4-operators-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Arithmetic operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "x, y = 5, 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "s = x + y\n",
    "d = x - y\n",
    "p = x * y\n",
    "q = x / y\n",
    "qf = x // y\n",
    "r = x % y\n",
    "e = x ** y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 5\n",
      "y = 3\n",
      "sum        = 8\n",
      "difference = 2\n",
      "product    = 15\n",
      "divide     = 1.6666666666666667\n",
      "quotient   = 1\n",
      "remainder  = 2\n",
      "power      = 125\n"
     ]
    }
   ],
   "source": [
    "print('x =', x)\n",
    "print('y =', y)\n",
    "print('sum        =', s)\n",
    "print('difference =', d)\n",
    "print('product    =', p)\n",
    "print('divide     =', q)\n",
    "print('quotient   =', qf)\n",
    "print('remainder  =', r)\n",
    "print('power      =', e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Relational operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 5\n",
      "y = 3\n"
     ]
    }
   ],
   "source": [
    "print('x =', x)\n",
    "print('y =', y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x > y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x != y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10 == 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 != 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 >= 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Chaining up of comparison operators\n",
    "If there are multiple operations connected with a `logical and`, they can be chained together into one expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "x = 56"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Check if `x` lies within 0 and 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yes\n"
     ]
    }
   ],
   "source": [
    "if x > 0 and x < 100:\n",
    "    print('yes')\n",
    "else:\n",
    "    print('no')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yes\n"
     ]
    }
   ],
   "source": [
    "if 0 < x < 100:\n",
    "    print('yes')\n",
    "else:\n",
    "    print('no')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Shorthand assignment operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13\n"
     ]
    }
   ],
   "source": [
    "x = 10\n",
    "x += 3  # this translates to x = x + 3\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "x = 20\n",
    "x *= 3\n",
    "print(x)\n",
    "x -= 50\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logical operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "x, y = 2, 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x != y and x < y and x+y > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x != y and x > y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == y or x*10 == y or y-x == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not x != y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Quick question\n",
    "What is the value of <font color=\"red\">2 * 5 ** 3</font> ?\n",
    "1. 1000\n",
    "2. 250\n",
    "3. I've never seen ** before! It's a syntax error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "250"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * 5 ** 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## The importance of operator precedence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<table>\n",
    "    <tr>\n",
    "        <th><font size=5>Symbol</font></th>\n",
    "        <th><font size=5>Operator</font></th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>( )</font></td>\n",
    "        <td><font size=4>Parentheses</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>**</font></td>\n",
    "        <td><font size=4>Exponent</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>+x, -x, ~x</font></td>\n",
    "        <td><font size=4>Unary plus, Unary minus, Bitwise complement</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>*, /, //, %</font></td>\n",
    "        <td><font size=4>Multiplication, Division, Floor division, Modulus</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>+, -</font></td>\n",
    "        <td><font size=4>Addition, Subtraction</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>&</font></td>\n",
    "        <td><font size=4>Bitwise AND</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>^</font></td>\n",
    "        <td><font size=4>Bitwise XOR</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>|</font></td>\n",
    "        <td><font size=4>Bitwise OR</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>==, !=, >, >=, <, <=, is, is not, in, not in</font></td>\n",
    "        <td><font size=4>Comparisions, Identity, Membership operators</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>not</font></td>\n",
    "        <td><font size=4>Logical NOT</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>and</font></td>\n",
    "        <td><font size=4>Logical AND</font></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><font size=4>or</font></td>\n",
    "        <td><font size=4>Logical OR</font></td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Quick question\n",
    "What is the value of <font color=\"red\">2 ** 3 ** 4</font> ?\n",
    "1. 2417851639229258349412352\n",
    "2. 4096\n",
    "3. This should be illegal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2417851639229258349412352"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 ** 3 ** 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4096"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2 ** 3) ** 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The importance of operator associativity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can see that there are multiple operators in one group in the precedence table.  \n",
    "\n",
    "Associativity helps in determining the order of operations when two or more operators have the same precedence.  \n",
    "\n",
    "The associativity of the ** operator is from right to left."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Quick question\n",
    "What is the value of <font color=\"red\">5 * 2 // 3</font> ?\n",
    "1. 0\n",
    "2. 3\n",
    "3. I'd rather not answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 * 2 // 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 * (2 // 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The other operators have left to right associativity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Problems with floating point math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### What is 0.1 + 0.2 ?\n",
    "#### We all know that 0.1 + 0.2 is equal to 0.3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    ".1 + .2 == .3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30000000000000004"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    ".1 + .2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### This website gives a brief description of why this happens\n",
    "[0.30000000000000004.com](0.30000000000000004.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### How can we fix this problem?\n",
    "\n",
    "The `math` module in python provides a function called `isclose`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on built-in function isclose in module math:\n",
      "\n",
      "isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)\n",
      "    Determine whether two floating point numbers are close in value.\n",
      "    \n",
      "      rel_tol\n",
      "        maximum difference for being considered \"close\", relative to the\n",
      "        magnitude of the input values\n",
      "      abs_tol\n",
      "        maximum difference for being considered \"close\", regardless of the\n",
      "        magnitude of the input values\n",
      "    \n",
      "    Return True if a is close in value to b, and False otherwise.\n",
      "    \n",
      "    For the values to be considered close, the difference between them\n",
      "    must be smaller than at least one of the tolerances.\n",
      "    \n",
      "    -inf, inf and NaN behave similarly to the IEEE 754 Standard.  That\n",
      "    is, NaN is not close to anything, even itself.  inf and -inf are\n",
      "    only close to themselves.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from math import isclose\n",
    "\n",
    "help(isclose)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isclose(.1 + .2, .3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![questions.jpg](img/questions.jpg)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "livereveal": {
   "scroll": true,
   "theme": "sky"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}