hubble-radius.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to determine the horizon of the visible universe in a Jupyter Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 48 correlations converging the theoretical value of the horizon of the critical universe see [Observable_universe](https://en.wikipedia.org/wiki/Observable_universe) and [Schwarzschild_radius](https://en.wikipedia.org/wiki/Schwarzschild_radius)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# with $10^{-9}$  precision"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List of physical (NIST CODATA2018) and mathematical constants used:\n",
    "\n",
    "* $\\pi=3.141592653589793$\n",
    "* Euler natural logarithm $e=2.718281828459045$\n",
    "* Euler Mascheroni $\\gamma=0.5772156649015329$\n",
    "* Apery Constant $\\xi(3)=1.202056903159594$ [Apery Constant](https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant)\n",
    "* Atiyah's $\\Gamma=25.178097241906$ [Michael_Atiyah](https://en.wikipedia.org/wiki/Michael_Atiyah)\n",
    "* Lucas Mersenne number [Edouard Lucas](https://en.wikipedia.org/wiki/%C3%89douard_Lucas)\n",
    "* OM Monster [Monster_group](https://en.wikipedia.org/wiki/Monster_group) also known as Fischer–Griess monster\n",
    "* OB Baby Monster [Baby_monster_group](https://en.wikipedia.org/wiki/Baby_monster_group) baby monster group B\n",
    "* OP Pariah Group [Pariah_group](https://en.wikipedia.org/wiki/Pariah_group) six sporadic simple groups\n",
    "* Eddington Electric Constant $a=137.0359990836958$ also known as the inversed fine structure constant CODATA2018\n",
    "* $c=299792458.0$ m/s CODATA2018\n",
    "* $h=6.62607015.10^{-34}$ $J.Hz^{-1}$ Planck constant CODATA2018\n",
    "* $\\hbar=1.0545718176461565.10^{-34}$ $J.s$ Planck constant over 2 pi CODATA2018\n",
    "* $l_P=1.616255.10^{-35}$ m Planck length CODATA2018\n",
    "* $m_P=2.176434.10^{-8}$ kg Planck mass CODATA2018\n",
    "* ƛ$_e$ $=3.861 592 6796.10^{-13}$m Reduced (Electron) Compton Wavelength CODATA2018\n",
    "* ƛ$_p$ $=2.103 089 103 36.10^{-16}$m Reduced (Proton) Compton Wavelength CODATA2018\n",
    "* $\\lambda_{wi}=2.897771955.10^{-3}$ m K (exact) Wien wavelength displacement law constant CODATA2018\n",
    "* $k_B=1.380 649.10^{-23}$ J K^-1  (exact) Boltzmann constant CODATA2018\n",
    "* $t_K=9600.60(1)$s non-Doppler Kotov Periodicity (1000 ppb)\n",
    "* Fermi coupling constant : $1.1663787.10^{-5}$    (GeV)-2          (51 ppb)\n",
    "* Fermi's ratio   F = Fermi's mass / m_e = 573007.3625        (25 ppb)\n",
    "* Fermi-Atiyah's ratio : $F_A = (2\\Gamma . 137)^{3/2}$ ≈ 573007.3652        (0.22 ppb)\n",
    "* Mass of the electron $m_e=9.1093837015.10^{-31}$ kg CODATA2018\n",
    "* Mass of the proton $m_p=1.672 621 923 69.10^{-27}$ kg CODATA2018\n",
    "* Magnetic Moment of the electron/Bohr magneton: $d_e$ ≈ 1.00115965218128 (2 × 10-4  ppb)\n",
    "* Magnetic moment anomaly $1159.65218091.10^{−6}$ ± 0.00000026 [Particle Data Group Leptons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-leptons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "\n",
    "* $G=6.67545372.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$ Newtonian constant of gravitation estimate by Francis M. Sanchez (Jan 2020)\n",
    "* Galaxies Doppler radius $R=c.f /\\Delta.f$=Universe Schwarzschild radius: $2G.M/c^2$\n",
    "* Hubble-Lemaître radius: $c/H_0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from decimal import Decimal\n",
    "from scipy import constants\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sympy as sy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sets and fixes the table of constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299792458.0\n",
      "6.62607015e-34\n",
      "1.0545718176461565e-34\n",
      "137.0359990836958\n",
      "1.00115965218128\n",
      "1.202056903159594\n",
      "1.6449340668482264\n",
      "2.718281828459045\n",
      "0.5772156649015329\n",
      "25.178097241906\n",
      "573007.364905975\n",
      "3.8615926796089057e-13\n",
      "6.739167620022749e-19\n",
      "2.1030891033555923e-16\n",
      "1837.152646 1836.15267343 1838.68366173\n",
      "9.1093837015e-31 1.67262192369e-27 1.67492749804e-27\n",
      "1.6735328361530618e-27\n",
      "1.000027430752471\n",
      "328337440236.48914\n",
      "8.434502897752472\n",
      "113.91063459990004\n",
      "1.380649e-23 2.72582 9600.591457\n",
      "0.0008400718024707187\n",
      "0.005278326806259892\n",
      "6.67545372e-11\n",
      "1.6163947113699356e-35\n",
      "2.176434e-08\n",
      "0.0010630824999999999\n",
      "2878184911147.8315\n",
      "1.1761048867371158e-24\n",
      "2.389015908333496e+22\n",
      "6.739167620022749e-19\n",
      "0.002897771955\n",
      "4.965114232061555\n",
      "2.4263102386830926e-12\n",
      "0.0013440173951173593\n",
      "157705.2404352378\n",
      "178450\n",
      "206.7682869\n",
      "3477.441701\n",
      "50796495.669951715\n",
      "5.294654020152911e-11\n",
      "2.817940326213412e-15\n",
      "1.7128941663434102e+26\n",
      "9.075773400070832e+86\n",
      "8.792233511611562e+52\n",
      "3.8499570411855345e+87\n",
      "1.4923654623153317e+26\n",
      "3814279.1047601975\n",
      "170141183460469231731687303715884105727\n",
      "15747724136275002577605653961181555468044717914527116709366231425076185631031296\n",
      "808017424794512875886459904961710757005754368000000000\n",
      "4154781481226426191177580544000000\n",
      "2663849798329448283764291471531459318169741293570162121768960000000000000\n",
      "8.724905575508272139543742768E+292\n",
      "2.937238508642020695790261107E+365\n"
     ]
    }
   ],
   "source": [
    "c=constants.c\n",
    "print(c)\n",
    "h=constants.h\n",
    "print(h)\n",
    "hbar=constants.hbar\n",
    "print(hbar)\n",
    "a=137.0359990836958\n",
    "print(a)\n",
    "d_e=1.00115965218128\n",
    "print(d_e)\n",
    "zeta3=1.202056903159594\n",
    "print(zeta3)\n",
    "zeta2=np.pi**2/6\n",
    "print(zeta2)\n",
    "#print(c,h,hbar,a,d_e,xi3,xi2)\n",
    "e=np.e\n",
    "print(e)\n",
    "gamma=np.euler_gamma\n",
    "print(gamma)\n",
    "Gamma=(constants.fine_structure**-1*gamma)/np.pi\n",
    "print(Gamma)\n",
    "# F**(2/3)=2*137*Gamma\n",
    "# Fermi's mass given by \n",
    "F=(2*137*Gamma)**1.5\n",
    "print(F)\n",
    "lambdabare=constants.hbar/(constants.m_e*constants.c)\n",
    "print(lambdabare)\n",
    "lambdabar_F=lambdabare/F\n",
    "print(lambdabar_F)\n",
    "lambdabar_p=(constants.hbar/(constants.m_p*constants.c))\n",
    "print(lambdabar_p)\n",
    "H=1837.152646   # (0.06 ppb)\n",
    "p=1836.15267343 # 1836.1526734400013 #(0.06 ppb)\n",
    "n=1838.68366173 # 1838.6836617324586 #(0.5 ppb)\n",
    "print(H,p,n)\n",
    "m_e=constants.m_e\n",
    "m_p=constants.m_p\n",
    "m_n=constants.m_n\n",
    "print(m_e,m_p,m_n)\n",
    "m_H=1837.152645*constants.m_e\n",
    "print(m_H)\n",
    "beta=(H-p)**(-1)\n",
    "print(beta)\n",
    "a_w=F**2\n",
    "print(a_w)\n",
    "a_s=a_w/(2*np.pi*(p*H)**(3/2))\n",
    "print(a_s)\n",
    "j=(8*np.pi**2)/np.log(2)\n",
    "print(j)\n",
    "k_B=constants.Boltzmann\n",
    "T_cmb=2.72582\n",
    "t_k=9600.591457\n",
    "T_cnb=1.9454\n",
    "print(k_B,T_cmb,t_k,T_cnb)\n",
    "lambdabar_cmb=(constants.hbar*constants.c)/(k_B*T_cmb)\n",
    "print(lambdabar_cmb)\n",
    "lambda_cmb=lambdabar_cmb*2*np.pi\n",
    "print(lambda_cmb)\n",
    "lambdabar_cnb=hbar* c / k_B * T_cnb\n",
    "print(lambdabar_cnb)\n",
    "# Planck's length CODATA2018 (hbar.G/c^3)^1/2 = 1.61639471.10^-35\n",
    "# l_P=1.616255*10**(-35) CODATA2018\n",
    "G_s=6.67545372*10**-11\n",
    "print(G_s)\n",
    "l_P=((constants.hbar*G_s)/constants.c**3)**0.5\n",
    "print(l_P)\n",
    "# Planck's mass\n",
    "m_P=2.176434*10**(-8)\n",
    "print(m_P)\n",
    "l_wi=1.0630825*10**-3\n",
    "print(l_wi)\n",
    "l_K=9600.591457*c\n",
    "print(l_K)\n",
    "ƛ_w=(constants.hbar/(constants.m_e*constants.c))/F**2\n",
    "print(ƛ_w)\n",
    "lambdabar_w=(constants.hbar/(constants.m_e*constants.c))/F**2\n",
    "P=lambdabare/l_P\n",
    "print(P)\n",
    "lambdabar_F=lambdabare/F\n",
    "print(lambdabar_F)\n",
    "#2.897 771 955... e-3 m.K - NIST CODATA 2018\n",
    "b=2.897771955*10**(-3)\n",
    "#lambdawien=(h*c)/(k_B*)\n",
    "# b=lambda/lambdawien\n",
    "print(b)\n",
    "𝜔=(h*c)/(k_B*b)\n",
    "print(𝜔)\n",
    "lambda_e=lambdabare*2*np.pi\n",
    "print(lambda_e)\n",
    "l_ph=(lambdabare*(np.pi*(a**2))**2)\n",
    "print(l_ph)\n",
    "aprime=137.1106292\n",
    "W=137**2*Gamma/3*d_e\n",
    "print(W)\n",
    "Z=178450\n",
    "print(Z)\n",
    "μ=206.7682869\n",
    "print(μ)\n",
    "τ=3477.441701\n",
    "print(τ)\n",
    "s_4=2*np.pi**2*a**3\n",
    "print(s_4)\n",
    "# Hydrogen Atom Radius\n",
    "r_H=(lambdabare*aprime)\n",
    "print(r_H)\n",
    "r_e=(lambdabare/a)\n",
    "print(r_e)\n",
    "R_N=2*constants.hbar**2/(G_s*((a)*constants.m_e)**3)\n",
    "print(R_N)\n",
    "R_GC=R_N**2/(2*l_P)\n",
    "print(R_GC)\n",
    "M_U=(m_P**4)/(constants.m_e*constants.m_p*constants.m_n)\n",
    "print(M_U)\n",
    "n_ph=(4*np.pi/3)*(lambdabare*2**128/(1+(137**2 + np.pi**2 + e**2)/(H*p) )/l_ph )**3\n",
    "print(n_ph)\n",
    "R1=(np.exp(((a*((1+1/p))*(((np.pi**2)/6)-1))+1)-gamma))*lambdabare\n",
    "print(R1)\n",
    "E_3=e**e**e\n",
    "print(E_3)\n",
    "#E_4=e**e**e**e\n",
    "Lucas=(2**127)-1\n",
    "print(Lucas)\n",
    "N_Edd=136*2**256\n",
    "print(N_Edd)\n",
    "OM=2**46 * 3**20 * 5**9 * 7**6 * 11**2 * 13**3 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 #  Monster Sporadic Group Order 808017424794512875886459904961710757005754368000000000\n",
    "print(OM)\n",
    "OB=2**41 * 3**13 * 5**6 * 7**2 * 11 * 13 * 17 * 19 * 23 * 31 * 47 # Baby Monster Sporadic Group Order 4154781481226426191177580544000000\n",
    "print(OB)\n",
    "OP=2**8 * 3**7 * 5**6 * 7 * 11 * 31 * 37 * 67 * 2**9 * 3**4 * 5 * 7**3 * 11 * 19 * 31 * 2**14 * 3**3 * 5**3 * 7 * 13 * 29 * 2**21 * 3**3 * 5 * 7 * 11**3 * 23 * 29 * 31 * 37 * 43 * 2**7 * 3**5 * 5 * 17 * 19 * 2**3 * 3 * 5 * 7 * 11 * 19 #  Pariah Sporadic Group Order\n",
    "print(OP)\n",
    "xHappy = Decimal(674.5210288)\n",
    "Happy=np.exp(xHappy) # Happy Family Sporadic Group Order 8.7249055755086e292\n",
    "print(Happy)\n",
    "xTSSPG=Decimal(841.5210288)  #  exp(841.2869278)\n",
    "TSSPG=np.exp(xTSSPG)  # 26 Sporadic Group Order: 2.3241836455143e+365\n",
    "print(TSSPG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# URL= 'https://github.com/laguer/hubble-table/hubble-table.csv'\n",
    "URL= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/hubble-table.csv'\n",
    "from urllib.request import urlretrieve\n",
    "urlretrieve (URL, 'hubble-table.csv')\n",
    "df = pd.read_csv(\"hubble-table.csv\", dtype = {\"Gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [50,51], sep = \",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "URL1= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/hubble-table1.csv'\n",
    "from urllib.request import urlretrieve\n",
    "urlretrieve (URL1, 'hubble-table1.csv')\n",
    "df1 = pd.read_csv(\"hubble-table1.csv\", dtype = {\"Gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [50,51], sep = \",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "URL2= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/hubble-table2.csv'\n",
    "from urllib.request import urlretrieve\n",
    "urlretrieve (URL2, 'hubble-table2.csv')\n",
    "df2 = pd.read_csv(\"hubble-table2.csv\", dtype = {\"gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [28,29,33], sep = \",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# URL= 'https://github.com/laguer/hubble-table/hubble-table.csv'\n",
    "URL3= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/hubble-table3.csv'\n",
    "from urllib.request import urlretrieve\n",
    "urlretrieve (URL3, 'hubble-table3.csv')\n",
    "df3 = pd.read_csv(\"hubble-table3.csv\", dtype = {\"Gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [50,51], sep = \",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('constant-table.csv', <http.client.HTTPMessage at 0x7f622a908050>)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# URL= 'https://github.com/laguer/hubble-table/hubble-table.csv'\n",
    "URL4= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/constant-table.csv'\n",
    "from urllib.request import urlretrieve\n",
    "urlretrieve (URL4, 'constant-table.csv')\n",
    "#df4 = pd.read_csv(\"constant-table.csv\", dtype = {\"Gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [50,51], sep = \",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.938504169672099"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambda_e*(OM)**(7/10)/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th>PlainFormula</th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>$$2\\hbar^2/(G.m_e.m_p.m_n)$$</td>\n",
       "      <td>2*hbar**2/(G_s*m_e*m_p*m_n)</td>\n",
       "      <td>1.380048e+10</td>\n",
       "      <td>1.305626e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$$2\\hbar^2/(G.m_e.m_p^2)$$</td>\n",
       "      <td>2*hbar**2/(G_s*m_e*m_p**2)</td>\n",
       "      <td>1.380048e+10</td>\n",
       "      <td>1.305626e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2/6})$$</td>\n",
       "      <td>lambdabare*(np.exp(2**(6+(1/2)))/6)</td>\n",
       "      <td>1.382101e+10</td>\n",
       "      <td>1.307569e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$$ƛ_e(τ/μ)^{32}/ω$$</td>\n",
       "      <td>lambdabare*(τ/μ)**32/ω</td>\n",
       "      <td>1.379565e+10</td>\n",
       "      <td>1.305170e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$$(2ƛ_e/3)(ƛ_{CMB} /ƛ_{H2})^3$$</td>\n",
       "      <td>(2*lambdabare/3)*(lambdabar_cmb/lambdabar_H2)**3</td>\n",
       "      <td>1.390000e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$$ƛ_e s_4^5$$</td>\n",
       "      <td>lambdabare*s_4**5</td>\n",
       "      <td>1.380418e+10</td>\n",
       "      <td>1.305976e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>$$ƛ_p(WZ)^4$$</td>\n",
       "      <td>lambdabar_p*(W*Z)**4</td>\n",
       "      <td>1.394388e+10</td>\n",
       "      <td>1.319193e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>$$ƛ_e^{11/3} /l_P^2 ƛ_{CMB}^{2/3}$$</td>\n",
       "      <td>lambdabare**(11/3)/l_P**2*lambdabar_cmb**(2/3)</td>\n",
       "      <td>1.387000e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>$$2ƛ_{CNB}^6/ƛ_e^3 ƛ_{CMB}^2$$</td>\n",
       "      <td>2*lambdabar_cnb**6/lambdabare**3*lambdabar_cmb**2</td>\n",
       "      <td>1.383000e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>$$2ƛ_e a_s^2 W^7$$</td>\n",
       "      <td>2*lambdabare*a_s**2*W**7</td>\n",
       "      <td>1.409009e+10</td>\n",
       "      <td>1.333025e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>$$ƛ_e(FZ)^{7/2}$$</td>\n",
       "      <td>lambdabare*(F*Z)**(7/2)</td>\n",
       "      <td>1.395438e+10</td>\n",
       "      <td>1.320186e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>$$2^{128}.ƛ_e$$</td>\n",
       "      <td>2**128*lambdabare</td>\n",
       "      <td>1.388933e+10</td>\n",
       "      <td>1.314032e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>$$ƛ_e\\pi^{155/2}$$</td>\n",
       "      <td>lambdabare*np.pi**(155/2)</td>\n",
       "      <td>1.380247e+10</td>\n",
       "      <td>1.305815e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>$$4P^3l_{Wi}ƛ_e/R_N$$</td>\n",
       "      <td>(4*P**3*l_wi*lambdabare)/R_N</td>\n",
       "      <td>1.381641e+10</td>\n",
       "      <td>1.307134e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>$$(2\\pi^{32}Pƛ_e )^2 /R_N$$</td>\n",
       "      <td>(2*np.pi**32*P*lambdabare)**2/R_N</td>\n",
       "      <td>1.380000e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>$$R_N a^a /\\Pi_{happy}$$</td>\n",
       "      <td>R_N*a**a/OP</td>\n",
       "      <td>1.381411e+10</td>\n",
       "      <td>1.306916e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>$$R_N (R_{GC} /l_P )^3 /\\Pi^{26}$$</td>\n",
       "      <td>R_N*(R_GC/l_P)**3/TSSPG</td>\n",
       "      <td>1.379000e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>$$ƛ_FP^3/p^7$$</td>\n",
       "      <td>lambdabar_F*P**3/p**7</td>\n",
       "      <td>1.380312e+10</td>\n",
       "      <td>1.305876e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>$$ƛ_FP^2e/8$$</td>\n",
       "      <td>lambdabar_F*P**2*e/8</td>\n",
       "      <td>1.381415e+10</td>\n",
       "      <td>1.306919e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>$$\\lambda_e(OM)^{7/10}$$</td>\n",
       "      <td>lambda_e*(OM)**(7/10)</td>\n",
       "      <td>1.393850e+10</td>\n",
       "      <td>1.318684e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>$$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$</td>\n",
       "      <td>((lambdabarRyd*n**4)**2)/lambdabar_p</td>\n",
       "      <td>1.381037e+10</td>\n",
       "      <td>1.306562e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>$$( λ_{CMB} /(j+1))^2 /l_P$$</td>\n",
       "      <td>(lambda_cmb/(j+1))**2/l_P</td>\n",
       "      <td>1.379749e+10</td>\n",
       "      <td>1.305343e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>$$((20/3)*N_Edd*G*m_H)/c^2$$</td>\n",
       "      <td>((20/3)*N_Edd*G_s*m_H)/constants.c**2</td>\n",
       "      <td>1.379353e+10</td>\n",
       "      <td>1.304969e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>$$(\\hbar/(m_e.c))*(2.R/R_N)^{210}$$</td>\n",
       "      <td>(constants.hbar/(constants.m_e*constants.c))*(2*R/R_N)**210</td>\n",
       "      <td>1.385596e+10</td>\n",
       "      <td>1.310875e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>$$ƛ_e(\\tau/p)^{140}/2$$</td>\n",
       "      <td>lambdabare*(τ/p)**140/2</td>\n",
       "      <td>1.377087e+10</td>\n",
       "      <td>1.302825e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>$$R_N (OM.OB/n_{ph})^2$$</td>\n",
       "      <td>R_N*(OM*OB/n_ph)**2</td>\n",
       "      <td>1.376677e+10</td>\n",
       "      <td>1.302437e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>$$R_N (\\pi.OM.OB/3)^2 /exp(e^6)$$</td>\n",
       "      <td>R_N*(np.pi*OM*OB /3)**2/(np.exp(e**6))</td>\n",
       "      <td>1.389639e+10</td>\n",
       "      <td>1.314700e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   LaTeXFormula  \\\n",
       "0                  $$2\\hbar^2/(G.m_e.m_p.m_n)$$   \n",
       "1                    $$2\\hbar^2/(G.m_e.m_p^2)$$   \n",
       "2        $$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2/6})$$   \n",
       "3                           $$ƛ_e(τ/μ)^{32}/ω$$   \n",
       "4               $$(2ƛ_e/3)(ƛ_{CMB} /ƛ_{H2})^3$$   \n",
       "5                                 $$ƛ_e s_4^5$$   \n",
       "6                                 $$ƛ_p(WZ)^4$$   \n",
       "7           $$ƛ_e^{11/3} /l_P^2 ƛ_{CMB}^{2/3}$$   \n",
       "8                $$2ƛ_{CNB}^6/ƛ_e^3 ƛ_{CMB}^2$$   \n",
       "9                            $$2ƛ_e a_s^2 W^7$$   \n",
       "10                            $$ƛ_e(FZ)^{7/2}$$   \n",
       "11                              $$2^{128}.ƛ_e$$   \n",
       "12                           $$ƛ_e\\pi^{155/2}$$   \n",
       "13                        $$4P^3l_{Wi}ƛ_e/R_N$$   \n",
       "14                  $$(2\\pi^{32}Pƛ_e )^2 /R_N$$   \n",
       "15                     $$R_N a^a /\\Pi_{happy}$$   \n",
       "16           $$R_N (R_{GC} /l_P )^3 /\\Pi^{26}$$   \n",
       "17                               $$ƛ_FP^3/p^7$$   \n",
       "18                                $$ƛ_FP^2e/8$$   \n",
       "19                     $$\\lambda_e(OM)^{7/10}$$   \n",
       "20  $$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$   \n",
       "21                 $$( λ_{CMB} /(j+1))^2 /l_P$$   \n",
       "22                 $$((20/3)*N_Edd*G*m_H)/c^2$$   \n",
       "23          $$(\\hbar/(m_e.c))*(2.R/R_N)^{210}$$   \n",
       "24                      $$ƛ_e(\\tau/p)^{140}/2$$   \n",
       "25                     $$R_N (OM.OB/n_{ph})^2$$   \n",
       "26            $$R_N (\\pi.OM.OB/3)^2 /exp(e^6)$$   \n",
       "\n",
       "                                                    PlainFormula  \\\n",
       "0                                    2*hbar**2/(G_s*m_e*m_p*m_n)   \n",
       "1                                     2*hbar**2/(G_s*m_e*m_p**2)   \n",
       "2                            lambdabare*(np.exp(2**(6+(1/2)))/6)   \n",
       "3                                         lambdabare*(τ/μ)**32/ω   \n",
       "4               (2*lambdabare/3)*(lambdabar_cmb/lambdabar_H2)**3   \n",
       "5                                              lambdabare*s_4**5   \n",
       "6                                           lambdabar_p*(W*Z)**4   \n",
       "7                 lambdabare**(11/3)/l_P**2*lambdabar_cmb**(2/3)   \n",
       "8              2*lambdabar_cnb**6/lambdabare**3*lambdabar_cmb**2   \n",
       "9                                       2*lambdabare*a_s**2*W**7   \n",
       "10                                       lambdabare*(F*Z)**(7/2)   \n",
       "11                                             2**128*lambdabare   \n",
       "12                                     lambdabare*np.pi**(155/2)   \n",
       "13                                  (4*P**3*l_wi*lambdabare)/R_N   \n",
       "14                             (2*np.pi**32*P*lambdabare)**2/R_N   \n",
       "15                                                   R_N*a**a/OP   \n",
       "16                                       R_N*(R_GC/l_P)**3/TSSPG   \n",
       "17                                         lambdabar_F*P**3/p**7   \n",
       "18                                          lambdabar_F*P**2*e/8   \n",
       "19                                         lambda_e*(OM)**(7/10)   \n",
       "20                          ((lambdabarRyd*n**4)**2)/lambdabar_p   \n",
       "21                                     (lambda_cmb/(j+1))**2/l_P   \n",
       "22                         ((20/3)*N_Edd*G_s*m_H)/constants.c**2   \n",
       "23   (constants.hbar/(constants.m_e*constants.c))*(2*R/R_N)**210   \n",
       "24                                       lambdabare*(τ/p)**140/2   \n",
       "25                                           R_N*(OM*OB/n_ph)**2   \n",
       "26                        R_N*(np.pi*OM*OB /3)**2/(np.exp(e**6))   \n",
       "\n",
       "             gly             m  \n",
       "0   1.380048e+10  1.305626e+26  \n",
       "1   1.380048e+10  1.305626e+26  \n",
       "2   1.382101e+10  1.307569e+26  \n",
       "3   1.379565e+10  1.305170e+26  \n",
       "4   1.390000e+10  1.300000e+26  \n",
       "5   1.380418e+10  1.305976e+26  \n",
       "6   1.394388e+10  1.319193e+26  \n",
       "7   1.387000e+10  1.300000e+26  \n",
       "8   1.383000e+10  1.300000e+26  \n",
       "9   1.409009e+10  1.333025e+26  \n",
       "10  1.395438e+10  1.320186e+26  \n",
       "11  1.388933e+10  1.314032e+26  \n",
       "12  1.380247e+10  1.305815e+26  \n",
       "13  1.381641e+10  1.307134e+26  \n",
       "14  1.380000e+10  1.300000e+26  \n",
       "15  1.381411e+10  1.306916e+26  \n",
       "16  1.379000e+10  1.300000e+26  \n",
       "17  1.380312e+10  1.305876e+26  \n",
       "18  1.381415e+10  1.306919e+26  \n",
       "19  1.393850e+10  1.318684e+26  \n",
       "20  1.381037e+10  1.306562e+26  \n",
       "21  1.379749e+10  1.305343e+26  \n",
       "22  1.379353e+10  1.304969e+26  \n",
       "23  1.385596e+10  1.310875e+26  \n",
       "24  1.377087e+10  1.302825e+26  \n",
       "25  1.376677e+10  1.302437e+26  \n",
       "26  1.389639e+10  1.314700e+26  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "display = pd.options.display\n",
    "display.max_columns = (None)\n",
    "display.max_rows = 40\n",
    "display.max_colwidth = 100\n",
    "display.width = None\n",
    "\n",
    "#pd.set_option('display.width', 20)\n",
    "#pd.set_option('display.max_colwidth', None)\n",
    "df2.iloc[:,[0,1,2,3]]\n",
    "#print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        vertical-align: top;\n",
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th>PlainFormula</th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>$$(e^{e^{e}})^{\\sqrt a}).(a-136))^{1/2}ƛ_e$$</td>\n",
       "      <td>((e**e**e)**(np.sqrt(a))*(a-136))**(1/2)*lambdabare</td>\n",
       "      <td>1.381372e+10</td>\n",
       "      <td>1.306879e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$$(\\Pi_{26}^2 ( ƛ_e /j)^{18} R_N /2)^{1/19}$$</td>\n",
       "      <td>(TSSPG**2*(lambdabare/j)**18*R_N/2)**(1/19)</td>\n",
       "      <td>1.381400e+10</td>\n",
       "      <td>1.306000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$$ƛ_e \\Pi_{26}^{1/9}/(j+e)$$</td>\n",
       "      <td>lambdabare*TSSPG**(1/9)/(j+e)</td>\n",
       "      <td>1.381300e+10</td>\n",
       "      <td>1.306000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$$ƛ_e(a^a)^{5/38}$$</td>\n",
       "      <td>lambdabare*(a**a)**(5/38)</td>\n",
       "      <td>1.381084e+10</td>\n",
       "      <td>1.306606e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$$R1(8/\\sqrt(3a))^{1/7}$$</td>\n",
       "      <td>R1*(8/np.sqrt(3*a))**(1/7)</td>\n",
       "      <td>1.381186e+10</td>\n",
       "      <td>1.306703e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$$ƛ_e.exp((e^{4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$</td>\n",
       "      <td>np.exp(np.sqrt((e**(4*e-1/a)-np.log(P**4/a**3)**2)/2))*lambdabare</td>\n",
       "      <td>1.381169e+10</td>\n",
       "      <td>1.306719e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>$$ƛ_Fe(Pe^e)^2/\\sqrt(pn)$$</td>\n",
       "      <td>lambdabar_F*e*(P*e**e)**2/np.sqrt(p*n)</td>\n",
       "      <td>1.381261e+10</td>\n",
       "      <td>1.306774e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>$$(ƛ_e^2/l_P)(j/16)^{16}( e^e )^2.d_e\\sqrt(2)$$</td>\n",
       "      <td>(lambdabare**2/l_P)(j/16)**16( e**e )**2*d_e*np.sqrt(2)</td>\n",
       "      <td>1.381203e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>$$3^{1/137}R_{GC}^{2/3}r_e^{1/3} /l_K$$</td>\n",
       "      <td>3**(1/137)*R_GC**(2/3)*(lambdabare/a)**(4/3)/l_K/(constants.light_year*10**9)</td>\n",
       "      <td>1.381245e+10</td>\n",
       "      <td>1.306759e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>$$((a/\\sqrt(137)(4\\pi F)^2)ƛ_e^4 l_{ph}^3(\\lambda_{CMB}/l_P)^8 )^{1/7}$$</td>\n",
       "      <td>((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)</td>\n",
       "      <td>1.380699e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>$$R_N exp(-2/e^2 )$$</td>\n",
       "      <td>R_N*np.exp(-2/np.e**2)</td>\n",
       "      <td>1.381195e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>$$2\\beta ƛ_ej^{17}(4\\pi)^2\\sqrt(137)$$</td>\n",
       "      <td>2*beta*lambdabare*(j**17)*(4*np.pi)**2*np.sqrt(137)</td>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>$$ƛ_e(3j^j/(2H)^{1/6} $$</td>\n",
       "      <td>lambdabare*(3*j**j/(2*H))**(1/6)</td>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>$$(\\beta FP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$</td>\n",
       "      <td>beta*F*P**(3/2)*(n/p)**(7/2)/(2*np.pi)*lambdabare</td>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306716e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>$$2(l_K /F)^2 /ƛ_e$$</td>\n",
       "      <td>2*(l_K/F)**2/lambdabare</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                LaTeXFormula  \\\n",
       "0                               $$(e^{e^{e}})^{\\sqrt a}).(a-136))^{1/2}ƛ_e$$   \n",
       "1                              $$(\\Pi_{26}^2 ( ƛ_e /j)^{18} R_N /2)^{1/19}$$   \n",
       "2                                               $$ƛ_e \\Pi_{26}^{1/9}/(j+e)$$   \n",
       "3                                                        $$ƛ_e(a^a)^{5/38}$$   \n",
       "4                                                  $$R1(8/\\sqrt(3a))^{1/7}$$   \n",
       "5                            $$ƛ_e.exp((e^{4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$   \n",
       "6                                                 $$ƛ_Fe(Pe^e)^2/\\sqrt(pn)$$   \n",
       "7                            $$(ƛ_e^2/l_P)(j/16)^{16}( e^e )^2.d_e\\sqrt(2)$$   \n",
       "8                                    $$3^{1/137}R_{GC}^{2/3}r_e^{1/3} /l_K$$   \n",
       "9   $$((a/\\sqrt(137)(4\\pi F)^2)ƛ_e^4 l_{ph}^3(\\lambda_{CMB}/l_P)^8 )^{1/7}$$   \n",
       "10                                                      $$R_N exp(-2/e^2 )$$   \n",
       "11                                    $$2\\beta ƛ_ej^{17}(4\\pi)^2\\sqrt(137)$$   \n",
       "12                                                  $$ƛ_e(3j^j/(2H)^{1/6} $$   \n",
       "13                                  $$(\\beta FP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$   \n",
       "14                                                      $$2(l_K /F)^2 /ƛ_e$$   \n",
       "\n",
       "                                                                                    PlainFormula  \\\n",
       "0                                            ((e**e**e)**(np.sqrt(a))*(a-136))**(1/2)*lambdabare   \n",
       "1                                                    (TSSPG**2*(lambdabare/j)**18*R_N/2)**(1/19)   \n",
       "2                                                                  lambdabare*TSSPG**(1/9)/(j+e)   \n",
       "3                                                                      lambdabare*(a**a)**(5/38)   \n",
       "4                                                                     R1*(8/np.sqrt(3*a))**(1/7)   \n",
       "5                              np.exp(np.sqrt((e**(4*e-1/a)-np.log(P**4/a**3)**2)/2))*lambdabare   \n",
       "6                                                         lambdabar_F*e*(P*e**e)**2/np.sqrt(p*n)   \n",
       "7                                        (lambdabare**2/l_P)(j/16)**16( e**e )**2*d_e*np.sqrt(2)   \n",
       "8                  3**(1/137)*R_GC**(2/3)*(lambdabare/a)**(4/3)/l_K/(constants.light_year*10**9)   \n",
       "9    ((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)   \n",
       "10                                                                        R_N*np.exp(-2/np.e**2)   \n",
       "11                                           2*beta*lambdabare*(j**17)*(4*np.pi)**2*np.sqrt(137)   \n",
       "12                                                              lambdabare*(3*j**j/(2*H))**(1/6)   \n",
       "13                                             beta*F*P**(3/2)*(n/p)**(7/2)/(2*np.pi)*lambdabare   \n",
       "14                                                                       2*(l_K/F)**2/lambdabare   \n",
       "\n",
       "             gly             m  \n",
       "0   1.381372e+10  1.306879e+26  \n",
       "1   1.381400e+10  1.306000e+26  \n",
       "2   1.381300e+10  1.306000e+26  \n",
       "3   1.381084e+10  1.306606e+26  \n",
       "4   1.381186e+10  1.306703e+26  \n",
       "5   1.381169e+10  1.306719e+26  \n",
       "6   1.381261e+10  1.306774e+26  \n",
       "7   1.381203e+10  1.306715e+26  \n",
       "8   1.381245e+10  1.306759e+26  \n",
       "9   1.380699e+10  1.306715e+26  \n",
       "10  1.381195e+10  1.300000e+26  \n",
       "11  1.381199e+10  1.306715e+26  \n",
       "12  1.381199e+10  1.306715e+26  \n",
       "13  1.381199e+10  1.306716e+26  \n",
       "14  1.381198e+10  1.306714e+26  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.read_csv(\"hubble-table1.csv\", dtype = {\"gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [17], sep = \",\")\n",
    "#df1.head (20)\n",
    "df1.iloc[:,[0,1,2,3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Decimal('2.937238508642020695790261107E+365')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TSSPG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Infinity\n"
     ]
    }
   ],
   "source": [
    "R13 = Decimal(lambdabare*2.937238508642020695790261107e+365**(1/9)/(j+e))\n",
    "#lambdabare*2.937238508642020695790261107e+365**(1/9)/(j+e)\t\n",
    "print(R13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th>PlainFormula</th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>$$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$</td>\n",
       "      <td>((1-(137**2 + np.pi**2 + e**2 )/(p*H))*2**128)*lambdabare</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$$(11/4)^{3/610}R1^2 /R_N$$</td>\n",
       "      <td>(11/4)**(3/610)*R1/R_N</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$</td>\n",
       "      <td>lambdabare*2**137*(gamma*n**3)**2/(137**3*Gamma**11)</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$$ƛ_e 2^{128} / d_e^2 (H /p )^6$$</td>\n",
       "      <td>lambdabare*2**128/d_e**2 *(H /p )**6</td>\n",
       "      <td>1.390251e+10</td>\n",
       "      <td>1.315279e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$</td>\n",
       "      <td>((constants.hbar/(constants.m_e*constants.c))*np.exp(2**(6+(1/2)))/6)/(1+np.sqrt(137**2+np.sqrt...</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$</td>\n",
       "      <td>2*lambdabare*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5/np.log(2-((a**2*j)**-1)))**2</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                          LaTeXFormula  \\\n",
       "0                  $$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$   \n",
       "1                                          $$(11/4)^{3/610}R1^2 /R_N$$   \n",
       "2                 $$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$   \n",
       "3                                    $$ƛ_e 2^{128} / d_e^2 (H /p )^6$$   \n",
       "4                        $$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$   \n",
       "5  $$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$   \n",
       "\n",
       "                                                                                          PlainFormula  \\\n",
       "0                                            ((1-(137**2 + np.pi**2 + e**2 )/(p*H))*2**128)*lambdabare   \n",
       "1                                                                               (11/4)**(3/610)*R1/R_N   \n",
       "2                                                 lambdabare*2**137*(gamma*n**3)**2/(137**3*Gamma**11)   \n",
       "3                                                                 lambdabare*2**128/d_e**2 *(H /p )**6   \n",
       "4   ((constants.hbar/(constants.m_e*constants.c))*np.exp(2**(6+(1/2)))/6)/(1+np.sqrt(137**2+np.sqrt...   \n",
       "5                         2*lambdabare*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5/np.log(2-((a**2*j)**-1)))**2   \n",
       "\n",
       "            gly             m  \n",
       "0  1.381198e+10  1.306714e+26  \n",
       "1  1.381198e+10  1.306714e+26  \n",
       "2  1.381198e+10  1.306714e+26  \n",
       "3  1.390251e+10  1.315279e+26  \n",
       "4  1.381198e+10  1.306714e+26  \n",
       "5  1.381198e+10  1.306714e+26  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = pd.read_csv(\"hubble-table3.csv\", dtype = {\"gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [50,51], sep = \",\")\n",
    "df3.iloc[:,[0,1,2,3]]\n",
    "#df3.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Pick a formula from the above table, select it from the \"PlainFormula\" column and Copy / paste it into the cell below to get the result in meter :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.315279188467532e+26"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example\n",
    "lambdabare*2**128/d_e**2 *(m_H /m_p )**6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Divide the result by:\n",
    "/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.902511991854007"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example\n",
    "lambdabare*2**128/d_e**2 *(m_H /m_p )**6/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2.700000e+01</td>\n",
       "      <td>2.700000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.384332e+10</td>\n",
       "      <td>1.307980e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.252979e+07</td>\n",
       "      <td>7.685448e+23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.376677e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.380024e+10</td>\n",
       "      <td>1.303897e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.381411e+10</td>\n",
       "      <td>1.305876e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.387966e+10</td>\n",
       "      <td>1.309222e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.409009e+10</td>\n",
       "      <td>1.333025e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                gly             m\n",
       "count  2.700000e+01  2.700000e+01\n",
       "mean   1.384332e+10  1.307980e+26\n",
       "std    7.252979e+07  7.685448e+23\n",
       "min    1.376677e+10  1.300000e+26\n",
       "25%    1.380024e+10  1.303897e+26\n",
       "50%    1.381411e+10  1.305876e+26\n",
       "75%    1.387966e+10  1.309222e+26\n",
       "max    1.409009e+10  1.333025e+26"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Stat Table 1\n",
    "#print(df2.describe())\n",
    "#df2.describe();\n",
    "pd.set_option('display.precision', 6)\n",
    "df2.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.500000e+01</td>\n",
       "      <td>1.500000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.381194e+10</td>\n",
       "      <td>1.306182e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.581344e+06</td>\n",
       "      <td>1.729917e+23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.380699e+10</td>\n",
       "      <td>1.300000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.381191e+10</td>\n",
       "      <td>1.306654e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.381253e+10</td>\n",
       "      <td>1.306717e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.381400e+10</td>\n",
       "      <td>1.306879e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                gly             m\n",
       "count  1.500000e+01  1.500000e+01\n",
       "mean   1.381194e+10  1.306182e+26\n",
       "std    1.581344e+06  1.729917e+23\n",
       "min    1.380699e+10  1.300000e+26\n",
       "25%    1.381191e+10  1.306654e+26\n",
       "50%    1.381199e+10  1.306715e+26\n",
       "75%    1.381253e+10  1.306717e+26\n",
       "max    1.381400e+10  1.306879e+26"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Stat Table 2\n",
    "#print(df1.describe())\n",
    "#df1.describe();\n",
    "pd.set_option('display.precision', 6)\n",
    "df1.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>6.000000000e+00</td>\n",
       "      <td>6.000000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.382706598e+10</td>\n",
       "      <td>1.308141445e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.696086888e+07</td>\n",
       "      <td>3.496768185e+23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.381197653e+10</td>\n",
       "      <td>1.306713872e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.381197677e+10</td>\n",
       "      <td>1.306713895e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.381197680e+10</td>\n",
       "      <td>1.306713898e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.381197692e+10</td>\n",
       "      <td>1.306713909e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.390251204e+10</td>\n",
       "      <td>1.315279193e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   gly                m\n",
       "count  6.000000000e+00  6.000000000e+00\n",
       "mean   1.382706598e+10  1.308141445e+26\n",
       "std    3.696086888e+07  3.496768185e+23\n",
       "min    1.381197653e+10  1.306713872e+26\n",
       "25%    1.381197677e+10  1.306713895e+26\n",
       "50%    1.381197680e+10  1.306713898e+26\n",
       "75%    1.381197692e+10  1.306713909e+26\n",
       "max    1.390251204e+10  1.315279193e+26"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Stat Table 3\n",
    "#print(df3.describe())\n",
    "#df3.describe();\n",
    "pd.set_option('display.precision', 9)\n",
    "df3.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# END OF PART 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import host_subplot\n",
    "import mpl_toolkits.axisartist as AA\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(df2.iloc[:,[3,3]], df2.iloc[:,[2,2]], s=12 )\n",
    "plt.ylabel('Value displayed in $10^{10}$ Gly')\n",
    "plt.xlabel('Distance displayed in $10^{26}$m')\n",
    "plt.title('Hubble distance table', fontsize=18, color=\"black\")\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import host_subplot\n",
    "import mpl_toolkits.axisartist as AA\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(df1.iloc[:,[3,3]], df1.iloc[:,[2,2]], s=12 )\n",
    "plt.ylabel('Value displayed in $10^{10}$ Gly')\n",
    "#plt.xlabel('Distance displayed in $1.306.10^{26}$m')\n",
    "plt.title('Hubble distance table', fontsize=18, color=\"black\")\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$</th>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$((11/4)^{3/610}.R1^2)/R_N$$</th>\n",
       "      <td>1.381196e+10</td>\n",
       "      <td>1.306710e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$((a/\\sqrt(137)(4\\pi F)^2)ƛ_e^4 l_{ph}^3(\\lambda_{CMB}/l_P)^8 )^(1/7)$$</th>\n",
       "      <td>2.761399e+10</td>\n",
       "      <td>2.613431e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l_{ph}^3(ƛ_{CMB}/l_P)^8)^{1/7}$$</th>\n",
       "      <td>2.761399e+10</td>\n",
       "      <td>2.612485e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$(\\beta FP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$</th>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306716e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$(e^{e^{e}})^{\\sqrt a}).(a-136))^{1/2}ƛ_e$$</th>\n",
       "      <td>2.762744e+10</td>\n",
       "      <td>2.613757e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e\\sqrt(2)$$</th>\n",
       "      <td>2.762405e+10</td>\n",
       "      <td>2.613431e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$2(l_K /F)^2 /ƛ_e$$</th>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$2\\beta ƛ_ej^{17}(4\\pi)^2\\sqrt(137)$$</th>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$2\\hbar^2/(G.m_e.m_p.m_n)$$</th>\n",
       "      <td>1.380048e+10</td>\n",
       "      <td>1.305626e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$</th>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$3^{1/137}R_{GC}^{2/3}r_e^{1/3} /l_K$$</th>\n",
       "      <td>2.762490e+10</td>\n",
       "      <td>2.613518e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$4P^3l_{Wi}ƛ_e/R_N$$</th>\n",
       "      <td>1.381641e+10</td>\n",
       "      <td>1.307134e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R1(8/\\sqrt(3a))^{1/7}$$</th>\n",
       "      <td>1.381186e+10</td>\n",
       "      <td>1.306000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R_N a^a /\\Pi_{happy}$$</th>\n",
       "      <td>1.381100e+10</td>\n",
       "      <td>1.306000e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$</th>\n",
       "      <td>1.381037e+10</td>\n",
       "      <td>1.306562e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R_{a}=ƛ_e.(2.\\pi^2.a^3)^5$$</th>\n",
       "      <td>4.141253e+10</td>\n",
       "      <td>3.917928e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R_{kotov-fermi}=\\frac{2.(c.t_k)^2/ƛ_e}{F^2}$$</th>\n",
       "      <td>2.762395e+10</td>\n",
       "      <td>2.613428e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R_{ƛ_w}=ƛ_e/F^2.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$</th>\n",
       "      <td>2.762395e+10</td>\n",
       "      <td>2.613428e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$R_{ƛ_w}=ƛ_w.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$</th>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_FP^2e/8$$</th>\n",
       "      <td>1.381415e+10</td>\n",
       "      <td>1.306919e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_FP^3/p^7$$</th>\n",
       "      <td>1.380312e+10</td>\n",
       "      <td>1.305876e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_Fe(Pe^e)^2/\\sqrt(pn)$$</th>\n",
       "      <td>2.762523e+10</td>\n",
       "      <td>2.613548e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e 2^{128} / d_e^2 (H /p )^6$$</th>\n",
       "      <td>1.390251e+10</td>\n",
       "      <td>1.315279e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e 2^{128}(1 - (137^2 + \\pi^2 + e^2 )/pH)$$</th>\n",
       "      <td>1.381241e+10</td>\n",
       "      <td>1.306754e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$</th>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2}/6)$$</th>\n",
       "      <td>1.382101e+10</td>\n",
       "      <td>1.307569e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$</th>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e(3j^j/(2H)^{1/6} $$</th>\n",
       "      <td>1.381199e+10</td>\n",
       "      <td>1.306715e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e(a^a)^{5/38}$$</th>\n",
       "      <td>2.762167e+10</td>\n",
       "      <td>2.613212e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e.exp((e^{4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$</th>\n",
       "      <td>1.381169e+10</td>\n",
       "      <td>1.306719e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e2^{128}/(1+(137^2 + \\pi^2 + e^2 )/pH)$$</th>\n",
       "      <td>2.762481e+10</td>\n",
       "      <td>2.613509e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$$ƛ_e\\pi^{155/2}$$</th>\n",
       "      <td>1.380247e+10</td>\n",
       "      <td>1.305815e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                   Gly  \\\n",
       "LaTeXFormula                                                                             \n",
       "$$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$                       1.381198e+10   \n",
       "$$((11/4)^{3/610}.R1^2)/R_N$$                                             1.381196e+10   \n",
       "$$((a/\\sqrt(137)(4\\pi F)^2)ƛ_e^4 l_{ph}^3(\\lambda_{CMB}/l_P)^8 )^(1/7)$$  2.761399e+10   \n",
       "$$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l_{ph}^3(ƛ_{CMB}/l_P)^8)^{1/7}$$          2.761399e+10   \n",
       "$$(\\beta FP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$                                  1.381199e+10   \n",
       "$$(e^{e^{e}})^{\\sqrt a}).(a-136))^{1/2}ƛ_e$$                              2.762744e+10   \n",
       "$$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e\\sqrt(2)$$                             2.762405e+10   \n",
       "$$2(l_K /F)^2 /ƛ_e$$                                                      1.381198e+10   \n",
       "$$2\\beta ƛ_ej^{17}(4\\pi)^2\\sqrt(137)$$                                    1.381199e+10   \n",
       "$$2\\hbar^2/(G.m_e.m_p.m_n)$$                                              1.380048e+10   \n",
       "$$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$       1.381198e+10   \n",
       "$$3^{1/137}R_{GC}^{2/3}r_e^{1/3} /l_K$$                                   2.762490e+10   \n",
       "$$4P^3l_{Wi}ƛ_e/R_N$$                                                     1.381641e+10   \n",
       "$$R1(8/\\sqrt(3a))^{1/7}$$                                                 1.381186e+10   \n",
       "$$R_N a^a /\\Pi_{happy}$$                                                  1.381100e+10   \n",
       "$$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$                               1.381037e+10   \n",
       "$$R_{a}=ƛ_e.(2.\\pi^2.a^3)^5$$                                             4.141253e+10   \n",
       "$$R_{kotov-fermi}=\\frac{2.(c.t_k)^2/ƛ_e}{F^2}$$                           2.762395e+10   \n",
       "$$R_{ƛ_w}=ƛ_e/F^2.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$                2.762395e+10   \n",
       "$$R_{ƛ_w}=ƛ_w.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$                    1.381198e+10   \n",
       "$$ƛ_FP^2e/8$$                                                             1.381415e+10   \n",
       "$$ƛ_FP^3/p^7$$                                                            1.380312e+10   \n",
       "$$ƛ_Fe(Pe^e)^2/\\sqrt(pn)$$                                                2.762523e+10   \n",
       "$$ƛ_e 2^{128} / d_e^2 (H /p )^6$$                                         1.390251e+10   \n",
       "$$ƛ_e 2^{128}(1 - (137^2 + \\pi^2 + e^2 )/pH)$$                            1.381241e+10   \n",
       "$$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$                      1.381198e+10   \n",
       "$$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2}/6)$$                                    1.382101e+10   \n",
       "$$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$                             1.381198e+10   \n",
       "$$ƛ_e(3j^j/(2H)^{1/6} $$                                                  1.381199e+10   \n",
       "$$ƛ_e(a^a)^{5/38}$$                                                       2.762167e+10   \n",
       "$$ƛ_e.exp((e^{4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$                           1.381169e+10   \n",
       "$$ƛ_e2^{128}/(1+(137^2 + \\pi^2 + e^2 )/pH)$$                              2.762481e+10   \n",
       "$$ƛ_e\\pi^{155/2}$$                                                        1.380247e+10   \n",
       "\n",
       "                                                                                     m  \n",
       "LaTeXFormula                                                                            \n",
       "$$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$                       1.306714e+26  \n",
       "$$((11/4)^{3/610}.R1^2)/R_N$$                                             1.306710e+26  \n",
       "$$((a/\\sqrt(137)(4\\pi F)^2)ƛ_e^4 l_{ph}^3(\\lambda_{CMB}/l_P)^8 )^(1/7)$$  2.613431e+26  \n",
       "$$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l_{ph}^3(ƛ_{CMB}/l_P)^8)^{1/7}$$          2.612485e+26  \n",
       "$$(\\beta FP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$                                  1.306716e+26  \n",
       "$$(e^{e^{e}})^{\\sqrt a}).(a-136))^{1/2}ƛ_e$$                              2.613757e+26  \n",
       "$$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e\\sqrt(2)$$                             2.613431e+26  \n",
       "$$2(l_K /F)^2 /ƛ_e$$                                                      1.306714e+26  \n",
       "$$2\\beta ƛ_ej^{17}(4\\pi)^2\\sqrt(137)$$                                    1.306715e+26  \n",
       "$$2\\hbar^2/(G.m_e.m_p.m_n)$$                                              1.305626e+26  \n",
       "$$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$       1.306714e+26  \n",
       "$$3^{1/137}R_{GC}^{2/3}r_e^{1/3} /l_K$$                                   2.613518e+26  \n",
       "$$4P^3l_{Wi}ƛ_e/R_N$$                                                     1.307134e+26  \n",
       "$$R1(8/\\sqrt(3a))^{1/7}$$                                                 1.306000e+26  \n",
       "$$R_N a^a /\\Pi_{happy}$$                                                  1.306000e+26  \n",
       "$$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$                               1.306562e+26  \n",
       "$$R_{a}=ƛ_e.(2.\\pi^2.a^3)^5$$                                             3.917928e+26  \n",
       "$$R_{kotov-fermi}=\\frac{2.(c.t_k)^2/ƛ_e}{F^2}$$                           2.613428e+26  \n",
       "$$R_{ƛ_w}=ƛ_e/F^2.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$                2.613428e+26  \n",
       "$$R_{ƛ_w}=ƛ_w.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$                    1.306714e+26  \n",
       "$$ƛ_FP^2e/8$$                                                             1.306919e+26  \n",
       "$$ƛ_FP^3/p^7$$                                                            1.305876e+26  \n",
       "$$ƛ_Fe(Pe^e)^2/\\sqrt(pn)$$                                                2.613548e+26  \n",
       "$$ƛ_e 2^{128} / d_e^2 (H /p )^6$$                                         1.315279e+26  \n",
       "$$ƛ_e 2^{128}(1 - (137^2 + \\pi^2 + e^2 )/pH)$$                            1.306754e+26  \n",
       "$$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$                      1.306714e+26  \n",
       "$$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2}/6)$$                                    1.307569e+26  \n",
       "$$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$                             1.306714e+26  \n",
       "$$ƛ_e(3j^j/(2H)^{1/6} $$                                                  1.306715e+26  \n",
       "$$ƛ_e(a^a)^{5/38}$$                                                       2.613212e+26  \n",
       "$$ƛ_e.exp((e^{4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$                           1.306719e+26  \n",
       "$$ƛ_e2^{128}/(1+(137^2 + \\pi^2 + e^2 )/pH)$$                              2.613509e+26  \n",
       "$$ƛ_e\\pi^{155/2}$$                                                        1.305815e+26  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.pivot_table(df, index=['LaTeXFormula'], aggfunc='sum')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pd.set_option('display.max_rows', df.shape[0]+1)\n",
    "#print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"hubble-table.csv\", dtype = {\"Gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [50,51], sep = \",\")\n",
    "display = pd.options.display\n",
    "#display.max_columns = (None)\n",
    "#display.max_rows = 24\n",
    "#display.max_colwidth = 50\n",
    "\n",
    "#pd.set_option('display.max_rows', df.shape[0]+1)\n",
    "pd.set_option('display.max_rows', None)\n",
    "pd.set_option('display.max_columns', None)\n",
    "pd.set_option('display.width', None)\n",
    "pd.set_option('display.max_colwidth', 80)\n",
    "pd.set_option('display.precision', 9)\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import host_subplot\n",
    "import mpl_toolkits.axisartist as AA\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(df2.iloc[:,[3,3]], df2.iloc[:,[2,2]], s=12 )\n",
    "plt.ylabel('Value displayed in $10^{10}$ Gly')\n",
    "plt.xlabel('Distance displayed in $10^{26}$m')\n",
    "plt.title('Hubble distance table', fontsize=18, color=\"black\")\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import host_subplot\n",
    "import mpl_toolkits.axisartist as AA\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.scatter(df3.iloc[:,[3,3]], df3.iloc[:,[2,2]], s=12 )\n",
    "plt.ylabel('Value displayed in $10^{10}$ Gly')\n",
    "plt.xlabel('Distance displayed in $10^{26}$m')\n",
    "plt.title('Hubble distance table', fontsize=18, color=\"black\")\n",
    "ax.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Pick a formula from the above table, select it from the \"PlainFormula\" column and Copy / paste it into the cell below to get the result in meter :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import quantities as pq\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UnitConstant('Planck_constant', 6.62606896e-34 * s*J, 'h')\n",
      "UnitConstant('Boltzmann_constant', 1.3806504e-23 * J/K, 'k')\n"
     ]
    }
   ],
   "source": [
    "print(repr(pq.constants.Planck_constant))\n",
    "print(repr(pq.constants.Boltzmann_constant))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [],
   "source": [
    "def B(wl,T):\n",
    "    '''wl is an array of wavelengths with units of length\n",
    "    T is a temperature in Kelvin\n",
    "    the result is an array of s.r. with units W/(m**2 * nm * sr)\n",
    "    '''\n",
    "    I = 2 * pq.constants.h * (pq.c)**2 / wl**5 *  \\\n",
    "        1 / (np.exp((pq.constants.h*pq.c \\\n",
    "        / (wl*pq.constants.k*T)).simplified)-1)\n",
    "    return I.rescale(pq.watt/(pq.m**2 * pq.nm *pq.sr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(26421.6296097) * W/(m**2*nm*sr)"
      ]
     },
     "execution_count": 300,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B( 5000 *pq.angstrom, 5780 *pq.K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [],
   "source": [
    "#T0 = 2.7255 * pq.Kelvin\n",
    "T1 = 4000 * pq.Kelvin\n",
    "T2 = 5000 * pq.Kelvin\n",
    "T3 = 6000 * pq.Kelvin\n",
    "T4 = 7000 * pq.Kelvin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "wl = np.arange(10,2000,10) * pq.nm\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "ax.plot(wl, B(wl,T4), label='7000K')\n",
    "ax.plot(wl, B(wl,T3), label='6000K')\n",
    "ax.plot(wl, B(wl,T2), label='5000K')\n",
    "ax.plot(wl, B(wl,T1), label='4000K')\n",
    "#ax.plot(wl, B(wl,T0), label='2.7255K')\n",
    "ax.legend()\n",
    "ax.set_title('Blackbody radiation')\n",
    "ax.title.set_fontsize(20)\n",
    "ax.set_xlabel('wavelength in nm')\n",
    "ax.xaxis.label.set_fontsize(15)\n",
    "ax.set_ylabel('spectral radiance $(W m^{-2}nm^{-1}sr^{-1})$')\n",
    "ax.yaxis.label.set_fontsize(15)\n",
    "ax.axvspan(0,400,facecolor = 'violet',alpha = 0.6)\n",
    "ax.axvspan(400,700, facecolor='yellow', alpha = 0.5)\n",
    "ax.axvspan(700,2000, facecolor ='red', alpha = 0.3)\n",
    "ax.text(150,6e4, 'UV', fontsize=30, color = 'b')\n",
    "ax.text(1200,6e4, 'IR', fontsize=30, color = 'r')\n",
    "ax.text(420,6e4, 'VISIBLE', fontsize=20, color = 'green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UnitConstant('Wien_wavelength_displacement_law_constant', 0.0028977685 * m*K, 'b')\n"
     ]
    }
   ],
   "source": [
    "print(repr(pq.constants.b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3219 Angstrom\n"
     ]
    }
   ],
   "source": [
    "l_max = pq.constants.b/(9000 * pq.K)\n",
    "print('%d Angstrom' %l_max.rescale(pq.angstrom))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Its effective temperature will be: 7244 K\n"
     ]
    }
   ],
   "source": [
    "# Suppose that the radiation from a SN Type 1a  has its maximum intensity at 400 nm\n",
    "lmax  = 400 * pq.nm\n",
    "T = pq.constants.b / lmax\n",
    "print(\"Its effective temperature will be: %d K\" %T.simplified)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 sigma (Stefan_Boltzmann_constant) = 5.6704e-08 kg/(s**3*K**4)\n"
     ]
    }
   ],
   "source": [
    "print(pq.constants.sigma, '=', pq.constants.sigma.simplified)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.30671e+26 m\n"
     ]
    }
   ],
   "source": [
    "# We will need the value of the radius of the Sun:\n",
    "#sun_radius = 695000000.0 * pq.m\n",
    "#l_sun = 3.839e26 * pq.watt\n",
    "hubble_radius = 1.30671*10**26 * pq.m\n",
    "print(hubble_radius)\n",
    "#l_sun = 3.839e26 * pq.watt\n",
    "#temp_sun = (l_sun/(4 * np.pi * sun_radius**2 * pq.constants.sigma))**(1./4)\n",
    "#print (temp_sun.simplified)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0010630813846842417 m*K\n"
     ]
    }
   ],
   "source": [
    "TCMB = 2.7255 *pq.K\n",
    "lmax = pq.constants.b / T_cmb\n",
    "print (lmax.simplified)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "wl = np.arange(0.1,10,0.1) * pq.mm\n",
    "I = B(wl,TCMB).rescale(pq.watt/(pq.m**2 * pq.mm * pq.sr))\n",
    "fig, ax = plt.subplots(figsize=(10, 8))\n",
    "ax.plot(wl, I*1e7)\n",
    "ax.set_title('Blackbody spectrum at T = 2.7255 K \\\n",
    "\\n (wavelength in mm)')\n",
    "ax.title.set_fontsize(20)\n",
    "ax.set_xlabel('Wavelength in mm')\n",
    "ax.xaxis.label.set_fontsize(15)\n",
    "ax.set_ylabel('Spectral Radiance ($10^{-7} W m^{-2} mm^{-1} sr^{-1}$)')\n",
    "ax.yaxis.label.set_fontsize(15)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3067030578901262e+26"
      ]
     },
     "execution_count": 309,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R1*(8/np.sqrt(3*a))**(1/7)#/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976767663971"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#2 ƛ e (pn/H^2)(g(5)/ln (2 – 1/a^2 j))^2\n",
    "2*lambdabare*(p*n/H**2)*((np.exp(2**(5+(1/2)))/5)/np.log(2-1/(a**2*j)))**2/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976769267615"
      ]
     },
     "execution_count": 316,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example\n",
    "2*(c*t_k)**2/lambdabare/F**2/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th>PlainFormula</th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>$$2\\hbar^2/(G.m_e.m_p.m_n)$$</td>\n",
       "      <td>2*hbar**2/(G_s*m_e*m_p*m_n)</td>\n",
       "      <td>1.380048e+10</td>\n",
       "      <td>1.305626e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$$2\\hbar^2/(G.m_e.m_p^2)$$</td>\n",
       "      <td>2*hbar**2/(G_s*m_e*m_p**2)</td>\n",
       "      <td>1.380048e+10</td>\n",
       "      <td>1.305626e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2/6})$$</td>\n",
       "      <td>lambdabare*(np.exp(2**(6+(1/2)))/6)</td>\n",
       "      <td>1.382101e+10</td>\n",
       "      <td>1.307569e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$$ƛ_e s_4^5$$</td>\n",
       "      <td>lambdabare*s_4**5</td>\n",
       "      <td>1.380418e+10</td>\n",
       "      <td>1.305976e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$$ƛ_p(WZ)^4$$</td>\n",
       "      <td>lambdabar_p*(W*Z)**4</td>\n",
       "      <td>1.394388e+10</td>\n",
       "      <td>1.319193e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$$2^{128}.ƛ_e$$</td>\n",
       "      <td>2**128*lambdabare</td>\n",
       "      <td>1.388933e+10</td>\n",
       "      <td>1.314032e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>$$ƛ_e(τ/μ)^{32}/ω$$</td>\n",
       "      <td>lambdabare*(τ/μ)**32/ω</td>\n",
       "      <td>1.379565e+10</td>\n",
       "      <td>1.305170e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>$$2ƛ_e a_s^2 W^7$$</td>\n",
       "      <td>2*lambdabare*a_s**2*W**7</td>\n",
       "      <td>1.409009e+10</td>\n",
       "      <td>1.333025e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>$$ƛ_e(FZ)^{7/2}$$</td>\n",
       "      <td>lambdabare*(F*Z)**(7/2)</td>\n",
       "      <td>1.395438e+10</td>\n",
       "      <td>1.320186e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>$$\\lambda_e(OM)^{7/10}$$</td>\n",
       "      <td>lambda_e*(OM)**(7/10)</td>\n",
       "      <td>1.393850e+10</td>\n",
       "      <td>1.318684e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>$$R_N (OM.OB/n_{ph})^2$$</td>\n",
       "      <td>R_N*(OM*OB/n_ph)**2</td>\n",
       "      <td>1.376677e+10</td>\n",
       "      <td>1.302437e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>$$R_N (\\pi.OM.OB/3)^2 /exp(e^6)$$</td>\n",
       "      <td>R_N*(np.pi*OM*OB /3)**2/(np.exp(e**6))</td>\n",
       "      <td>1.389639e+10</td>\n",
       "      <td>1.314700e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>$$ƛ_e 2^{128} / d_e^2 (H /p )^6$$</td>\n",
       "      <td>lambdabare*2**128/d_e**2 *(H /p )**6</td>\n",
       "      <td>1.390251e+10</td>\n",
       "      <td>1.315279e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>$$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l_{ph}^3(ƛ_{CMB}/l_P)^8)^{1/7}$$</td>\n",
       "      <td>((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)</td>\n",
       "      <td>1.380699e+10</td>\n",
       "      <td>1.306242e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>$$4P^3l_{Wi}ƛ_e/R_N$$</td>\n",
       "      <td>(4*P**3*l_wi*lambdabare)/R_N</td>\n",
       "      <td>1.381641e+10</td>\n",
       "      <td>1.307134e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>$$R_{a}=ƛ_e.(2.\\pi^2.a^3)^5$$</td>\n",
       "      <td>((constants.pi**2*(2*(1/constants.fine_structure)**3))**5)*(constants.hbar/(constants.m_e*constants.c))</td>\n",
       "      <td>1.380418e+10</td>\n",
       "      <td>1.305976e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>$$ƛ_FP^2e/8$$</td>\n",
       "      <td>lambdabar_F*P**2*e/8</td>\n",
       "      <td>1.381415e+10</td>\n",
       "      <td>1.306919e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>$$ƛ_FP^3/p^7$$</td>\n",
       "      <td>lambdabar_F*P**3/p**7</td>\n",
       "      <td>1.380312e+10</td>\n",
       "      <td>1.305876e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>$$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$</td>\n",
       "      <td>((lambdabarRyd*n**4)**2)/lambdabar_p</td>\n",
       "      <td>1.381037e+10</td>\n",
       "      <td>1.306562e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>$$R_{ƛ_w}=ƛ_w.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$</td>\n",
       "      <td>(((2**70*np.euler_gamma*n**3)/Gamma**4)**2)*ƛ_w</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                        LaTeXFormula  \\\n",
       "0                                       $$2\\hbar^2/(G.m_e.m_p.m_n)$$   \n",
       "1                                         $$2\\hbar^2/(G.m_e.m_p^2)$$   \n",
       "2                             $$ƛ_e g(6) and g(6)=𝑒𝑥𝑝(2^{6+1/2/6})$$   \n",
       "3                                                      $$ƛ_e s_4^5$$   \n",
       "4                                                      $$ƛ_p(WZ)^4$$   \n",
       "5                                                    $$2^{128}.ƛ_e$$   \n",
       "6                                                $$ƛ_e(τ/μ)^{32}/ω$$   \n",
       "7                                                 $$2ƛ_e a_s^2 W^7$$   \n",
       "8                                                  $$ƛ_e(FZ)^{7/2}$$   \n",
       "9                                           $$\\lambda_e(OM)^{7/10}$$   \n",
       "10                                          $$R_N (OM.OB/n_{ph})^2$$   \n",
       "11                                 $$R_N (\\pi.OM.OB/3)^2 /exp(e^6)$$   \n",
       "12                                 $$ƛ_e 2^{128} / d_e^2 (H /p )^6$$   \n",
       "13  $$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l_{ph}^3(ƛ_{CMB}/l_P)^8)^{1/7}$$   \n",
       "14                                             $$4P^3l_{Wi}ƛ_e/R_N$$   \n",
       "15                                     $$R_{a}=ƛ_e.(2.\\pi^2.a^3)^5$$   \n",
       "16                                                     $$ƛ_FP^2e/8$$   \n",
       "17                                                    $$ƛ_FP^3/p^7$$   \n",
       "18                       $$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$   \n",
       "19            $$R_{ƛ_w}=ƛ_w.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$   \n",
       "\n",
       "                                                                                                PlainFormula  \\\n",
       "0                                                                                2*hbar**2/(G_s*m_e*m_p*m_n)   \n",
       "1                                                                                 2*hbar**2/(G_s*m_e*m_p**2)   \n",
       "2                                                                        lambdabare*(np.exp(2**(6+(1/2)))/6)   \n",
       "3                                                                                          lambdabare*s_4**5   \n",
       "4                                                                                       lambdabar_p*(W*Z)**4   \n",
       "5                                                                                          2**128*lambdabare   \n",
       "6                                                                                     lambdabare*(τ/μ)**32/ω   \n",
       "7                                                                                   2*lambdabare*a_s**2*W**7   \n",
       "8                                                                                    lambdabare*(F*Z)**(7/2)   \n",
       "9                                                                                      lambda_e*(OM)**(7/10)   \n",
       "10                                                                                       R_N*(OM*OB/n_ph)**2   \n",
       "11                                                                    R_N*(np.pi*OM*OB /3)**2/(np.exp(e**6))   \n",
       "12                                                                      lambdabare*2**128/d_e**2 *(H /p )**6   \n",
       "13               ((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)   \n",
       "14                                                                              (4*P**3*l_wi*lambdabare)/R_N   \n",
       "15   ((constants.pi**2*(2*(1/constants.fine_structure)**3))**5)*(constants.hbar/(constants.m_e*constants.c))   \n",
       "16                                                                                      lambdabar_F*P**2*e/8   \n",
       "17                                                                                     lambdabar_F*P**3/p**7   \n",
       "18                                                                      ((lambdabarRyd*n**4)**2)/lambdabar_p   \n",
       "19                                                           (((2**70*np.euler_gamma*n**3)/Gamma**4)**2)*ƛ_w   \n",
       "\n",
       "             gly             m  \n",
       "0   1.380048e+10  1.305626e+26  \n",
       "1   1.380048e+10  1.305626e+26  \n",
       "2   1.382101e+10  1.307569e+26  \n",
       "3   1.380418e+10  1.305976e+26  \n",
       "4   1.394388e+10  1.319193e+26  \n",
       "5   1.388933e+10  1.314032e+26  \n",
       "6   1.379565e+10  1.305170e+26  \n",
       "7   1.409009e+10  1.333025e+26  \n",
       "8   1.395438e+10  1.320186e+26  \n",
       "9   1.393850e+10  1.318684e+26  \n",
       "10  1.376677e+10  1.302437e+26  \n",
       "11  1.389639e+10  1.314700e+26  \n",
       "12  1.390251e+10  1.315279e+26  \n",
       "13  1.380699e+10  1.306242e+26  \n",
       "14  1.381641e+10  1.307134e+26  \n",
       "15  1.380418e+10  1.305976e+26  \n",
       "16  1.381415e+10  1.306919e+26  \n",
       "17  1.380312e+10  1.305876e+26  \n",
       "18  1.381037e+10  1.306562e+26  \n",
       "19  1.381198e+10  1.306714e+26  "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "display = pd.options.display\n",
    "display.max_columns = (None)\n",
    "display.max_rows = 35\n",
    "display.max_colwidth = 199\n",
    "display.width = None\n",
    "\n",
    "df2 = pd.read_csv(\"hubble-table2.csv\", dtype = {\"gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [29,31], sep = \",\")\n",
    "df3 = pd.read_csv(\"hubble-table3.csv\", dtype = {\"gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [30,31], sep = \",\")\n",
    "df2.head (20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.939837402842264e+30"
      ]
     },
     "execution_count": 320,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*lambdabare*2**128*((137**2 + np.pi**2 + e**2 )/p*H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-18795.489696091594"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1 - (137**2 + np.pi**2 + e**2 )/p*H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3140318971018876e+26"
      ]
     },
     "execution_count": 322,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdabare*2**128*1-(137**2 + np.pi**2 + e**2 )/(p*H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3067544300679512e+26"
      ]
     },
     "execution_count": 323,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdabare*2**128/(1+(137**2 + np.pi**2 + e**2)/(H*p) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976831988007"
      ]
     },
     "execution_count": 324,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((1-(137**2 + np.pi**2 + e**2 )/(p*H))*2**128)*lambdabare/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.812405224471854"
      ]
     },
     "execution_count": 325,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdabare*2**128/(1+(137**2 + np.pi**2 + e**2)/(H*p) )/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3152791928061182e+26"
      ]
     },
     "execution_count": 326,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdabare*2**128 / d_e**2 * (H /p )**6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3067153891523966e+26"
      ]
     },
     "execution_count": 327,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#ƛ_e(3j^j/(2H)^{1/6} \n",
    "lambdabare*(3*j**j/(2*H))**(1/6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th>PlainFormula</th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>$$(11/4)^{3/610}R1^2 /R_N$$</td>\n",
       "      <td>(11/4)**(3/610)*R1/R_N</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$</td>\n",
       "      <td>lambdabare*2**137*(gamma*n**3)**2/(137**3*Gamma**11)</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$</td>\n",
       "      <td>((1-(137**2 + np.pi**2 + e**2 )/(p*H))*2**128)*lambdabare</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$</td>\n",
       "      <td>((constants.hbar/(constants.m_e*constants.c))*np.exp(2**(6+(1/2)))/6)/(1+np.sqrt(137**2+np.sqrt(136))/(j*n))</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$</td>\n",
       "      <td>2*lambdabare*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5/np.log(2-((a**2*j)**-1)))**2</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$$R_{ƛ_w}=ƛ_e/F^2.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$</td>\n",
       "      <td>(((2**70*np.euler_gamma*n**3)/Gamma**4)**2)*(lambdabare/F**2)</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>$$2(l_K /F)^2 /ƛ_e$$</td>\n",
       "      <td>2*(l_K/F)**2/lambdabare</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                          LaTeXFormula  \\\n",
       "0                                          $$(11/4)^{3/610}R1^2 /R_N$$   \n",
       "1                 $$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$   \n",
       "2                  $$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$   \n",
       "3                        $$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$   \n",
       "4  $$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$   \n",
       "5           $$R_{ƛ_w}=ƛ_e/F^2.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$   \n",
       "6                                                 $$2(l_K /F)^2 /ƛ_e$$   \n",
       "\n",
       "                                                                                                    PlainFormula  \\\n",
       "0                                                                                         (11/4)**(3/610)*R1/R_N   \n",
       "1                                                           lambdabare*2**137*(gamma*n**3)**2/(137**3*Gamma**11)   \n",
       "2                                                      ((1-(137**2 + np.pi**2 + e**2 )/(p*H))*2**128)*lambdabare   \n",
       "3   ((constants.hbar/(constants.m_e*constants.c))*np.exp(2**(6+(1/2)))/6)/(1+np.sqrt(137**2+np.sqrt(136))/(j*n))   \n",
       "4                                   2*lambdabare*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5/np.log(2-((a**2*j)**-1)))**2   \n",
       "5                                                  (((2**70*np.euler_gamma*n**3)/Gamma**4)**2)*(lambdabare/F**2)   \n",
       "6                                                                                        2*(l_K/F)**2/lambdabare   \n",
       "\n",
       "            gly             m  \n",
       "0  1.381198e+10  1.306714e+26  \n",
       "1  1.381198e+10  1.306714e+26  \n",
       "2  1.381198e+10  1.306714e+26  \n",
       "3  1.381198e+10  1.306714e+26  \n",
       "4  1.381198e+10  1.306714e+26  \n",
       "5  1.381198e+10  1.306714e+26  \n",
       "6  1.381198e+10  1.306714e+26  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = pd.read_csv(\"hubble-table3.csv\", dtype = {\"gly\" : \"float64\",\"m\" : \"float64\"}, skiprows = [11,31], sep = \",\")\n",
    "df3.head (11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                gly             m\n",
      "count  7.000000e+00  7.000000e+00\n",
      "mean   1.381198e+10  1.306714e+26\n",
      "std    1.427988e+02  1.350981e+18\n",
      "min    1.381198e+10  1.306714e+26\n",
      "25%    1.381198e+10  1.306714e+26\n",
      "50%    1.381198e+10  1.306714e+26\n",
      "75%    1.381198e+10  1.306714e+26\n",
      "max    1.381198e+10  1.306714e+26\n"
     ]
    }
   ],
   "source": [
    "print(df3.describe())\n",
    "df3.describe();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import host_subplot\n",
    "import mpl_toolkits.axisartist as AA\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "#ax.set_xscale('linear', basex=2)\n",
    "#ax.set_yscale('linear', basey=2)\n",
    "ax.scatter(df2.iloc[:,[3,3]], df2.iloc[:,[2,2]], s=12 )\n",
    "plt.ylabel('Value displayed in $10^{10}$ Gly')\n",
    "plt.xlabel('Distance displayed in $10^{26}$m')\n",
    "plt.title('Hubble distance table', fontsize=18, color=\"black\")\n",
    "ax.grid()\n",
    "#host = host_subplot(111, axes_class=AA.Axes)\n",
    "#par2 = host.twiny()\n",
    "#p3, = par2.plot([0, 10, 14], [0, 1.6, 83096], label=\"Velocity\")\n",
    "#ax.set_xlim(13.795*10**9, 13.905*10**9)\n",
    "#par2.set_xlim(-0.5, 8)\n",
    "#par2.set_ylim(0, 10e99)\n",
    "\n",
    "#host.legend()\n",
    "#plt.colorbar(label='log$_{10}$(population)')\n",
    "#host.axis[\"bottom\"].label.set_color(p1.get_color())\n",
    "#par2.axis[\"bottom\"].label.set_color(p3.get_color())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                gly             m\n",
      "count  2.700000e+01  2.700000e+01\n",
      "mean   1.384332e+10  1.307980e+26\n",
      "std    7.252979e+07  7.685448e+23\n",
      "min    1.376677e+10  1.300000e+26\n",
      "25%    1.380024e+10  1.303897e+26\n",
      "50%    1.381411e+10  1.305876e+26\n",
      "75%    1.387966e+10  1.309222e+26\n",
      "max    1.409009e+10  1.333025e+26\n"
     ]
    }
   ],
   "source": [
    "print(df2.describe())\n",
    "df2.describe();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>7.000000000e+00</td>\n",
       "      <td>7.000000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.381197679e+10</td>\n",
       "      <td>1.306713897e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.427988289e+02</td>\n",
       "      <td>1.350981226e+18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.381197653e+10</td>\n",
       "      <td>1.306713872e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.381197677e+10</td>\n",
       "      <td>1.306713895e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.381197677e+10</td>\n",
       "      <td>1.306713895e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.381197689e+10</td>\n",
       "      <td>1.306713906e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.381197695e+10</td>\n",
       "      <td>1.306713912e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   gly                m\n",
       "count  7.000000000e+00  7.000000000e+00\n",
       "mean   1.381197679e+10  1.306713897e+26\n",
       "std    1.427988289e+02  1.350981226e+18\n",
       "min    1.381197653e+10  1.306713872e+26\n",
       "25%    1.381197677e+10  1.306713895e+26\n",
       "50%    1.381197677e+10  1.306713895e+26\n",
       "75%    1.381197689e+10  1.306713906e+26\n",
       "max    1.381197695e+10  1.306713912e+26"
      ]
     },
     "execution_count": 337,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LaTeXFormula      object\n",
       " PlainFormula     object\n",
       " Gly             float64\n",
       " m               float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LaTeXFormula      object\n",
       " PlainFormula     object\n",
       " gly             float64\n",
       " m               float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 339,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LaTeXFormula      object\n",
       " PlainFormula     object\n",
       " gly             float64\n",
       " m               float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 340,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df4.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df.plot(style=['o','rx'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   gly                m\n",
      "count  7.000000000e+00  7.000000000e+00\n",
      "mean   1.381197679e+10  1.306713897e+26\n",
      "std    1.427988289e+02  1.350981226e+18\n",
      "min    1.381197653e+10  1.306713872e+26\n",
      "25%    1.381197677e+10  1.306713895e+26\n",
      "50%    1.381197677e+10  1.306713895e+26\n",
      "75%    1.381197689e+10  1.306713906e+26\n",
      "max    1.381197695e+10  1.306713912e+26\n"
     ]
    }
   ],
   "source": [
    "print(df3.describe())\n",
    "df3.describe();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LaTeXFormula</th>\n",
       "      <th>gly</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>$$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$$(11/4)^{3/610}R1^2 /R_N$$</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$$ƛ_e 2^{128} / d_e^2 (H /p )^6$$</td>\n",
       "      <td>1.390251e+10</td>\n",
       "      <td>1.315279e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$</td>\n",
       "      <td>1.381198e+10</td>\n",
       "      <td>1.306714e+26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                          LaTeXFormula  \\\n",
       "0                  $$((1-(137^2 + np.pi^2 + e^2 )/(p.H)).2^{128})ƛ_e$$   \n",
       "1                                          $$(11/4)^{3/610}R1^2 /R_N$$   \n",
       "2                 $$ƛ_e 2^{137} (\\gamma n^3 )^2 /(137^3 \\Gamma^{11})$$   \n",
       "3                                    $$ƛ_e 2^{128} / d_e^2 (H /p )^6$$   \n",
       "4                        $$ƛ_e g(6)/ (1 + \\sqrt(137 +\\sqrt(136))/jn)$$   \n",
       "5  $$2ƛ_e(pn/H^2)(g(5)/ln (2-1/a^2.j))^2 and g(5)=exp(2^{(5+1/2)/5})$$   \n",
       "\n",
       "            gly             m  \n",
       "0  1.381198e+10  1.306714e+26  \n",
       "1  1.381198e+10  1.306714e+26  \n",
       "2  1.381198e+10  1.306714e+26  \n",
       "3  1.390251e+10  1.315279e+26  \n",
       "4  1.381198e+10  1.306714e+26  \n",
       "5  1.381198e+10  1.306714e+26  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df.order(-gly, m)\n",
    "#df.sort_values(by='gly', axis=1, ascending=True, inplace=True)\n",
    "#df.sort(['gly', 'm'], ascending=[True, False])\n",
    "#df1 = df.sort(['gly', 'm'], ascending=[True, False])\n",
    "#stacked_df=df.stack()\n",
    "#stacked_df\n",
    "df3.iloc[:,[0,2,3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [],
   "source": [
    "#m, gly = distance['m'], distance['gly']\n",
    "#gly, m = distance['gly'], distance['m']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x490 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "w = 5\n",
    "h = 3.5\n",
    "d = 140\n",
    "plt.figure(figsize=(w, h), dpi=d)\n",
    "table3=df.iloc[:,[3,3]]\n",
    "table4=df.iloc[:,[2,2]]\n",
    "for area in [13.81190, 13.81195, 13.81199]:\n",
    "    plt.scatter([],[], c='k', alpha=0.6, s=area,\n",
    "                label=str(area) + ' Gly')\n",
    "#plt.scatter(df3.iloc[:,[2,2]], df3.iloc[:,[3,3]], label=None,\n",
    "plt.scatter(df.iloc[:,[3,3]], df.iloc[:,[2,2]],label=None,            \n",
    "#            c=np.log10(table4), cmap='viridis',\n",
    "            cmap='viridis',\n",
    "            s=area, linewidth=0, alpha=0.6)\n",
    "#plt.scatter(df3.iloc[:,[2,2]], df3.iloc[:,[3,3]], s=3 )\n",
    "#plt.ylabel('Value displayed in $10^{10}Gly$')\n",
    "#plt.xlabel('Value displayed in $10^{26}m$')\n",
    "plt.title('Hubble Table', fontsize=14, color=\"black\")\n",
    "\n",
    "plt.legend(scatterpoints=1, frameon=False, labelspacing=1, title='Hubble radius')\n",
    "plt.colorbar(label='')\n",
    "plt.clim(1.378,1.392)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "df = df.convert_dtypes(convert_integer=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3071337184211224e+26"
      ]
     },
     "execution_count": 348,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example\n",
    "(4*P**3*l_wi*lambdabare)/R_N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.813717718551707"
      ]
     },
     "execution_count": 349,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((e**e**e)**(np.sqrt(a))*(a-136))**(1/2)*lambdabare/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3814279.1047601975"
      ]
     },
     "execution_count": 350,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e**e**e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$E_3=e^{e^{e}} \\approx E_4^{(1/ap)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To be tested on Julia\n",
    "#e**e**e**e**(1/a*p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install tabulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import pandas as pd\n",
    "#from io import StringIO\n",
    "#from tabulate import tabulate\n",
    "\n",
    "#df = pd.read_csv(\"hubble-table.csv\", dtype = {\"gly_value\" : \"float64\",\"m_value\" : \"float64\"}, skiprows = [22], sep = \",\")\n",
    "#print(tabulate(df, headers='keys', tablefmt='psql'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Print the last 20 constants of the constant table used in the calculation given above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symbol</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>n</td>\n",
       "      <td>1838.68366173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>m_e</td>\n",
       "      <td>constants.m_e</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>m_p</td>\n",
       "      <td>constants.m_p</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>m_n</td>\n",
       "      <td>constants.m_n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>beta</td>\n",
       "      <td>(H-p)**(-1)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>j</td>\n",
       "      <td>(8*np.pi**2)/np.log(2)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>k_B</td>\n",
       "      <td>constants.Boltzmann</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>T_cmb</td>\n",
       "      <td>2.7255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>l_P</td>\n",
       "      <td>((constants.hbar*G_s)/constants.c**3)**0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>ƛ_w</td>\n",
       "      <td>(constants.hbar/(constants.m_e*constants.c))/F**2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>b</td>\n",
       "      <td>2.897771955*10**(-3)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>𝜔</td>\n",
       "      <td>(h*c)/(k_B*b)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>l_ph</td>\n",
       "      <td>(lambdabare*(np.pi*(a**2))**2)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>aprime</td>\n",
       "      <td>137.1106292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>r_H</td>\n",
       "      <td>(lambdabare*aprime)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>G_s</td>\n",
       "      <td>6.67545372e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>Lucas</td>\n",
       "      <td>170141183460469231731687303715884105727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>OM</td>\n",
       "      <td>808017424794512875886459904961710757005754368000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>OB</td>\n",
       "      <td>4154781481226426191177580544000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>OP</td>\n",
       "      <td>2663849798329448283764291471531459318169741293570162121768960000000000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    symbol  \\\n",
       "15       n   \n",
       "16     m_e   \n",
       "17     m_p   \n",
       "18     m_n   \n",
       "19    beta   \n",
       "20       j   \n",
       "21     k_B   \n",
       "22   T_cmb   \n",
       "23     l_P   \n",
       "24     ƛ_w   \n",
       "25       b   \n",
       "26       𝜔   \n",
       "27    l_ph   \n",
       "28  aprime   \n",
       "29     r_H   \n",
       "30     G_s   \n",
       "31   Lucas   \n",
       "32      OM   \n",
       "33      OB   \n",
       "34      OP   \n",
       "\n",
       "                                                                        value  \n",
       "15                                                             1838.68366173   \n",
       "16                                                              constants.m_e  \n",
       "17                                                              constants.m_p  \n",
       "18                                                              constants.m_n  \n",
       "19                                                                (H-p)**(-1)  \n",
       "20                                                     (8*np.pi**2)/np.log(2)  \n",
       "21                                                        constants.Boltzmann  \n",
       "22                                                                     2.7255  \n",
       "23                                 ((constants.hbar*G_s)/constants.c**3)**0.5  \n",
       "24                          (constants.hbar/(constants.m_e*constants.c))/F**2  \n",
       "25                                                       2.897771955*10**(-3)  \n",
       "26                                                              (h*c)/(k_B*b)  \n",
       "27                                             (lambdabare*(np.pi*(a**2))**2)  \n",
       "28                                                                137.1106292  \n",
       "29                                                        (lambdabare*aprime)  \n",
       "30                                                             6.67545372e-11  \n",
       "31                                    170141183460469231731687303715884105727  \n",
       "32                     808017424794512875886459904961710757005754368000000000  \n",
       "33                                         4154781481226426191177580544000000  \n",
       "34  2663849798329448283764291471531459318169741293570162121768960000000000000  "
      ]
     },
     "execution_count": 354,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df1 = pd.read_csv(\"constant-table.csv\", dtype = {\"value\" : \"float64\"}, skiprows = [2], sep = \",\")\n",
    "df4 = pd.read_csv(\"constant-table.csv\", dtype = {\"value\" : \"float64\"}, skiprows = [11], sep = \",\")\n",
    "#df = pd.to_csv('hubble-table.csv', float_format='%.3f')\n",
    "#df1.head ()\n",
    "df4.tail(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "symbol    object\n",
       " value    object\n",
       "dtype: object"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df4.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3**210"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.67545372e-11\n"
     ]
    }
   ],
   "source": [
    "# Using G_s the Newtonian constant of gravitation estimate by Francis M. Sanchez (Jan 2020)\n",
    "G_s=6.67545372*10**-11\n",
    "print(G_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hubble Radius calculus\n",
    "$$R_H=\\frac{2.\\hbar^2}{G.m_e.m_p.m_n}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### https://fr.wikipedia.org/wiki/Analyse_dimensionnelle#Cosmologie:_Rayon_de_Hubble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3056258355517771e+26\n"
     ]
    }
   ],
   "source": [
    "R_H=2*constants.hbar**2/(G_s*constants.m_e*constants.m_p*constants.m_n)\n",
    "print(R_H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Yields 13.802861522337478 Gly (G) and 13.80047597102314 Gyr (G_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.80047597102314"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_H/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nambu Universe Radius calculus in 3 minutes (method 2)\n",
    "$$R_N=\\frac{2.\\hbar^2}{G.(m_N)^3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### https://en.wikipedia.org/wiki/Yoichiro_Nambu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With Nambu mass $$m_N=m_e.a$$ and $$a=1/\\alpha$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137.0359990836958\n"
     ]
    }
   ],
   "source": [
    "a=(1/constants.fine_structure)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2483134965717876e-28\n"
     ]
    }
   ],
   "source": [
    "m_N=constants.m_e*a\n",
    "print(m_N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7128941663434102e+26\n"
     ]
    }
   ],
   "source": [
    "R_N=2*constants.hbar**2/(G_s*((a)*constants.m_e)**3)\n",
    "print(R_N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 18.10530562420883 Gly with method 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.10530562420883"
      ]
     },
     "execution_count": 363,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_N/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$R_N'=ƛ_e(2R/R_N)^{210}$$ and $$R=\\frac{2.\\hbar^2}{G.m_e.m_p.m_H}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$H=p+1-\\frac{1/2}{a'^2}$$ and $a'=H/p=137.11$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.67262192369e-27"
      ]
     },
     "execution_count": 364,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# proton mass 1.672 621 923 69 e-27\n",
    "constants.m_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6735328361530618e-27\n"
     ]
    }
   ],
   "source": [
    "H=constants.m_e*1837.152645\n",
    "print(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067138970179814e+26\n"
     ]
    }
   ],
   "source": [
    "R=2*constants.hbar**2/(G_s*constants.m_e*constants.m_p*H)\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3108749648748815e+26\n"
     ]
    }
   ],
   "source": [
    "R_Nprime=(constants.hbar/(constants.m_e*constants.c))*(2*R/R_N)**210\n",
    "print(R_Nprime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.855959311747384 Gly with method 2'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.855959311747384"
      ]
     },
     "execution_count": 368,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_Nprime/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eddington Universe Radius calculus in 3 minutes (method 3)\n",
    "$$R_{Edd}=\\frac{2.\\hbar^2}{G.m_e.m_p^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### https://en.wikipedia.org/wiki/Eddington_number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15747724136275002577605653961181555468044717914527116709366231425076185631031296\n"
     ]
    }
   ],
   "source": [
    "# Number of Hydrogen Atoms of mass m_H in the visible universe\n",
    "N_Edd=136*2**256\n",
    "print(N_Edd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6735328361530618e-27\n"
     ]
    }
   ],
   "source": [
    "m_H=1837.152645*constants.m_e\n",
    "print(m_H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.666666666666667"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "20/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_Edd=(6.666666666666667*N_Edd*G_s*m_H)/constants.c**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.793532128031092 Gly for R_Edd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.793532128031092"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_Edd/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3049688972818604e+26\n"
     ]
    }
   ],
   "source": [
    "R_Edd2=2*constants.hbar**2/(G_s*constants.m_e*constants.m_p**2)\n",
    "print(R_Edd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.819498813523245 Gly for R_Edd2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.819498813523245"
      ]
     },
     "execution_count": 375,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_Edd2/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Francis M. Sanchez Universe Radius calculus in 3 minutes (method 4)\n",
    "$$R_{Francis.M.Sanchez}=ƛ_e.g(6)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $$g(k)=exp(2^{k+1/2})/k$$ when $$k=6$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and ƛ$_e=\\frac{\\hbar}{m_e.c}$ as the reduced Compton (electron) wavelength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8615926796089057e-13"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reduced Compton Wavelength\n",
    "(constants.hbar/(constants.m_e*constants.c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.307568892158173e+26\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import constants\n",
    "R_FMS=(constants.hbar/(constants.m_e*constants.c))*np.exp(2**(6+(1/2)))/6\n",
    "print(R_FMS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.821014095558315 Gly with method 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.821014095558315"
      ]
     },
     "execution_count": 378,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_FMS/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on Rydberg reduced wavelength (method 5) \n",
    "$$R_{Rydberg}=\\frac{(ƛ_{Ryd}.n^4)^2}{ƛ_p}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137.0359990836958\n"
     ]
    }
   ],
   "source": [
    "a=constants.fine_structure**-1\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18778.865044866678"
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1838.6836617324586\n"
     ]
    }
   ],
   "source": [
    "# n equals mass ratio between Neutron and Electron\n",
    "n=(constants.m_n)/(constants.m_e)\n",
    "print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11429522003521.688"
      ]
     },
     "execution_count": 382,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4503265557724145e-08\n"
     ]
    }
   ],
   "source": [
    "lambdabarRyd=2*(constants.hbar/(constants.m_e*constants.c))*(a**2)\n",
    "print(lambdabarRyd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1030891033555923e-16\n"
     ]
    }
   ],
   "source": [
    "lambdabar_p=(constants.hbar/(constants.m_p*constants.c))\n",
    "print(lambdabar_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3065621143319103e+26\n"
     ]
    }
   ],
   "source": [
    "R_Ryd=((lambdabarRyd*n**4)**2)/lambdabar_p\n",
    "print(R_Ryd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.810372445537942 Gly with method 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.810372445537942"
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Incorrect result , method to be modified\n",
    "R_Ryd/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on pi (method 6) \n",
    "$$R_{\\pi}=ƛ_e.\\pi^{155/2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3058148293550039e+26\n"
     ]
    }
   ],
   "source": [
    "R_pi=(constants.hbar/(constants.m_e*constants.c))*constants.pi**(155/2)\n",
    "print(R_pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.802473637099501 Gly with method 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.802473637099501"
      ]
     },
     "execution_count": 388,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_pi/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on 2 (method 7) \n",
    "$$R_{2}=ƛ_e.2^{128}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3140318971018876e+26\n"
     ]
    }
   ],
   "source": [
    "R_2=(constants.hbar/(constants.m_e*constants.c))*2**128\n",
    "print(R_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One obtains 13.889328111716429 Gly with method 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.889328111716429"
      ]
     },
     "execution_count": 390,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_2/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on Fermi's mass and Kotov period (method 8) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$R_{kotov-fermi}=\\frac{2.(c.t_k)^2/ƛ_e}{F^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fermi's mass given by the relation: $$F=(2\\times 137 \\times \\Gamma)^{3/2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.178097241906\n"
     ]
    }
   ],
   "source": [
    "# Atiyah's Gamma\n",
    "Gamma=a*np.euler_gamma/np.pi\n",
    "print(Gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "573007.364905975\n"
     ]
    }
   ],
   "source": [
    "# F**(2/3)=2*137*Gamma\n",
    "# Fermi's mass given by \n",
    "F=(2*137*Gamma)**1.5\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3067162206121416e+26"
      ]
     },
     "execution_count": 393,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((2*(constants.c*9600.6)**2)/(constants.hbar/(constants.m_e*constants.c)))/F**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067162206121416e+26\n"
     ]
    }
   ],
   "source": [
    "R_kf=(2*(constants.c*9600.6)**2)/(constants.hbar/(constants.m_e*constants.c)) / F**2\n",
    "print(R_kf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://en.wikipedia.org/wiki/Light-year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9460730472580800.0"
      ]
     },
     "execution_count": 395,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://en.wikipedia.org/wiki/Light-year\n",
    "constants.light_year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.812001350205271"
      ]
     },
     "execution_count": 396,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_kf/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on \"a\"  (method 9) \n",
    "$$a=1/\\alpha$$ $\\alpha$ being the fine structure constant  $$R_{a}=ƛ_e.(2.\\pi^2.a^3)^5$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8615926796089057e-13\n"
     ]
    }
   ],
   "source": [
    "lambdabare=(constants.hbar/(constants.m_e*constants.c))\n",
    "print(lambdabare)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2276645699260076e+33"
      ]
     },
     "execution_count": 398,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2*constants.pi**2)*((1/constants.fine_structure)**3)**5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3059760854303987e+26\n"
     ]
    }
   ],
   "source": [
    "R_a=((constants.pi**2*(2*(1/constants.fine_structure)**3))**5)*(constants.hbar/(constants.m_e*constants.c))\n",
    "print(R_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.80417811516134"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_a/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on $\\lambda_{CMB}$ (method 10) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$l_P$ is the Planck length , $j$ is the sternheimer constant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$R_{cmb} = \\frac{(\\lambda_{cmb}/(j+1))^2}{l_P}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "113.91063459990004\n"
     ]
    }
   ],
   "source": [
    "j=(8*np.pi**2)/np.log(2)\n",
    "print(j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.380649e-23 2.72582\n"
     ]
    }
   ],
   "source": [
    "k_B=constants.Boltzmann\n",
    "T_cmb=2.72582\n",
    "print(k_B,T_cmb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0008400718024707187\n"
     ]
    }
   ],
   "source": [
    "lambdabar_cmb=(constants.hbar*constants.c)/(k_B*T_cmb)\n",
    "print(lambdabar_cmb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.005278326806259892\n"
     ]
    }
   ],
   "source": [
    "lambda_cmb=lambdabar_cmb*2*np.pi\n",
    "print(lambda_cmb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6163947113699356e-35\n"
     ]
    }
   ],
   "source": [
    "# Planck's length CODATA2018 (hbar.G/c^3)^1/2 = 1.61639471.10^-35\n",
    "# l_P=1.616255*10**(-35) CODATA2018\n",
    "l_P=((constants.hbar*G_s)/constants.c**3)**0.5\n",
    "print(l_P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3053431213288355e+26\n"
     ]
    }
   ],
   "source": [
    "R_cmb=((lambda_cmb/(j+1))**2)/l_P\n",
    "print(R_cmb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.79748767932874"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_cmb/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on $ƛ_w$, $\\gamma$ and $\\Gamma$ (method 11) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$R_{ƛ_w}=ƛ_w.(\\frac{2^{70}.\\gamma.n^3}{\\Gamma^4})^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ƛ_w=ƛ_e/F^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137.0359990836958\n"
     ]
    }
   ],
   "source": [
    "a=constants.fine_structure**-1\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.178097241906\n"
     ]
    }
   ],
   "source": [
    "# Atiyah's Gamma\n",
    "Gamma=a*np.euler_gamma/np.pi\n",
    "print(Gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 411,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1761048867371158e-24\n"
     ]
    }
   ],
   "source": [
    "ƛ_w=(constants.hbar/(constants.m_e*constants.c))/F**2\n",
    "print(ƛ_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.306713911982143e+26\n"
     ]
    }
   ],
   "source": [
    "R_w=(((2**70*np.euler_gamma*n**3)/Gamma**4)**2)*ƛ_w\n",
    "print(R_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976947966931"
      ]
     },
     "execution_count": 414,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_w/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R =$  ƛe $ g(6)/ (1 + √(137^2+√136)/jn)$ (method 12) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $$g(k)=exp(2^{k+1/2})/k$$ when $$k=6$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and ƛ$_e=\\frac{\\hbar}{m_e.c}$ as the reduced Compton (electron) wavelength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067138950061914e+26\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import constants\n",
    "R_12=((constants.hbar/(constants.m_e*constants.c))*np.exp(2**(6+(1/2)))/6)/(1+np.sqrt(137**2+np.sqrt(136))/(j*n))\n",
    "print(R_12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.675453730277392e-11\n"
     ]
    }
   ],
   "source": [
    "G_12=2*constants.hbar**2/(R_12*m_e*m_p*m_H)\n",
    "print(G_12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0006543109055848"
      ]
     },
     "execution_count": 417,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1+np.sqrt(137**2+np.sqrt(136))/(j*n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976768530982"
      ]
     },
     "execution_count": 418,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_12/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R =  \\frac{2.ƛe(p.n/H^2).g(5)^2}{ln^2 (2 – 1/j.a^2)} $ (method 13) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $$g(k)=exp(2^{k+1/2})/k$$ when $$k=5$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and ƛ$_e=\\frac{\\hbar}{m_e.c}$ as the reduced Compton (electron) wavelength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import constants\n",
    "# R_13=(2*(constants.hbar/(constants.m_e*constants.c))*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5)**2)/(np.log(2-1/(j*a**2)))**2\n",
    "# print(R_13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [],
   "source": [
    "#R_13/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {},
   "outputs": [],
   "source": [
    "#(2*(constants.hbar/(constants.m_e*constants.c))*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.480452689883273"
      ]
     },
     "execution_count": 422,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.log(2-1/(j*a**2)))**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {},
   "outputs": [],
   "source": [
    "#G_13=2*constants.hbar**2/(R_13*m_e*m_p*m_H)\n",
    "#print(G_13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R_N(O_M O_B/n_{ph})^2$ (method 14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8379999999999998e+87\n"
     ]
    }
   ],
   "source": [
    "n_ph=3.838*10**87\n",
    "print(n_ph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7128941663434102e+26"
      ]
     },
     "execution_count": 425,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3105645508705246e+26\n"
     ]
    }
   ],
   "source": [
    "R_14=R_N*(OM*OB/n_ph)**2\n",
    "print(R_14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.852678233132401"
      ]
     },
     "execution_count": 427,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_14/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\lambda_e OM^{7/10}$ (method 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_e=lambdabare*2*np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3186843114021136e+26\n"
     ]
    }
   ],
   "source": [
    "#lambda_e*OM**(7/10)\n",
    "R_15=lambda_e*OM**(7/10)\n",
    "print(R_15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.938504169672099"
      ]
     },
     "execution_count": 430,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_15/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $(2\\pi^{32}Pƛe)^2/R_N$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.389015908333496e+22\n"
     ]
    }
   ],
   "source": [
    "# \n",
    "P=lambdabare/l_P\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3058470789771101e+26\n"
     ]
    }
   ],
   "source": [
    "# Radius in m\n",
    "R_16=((2*np.pi**32)*P*lambdabare)**2/R_N\n",
    "print(R_16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.802814515874134"
      ]
     },
     "execution_count": 433,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_16/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $ƛ_FP^3/p^7$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.389015908333496e+22"
      ]
     },
     "execution_count": 434,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.30587575365127e+26\n"
     ]
    }
   ],
   "source": [
    "R_17=(lambdabar_F*P**3)/p**7\n",
    "print(R_17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.803117607419157"
      ]
     },
     "execution_count": 436,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_17/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $ƛ_FP^2e/8$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3069194966342527e+26\n"
     ]
    }
   ],
   "source": [
    "R_18=(lambdabar_F*(P**2)*np.e)/8\n",
    "print(R_18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.814149979454358"
      ]
     },
     "execution_count": 438,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_18/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $4P^3l_{Wi}ƛe/R_N$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0010632074683544304"
      ]
     },
     "execution_count": 439,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# l_wi\n",
    "((2.897771955*10**-3)/2.7255)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0010630824999999999\n"
     ]
    }
   ],
   "source": [
    "# l_wi=constants.Wien\n",
    "l_wi=1.0630825*10**-3\n",
    "print(l_wi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3071337184211224e+26\n"
     ]
    }
   ],
   "source": [
    "R_19=(4*P**3*l_wi*lambdabare)/R_N\n",
    "print(R_19)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.816414305528234"
      ]
     },
     "execution_count": 442,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_19/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $ƛe.exp((e^{4e-1/a}-ln^2(P^4/a^3))/2)^{1/2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52356.42609346239"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(e**(4*e-1/a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2658205894579623e+83"
      ]
     },
     "execution_count": 444,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P**4/a**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36614.930925762965"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(P**4/a**3)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3066870223677776e+26\n"
     ]
    }
   ],
   "source": [
    "R_20=np.exp(np.sqrt((e**(4*e-1/a)-np.log(P**4/a**3)**2)/2))*lambdabare\n",
    "print(R_20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3066870223677776e+26\n"
     ]
    }
   ],
   "source": [
    "# R_20=(lambdabare*np.exp((e**(4*e-1/a)-np.log(P**4/a**3)**2))/2)**0.5\n",
    "print(R_20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811692724518824"
      ]
     },
     "execution_count": 448,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_20/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $ƛ_F(Pe^e)^2/√(pn)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.739167620022749e-19\n"
     ]
    }
   ],
   "source": [
    "lambdabar_f=lambdabare/F\n",
    "print(lambdabar_f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.939073444929389e+44"
      ]
     },
     "execution_count": 450,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e*(P*e**e)**2/np.sqrt(p*n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067740972914103e+26\n"
     ]
    }
   ],
   "source": [
    "R_21=lambdabar_f*e*(P*e**e)**2/np.sqrt(p*n)\n",
    "print(R_21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.812613107187849"
      ]
     },
     "execution_count": 452,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_21/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1189663868972993e+292"
      ]
     },
     "execution_count": 453,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a**a/np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Measurement Confirmation of the methods given above by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirmation Measurement #1 (WMAP)\n",
    "https://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe\n",
    "\n",
    "$R_{wmap}=13.74$ Â±0.11 Gly (over 9 years)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirmation Measurement #2\n",
    "https://en.wikipedia.org/wiki/Type_Ia_supernova\n",
    "Universe Radius measurement based on supernovae 1a\n",
    "$$R_{SN1a}=13.6(6)Gly$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirmation Measurement #3 (Planck Space Observatory)\n",
    "https://en.wikipedia.org/wiki/Planck_(spacecraft)\n",
    "13.8 billion years (as of 2015) – 13.799±0.021 billion (109) years within the Lambda-CDM concordance model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$R_{Planck}=13.799±0.021 Gly$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirmation Measurement #4 (James Webb Space Telescope)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### https://en.wikipedia.org/wiki/James_Webb_Space_Telescope"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Measurements due to start in 2021"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other estimates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Universe mass calculus given by the relation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$m_P$ is the Planck Mass , $m_e$ the electron mass, $m_p$ the proton mass, $m_n$ the neutron mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\frac{m_P^4}{m_e\\cdot m_p\\cdot\\ m_n} = M_U \\\\\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "\\begin{align}\n",
    "\\frac{m_P^4}{m_e\\cdot m_p\\cdot\\ m_n} = M_U \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.176434e-08\n"
     ]
    }
   ],
   "source": [
    "# Planck's mass\n",
    "m_P=2.176434*10**(-8)\n",
    "print(m_P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2437889614753534e-31\n"
     ]
    }
   ],
   "source": [
    "print(m_P**4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5520124761382513e-84"
      ]
     },
     "execution_count": 457,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constants.m_e*constants.m_p*constants.m_n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Universe Mass $8.792233511611562.10^{52}$ kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.792233511611562e+52\n"
     ]
    }
   ],
   "source": [
    "M_U=(m_P**4)/(constants.m_e*constants.m_p*constants.m_n)\n",
    "print(M_U)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GrandCosmos radius calculus given by the relation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R_{GC} = R_N^2/(2.l_P)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.075773400070832e+86\n"
     ]
    }
   ],
   "source": [
    "R_GC=R_N**2/(2*l_P)\n",
    "print(R_GC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.59310005329329e+61"
      ]
     },
     "execution_count": 460,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_GC/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Volume calculus of R_GC: $V_{GC}=(R_{GC}/r_H)^3(4\\pi/3)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137.11\n"
     ]
    }
   ],
   "source": [
    "#aprime=a/(H/p)\n",
    "aprime=137.11\n",
    "print(aprime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.2946297230117714e-11\n"
     ]
    }
   ],
   "source": [
    "# Hydrogen Atom Radius\n",
    "r_H=(lambdabare*aprime)\n",
    "print(r_H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.109758578455705e+292\n"
     ]
    }
   ],
   "source": [
    "# Volume of R_GC\n",
    "V_GC=((R_GC/r_H)**3)*(4*np.pi/3)\n",
    "print(V_GC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1189663868972993e+292"
      ]
     },
     "execution_count": 464,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a**a/np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{eqnarray}\n",
       "\\ (R_{GC}/r_H)^3(4\\pi/3) \\approx a^a/\\pi \\\\\n",
       "\\end{eqnarray}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 465,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "\\ (R_{GC}/r_H)^3(4\\pi/3) \\approx a^a/\\pi \\\\\n",
    "\\end{eqnarray}\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [],
   "source": [
    "aprime=137.1106292"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1837.15266013165\n"
     ]
    }
   ],
   "source": [
    "H=p+1 -1/(2*(aprime))**2\n",
    "print(H)\n",
    "# p + 1 – 1/2(aH/p)^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "292.8061605778735"
      ]
     },
     "execution_count": 468,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fermi's Energy in GeV\n",
    "np.sqrt(1/(1.1663787*10**-5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "573007.3624962899"
      ]
     },
     "execution_count": 469,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ratio of Fermi/Electron (electron in MeV)\n",
    "(np.sqrt(1/(1.1663787*10**-5))/0.510998950)*1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$A*OP=1.432938112.10^{365}=\\Pi_{Pariah}.a^a=(R_{GC}/l_P)^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 470,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2663849798329448283764291471531459318169741293570162121768960000000000000"
      ]
     },
     "execution_count": 470,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 471,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.656929234280262e+292\n"
     ]
    }
   ],
   "source": [
    "A=a**a\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$((a/√137(4\\pi.F)^2)ƛe^4l{ph}^3(ƛ_{CMB}/l_P)^8)^{1/7}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $l_{ph}=(ƛe(\\pi a^2)^2)^{-3}  $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 472,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8615926796089057e-13"
      ]
     },
     "execution_count": 472,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdabare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 473,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0013440173951173593\n"
     ]
    }
   ],
   "source": [
    "# 0.0013440173951173593\n",
    "l_ph=(lambdabare*(np.pi*(a**2))**2)\n",
    "print(l_ph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 474,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12771295365.93782\n"
     ]
    }
   ],
   "source": [
    "l_ph1=(lambdabare*(np.pi*(a**2)**2))**-3\n",
    "print(l_ph1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.83988529656067e-40\n"
     ]
    }
   ],
   "source": [
    "l_ph2=(lambdabare*(np.pi*(a**2)**2)**-3)\n",
    "print(l_ph2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 𝜉(3)=1.202056903159594\n",
    "apery=1.202056903159594"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.020712279754473314\n"
     ]
    }
   ],
   "source": [
    "# l_ph^-3=16𝜋𝜉(3))/l_{CMB}^3\n",
    "l_ph3=lambda_cmb/(16*np.pi*apery)**(-1/3)\n",
    "print(l_ph3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.8736403508066634e+195"
      ]
     },
     "execution_count": 478,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.863350346618644"
      ]
     },
     "execution_count": 479,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a/np.sqrt(137*4*np.pi**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 480,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.223647026545871e-50"
      ]
     },
     "execution_count": 480,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdabare**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4278098495001795e-09"
      ]
     },
     "execution_count": 481,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l_ph**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07414035459408844"
      ]
     },
     "execution_count": 482,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a/(np.sqrt(137)*(4*np.pi)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3062424977649562e+26"
      ]
     },
     "execution_count": 483,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "metadata": {},
   "outputs": [],
   "source": [
    "#((a/np.sqrt(137)*(4*np.pi*F)**2)*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3062424977649562e+26"
      ]
     },
     "execution_count": 485,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a/(np.sqrt(137)*(4*np.pi*F)**2)*(lambdabare**4)*(l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_22=((a/(np.sqrt(137)*(4*np.pi*F)**2)*lambdabare**4*l_ph**3)*(lambdabar_cmb/l_P)**8)**(1/7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.806994095759556"
      ]
     },
     "execution_count": 487,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_22/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R_{23}=(x.R1^2)/R_N$\n",
    "* With $x=(11/4)^{3/610}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.499978924038854"
      ]
     },
     "execution_count": 488,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((1/np.log(2))**2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 489,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4923645070720404e+26 1.7128941630000002e+26 1.0049874827424896\n"
     ]
    }
   ],
   "source": [
    "R1=(np.exp((((a*H)/p*0.6449340668482264)+1)-gamma))*lambdabare\n",
    "x=(11/4)**(3/610)\n",
    "RN=1.712894163*10**26 \n",
    "print(R1,RN,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0049874827424896"
      ]
     },
     "execution_count": 490,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(11/4)**(3/610)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "metadata": {},
   "outputs": [],
   "source": [
    "# R_1=1.492365475 × 10^26 \n",
    "R_23=(x*R1**2)/RN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 492,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811958871705365"
      ]
     },
     "execution_count": 492,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "R_23/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mono-electron universe radius calculus \n",
    "$ƛe.exp((\\pi^2/6-1).(aH/p) + 1 - \\gamma )$\n",
    "* With $a \\approx a.H/p \\approx a.((1+1/p)) \\approx a.(1/(1/p+1))$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "136.96140756984636"
      ]
     },
     "execution_count": 493,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*(1/(1/p+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 494,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "137.11063122135334"
      ]
     },
     "execution_count": 494,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*((1+1/p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 495,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "137.11063022886907"
      ]
     },
     "execution_count": 495,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a*H)/p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6449340668482264"
      ]
     },
     "execution_count": 496,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(((np.pi**2)/6)-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4923654623153317e+26\n",
      "1.4923645070720404e+26\n"
     ]
    }
   ],
   "source": [
    "# monoelectronic universe radius in m\n",
    "R1prime=(np.exp((((a*H)/p*(((np.pi**2)/6)-1))+1)-gamma))*lambdabare\n",
    "R1=(np.exp(((a*((1+1/p))*(((np.pi**2)/6)-1))+1)-gamma))*lambdabare\n",
    "print(R1)\n",
    "print(R1prime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.774315383368366\n",
      "15.774305286438809\n"
     ]
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "GlyR1=R1/(constants.light_year*10**9)\n",
    "GlyR1prime=R1prime/(constants.light_year*10**9)\n",
    "print(GlyR1)\n",
    "print(GlyR1prime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6580092611335417e+26"
      ]
     },
     "execution_count": 499,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3.8610**38  ƛe.exp((\\pi^2/6-1).(aH/p) + 1 - \\gamma )\n",
    "(np.exp(((a*H)/p)*((np.pi**(2)/6)-1)+1)-gamma)*lambdabare"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$sin^2.\\theta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9124443057840286"
      ]
     },
     "execution_count": 500,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1/np.log(2))**(-1/4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "136.9957461328975"
      ]
     },
     "execution_count": 501,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log((OM*OB)/2)/(np.log(np.log(2)))/-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $2βƛ_e j^{17} (4π)^2 √137$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000132985268892\n"
     ]
    }
   ],
   "source": [
    "beta=(H-p)**(-1)\n",
    "print(beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_j17=(2*beta*lambdabare*j**17*(4*np.pi)**2)*np.sqrt(137)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.811797040850742\n",
      "15.774305286438809\n"
     ]
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "GlyRj17=R_j17/(constants.light_year*10**9)\n",
    "GlyR1prime=R1prime/(constants.light_year*10**9)\n",
    "print(GlyRj17)\n",
    "print(GlyR1prime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $(ƛ_e^2 /l_P )(j/16)^{16} ( e^e )^2 d_e √2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 505,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6163947113699356e-35"
      ]
     },
     "execution_count": 505,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l_P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 506,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rj16=(lambdabare**2/l_P*((j/16)**16)*(e**e)**2)*(d_e)*np.sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 507,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43562081064894.15"
      ]
     },
     "execution_count": 507,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(j/16)**16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 508,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "229.65166408352397"
      ]
     },
     "execution_count": 508,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(e**e)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 509,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.00115965218128"
      ]
     },
     "execution_count": 509,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 510,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.811797040850742\n",
      "13.812025973801315\n"
     ]
    }
   ],
   "source": [
    "# Radius in Gly\n",
    "GlyRj17=R_j17/(constants.light_year*10**9)\n",
    "GlyRj16=Rj16/(constants.light_year*10**9)\n",
    "print(GlyRj17)\n",
    "print(GlyRj16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $ƛ_e(3j^j /2H)^{1/6}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 511,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067153874771553e+26\n"
     ]
    }
   ],
   "source": [
    "# Radius in m\n",
    "Rjj=lambdabare*((3*j**j)/(2*H))**(1/6)\n",
    "print(Rjj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 512,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.811992543961518\n"
     ]
    }
   ],
   "source": [
    "# Distance Radius Length in Gly\n",
    "GlyRjj=Rjj/(constants.light_year*10**9)\n",
    "print(GlyRjj)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Electric Constant \"a\" calculus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$a \\approx (\\frac{\\lambda_{cmb}^5.l_{Wien}^4/l_{ph}^9}{\\pi^3})^2 \\approx (16\\xi(3)^3/\\omega^4)^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 513,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "137.0359990836958"
      ]
     },
     "execution_count": 513,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "139.09491763634472"
      ]
     },
     "execution_count": 514,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(((lambda_cmb**5*l_wi**4)/l_ph**9)/np.pi**3)**2\n",
    "#lambda**5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.002897771955\n"
     ]
    }
   ],
   "source": [
    "#2.897 771 955... e-3 m.K - NIST CODATA 2018\n",
    "b=2.897771955*10**(-3)\n",
    "#lambdawien=(h*c)/(k_B*)\n",
    "# b=lambda/lambdawien\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6226555739400742e+34\n"
     ]
    }
   ],
   "source": [
    "𝜔=(h*c)/(k_B*b)\n",
    "print(𝜔)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 517,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2612052226456562e-268"
      ]
     },
     "execution_count": 517,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(((16*apery)**3)/𝜔**4)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wien Constant\n",
    "$ω = hc/k_B \\lambda_{wien} = 5(1-e^{-ω} )$\n",
    "(official value : $hc/bk_B$ = 4.9651141632 : )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 518,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.002897771955\n"
     ]
    }
   ],
   "source": [
    "#2.897 771 955... e-3 m.K - NIST CODATA 2018\n",
    "b=2.897771955*10**(-3)\n",
    "#lambdawien=(h*c)/(k_B*)\n",
    "# b=lambda/lambdawien\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 519,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6226555739400742e+34\n"
     ]
    }
   ],
   "source": [
    "𝜔=(h*c)/(k_B*b)\n",
    "print(𝜔)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.599857769787976e+31\n"
     ]
    }
   ],
   "source": [
    "𝜆=(h*c)/k_B\n",
    "print(𝜆)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.965114231744277\n"
     ]
    }
   ],
   "source": [
    "𝜔1=5*(1-np.e**-(4.9651142317443))\n",
    "print(𝜔1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following example, one can write the equation with Latex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 522,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{eqnarray}\n",
       "\\ T^2=L^3=M^5=F^7 \\\\\n",
       "\\ R_U = \\frac{2\\cdot \\hbar^2}{G.m_e.m_p.m_n} \\\\\n",
       "\\ M_U = \\frac{{R}{c}^2}{2G} = \\frac{{m_P}^4}{m_em_pm_n} \\\\\n",
       "\\frac{r_H}{ƛ_e} = \\frac{\\sum\\frac{1}{n}}{\\sum\\frac{1}{n^2}}\\\\\n",
       "\\end{eqnarray}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 522,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "\\ T^2=L^3=M^5=F^7 \\\\\n",
    "\\ R_U = \\frac{2\\cdot \\hbar^2}{G.m_e.m_p.m_n} \\\\\n",
    "\\ M_U = \\frac{{R}{c}^2}{2G} = \\frac{{m_P}^4}{m_em_pm_n} \\\\\n",
    "\\frac{r_H}{ƛ_e} = \\frac{\\sum\\frac{1}{n}}{\\sum\\frac{1}{n^2}}\\\\\n",
    "\\end{eqnarray}\"\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":star:\n",
    "\n",
    "# Docs\n",
    "\n",
    "This project aims at providing a repository dedicated to Dr Francis Michel Sanchez's work in holography and cosmology; it is just a mere continuation of what was initiated and published in a set of theoritical physics articles.\n",
    "\n",
    "\n",
    "## Publications\n",
    "* Please, cite this paper (http://vixra.org/pdf/1811.0146v8.pdf) if you employ this package in your research work.\n",
    "* [Vixra Publications](http://vixra.org/author/francis_m_sanchez)\n",
    "* [Rxiv Publications](http://rxiv.org/author/f_m_sanchez)\n",
    "* [Nature: Observations of solar oscillations with periods of 160 minutes](https://www.nature.com/articles/277635a0)\n",
    "* [A coherent resonant cosmology approach and its implications in microphysics and Biophysics Pages 375-407 of Quantum Systems in Physics, Chemistry](https://www.springer.com/fr/book/9783319502540?token=gbgen&wt_mc=GoogleBooks.GoogleBooks.3.EN#)\n",
    "* [From Coherent Cosmic Oscillations to the Steady-State Cyclic Ultrafast](https://rxiv.org/abs/1401.0228)\n",
    "* [Evidence for a Steady-State, Holographic, Tachyonic and Super-Symmetric Cosmology](https://www.researchgate.net/publication/267430152_Evidence_for_a_Steady-State_Holographic_Tachyonic_and_Super-Symmetric_Cosmology)\n",
    "* [academia.edu Correcting Five Historical Faults in Modern Cosmology](https://www.academia.edu/30843365/Correcting_Five_Historical_Faults_in_Modern_Cosmology)\n",
    "\n",
    "## Videos\n",
    "\n",
    "* [L'enigme des grands nombres Part1](https://www.youtube.com/watch?v=ev_eIqLtK8s)\n",
    "* [L'enigme des grands nombres Part2](https://www.youtube.com/watch?v=i4w392nYqns)\n",
    "* [L'enigme des grands nombres Part3](https://www.youtube.com/watch?v=b4WvI0yVXnE)\n",
    "* [Exposés de Francis Sanchez playlist created by J.Bailhache](https://www.youtube.com/playlist?list=PLQXUNrzoAeFbmfHo3jgWzzExlVoBn2JUw)\n",
    "* [Khelif/Torgoz/Sanchez' Debate on LE FORMALISME EN PHYSIQUE ET EN SCIENCE](https://www.youtube.com/watch?v=TEK2hCI2we0)\n",
    "\n",
    "* [La science du 3eme millenaire playlist created by J.Bailhache](https://www.youtube.com/playlist?list=PLQXUNrzoAeFbLOuEsltAUWJWCcAEgeGJE)\n",
    "* [Francis Sanchez Cosmologie 23/03/2017](https://www.youtube.com/watch?v=NmvvIQjxBw8)\n",
    "* [La complexité mathématique face à la simplicité cosmique - Exposé de Francis Sanchez](https://www.youtube.com/watch?v=dyUlUahgHGg)\n",
    "* [La méthode scientifique en question et les constantes fondamentales - Exposé](https://www.youtube.com/watch?v=zUt1hxTdiuA)\n",
    "* [Jean Maruani chez lui et Francis Sanchez autour du nombre 237 29. 12. 17](https://www.youtube.com/watch?v=05g416VWjnw)\n",
    "* [Pr. Michel Grosmann: Holographie quanto-cosmique](https://www.youtube.com/watch?v=M7bJnekDIt0)\n",
    "* [Pr. Renée Veysseyre: La constante d'Atiyah réunifie Physique et Mathématique](https://www.youtube.com/watch?v=mbPpKqakDAU)\n",
    "* [Christian Bizouard, astronome: Omniprésence astrophysique du cycle de Kotov](https://www.youtube.com/watch?v=DGeBC73kKvQ)\n",
    "* [Pr. Francis Sanchez: Historique, Principe Calculatoire, Axe Topologique et Principe Holique](https://www.youtube.com/watch?v=IgKSrfsqFEs)\n",
    "\n",
    "## Books\n",
    "\n",
    "* [Bizouard, Kotov, Sanchez wrote in 20th Natural Philosophy Alliance Proceedings by David de Hilster, published by Lulu.com in 2013]()\n",
    "* [Quantum Systems in Physics, Chemistry, Springer Ed](https://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9783319502557)\n",
    "* [The Worldwide List of Alternative Theories and Critics](https://books.google.com/books?isbn=2902425171)\n",
    "* [The Dirac Electron: From Quantum Chemistry to Holistic Cosmology by J.Maruani](https://onlinelibrary.wiley.com/doi/abs/10.1002/jccs.201500374#)\n",
    "* [solar 22 years cycle](https://link.springer.com/article/10.1007%2Fs10509-016-2985-8)\n",
    "* [Current Issues in Cosmology](https://www.cambridge.org/gb/academic/subjects/physics/cosmology-relativity-and-gravitation/current-issues-cosmology?format=HB&isbn=9780521858984)\n",
    "* ```@inproceedings{Sanchez2015RemarkablePO,\n",
    "  title=Remarkable Properties of the Eddington Number 137 and Electric Parameter 137 . 036 excluding the Multiverse Hypothesis},\n",
    "  author={Francis M. Sanchez and Valery A. Kotov,\n",
    "  year=2015```\n",
    "\n",
    "## Papers\n",
    "\n",
    "* [College de France (2004): Discussions sur les oscillations cosmiques, les nombres sans dimension et les periodicites en microphysique et cosmologie - College de France 27th Feb 2004](https://lempel.pagesperso-orange.fr/occ_cdf.pdf)\n",
    "\n",
    "More to come soon stay tuned.../.:stars:."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{eqnarray}\n",
       "T^2=L^3=M^5=F^7 \\\\\n",
       "\\frac{m_p^4}{m_p\\cdot m_H\\cdot\\ m_e} = M_U \\\\\n",
       "\\frac{\\pi_Pt}{\\pi_Bb} = 6 \\cdot \\frac{\\pi^5}{p_H^9} \\\\\n",
       "\\end{eqnarray}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 523,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write your equation in a dedicated cell with latex\n",
    "\n",
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "T^2=L^3=M^5=F^7 \\\\\n",
    "\\frac{m_p^4}{m_p\\cdot m_H\\cdot\\ m_e} = M_U \\\\\n",
    "\\frac{\\pi_Pt}{\\pi_Bb} = 6 \\cdot \\frac{\\pi^5}{p_H^9} \\\\\n",
    "\\end{eqnarray}\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{eqnarray}\n",
       "S = \\frac{c^3 k A}{4 \\hbar G} \\\\\n",
       "\\end{eqnarray}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 524,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Write Bekenstein-Hawking Entropy \n",
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "S = \\frac{c^3 k A}{4 \\hbar G} \\\\\n",
    "\\end{eqnarray}\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}