBIQMo//M/15EBEIGBDIAI+MjAZIDLGfjeRzs9aNe7GmlWM5pZS1VaaUbqVneru9WSZvdub28f1FQl4Evg/Pz8h56fq/zlv0+tC/6hYP5Vfqn6P8Af8FNTlYBJoFGSowzKdiScTxq8KJ5LVeFMErU0CaAkP+2hbymFBcdPlc98HFXhfGnc47oU41Dsv1RGQW70/J/Ky0ZxVM2TqsLlkePssUixiNdeq8TDXaj8NARTVeF6SFWT8VZgP1S+6wE+OIjoImb6qnyi+k3igMReXxJhortXhYsW1aJjo2yPpqpsUImSKZ+q+lVltNKpL94N2CUl1TNKyBLbldiNBne2VeG6ROi1S5gv9His0m3xvabJVUUjATue+KPy00gCW+8mWLwkhvULXAk4gkPtB1trYysBCd2s/KR9OVBFYx0qoyhbJeFwS77KV5GIHqvft6bvmeCC3ioS51K36uGWxBF8eK/Wd5qEpeUmCNG/kaXNJr4/lgUkO88r0f0pQoFQcg588eSXC/B+v8Jhu154wYDwtld79aahW6ASFkcFTMZfqg+qcMKPN0JJCNw/63nr3aJwMNlMeuzSqu7DpN4KJ+IHu/4YhtX+WMXrlaDxEK/7Y4mHZDxllrcsSbjwNvDwWPXsy2QKkb1iOBFNQJnr+gP3DT7y5JJ4JXZjwi7GIK6RbVYv2igZHhPPWTT1UjhRzLqc5fpDwngjXEWtrmMGztT+RXRmVYLAmMj2O+0aE2PMlQgJcuLrRVeSwkkAxAGcx7gzGerKeIBdTha/jcWjM2TJFeXIeQALrofCu3S3ORZTNs6BVWJKEYsnGvz6I4aWMfp4xpRz4oOkNzLOvvSBt8HNxmHrjUiQiUBjksJ5eNoDQu/dLlaPYaqZqE7+1I84lM3U01UYPQ/+4aHG2OsgEsNxPHX0G6w5WeHEFDHGoNcfg3GbjhhvkBKrIhvCjjsxaYQypFOXDsFOtWgcl6xwIrj1bhIiFp39+iNdjoNBoEApy2mngkpm7HiJfZ/3pbrBwdkah7QpmxlnCILhhCHFkPqSegcuadPQQA9+/XGHynIvMKg73ipAToyC0qf3LQLKIniUlpyajJc+sKljre3vPJyYQLC4WpSJQ0eOKlxq2t6rNIsc/PrDH9/oKFiyDG1MohUFIshHhkwk3gMZfVvlQ8/tLYLqz5STg3fB2C5WQyQnU7hHyZCZAJzCCRcXtew+2TJzZ9gqnOr8CaLdSqsPS0zKMqPu65NwIYBep/eCZUlhslMSX1CY4QTh1M+8wHWoo/o5eahERk9Ubrw+UtsbZT7hyb4LDdFobRqX2JtHjKNIOhABCNZcPMIyKzCCeJdFwQxhjnKESUudlJj4DZw3q/w3cxAyvI/qk3MO/l6lYaxnPNy1mDHXjje7WBkcL7L6bqXLTj7asnNHQTZwi5xMjhu6OI/8nUbJ/IWyfT6EkY/p9VKNaRM/ye/3xbQTqEoEBiHtZ9N6R4DKu5zWJXSzSLaUdk6O5EQfVorPHZxZ/NX7FoE5USYWxCDY7bbhTsfYk2jGw1kitiHGubEXKlFC1n0nKO998apoGjSGS2TwmP6iqTVM1blG8mVJ+9aeTDiYC7IfZzN8ZxKsGU9wI9SJaIsOvsJhobOI3+BXwht6CTJlsaU1JOal+E204XVQCsMRgh2zzXgpRte+x+2SskloeDdy1zLhodip6nXDjXmFEHOtsUpu9F972xBCMFKb8WK8jTTsn2F8D8cuifM2vgT5rWwfALbLxB+w3a9JDnZ9Z3IIMY3s3grGXRupTF7uQsgzthX3cK3CIWAx1p5R6RnFI6Zb8nwZmZ8DKnjHewVTIyOW1akn48XtlEsQ65ZUCQzr5CsHl1TH9WKt9/E4ZCGExS8T4zYE/ssZ1/l7I58p4VyKJKdwGplY7dKjwP6h1HWu5IHsZBUjZLdpsc/cmWSe2cwUS7akEoMQ6HK+Q8yCx7uXsdvKTHxAFspM1KyNrzEallT3tbbKIskpnIiZtTCHkpzkwsYBwyM+m7uMMBpSUUdiS+qClPq7TgJ8+cGV39yTOyuUARXdBFaF61YjllXiOPMQ3RDT7LHunnx0SqvCdYicZVVdOFcrGvt0kBlsFg/E5g9UFg8LqsIFp2rRqImyTdVRRPcpdjkTUadTIKwqXPwsuJuY+O7T6Nl4N87eins3JFIVLlIvNGH27ZpbniLBinYTzYciAO/W3iAVJUiDV4VLm4ETdecTcSZy0kk0cljNhxenqhfdmfqCqgrnS6OjroljA8HxAp98T/32geMcPtCcxFJqoq0KZ5KILBtvwRI1WS/XGAPK1n69Hcne4N3+B377TyvSlRQgAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle y^{t - 1}=\\left(t^{\\frac{t}{t - 1}}\\right)^{t - 1}$"
      ],
      "text/plain": [
       "y**(t - 1)=(t**(t/(t - 1)))**(t - 1)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq2.ope4('P',(t-1),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "34561d07-4f48-4137-a39b-ef62a73ead2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y^{t - 1}=t^{t}$"
      ],
      "text/plain": [
       "y**(t - 1)=t**t"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq2.polymath('O',1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "cc05cb06-0784-4e19-a4d5-35be7e6d1126",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(y^{t - 1}\\right)^{\\frac{1}{t}}=\\left(t^{t}\\right)^{\\frac{1}{t}}$"
      ],
      "text/plain": [
       "(y**(t - 1))**(1/t)=(t**t)**(1/t)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq2.ope4('P',1/t,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "90c5d4b9-5629-4c44-89f4-d8a01687875b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y^{\\frac{t - 1}{t}}=t$"
      ],
      "text/plain": [
       "y**((t - 1)/t)=t"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq2.polymath('O',1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "cde2d09e-91ca-448b-a0c7-a82e788efe57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle remmeber\\;that\\;t=\\;x^{t - 1}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['remmeber that t=',kpow(x,t-1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d4fce531-bec5-4ee8-85ed-cee411ce256c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y^{\\frac{t - 1}{t}}=x^{t - 1}$"
      ],
      "text/plain": [
       "y**((t - 1)/t)=x**(t - 1)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq3=polyclass(Eq2.q1,kpow(x,t-1));Eq3.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "c89866f9-99f6-406b-a41e-48d7a9b4ba88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left(y^{\\frac{t - 1}{t}}\\right)^{\\frac{t}{t - 1}}=\\left(x^{t - 1}\\right)^{\\frac{t}{t - 1}}$"
      ],
      "text/plain": [
       "(y**((t - 1)/t))**(t/(t - 1))=(x**(t - 1))**(t/(t - 1))"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq3.ope4('P',t/(t-1),1) # New Eq3 po to (t/(t-1)) to eliminate expone"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "9a76f4b5-66b9-45d0-9a46-08bbafd065a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y=x^{t}$"
      ],
      "text/plain": [
       "y=x**t"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq3.polymath('O',1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "cc4360aa-db53-4d51-9cd5-172c91808bab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle upper\\;cell\\;we\\;find\\;that\\;x^{t}\\;=\\;t x\\;subs\\;this\\;data\\;in\\;Eq3\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp(['upper cell we find that  ',kpow(x,t),'=',x*t,' subs this data in Eq3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "bb1140e7-4f28-416b-8b15-4ec2da6ca1cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle y=t x$"
      ],
      "text/plain": [
       "y=t*x"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq3.subs(kpow(x,t),x*t,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "f19675d7-b634-4243-8834-a9eb58a3eae3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t=\\;\\frac{y}{x}\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# applied simple solve\n",
    "show_exp([' t=',Eq3.solve(t) ])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a8b32ee-e98f-4741-ad4b-b93d3edb139b",
   "metadata": {},
   "source": [
    " <img src=\"images/linep.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f7cb7b7-09be-49fc-b62e-c6da299c5769",
   "metadata": {},
   "source": [
    " <img src=\"images/p6.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7bbd39b-b5bd-488e-b6f2-3673bb59478d",
   "metadata": {},
   "source": [
    " <img src=\"images/lines.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "7d81a29d-30a3-4fe3-8345-a78ee5d19c25",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#  w will be 4*x+2 but define later\n",
    "w,x=symbols('w x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "87aa80c4-d157-4f0f-8632-fa6499c14eed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{w}{3}=x^{\\frac{w}{2} - \\frac{3}{2}}$"
      ],
      "text/plain": [
       "w/3=x**(w/2 - 3/2)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P=polyclass(w/3,kpow(rpow(x,2),w-3));P.Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "3efc8028-4ff4-479d-8332-c22526494e71",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.Q=expand(P.ope4('P',2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "c01ff4b1-4dee-484d-9aea-51a865a98f0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle w^{2} x^{3}=9 x^{w}$"
      ],
      "text/plain": [
       "w**2*x**3=9*x**w"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.ope4('M',9*x**3,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "9357bbf4-2a95-4e99-b91d-699a23ef6662",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 9 x^{3}=9 x^{3}$"
      ],
      "text/plain": [
       "9*x**3=9*x**3"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.evalue_if(w,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "4b00cb73-14fd-400f-aed2-36dcd7a2e253",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAArCAYAAACuAHIQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFUlEQVQ4Ee2VwQ3CMAxFW8QAiBEYARiBEUBsQDeAY3tmA2AERoANkBiBEaAblPdREzkKba8IsPTlxP6xm8Rx06qqEitFUYyZH8GEcWl9fU0wDlAHcAdTMAKROLIiLORl4Rql6JH0IkuL4U+2h/Mhp5G6QuKaVTyqEdWG9A1cwQXfFp14siZd8iEb/PrPSPM8D3tBy8387g1Sw2Ows4fTVht6DMNOMhHVHCOJIis9LHVVIZCIjHfJgn3AqicBuU4fbMou8mSIIxwlWq/6rXgy3qwpvVv5IkNaYWhM78l1+kFbekdWPc+YZM5g9Jyxju8MbgTbJGpf70CQBzhan92gCfoaqt8JXqKXQjptVM3R/Qv1GSfs2ycS3W/ByGkKBAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\frac{1}{4}$"
      ],
      "text/plain": [
       "1/4"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csolve(4*x+2-3,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "96e7907a-70f6-4eca-b271-b413d5ed6902",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle if\\;K=\\;\\left(\\frac{1}{x}\\right)^{\\frac{1}{x}}\\;then\\;...\\;K=\\;256.0\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=kpow(1/x,1/x)\n",
    "show_exp(['if  K=',k,'then ... K=',k.subs(x,1/4)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dd60af1-b012-4ee9-a5db-fa895985930f",
   "metadata": {},
   "source": [
    " <img src=\"images/linep.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e95077f-550a-4750-9739-97d86b30ecc4",
   "metadata": {},
   "source": [
    " <img src=\"images/p14.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a31f799b-81ce-4924-9909-3cae67b9e850",
   "metadata": {},
   "source": [
    " <img src=\"images/lines.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "a8d789c9-1c66-4a46-8dd2-ac129d6c97a5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#  w will be 4*x+2 but define later\n",
    "w,x,m=symbols('w x m')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a3935ec-a299-4115-913e-2320301e6c5a",
   "metadata": {},
   "source": [
    " <img src=\"images/p14e1.png\" alt=\"ml\" style=\"width : 80%;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "0b76c1bd-9ccc-4880-9241-c74a3e8653e0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "e1,e2,e3,e4,e5=kpow(x,-1/w+w),kpow(x,-w),kpow(x,1/w),kpow(x,-1/w),kpow(x,w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "f58e8c7b-993c-41b0-a780-7699815a4f84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{w - \\frac{1}{w}} \\left(x^{\\frac{1}{w}} + x^{- w}\\right)}{x^{w} + x^{- \\frac{1}{w}}}$"
      ],
      "text/plain": [
       "     1              \n",
       " w - ─              \n",
       "     w ⎛w ___    -w⎞\n",
       "x     ⋅⎝╲╱ x  + x  ⎠\n",
       "────────────────────\n",
       "           -1       \n",
       "           ───      \n",
       "      w     w       \n",
       "     x  + x         "
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1*((e2+e3)/(e4+e5)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "2f0ae578-8a4a-4298-831f-7267a73fd559",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABgAAAAOCAYAAAA1+Nx+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAiElEQVQ4EWP8//8/A7VAQ0ODEdCs1UBsDGR/AJnLAiIoAUCDBID6ZwPxOyA2AWIlIIYDalgAcmkoyESgZWVACuQLOGCCs2jEGLWAYMDSPIhYoMlsL9ApoORGLAgF6jtHjGKQBaBkZkyMYnLU0DyIhr4FjNQo7IDxCCrgQIkEVBaB6HtADEoEpwEsISASVdEGngAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e7=-1*simplify(e1*((e2+e3)/(e4+e5)));e7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f71af8f7-4e30-48dd-8331-dd1848d16575",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "6e60aac2-5900-4de3-83c7-415fcfd2528c",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle YOU..\\;WANT...\\;MORE....\\;see\\;some\\;super\\;easy\\;problems\\;and\\;try\\;solve\\;whatever\\;method\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Haber\\;trata\\;de\\;resolver\\;con\\;cualquier\\;chucha\\;metodo\\;que\\;quieras\\;haber\\;si\\;puedes..\\;$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_exp([' YOU.. WANT...  MORE.... see some super easy problems and try solve whatever method'])\n",
    "show_exp([' Haber trata de resolver  con cualquier chucha metodo que quieras haber si puedes..'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37a55d94-4586-4bd4-ac6d-4c364b470606",
   "metadata": {},
   "source": [
    " <img src=\"images/pp1.png\" alt=\"ml\" style=\"width : 100%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1994f6ef-95b1-4c1e-9095-3a8202809f85",
   "metadata": {
    "tags": []
   },
   "source": [
    "#####  Coming soon\n",
    "     * polynomies\n",
    "     * Functions\n",
    "     * Factorize\n",
    "     * Y muchas wevadas masssss\n",
    "     "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9605634c-4e49-46c7-b405-a7c7c323a0c4",
   "metadata": {},
   "source": [
    "#####  some help or propose how to improve the library weite to aldotb@gmail.com\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "474b2b03-25de-4941-8628-c2c9e59b49d2",
   "metadata": {},
   "source": [
    "# eternal life to the nerds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76f077e0-6de5-4938-8bcf-b66189c9eaa1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}