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| { | |
| "worksheets": [ | |
| { | |
| "cells": [ | |
| { | |
| "metadata": {}, | |
| "cell_type": "heading", | |
| "source": "How to plot a mixture distribution with sympy.stats?", | |
| "level": 1 | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "( Q asked on stackoverflow [here](http://stackoverflow.com/questions/21187257/plotting-a-mixture-distribution-in-sympy-stats) )\n\n\n( Nbviewer gist [here](http://nbviewer.ipython.org/8472940) )\n" | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "I'd like create a mixture of two Gamma distributions and plot the result, evaluated over a given range. \n\nIt would appear that sympy.stats is capable of this because it is able to compute the expectation of the mixture and sample from it. I'm quite new to sympy, so not sure if there is a preferred way fo evaluating and plotting in this situation than the one I've been using. " | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "%matplotlib inline\nfrom matplotlib import pyplot as plt\nfrom sympy.stats import Gamma, E, density\nimport numpy as np", | |
| "prompt_number": 17, | |
| "outputs": [], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "G1 = Gamma(\"G1\", 5, 2.5)\nG2 = Gamma(\"G2\", 4, 1.5)\nf1 = 0.7; f2 = 1-f1\nG3 = f1*G1 + f2*G2", | |
| "prompt_number": 18, | |
| "outputs": [], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "E(G1)", | |
| "prompt_number": 19, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 19, | |
| "metadata": {}, | |
| "text": "12.5000000000000" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "E(G2)", | |
| "prompt_number": 20, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 20, | |
| "metadata": {}, | |
| "text": "6.00000000000000" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "E(G3)", | |
| "prompt_number": 21, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 21, | |
| "metadata": {}, | |
| "text": "10.5500000000000" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "u = np.linspace(0, 50)", | |
| "prompt_number": 28, | |
| "outputs": [], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "D1 = density(G1); D2 = density(G2); D3 = density(G3)\nv1 = [D1.args[1].subs(D1.args[0][0], i).evalf() for i in u]\nv2 = [D2.args[1].subs(D2.args[0][0], i).evalf() for i in u]\nv3 = [D3.args[1].subs(D3.args[0][0], i).evalf() for i in u]", | |
| "prompt_number": 29, | |
| "outputs": [], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "v1", | |
| "prompt_number": 33, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 33, | |
| "metadata": {}, | |
| "text": "[0,\n 0.000307553984814345,\n 0.00327173625935800,\n 0.0110123566845358,\n 0.0231404692844916,\n 0.0375620390900627,\n 0.0517858478085959,\n 0.0637874433070857,\n 0.0723502322240752,\n 0.0770525410243172,\n 0.0780825294694007,\n 0.0760083947451664,\n 0.0715735816142722,\n 0.0655447817191453,\n 0.0586156791281693,\n 0.0513574723268386,\n 0.0442033802584350,\n 0.0374548603738045,\n 0.0312996487240068,\n 0.0258345435678841,\n 0.0210883848238073,\n 0.0170426631613099,\n 0.0136485951269554,\n 0.0108404052522789,\n 0.00854507909297817,\n 0.00668910635070771,\n 0.00520281524658211,\n 0.00402287941768388,\n 0.00309350647988072,\n 0.00236672524055183,\n 0.00180209555684927,\n 0.00136608121225559,\n 0.00103125627132848,\n 0.000775459989623755,\n 0.000580973401685295,\n 0.000433760204738518,\n 0.000322793274184694,\n 0.000239473971336639,\n 0.000177142493158015,\n 0.000130672361763257,\n 9.61395807594342e-5,\n 7.05561104930834e-5,\n 5.16574914577272e-5,\n 3.77352228782767e-5,\n 2.75055763290812e-5,\n 2.00076943650500e-5,\n 1.45249706109059e-5,\n 1.05247627207562e-5,\n 7.61242062805297e-6,\n 5.49640965983615e-6]" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "plt.plot(u, v1)", | |
| "prompt_number": 30, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 30, | |
| "metadata": {}, | |
| "text": "[<matplotlib.lines.Line2D at 0x7f7fb8118e10>]" | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "metadata": {}, | |
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| |
| "text": "<matplotlib.figure.Figure at 0x5815ad0>" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "plt.plot(u, v2)", | |
| "prompt_number": 31, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 31, | |
| "metadata": {}, | |
| "text": "[<matplotlib.lines.Line2D at 0x7f7fb8145e10>]" | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "metadata": {}, | |
| "png": 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dDvwFM/+Y6/1hM+xrMTNllmEuuppE8yBMWC0EfuQ8/xHNoRd0RcA8zNknsxLe\nD+P+6EHzGRUdgNGYo9uw7YufYQ4A+2Ou0H8NuJrw7Ye4jsCJzvMTgEsx432+2R9hvujqaeAz4CBm\n7OI6zEj7q3j8NKo8GIlpXazABFsd5rTcMO6Ps4DlmH3xHqZnDeHcF3EX0nwgGNb90B/z38QKzOnJ\n8bwM6/4QERERERERERERERERERERERERERERERERETm+/wd/Se02PgIRCQAAAABJRU5ErkJggg==\n", | |
| "text": "<matplotlib.figure.Figure at 0x7f7fb81246d0>" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "plt.plot(u, v3)", | |
| "prompt_number": 32, | |
| "outputs": [ | |
| { | |
| "ename": "TypeError", | |
| "evalue": "can't convert expression to float", | |
| "traceback": [ | |
| "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", | |
| "\u001b[1;32m<ipython-input-32-3f9b7696cd73>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", | |
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| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 235\u001b[0m \u001b[1;31m# to fail, and if it is we still need to check that it evalf'ed to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 236\u001b[0m \u001b[1;31m# a number.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 237\u001b[1;33m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 238\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Number\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/evalf.pyc\u001b[0m in \u001b[0;36mevalf\u001b[1;34m(self, n, subs, maxn, chop, strict, quad, verbose)\u001b[0m\n\u001b[0;32m 1272\u001b[0m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mevalf_table\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1273\u001b[0m \u001b[0m_create_evalf_table\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1274\u001b[1;33m \u001b[0mprec\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdps_to_prec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1275\u001b[0m options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,\n\u001b[0;32m 1276\u001b[0m 'strict': strict, 'verbose': verbose}\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/mpmath/libmp/libmpf.pyc\u001b[0m in \u001b[0;36mdps_to_prec\u001b[1;34m(n)\u001b[0m\n\u001b[0;32m 65\u001b[0m \"\"\"Return the number of bits required to represent n decimals\n\u001b[0;32m 66\u001b[0m accurately.\"\"\"\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m3.3219280948873626\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mrepr_dps\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;32m/usr/local/lib/python2.7/dist-packages/sympy/core/expr.pyc\u001b[0m in \u001b[0;36m__float__\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 240\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_number\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mas_real_imag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 241\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"can't convert complex to float\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 242\u001b[1;33m \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"can't convert expression to float\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 243\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 244\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m__complex__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", | |
| "\u001b[1;31mTypeError\u001b[0m: can't convert expression to float" | |
| ], | |
| "output_type": "pyerr" | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "metadata": {}, | |
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| "text": "<matplotlib.figure.Figure at 0x580c910>" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "Presumably the problem is that the mixture terms still contain free symbols" | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "v1[0].free_symbols", | |
| "prompt_number": 44, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 44, | |
| "metadata": {}, | |
| "text": "set()" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "v3[0].free_symbols", | |
| "prompt_number": 45, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 45, | |
| "metadata": {}, | |
| "text": "{x}" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": { | |
| "run_control": { | |
| "breakpoint": false | |
| } | |
| }, | |
| "cell_type": "code", | |
| "input": "v3[0:3]", | |
| "prompt_number": 36, | |
| "outputs": [ | |
| { | |
| "output_type": "pyout", | |
| "prompt_number": 36, | |
| "metadata": {}, | |
| "text": "[2.05628607127982e-5*exp(0.171428571428571*x)*Heaviside(0.428571428571429*x + oo)*x**4 - 2.05628607127982e-5*exp(0.171428571428571*x)*Heaviside(0.428571428571429*x)*x**4,\n -0.000340218355378489*(-0.428571428571429*x + 1.45772594752187)**4*exp(0.171428571428571*x)*Heaviside(0.428571428571429*x - 1.45772594752187) + 0.000340218355378489*(-0.428571428571429*x + 1.45772594752187)**4*exp(0.171428571428571*x)*Heaviside(0.428571428571429*x + oo),\n -0.000189899930942603*(-0.428571428571429*x + 2.91545189504373)**4*exp(0.171428571428571*x)*Heaviside(0.428571428571429*x - 2.91545189504373) + 0.000189899930942603*(-0.428571428571429*x + 2.91545189504373)**4*exp(0.171428571428571*x)*Heaviside(0.428571428571429*x + oo)]" | |
| } | |
| ], | |
| "language": "python", | |
| "collapsed": false | |
| }, | |
| { | |
| "metadata": {}, | |
| "cell_type": "markdown", | |
| "source": "...as I said, sympy.stats appears to be dealing with this ok somehow in computing the expectation, I assume. So I think I need to apply that machinery here in evaluating and plotting the mixture distribution (?)" | |
| } | |
| ], | |
| "metadata": {} | |
| } | |
| ], | |
| "metadata": { | |
| "gist_id": "8472940", | |
| "name": "", | |
| "css": [ | |
| "" | |
| ] | |
| }, | |
| "nbformat": 3 | |
| } |
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