1-python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some Python tips and tricks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook presents some tips and tricks in Python, including:\n",
    "* interactive Python\n",
    "* coding style (naming, documentation, spacing), see [PEP8](https://www.python.org/dev/peps/pep-0008/) for details\n",
    "* typing\n",
    "* data structures (lists, sets, dictionaries, tuples)\n",
    "* exceptions\n",
    "* functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IPython\n",
    "\n",
    "Interactive Python (as in this notebook) comes with many interesting features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# shell commands\n",
    "!ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# install package\n",
    "!pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# help\n",
    "max?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# timing a line of code\n",
    "%time s = sum(range(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "# timing a cell\n",
    "s = 0\n",
    "for i in range(1000):\n",
    "    s += i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naming should be **explicit** to make code easy to read and understand."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# variables in lower case\n",
    "value = 0\n",
    "max_value = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# constants in upper case\n",
    "MAX_COUNT = 10**5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# classes capitalized\n",
    "class Person:\n",
    "    def __init__(self, name, height, weight):\n",
    "        self.name = name\n",
    "        self.height = height\n",
    "        self.weight = weight\n",
    "    \n",
    "albert = Person('albert', 1.8, 75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# functions in lower case (and preferably starting with a verb)\n",
    "def get_body_mass_index(person):\n",
    "    return person.weight / person.height ** 2\n",
    "\n",
    "get_body_mass_index(albert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# simple variables in singular, lists in plural\n",
    "value = 4\n",
    "values = 10 * [value]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Docstring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_range(values):\n",
    "    \"\"\"Get the range of values (max - min)\n",
    "    Parameters\n",
    "    ----------\n",
    "    values: list\n",
    "        My list of \n",
    "    \n",
    "    \"\"\"\n",
    "    return max(values) - min(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_range(values=[1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_range([2, 5, 9, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_range?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_range??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spacing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = x*y + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = x * (y+2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "{'albert': 3, 'barbara': 4}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# no space for default value\n",
    "def reverse(word=None):\n",
    "    if word:\n",
    "        word = list(word)\n",
    "        word.reverse()\n",
    "        word = ''.join(word)\n",
    "    return word"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "reverse('albert')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T10:03:50.780109Z",
     "start_time": "2019-09-26T10:03:50.771736Z"
    }
   },
   "outputs": [],
   "source": [
    "# implicit typing\n",
    "for x in ['a', 0, 0., True]:\n",
    "    print(x, type(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# operations\n",
    "for x in [1, 1.]:\n",
    "    print(x, type(1 + x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T09:59:29.931984Z",
     "start_time": "2019-09-26T09:59:29.924680Z"
    }
   },
   "outputs": [],
   "source": [
    "# boolean casting\n",
    "for x in [1, 0, -1, 3, 0.1]:\n",
    "    print(x, bool(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-20T13:56:02.394722Z",
     "start_time": "2019-09-20T13:56:02.382420Z"
    }
   },
   "outputs": [],
   "source": [
    "a = [0, 1, 2, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a += 2 * [4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# last element\n",
    "a[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# writing\n",
    "a[5] = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-02T09:13:24.125150Z",
     "start_time": "2019-10-02T09:13:24.120162Z"
    }
   },
   "outputs": [],
   "source": [
    "# slicing (to)\n",
    "print(a)\n",
    "for i in [2, 0, -1, -2]:\n",
    "    print(i, a[:i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slicing (from)\n",
    "print(a)\n",
    "for i in [2, 0, -1, -2]:\n",
    "    print(i, a[i:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slicing (from, to)\n",
    "print(a)\n",
    "for i, j in [(2, 4), (2, None), (-2, None), (None, None)]:\n",
    "    print(i, j, a[i:j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-20T13:45:55.329021Z",
     "start_time": "2019-09-20T13:45:55.315794Z"
    }
   },
   "outputs": [],
   "source": [
    "# assignement\n",
    "b = a\n",
    "a[-1] = 6\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# copy\n",
    "b = a.copy()\n",
    "a[-1] = 7\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# shallow copy\n",
    "a = [0, 1]\n",
    "b = [2, 3]\n",
    "c = [a, b]\n",
    "d = c.copy()\n",
    "c[0].append(2)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# deep copy\n",
    "from copy import deepcopy\n",
    "a = [0, 1]\n",
    "b = [2, 3]\n",
    "c = [a, b]\n",
    "d = deepcopy(c)\n",
    "c[0].append(2)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# comprehension lists\n",
    "a = [i for i in range(10)]\n",
    "b = [2 * i for i in range(10) if i % 3 == 1]\n",
    "c = [i * j if i != j else i + j for i in range(10) for j in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# zip\n",
    "a = [2, 3, 5]\n",
    "b = [4, 5, 7]\n",
    "for x, y in zip(a, b):\n",
    "    z = x**2 + y**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [1, -1, 1]\n",
    "for x, y, z in zip(a, b, c):\n",
    "    t = x * y * z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# boolean lists\n",
    "a = [True, False, False]\n",
    "all(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "any(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "all([1, 2, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "any([1, 2, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T20:27:58.182750Z",
     "start_time": "2019-09-26T20:27:58.173349Z"
    }
   },
   "outputs": [],
   "source": [
    "# operations\n",
    "a = {1, 2, 3}\n",
    "a |= {3, 4}\n",
    "a &= {2, 3, 4}\n",
    "a -= {2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# comparison\n",
    "{2, 3, 4} >= {2, 3, 4}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# comprehension\n",
    "a = {i for i in range(10)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dictionaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T16:41:59.922504Z",
     "start_time": "2019-09-25T16:41:59.911610Z"
    }
   },
   "outputs": [],
   "source": [
    "a = {\n",
    "    \"alice\"  : 1,\n",
    "    \"bob\"    : 2,\n",
    "    \"charly\" : 4,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a.pop('alice')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-25T16:45:03.922819Z",
     "start_time": "2019-09-25T16:45:03.915030Z"
    }
   },
   "outputs": [],
   "source": [
    "for key in a:\n",
    "    print(key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for key, value in a.items():\n",
    "    print(key, value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a['david']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T11:54:34.389872Z",
     "start_time": "2019-09-26T11:54:34.377121Z"
    }
   },
   "outputs": [],
   "source": [
    "# dict with default value\n",
    "from collections import defaultdict\n",
    "\n",
    "a = defaultdict(lambda: 1)\n",
    "print(a[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = defaultdict(lambda: [1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# comprehension\n",
    "a = {i: i % 3 for i in range(10)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T11:38:16.776053Z",
     "start_time": "2019-09-26T11:38:16.772041Z"
    }
   },
   "source": [
    "## Tuples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = (1, 3)\n",
    "b = (1, 5, 9)\n",
    "c = tuple(2 * i for i in range(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read access\n",
    "c[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# no write access!\n",
    "c[1] = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# indexing a dictionary by tuples\n",
    "lengths = {x: len(x) for x in [a, b, c]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lengths[a]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# no indexing by list!\n",
    "d = [1, 2]\n",
    "lengths[d] = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# comprehension\n",
    "a = (i for i in range(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exceptions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "1 / 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T10:56:48.530241Z",
     "start_time": "2019-09-26T10:56:48.513813Z"
    }
   },
   "outputs": [],
   "source": [
    "def safe_divide(a, b):\n",
    "    try:\n",
    "        return a / b\n",
    "    except:\n",
    "        # what to do if b = 0\n",
    "        return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "safe_divide(1, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T09:28:51.802062Z",
     "start_time": "2019-09-26T09:28:51.798972Z"
    }
   },
   "outputs": [],
   "source": [
    "# function of a simple variable\n",
    "def is_odd(x):\n",
    "    x %= 2\n",
    "    return bool(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pass by copy\n",
    "x = 4\n",
    "is_odd(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-09-26T09:29:44.189369Z",
     "start_time": "2019-09-26T09:29:44.174954Z"
    }
   },
   "outputs": [],
   "source": [
    "# function of a dictionary\n",
    "def remove_keys_with_subword(dictionary, subword):\n",
    "    \"\"\"Remove all keys with given subword.\"\"\"\n",
    "    for key in list(dictionary.keys()):\n",
    "    # for key in dictionary not allowed!\n",
    "        if subword in key:\n",
    "            dictionary.pop(key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pass by reference\n",
    "d = {\"albert\": 3, \"barbara\": 4, \"balthazar\": 1}\n",
    "remove_keys_with_subword(d, \"ba\")\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# multiple parameters\n",
    "def get_harmonic_mean(x, y):\n",
    "    try:\n",
    "        return 1 / (1/x+1/y)\n",
    "    except:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pass as a tuple\n",
    "a = (2, 4)\n",
    "get_harmonic_mean(*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# arbitrary number of parameters\n",
    "def get_harmonic_mean(*args):\n",
    "    try:\n",
    "        s = 0\n",
    "        for x in args:\n",
    "            s += 1 / x\n",
    "        return 1 / s\n",
    "    except:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_harmonic_mean(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_harmonic_mean(0, 2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# multiple parameters\n",
    "def get_harmonic_mean(x, y):\n",
    "    try:\n",
    "        return 1 / (1/x+1/y)\n",
    "    except:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pass as a dictionary\n",
    "a = {\"x\": 2, \"y\": 4}\n",
    "get_harmonic_mean(**a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# named parameters\n",
    "def print_parameters(**kwargs):\n",
    "    for key, value in kwargs.items():\n",
    "        print(key, '=', value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print_parameters(name=\"albert\", age=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mixing both\n",
    "def compute(*args, **kwargs):\n",
    "    # get parameters\n",
    "    a = 1\n",
    "    b = 0\n",
    "    if kwargs:\n",
    "        if \"a\" in kwargs:\n",
    "            a = kwargs[\"a\"]\n",
    "        if \"b\" in kwargs:\n",
    "            b = kwargs[\"b\"]\n",
    "    # compute \n",
    "    try:\n",
    "        s = 0\n",
    "        for x in args:\n",
    "            s += 1 / x\n",
    "        return a / s + b\n",
    "    except:\n",
    "        return 0    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "compute(2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "compute(2, 4, b=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "compute(2, 4, a=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "compute(2, 4, a=3, b=2)"
   ]
  }
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