{"nbformat_minor": 0, "cells": [{"source": "The incomplete gamma isn't stable in the real domain:", "cell_type": "markdown", "metadata": {}}, {"execution_count": 43, "cell_type": "code", "source": "%display latex\nvar('k')\nR10 = RealField(1000)\nf(k, x) = log(gamma(k, x * k))\nf", "outputs": [{"execution_count": 43, "output_type": "execute_result", "data": {"text/plain": "(k, x) |--> log(gamma(k, k*x))", "text/html": ""}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 40, "cell_type": "code", "source": "def plot1(f): return sum(\n plot_semilogy(\n ## float: see http://trac.sagemath.org/ticket/18210\n f(R10(k)),\n (x, R10(0), R10(5/2)),\n color=color,\n legend_label='k=%i' % k,\n figsize=6,\n aspect_ratio=1.0,\n )\n for k, color in zip(\n [1, 2, 4, 8, 17, 26, 35, 48, 51, 100],\n ['blue', 'brown', 'red', 'green', 'black', 'yellow', 'orange', 'cyan', 'purple', 'magenta'],\n )\n)\nplot1(f)", "outputs": [{"output_type": "stream", "name": "stdout", "text": "verbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 12 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 45 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 50 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 52 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 65 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\n"}, {"execution_count": 40, "output_type": "execute_result", "data": {"image/png": 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Z2KetyWJCX3gTnhzbNAoNtAotNAqNvWiVzsddnaMSVQxhRESDXECFIi7eSI6s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\nKCIiIiICwFBEREREBIChiIiIiAgA8H8TmyLmIkYgfQAAAABJRU5ErkJggg==\n", "text/plain": "Graphics object consisting of 18 graphics primitives"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"source": "There's an obvious bite out of that plot.\nThe correct output is smooth and real.", "cell_type": "markdown", "metadata": {}}, {"source": "A 3d plot of the same:", "cell_type": "markdown", "metadata": {}}, {"execution_count": 44, "cell_type": "code", "source": "def plot2(f): return plot3d(f, (x, 0, 5/2), (k, 1, 101))\nplot2(f)", "outputs": [{"execution_count": 44, "output_type": "execute_result", "data": {"text/plain": "Graphics3d Object", "text/html": "\n