A comparison of factorial and exponent

FactAndExp

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   "source": [
    "import math"
   ]
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       "263130836933693530167218012160000000L"
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   "source": [
    "math.factorial(32)"
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   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
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     "text": [
      "/home/stefan/anaconda2/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: invalid value encountered in remainder\n",
      "  from ipykernel import kernelapp as app\n"
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/QzVvXjLXV829vH339TunJd3m2xEl9wi98Ybf8Wf06KQjSVbrZQjiUlpHJuvM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\nIjmk5C4ikkNK7iIiOaTkLiKSQ/8HPJo6fVtfF8wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f225e223850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.misc\n",
    "plt.plot(scipy.misc.factorial(x) % x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f225e0700d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 5, 40)\n",
    "plt.plot(scipy.misc.factorial(x) % np.exp2(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 1, 2.0, 1.0)\n",
      "(2, 2, 4.0, 2.0)\n",
      "(3, 6, 8.0, 6.0)\n",
      "(4, 24, 16.0, 8.0)\n",
      "(5, 120, 32.0, 24.0)\n",
      "(6, 720, 64.0, 16.0)\n",
      "(7, 5040, 128.0, 48.0)\n",
      "(8, 40320, 256.0, 128.0)\n",
      "(9, 362880, 512.0, 384.0)\n",
      "(10, 3628800, 1024.0, 768.0)\n",
      "(11, 39916800, 2048.0, 1280.0)\n",
      "(12, 479001600, 4096.0, 3072.0)\n",
      "(13, 6227020800, 8192.0, 3072.0)\n",
      "(14, 87178291200, 16384.0, 10240.0)\n",
      "(15, 1307674368000, 32768.0, 22528.0)\n",
      "(16, 20922789888000, 65536.0, 32768.0)\n",
      "(17, 355687428096000, 131072.0, 98304.0)\n",
      "(18, 6402373705728000, 262144.0, 196608.0)\n",
      "(19, 121645100408832000, 524288.0, 65536.0)\n",
      "(20, 2432902008176640000, 1048576.0, 262144.0)\n",
      "(21, 51090942171709440000L, 2097152.0, 262144.0)\n",
      "(22, 1124000727777607680000L, 4194304.0, 1572864.0)\n",
      "(23, 25852016738884976640000L, 8388608.0, 0.0)\n",
      "(24, 620448401733239439360000L, 16777216.0, 0.0)\n",
      "(25, 15511210043330985984000000L, 33554432.0, 0.0)\n",
      "(26, 403291461126605635584000000L, 67108864.0, 0.0)\n",
      "(27, 10888869450418352160768000000L, 134217728.0, 0.0)\n",
      "(28, 304888344611713860501504000000L, 268435456.0, 0.0)\n",
      "(29, 8841761993739701954543616000000L, 536870912.0, 0.0)\n",
      "(30, 265252859812191058636308480000000L, 1073741824.0, 0.0)\n",
      "(31, 8222838654177922817725562880000000L, 2147483648.0, 0.0)\n",
      "(32, 263130836933693530167218012160000000L, 4294967296.0, 0.0)\n",
      "(33, 8683317618811886495518194401280000000L, 8589934592.0, 0.0)\n",
      "(34, 295232799039604140847618609643520000000L, 17179869184.0, 0.0)\n",
      "(35, 10333147966386144929666651337523200000000L, 34359738368.0, 0.0)\n",
      "(36, 371993326789901217467999448150835200000000L, 68719476736.0, 0.0)\n",
      "(37, 13763753091226345046315979581580902400000000L, 137438953472.0, 0.0)\n",
      "(38, 523022617466601111760007224100074291200000000L, 274877906944.0, 0.0)\n",
      "(39, 20397882081197443358640281739902897356800000000L, 549755813888.0, 0.0)\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "for x in range(1, 40):\n",
    "    print(x,math.factorial(x),math.pow(2,x), math.factorial(x) % math.pow(2,x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(' 1', '                 1.0', '                 2.0', '                 1.0')\n",
      "(' 2', '                 2.0', '                 4.0', '                 2.0')\n",
      "(' 3', '                 6.0', '                 8.0', '                 6.0')\n",
      "(' 4', '                24.0', '                16.0', '                 8.0')\n",
      "(' 5', '               120.0', '                32.0', '                24.0')\n",
      "(' 6', '               720.0', '                64.0', '                16.0')\n",
      "(' 7', '              5040.0', '               128.0', '                48.0')\n",
      "(' 8', '             40320.0', '               256.0', '               128.0')\n",
      "(' 9', '            362880.0', '               512.0', '               384.0')\n",
      "('10', '           3628800.0', '              1024.0', '               768.0')\n",
      "('11', '          39916800.0', '              2048.0', '              1280.0')\n",
      "('12', '         479001600.0', '              4096.0', '              3072.0')\n",
      "('13', '        6227020800.0', '              8192.0', '              3072.0')\n",
      "('14', '       87178291200.0', '             16384.0', '             10240.0')\n",
      "('15', '     1.307674368e+12', '             32768.0', '             22528.0')\n",
      "('16', '    2.0922789888e+13', '             65536.0', '             32768.0')\n",
      "('17', '   3.55687428096e+14', '            131072.0', '             98304.0')\n",
      "('18', '   6.40237370573e+15', '            262144.0', '            196608.0')\n",
      "('19', '   1.21645100409e+17', '            524288.0', '             65536.0')\n",
      "('20', '   2.43290200818e+18', '           1048576.0', '            262144.0')\n",
      "('21', '   5.10909421717e+19', '           2097152.0', '            262144.0')\n",
      "('22', '   1.12400072778e+21', '           4194304.0', '           1572864.0')\n",
      "('23', '   2.58520167389e+22', '           8388608.0', '                 0.0')\n",
      "('24', '   6.20448401733e+23', '          16777216.0', '                 0.0')\n",
      "('25', '   1.55112100433e+25', '          33554432.0', '                 0.0')\n",
      "('26', '   4.03291461127e+26', '          67108864.0', '                 0.0')\n",
      "('27', '   1.08888694504e+28', '         134217728.0', '                 0.0')\n",
      "('28', '   3.04888344612e+29', '         268435456.0', '                 0.0')\n",
      "('29', '   8.84176199374e+30', '         536870912.0', '                 0.0')\n"
     ]
    }
   ],
   "source": [
    "from decimal import Decimal\n",
    "for x in range(1, 30):\n",
    "    \n",
    "    print (repr(x).rjust(2),str(scipy.misc.factorial(x)).rjust(20),repr(np.exp2(x)).rjust(20),str(scipy.misc.factorial(x) % np.exp2(x)).rjust(20) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "}\n",
       " \n",
       "div.text_cell_render h1 { /* Main titles bigger, centered */\n",
       "font-size: 2.2em;\n",
       "line-height:1.4em;\n",
       "text-align:center;\n",
       "}\n",
       " \n",
       "div.text_cell_render h2 { /*  Parts names nearer from text */\n",
       "margin-bottom: -0.4em;\n",
       "}\n",
       " \n",
       " \n",
       "div.text_cell_render { /* Customize text cells */\n",
       "font-family: 'Times New Roman';\n",
       "font-size:1.5em;\n",
       "line-height:1.4em;\n",
       "padding-left:3em;\n",
       "padding-right:3em;\n",
       "}\n",
       " \n",
       "#notebook li { /* More space between bullet points */\n",
       "margin-top:0.8em;\n",
       "}\n",
       "\n",
       "#notebook_panel {\n",
       "background : url('motivational_penguin.gif') no-repeat left center ;\n",
       "}\n",
       "div.cell.code_cell {  /* Areat containing both code and output */\n",
       "background-color:#F1F0FF; /* light blue */\n",
       "border-radius: 10px; /* rounded borders = friendlier */\n",
       "padding: 1em;\n",
       "}\n",
       "\n",
       "div.input_area {\n",
       "border-color: rgba(0,0,0,0.10);\n",
       "background: rbga(0,0,0,0.5);\n",
       "}\n",
       "\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "HTML(\"\"\"\n",
    "<style>\n",
    "\n",
    "\n",
    ".container { width:100% !important; }\n",
    "\n",
    "div#notebook { /* centers the page content */\n",
    "padding-left:2%;\n",
    "padding-right:2%;\n",
    "}\n",
    " \n",
    "div.cell { /* Tunes the space between cells */\n",
    "margin-top:1em;\n",
    "margin-bottom:1em;\n",
    "}\n",
    " \n",
    "div.text_cell_render h1 { /* Main titles bigger, centered */\n",
    "font-size: 2.2em;\n",
    "line-height:1.4em;\n",
    "text-align:center;\n",
    "}\n",
    " \n",
    "div.text_cell_render h2 { /*  Parts names nearer from text */\n",
    "margin-bottom: -0.4em;\n",
    "}\n",
    " \n",
    " \n",
    "div.text_cell_render { /* Customize text cells */\n",
    "font-family: 'Times New Roman';\n",
    "font-size:1.5em;\n",
    "line-height:1.4em;\n",
    "padding-left:3em;\n",
    "padding-right:3em;\n",
    "}\n",
    " \n",
    "#notebook li { /* More space between bullet points */\n",
    "margin-top:0.8em;\n",
    "}\n",
    "\n",
    "#notebook_panel {\n",
    "background : url('motivational_penguin.gif') no-repeat left center ;\n",
    "}\n",
    "div.cell.code_cell {  /* Areat containing both code and output */\n",
    "background-color:#F1F0FF; /* light blue */\n",
    "border-radius: 10px; /* rounded borders = friendlier */\n",
    "padding: 1em;\n",
    "}\n",
    "\n",
    "div.input_area {\n",
    "border-color: rgba(0,0,0,0.10);\n",
    "background: rbga(0,0,0,0.5);\n",
    "}\n",
    "\n",
    "</style>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 1.000000000000000000000000000000000000000, 1.000000000000000000000000000000000000000, 0)\n",
      "(1, 1.000000000000000000000000000000000000000, 2.718281828459045235360287471352662497757, 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000)\n",
      "(2, 2.000000000000000000000000000000000000000, 7.389056098930650227230427460575007813180, 2.0000000000000000000000000000000000000000000000000000000000000000000000000000000)\n",
      "(3, 6.000000000000000000000000000000000000000, 20.08553692318766774092852965458171789699, 6.0000000000000000000000000000000000000000000000000000000000000000000000000000000)\n",
      "(4, 24.00000000000000000000000000000000000000, 54.59815003314423907811026120286087840279, 24.000000000000000000000000000000000000000000000000000000000000000000000000000000)\n",
      "(5, 120.0000000000000000000000000000000000000, 148.4131591025766034211155800405522796235, 120.00000000000000000000000000000000000000000000000000000000000000000000000000000)\n",
      "(6, 720.0000000000000000000000000000000000000, 403.4287934927351226083871805433882796059, 316.57120650726487739161281945661172039410010264287079738603281167484881936600650)\n",
      "(7, 5040.000000000000000000000000000000000000, 1096.633158428458599263720238288121432442, 653.46736628616560294511904684751427023112346066554742486904303689551292267506748)\n",
      "(8, 40320.00000000000000000000000000000000000, 2980.957987041728274743592099452888673756, 1567.5461684575324283333027071124472411724167912731358712834741049595005727462221)\n",
      "(9, 362880.0000000000000000000000000000000000, 8103.083927575384007709996689432759965011, 6344.3071866831036607601456649585615394950521354090076499930017041560093096125075)\n",
      "(10, 3628800.000000000000000000000000000000000, 22026.46579480671651695790064528424436635, 16459.609651698491218904294173383923918023930556687903825390077743066737754390018)\n",
      "(11, 39916800.00000000000000000000000000000000, 59874.14171519781845532648579225778161426, 40621.617678252908752560462356317444902120922636514877254171422965007536804459785)\n",
      "(12, 479001600.0000000000000000000000000000000, 162754.7914190039208080052048984867831702, 14248.853871461062040681983753397130074075779124772584613961728109703430994776920)\n",
      "(13, 6227020800.000000000000000000000000000000, 442413.3920089205033261027759490882817844, 52307.474443915685103428516582433884692367197199753319042420270517287614632162153)\n",
      "(14, 87178291200.00000000000000000000000000000, 1202604.284164776777749236770767859449412, 304036.61116660418007725026710065263943798412297249744924870888271350298140644352)\n",
      "(15, 1307674368000.000000000000000000000000000, 3269017.372472110639301855046091721315506, 2038663.7063020664719444623896393713944677011099166640422994477266264737933692294)\n",
      "(16, 20922789888000.00000000000000000000000000, 8886110.520507872636763023740781450350803, 7248048.7089909822592141667768579678068461672728764254500920806389830106509423521)\n",
      "(17, 355687428096000.0000000000000000000000000, 24154952.75357529821477543518038582387987, 24075801.136441754815190680991928690542117698336346541130043674218568681647731871)\n",
      "(18, 6402373705728000.000000000000000000000000, 65659969.13733051113878650325906003356922, 56225824.635938471725699005806472146626457024095100264281674990489611574685933022)\n",
      "(19, 121645100408832000.0000000000000000000000, 178482300.9631872608449100337887227038836, 38278588.053993155642353629011523849161310615496360934593030295191791167276911731)\n",
      "(20, 2432902008176640000.000000000000000000000, 485165195.4097902779691068305415405586846, 92823441.235615631588603742876528595450107776279663762216601947516023056006954586)\n",
      "(21, 51090942171709440000.00000000000000000000, 1318815734.483214697209998883745302785091, 783325453.98928175979442051523900316132947991220632318456748890692140867149887925)\n",
      "(22, 1124000727777607680000.000000000000000000, 3584912846.131591561681159945978420689223, 2540560235.2432522840995588208719632146301112856049122148289800741730744150266130)\n",
      "(23, 25852016738884976640000.00000000000000000, 9744803446.248902600034632684822975277649, 7802402951.1106634724597606588004207085451883576147018248075723246961776135438794)\n",
      "(24, 620448401733239439360000.0000000000000000, 26489122129.84347229413916215281188234087, 1969330232.8714570298488704934807519289893108973693829734307933580303013412870301)\n",
      "(25, 15511210043330985984000000.00000000000000, 72004899337.38587252416135146612615791522, 62417263972.987210240748432650843034053406354090729481763727582715674543973385338)\n",
      "(26, 403291461126605635584000000.0000000000000, 195729609428.8387642697763978760953427920, 135141266248.59609120205882749685014675332071005756734909026733952741884555127853)\n",
      "(27, 10888869450418352160768000000.00000000000, 532048240601.7986166837473043411774416593, 404848021775.49236364461131504166473711923532505617879304430608636687251511624345)\n",
      "(28, 304888344611713860501504000000.0000000000, 1446257064291.475173677047422996928856902, 727759885867.03279017663177115593660825977298362386003095892149582743310696931256)\n",
      "(29, 8841761993739701954543616000000.000000000, 3931334297144.042074388620580843527685797, 1840487655805.9276637276194057232984309619200237104094497095033320323813505791152)\n",
      "(30, 265252859812191058636308480000000.0000000, 10686474581524.46214699046865074140165002, Mod(265252859812191058636308480000000, exp(30)))\n",
      "(31, 8222838654177922817725562880000000.000000, 29048849665247.42523108568211167982566676, Mod(8222838654177922817725562880000000, exp(31)))\n",
      "(32, 263130836933693530167218012160000000.0000, 78962960182680.69516097802263510822421996, Mod(263130836933693530167218012160000000, exp(32)))\n",
      "(33, 8683317618811886495518194401280000000.000, 214643579785916.0646242977615312608803692, Mod(8683317618811886495518194401280000000, exp(33)))\n",
      "(34, 295232799039604140847618609643520000000.0, 583461742527454.8814029027346103910190037, Mod(295232799039604140847618609643520000000, exp(34)))\n",
      "(35, 1.033314796638614492966665133752320000000e+40, 1586013452313430.728129644625774660125176, Mod(10333147966386144929666651337523200000000, exp(35)))\n",
      "(36, 3.719933267899012174679994481508352000000e+41, 4311231547115195.227113422292856925390789, Mod(371993326789901217467999448150835200000000, exp(36)))\n",
      "(37, 1.376375309122634504631597958158090240000e+43, 11719142372802611.30877293979119019452168, Mod(13763753091226345046315979581580902400000000, exp(37)))\n",
      "(38, 5.230226174666011117600072241000742912000e+44, 31855931757113756.22032867170129864599954, Mod(523022617466601111760007224100074291200000000, exp(38)))\n",
      "(39, 2.039788208119744335864028173990289735680e+46, 86593400423993746.95360693271926493424970, Mod(20397882081197443358640281739902897356800000000, exp(39)))\n",
      "(40, 8.159152832478977343456112695961158942720e+47, 235385266837019985.4078999107490348045089, Mod(815915283247897734345611269596115894272000000000, exp(40)))\n",
      "(41, 3.345252661316380710817006205344075166515e+49, 639843493530054949.2226634035155708188793, Mod(33452526613163807108170062053440751665152000000000, exp(41)))\n",
      "(42, 1.405006117752879898543142606244511569936e+51, 1739274941520501047.394681303611235226148, Mod(1405006117752879898543142606244511569936384000000000, exp(42)))\n",
      "(43, 6.041526306337383563735513206851399750727e+52, 4727839468229346561.474457562744280370820, Mod(60415263063373835637355132068513997507264512000000000, exp(43)))\n"
     ]
    }
   ],
   "source": [
    "import sympy as sy\n",
    "sy.init_printing() # enable pretty printing in IPython\n",
    "X= sy.symbols('X')\n",
    "\n",
    "\n",
    "expr = (sy.factorial(X))\n",
    "expr2 =(sy.exp(X))\n",
    "expr3 = (sy.factorial(X)) % (sy.exp(X))\n",
    "# The values:\n",
    "for k in range(44):\n",
    "    vX = k\n",
    "# substitute values into variables:\n",
    "    expr10 = expr.subs({X:vX})\n",
    "    expr20 = expr2.subs({X:vX})\n",
    "    expr30 = expr3.subs({X:vX})\n",
    "# evaluate to 150 digits with internal precision up to 100 digits:\n",
    "    print(vX,expr10.evalf(n=40, maxn=100),expr20.evalf(n=40, maxn=100), expr30.evalf(n=80, maxn=100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}