Created
March 22, 2014 21:11
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| { | |
| "metadata": { | |
| "name": "" | |
| }, | |
| "nbformat": 3, | |
| "nbformat_minor": 0, | |
| "worksheets": [ | |
| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$$f(f(x)) = -x$$\n", | |
| "\n", | |
| "$$g(x) = f(f(x))$$\n", | |
| "$$g(x) = -x$$\n", | |
| "$$g(x) + x = 0$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def f(x):\n", | |
| " if -1 < x < 1:\n", | |
| " return -1. / (2 * x)\n", | |
| " return 1. / (2 * x)" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 1 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "g = lambda x: f(f(x))" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 2 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def poka(g, x):\n", | |
| " print g(x) == -x\n", | |
| " print g(x) + x == 0\n", | |
| " print g(x), x, \"\\n\"" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 3 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "poka(g, -1.0)\n", | |
| "poka(g, 1.0)\n", | |
| "poka(g, 0.3)\n", | |
| "poka(g, -34.32)\n", | |
| "poka(g, -0.5)" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "True\n", | |
| "True\n", | |
| "1.0 -1.0 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "-1.0 1.0 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "-0.3 0.3 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "34.32 -34.32 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "0.5 -0.5 \n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 4 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "f = lambda x: -1. / (2 * x) if -1 < x < 1 else 1. / (2 * x)" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 5 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "g = lambda x: f(f(x))" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 6 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "poka(g, -1.0)\n", | |
| "poka(g, 1.0)\n", | |
| "poka(g, 0.3)\n", | |
| "poka(g, -34.32)\n", | |
| "poka(g, -0.5)" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "True\n", | |
| "True\n", | |
| "1.0 -1.0 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "-1.0 1.0 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "-0.3 0.3 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "34.32 -34.32 \n", | |
| "\n", | |
| "True\n", | |
| "True\n", | |
| "0.5 -0.5 \n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 7 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [] | |
| } | |
| ], | |
| "metadata": {} | |
| } | |
| ] | |
| } |
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