SciPy_SymPy/tutorial_exercises/Gotchas.ipynb

{
 "metadata": {
  "name": "Gotchas"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Gotchas"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Boilerplate to make the doctester work.  Run this cell first."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "import os\n",
      "sys.path.insert(1, os.path.join(os.path.pardir, \"ipython_doctester\"))\n",
      "from sympy import *\n",
      "from ipython_doctester import test\n",
      "# Work around a bug in IPython. This will disable the ability to paste things with >>>\n",
      "def notransform(line): return line\n",
      "from IPython.core import inputsplitter\n",
      "inputsplitter.transform_classic_prompt = notransform"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For each exercise, fill in the function according to its docstring. Execute the cell to see if you did it right. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Symbols"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What will be the output of the following code?\n",
      "\n",
      "    x = 3\n",
      "    y = symbols('y')\n",
      "    a = x + y\n",
      "    y = 5\n",
      "    print a\n",
      "\n",
      "Replace `???` in the below code with what you think the value of `a` will be.  Remember to define any Symbols you need!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@test\n",
      "def symbols_exercise():\n",
      "    \"\"\"\n",
      "    (This tests that your output is correct)\n",
      "\n",
      "    >>> def testfunc():\n",
      "    ...     x = 3\n",
      "    ...     y = symbols('y')\n",
      "    ...     a = x + y\n",
      "    ...     y = 5\n",
      "    ...     return a\n",
      "    >>> symbols_exercise() == testfunc()\n",
      "    True\n",
      "    \"\"\"\n",
      "    return ??? # Replace ??? with what you think the value of a is"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Equality"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a function that takes two expressions as input, and returns a tuple of two booleans. The first if they are equal symbolically, and the second if they are equal mathematically."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@test\n",
      "def equality_exercise(a, b):\n",
      "    \"\"\"\n",
      "    Determine if a = b symbolically and mathematically.\n",
      "\n",
      "    Returns a tuple of two booleans. The first is True if a = b symbolically,\n",
      "    the second is True if a = b mathematically.  Note the second may be False\n",
      "    but the two still equal if SymPy is not powerful enough.\n",
      "\n",
      "    Examples\n",
      "    ========\n",
      "\n",
      "    >>> x = symbols('x')\n",
      "    >>> equality_exercise(x, 2)\n",
      "    (False, False)\n",
      "    >>> equality_exercise((x + 1)**2, x**2 + 2*x + 1)\n",
      "    (False, True)\n",
      "    >>> equality_exercise(2*x, 2*x)\n",
      "    (True, True)\n",
      "    \"\"\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "`^` and `/`"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Correct the following functions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@test\n",
      "def operator_exercise1():\n",
      "    \"\"\"\n",
      "    >>> operator_exercise1()\n",
      "    x**2 + 2*x + 1/2\n",
      "    \"\"\"\n",
      "    x = symbols('x')\n",
      "    return x^2 + 2*x + 1/2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@test\n",
      "def operator_exercise2():\n",
      "    \"\"\"\n",
      "    >>> operator_exercise2()\n",
      "    (x**2/2 + 2*x + 3/4)**(3/2)\n",
      "    \"\"\"\n",
      "    x = symbols('x')\n",
      "    return (1/2*x^2 + 2*x + 3/4)^(3/2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}