{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2d0f01b9-41fd-4655-8491-e6cf81fc4a8a",
   "metadata": {},
   "source": [
    "(section:julia-language-notes)=\n",
    "# Notes on the Julia Language\n",
    "\n",
    "**Last revised on August 25, 2025**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "012dccb6-3dc6-47e0-a395-792913e7d1b3",
   "metadata": {},
   "source": [
    "These notes are not intended to teach the Julia language from scratch, or comprehensively;\n",
    "instead they are addressed to readers who already know somewhat similar tools like Matlab or \"Python Scientific\" (Python + Numpy + Matplotlib),\n",
    "and they focus on the parts of Julia actually used in this book.\n",
    "\n",
    "A very short version of the story is that what works in Matlab often also work in Julia;\n",
    "one design principle is offering familiarity for Matlab users by having the Matlab syntax work (at least as one option)\n",
    "except where that would get in the way of moderization.\n",
    "Though some syntax comes from Python and some from C.\n",
    "And one bit is from Perl.\n",
    "\n",
    "An intermediate version is this summary of\n",
    "[Julia's noteworthy differences from other languages](https://docs.julialang.org/en/v1/manual/noteworthy-differences/),\n",
    "with comparisons to Matlab and Python (and also to R and C/C++).\n",
    "\n",
    "For the full story, see resources like [the official Julia documentation](https://docs.julialang.org/en/v1/).\n",
    "(Don't read it all at once: the PDF version is over 1500 pages.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c2474a3-f0b3-4750-9274-91f4d7c59390",
   "metadata": {},
   "source": [
    "(charactersstrings)=\n",
    "## Characters and strings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01da9763-2872-4ef3-a08e-b442557188ea",
   "metadata": {},
   "source": [
    "The character set is Unicode via UTF-8, so Greek letters and much more are usable.\n",
    "\n",
    "I generally advise against going beyond plain old ASCII characters, but see the functions [plu](plu-factorization) and [forward_substitution](forward_substitution)\n",
    "in the collection {ref}`module:NumericalMethods`\n",
    "where Unicode is used to illustrate the possibility of following mathematical notation more closely.\n",
    "\n",
    "The usual style is that the names of variable and functions use only (Roman alphabet) letter, digits, and possibly underscores to separate words in names that are descriptive phrases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "577f9fe9-2eef-4cba-accf-53ae4625944c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "π/2 = 1.5707963267948966\n"
     ]
    }
   ],
   "source": [
    "println(\"π/2 = \", π/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbdae3ea-5761-42fb-8a22-d4c9cde72495",
   "metadata": {},
   "source": [
    "(That function `println` will be explained below in [Displaying values](displaying_values).)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c400e55-58d2-460d-803f-1bd48bd7e2b3",
   "metadata": {},
   "source": [
    "So not only is $\\pi$ is the character set; it is the name of predefined constant.\n",
    "(which can also be referred to as `pi`)\n",
    "\n",
    "Typing such characters is done using LaTeX notation and tabbing:\n",
    "for $\\pi$, type the three character sequence `\\pi` and then press TAB.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9d3e2ca-1501-4fc7-ad0e-bc50265fd8db",
   "metadata": {},
   "source": [
    "The above characters are in single right quotes (to be pedantic, apostrophes),\n",
    "whereas strings of characters must be surrounded, more properly, by double quote characters:\n",
    "\n",
    "    \"This is a string\"\n",
    "    'This is a syntax error'\n",
    "\n",
    "This one comes from C, I think."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f4c6f31-f84e-4f8f-b057-e7752c95d1fc",
   "metadata": {},
   "source": [
    "*Aside:* here is a quirky use of Unicode built in to Julia:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "60982206-a9f6-4e05-90c1-abee209d5945",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "√4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "675b65d6-70d4-4d51-9047-da30c22cda97",
   "metadata": {},
   "source": [
    "(concatenationduplication)=\n",
    "### String concatenation and duplication\n",
    "\n",
    "To concatenate two strings, \"multiply\" them with `*`. (Versus \"adding\" them as in Python.)\n",
    "\n",
    "Also, consistent with that, making multiple copies of a string is done by \"exponentiation\", with `^`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "a5c34482-e690-4076-aa51-18c0a924e303",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello world.\n",
      "Hello Hello Hello \n"
     ]
    }
   ],
   "source": [
    "greeting = \"Hello\"\n",
    "audience = \"world\"\n",
    "sentence = greeting * ' ' * audience * '.'\n",
    "println(sentence)\n",
    "println((greeting*' ')^3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aab74c65-6e9a-4a21-838d-c7f446613309",
   "metadata": {},
   "source": [
    "Note that single characters can also be concatenated into strings, and exponentiated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "e15abfcf-4aea-4cd3-86f1-47b63408cf5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"gamma\""
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma = 'g' * 'a' * 'm'^2 * 'a'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c0a79ee-7b1e-4b13-9ff7-d3e7ff555034",
   "metadata": {},
   "source": [
    "(displaying_values)=\n",
    "## Displaying values: `println`, `print` and just saying the name"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a054e84-2efb-49eb-be19-98a55265ac2a",
   "metadata": {},
   "source": [
    "We have seen above two basic ways of getting output displayed on the screen:\n",
    "- the function `println`\n",
    "- putting an expression on the last line of a cell (or typing it into the interactive Julia command line),\n",
    "which causes that expression to be evaluated and the result displayed.\n",
    "This is as in both Matlab and Python, and with the same method for supressing output: ending that line with a semi-colon.\n",
    "\n",
    "The basic usage of function `println` is as for the synonymous function in Matlab and `print` in Python:\n",
    "input is a sequence of strings whose values are ouptut on a line, after which output moves to a newline.\n",
    "\n",
    "There is also a variant `print` which does not go to a new line at the end; useful for assembling a line of output piece-by-piece:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "8578c611-7e38-4ed4-860e-075a417c7ea5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The end.\n",
      "\n",
      "That's all folks!\n"
     ]
    }
   ],
   "source": [
    "println(\"The\",\" end.\")\n",
    "println()\n",
    "print(\"That's\")\n",
    "print(\" all\")\n",
    "print(\" folks\")\n",
    "println(\"!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1124b4cb-b20f-48ec-a220-14af81d5d4ac",
   "metadata": {},
   "source": [
    "Note that in each case, the spaces must be explicitly specified.\n",
    "Also, the sequence of strings can be empty: get just a blank line with `println()`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8faa12d-a1fd-408a-8e33-0a713608df4f",
   "metadata": {},
   "source": [
    "(displaying_values_of_expressions)=\n",
    "## Displaying the values of variables and expressions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c0f0e34-d4ae-4e53-bab3-6ca660837bc4",
   "metadata": {},
   "source": [
    "As already seen above, there are several ways of display the value of a variable, or more generally of an expression.\n",
    "\n",
    "One is to put such expressions in the sequence of arguments to `println` (so I lied slightly about the arguments being strings):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "0c35bd73-6ba1-43e2-a970-22caea1d240a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 2 and its cube is 8\n"
     ]
    }
   ],
   "source": [
    "a = 2\n",
    "println(\"a = \", a, \" and its cube is \", a^3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "543409c2-a1ed-493a-829c-af9f0c4faeb2",
   "metadata": {},
   "source": [
    "Another is to use '$' interpolation, adopted from the Perl language:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "3af243bc-8a0f-43e9-ac9f-a664505c5b75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 2 and its cube is 8\n"
     ]
    }
   ],
   "source": [
    "println(\"a = $a and its cube is $(a^3)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8dfd54e-48e1-4fa0-a95a-b6314930a022",
   "metadata": {},
   "source": [
    "When the expression whose value to interpolate is just a variable name, it is enough to prefix that name by '$'.\n",
    "However more involved expressions must be parenthesised, as with `$(a^3)`.\n",
    "\n",
    "Fun fact: the string in the last example is an expression whose value is the string displayed,\n",
    "so its value can also be displayed by simply having it as the last (and semicolon-free) line of a cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "e3ced19f-ee9e-4eb6-8ee8-53476eafec3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a = 2 and its cube is 8\""
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"a = $a and its cube is $(a^3)\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97f766be-4253-42db-989c-9c6d23965486",
   "metadata": {},
   "source": [
    "This is useful to know since it reveals a nice \"orthogonality of features\":\n",
    "interpolation is not a special feature of function `println` but something that can be used in other situations;\n",
    "probably the most common use in this book will be putting annotations on graphs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91e09c65-d698-493b-be8a-ff17527b2536",
   "metadata": {},
   "source": [
    "Sometimes it is illuminating to use the \"last line automatic display\" feature rather than `print` because it reveals some information about the type of a quantity rather than just its value.\n",
    "This book uses that often when discussing Julia language features rather than when actually doing numerical computing;\n",
    "see for example the notes on [arrays](arrays) below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8eae473-3a09-45fd-8804-0c08316bd4a8",
   "metadata": {},
   "source": [
    "On the other hand, many expressions give output values that you might not expect, like the definitions of [functions](#functions1) and  function `plot` in the notes on [modules](modules) below;\n",
    "thus you might want to end many cells with a semi-colon to supress unneeded output.\n",
    "An end-of-line semi-colon never hurts, even where redundant, so you may type like a C programmer if you wish.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c331946e-a38c-4e1f-a490-9556158e3287",
   "metadata": {},
   "source": [
    "Semicolons can also be used to combine statements on a single line.\n",
    "This is often considered as poor style, but I sometimes find that it improves readability with several short and closely related statements:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "3dc6dc36-7cc8-44b7-a50c-8d664247cf25",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=1, b=3"
     ]
    }
   ],
   "source": [
    "a = 1; b = 3\n",
    "print(\"a=\",a,\", b=\",b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d36bbe6-35bc-4a30-8536-1d1db2480fc9",
   "metadata": {},
   "source": [
    "(boolean)=\n",
    "## Boolean values (true-false)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df8f14f0-ebfb-4419-8764-54faa6d3b770",
   "metadata": {},
   "source": [
    "These are `true` and `false` and nothing else:\n",
    "- not capitalized as they are in Python\n",
    "- not \"1\" and \"0\" or \"nonzero\" vs \"zero\" or any other laziness.\n",
    "\n",
    "The logical operators are much as in C: \"&&\", \"||\", \"&\", \"|\", and \"!\" for negation.\n",
    "\n",
    "Be careful with that last one; logical negation is not \"~\" as in Matlab.\n",
    "\n",
    "The doubled forms \"&&\" and \"||\" use lazy or \"short-circuiting\" evaluation:\n",
    "if the value the left-hand term determines the truth value of the whole, then the second term is not evaluated.\n",
    "For example, the following avoids division by zero:\n",
    "\n",
    "    if q != 0 && -1 < p/q < 1\n",
    "        println(\"$p/$q is a proper fraction\")\n",
    "    else\n",
    "        println(\"$p/$q is not a proper fraction\")\n",
    "    end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6af0c22a-40e0-4562-9202-b1f7a7062c65",
   "metadata": {},
   "source": [
    "(comparisons)=\n",
    "## Comparisons\n",
    "\n",
    "The usual comparisons of numbers and tests for equality exist,\n",
    "\n",
    "    < <= == >= !=\n",
    "with a couple of extra twists."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c0c295d-efb6-4503-91ae-1b847aeb728f",
   "metadata": {},
   "source": [
    "the first is the comparisons can be chained, as seen above:\n",
    "\n",
    "    -1 < p/q < 1\n",
    "is equivalant to\n",
    "\n",
    "    -1 < p/q && p/q < 1\n",
    "but both more readable and more efficient, because the middle term is only evaluated once.\n",
    "Like `&&`, this is short-circuiting.\n",
    "\n",
    "(This one comes from Python, the only other language I know of with this feature.)\n",
    "\n",
    "This can even be done in cases where usual mathematical style forbids, with reversing of the direction of the inequalities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "41659188-b8b6-4d26-a1e4-5162fa3fc1e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 < 4 > 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bbeee8b-4461-4ae7-a02a-973efe022c41",
   "metadata": {},
   "source": [
    "The second extra is the function `isequal(a, b)`.\n",
    "This is mostly the same as `==` but with some special handling for the special values `-0.0` and `NaN` of IEEE floating point numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "fdd34738-942c-41fb-989b-05ad2fb619c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NaN == NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "f5086d3e-6abb-4e5e-8ec4-ff94e94eac00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isequal(NaN, NaN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "09876cd6-53f0-421f-abc8-49793f3f6523",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-0.0 == 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "8a5a43cf-cc88-4a67-9760-fddd972be43f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isequal(-0.0, 0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9f7f107-f031-47ea-b296-b0ea23cbf32a",
   "metadata": {},
   "source": [
    "(numbers)=\n",
    "## Numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49576fca-2cc3-4ecb-a9eb-cb14a9a63ea2",
   "metadata": {},
   "source": [
    "As just mentioned, the default floating point numbers and arithmetic are IEEE Float64, and the default integers are Int64;\n",
    "others are available (like Int32 and unsigned integers) but they will not be mentioned again in this book.\n",
    "\n",
    "Thus the main novelty here is a notation:\n",
    "the underscore can be used within numbers to improve readabilty, as commas are (and periods in some countries.)\n",
    "They can be put wherever you like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "730a7c50-64d2-4c96-aad4-8d399a4899a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "two_thousand_million is 2000000000\n",
      "In the Indian number naming system, one crore is 10000000\n",
      "pi is approximately 3.14159265\n"
     ]
    }
   ],
   "source": [
    "two_thousand_million = 2_000_000000  # British English\n",
    "println(\"two_thousand_million is \",two_thousand_million)\n",
    "crore = 1_00_00_000  # This is where Indian style puts the commas\n",
    "println(\"In the Indian number naming system, one crore is $crore\")\n",
    "almostpi = 3.1415_9265\n",
    "println(\"pi is approximately $almostpi\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da2d7605-f78b-45ec-97e7-84007a64dd0a",
   "metadata": {},
   "source": [
    "A point on recommended style: although floating point numbers can be typed with the decimal point at the beginning or the end,\n",
    "as with `2.` and `.5`,\n",
    "it is recommended style to always have digits around the decimal point, as with `2.0` and `0.5`.\n",
    "\n",
    "One reason is that the period '.' is used with many other meanings, so this style helps to avoid ambiguities;\n",
    "see below about [vectorization](vectorization-and-broadcasting)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0ef33b-cea6-426d-a45a-931138978ffa",
   "metadata": {},
   "source": [
    "(complexnumbers)=\n",
    "### Complex numbers\n",
    "\n",
    "Julia uses `im` for the square root of -1 rather than `i` or `j`, and `im` cannot be used as the name of a variable.\n",
    "\n",
    "In general, the complex number $a + b i$ is expressed as `a + bim` where 'b' is a literal number,\n",
    "not the name of a variable.\n",
    "Then `im` is immediately juxtaposed with that number, no intervening space allowed)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "6e5a91f6-2561-4c3f-ae2a-4450ac1fcb6a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z = 3 + 4im\n",
      "Its absolute value is 5.0\n"
     ]
    }
   ],
   "source": [
    "z = 3 + 4im\n",
    "println(\"z = \", z)\n",
    "println(\"Its absolute value is \", abs(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9beb0e0-be42-438a-ad0e-c8b02a09087a",
   "metadata": {},
   "source": [
    "As you might expect, imaginary numbers can be written without the real part $a$, as `bim` and when $b=1$, it can be ommited\n",
    "\n",
    "However, the imaginary part `b` is always needed, even when $b = 0$, to announce that the nuber is to br treated a complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "e32a7e01-38ba-420f-a830-679746dc889c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 + 2im\n"
     ]
    }
   ],
   "source": [
    "println(2im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "dfe621bb-b62f-4613-89f9-4c7cba3619f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "im\n"
     ]
    }
   ],
   "source": [
    "println(im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "cf0c7adb-05b0-4f4d-88b9-b2c848e3945b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1 + 0im\n"
     ]
    }
   ],
   "source": [
    "println(im^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "89ade22c-7be3-417c-ab72-5d8d4fb1de0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 - 1im\n"
     ]
    }
   ],
   "source": [
    "println(-1im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "69bc8855-0616-49a6-9fe5-460826412052",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 - 1im\n"
     ]
    }
   ],
   "source": [
    "println(-im)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91405090-f361-4c95-8ee7-5eb60915ff33",
   "metadata": {},
   "source": [
    "However, the imaginary part `b` is always needed, even when $b = 0$, to announce that the number is to be treated a complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "8210a17f-9fff-4019-ae72-ec79408a2f21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0 + 1.0im"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(-1 + 0im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "24044af1-f4b9-4374-9cbc-23b081dfaada",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "DomainError with -1.0:\nsqrt was called with a negative real argument but will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).",
     "output_type": "error",
     "traceback": [
      "DomainError with -1.0:\nsqrt was called with a negative real argument but will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).",
      "",
      "Stacktrace:",
      " [1] throw_complex_domainerror(f::Symbol, x::Float64)",
      "   @ Base.Math ./math.jl:33",
      " [2] sqrt",
      "   @ ./math.jl:608 [inlined]",
      " [3] sqrt(x::Int64)",
      "   @ Base.Math ./math.jl:1531",
      " [4] top-level scope",
      "   @ In[107]:1"
     ]
    }
   ],
   "source": [
    "sqrt(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12400d8a-48f2-426d-b380-fce463b25ba5",
   "metadata": {},
   "source": [
    "The name `im` is reserved for this role; it cannot be used as a variable name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "5e7327ae-e6cd-495b-906e-1602dc02cef8",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "cannot assign a value to imported variable Base.im from module Main",
     "output_type": "error",
     "traceback": [
      "cannot assign a value to imported variable Base.im from module Main",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[108]:1"
     ]
    }
   ],
   "source": [
    "im = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7bae82f-ee7a-4931-aae2-b681a4b729f2",
   "metadata": {},
   "source": [
    "(arithemeticoperators)=\n",
    "## Arithemetic operators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e26117ca-c1d8-4b1d-878b-601216e8d1d6",
   "metadata": {},
   "source": [
    "With arithmetic on numbers, the main items to note are\n",
    "1. exponentiation\n",
    "2. division with integers, and\n",
    "3. multiplication by juxtoposition\n",
    "\n",
    "- Exponentiation $a^b$ is given by `a^b` (as in Matlab and different from Python's `a**b`).\n",
    "\n",
    "- `p/q` with `p` and `q` both integers promotes to floating point arithmetic.\n",
    "\n",
    "- To do integer division with integer result, use `p ÷ q` (or `div(p,q)` to avoid that Unicode: all operators also have function forms).\n",
    "\n",
    "- The remainder is given by `p%q`, or `rem(p,q)`. Thus `(p ÷ q)* q + p%q = p`\n",
    "\n",
    "- There is also \"backward division\": `q\\p` is the same as `p/q`; see below.\n",
    "\n",
    "- The product of a literal number by a variable or function value can be indicated by juxtoposition, no '*' needed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "04a16b88-4fb8-4d87-b4c9-394a01a20041",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.283185307179586\n",
      "3.9999999999999996\n"
     ]
    }
   ],
   "source": [
    "println(2π)\n",
    "println(4tan(pi/4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e437cd10-1c9c-4c05-a88e-c9ab370e8540",
   "metadata": {},
   "source": [
    "(arrays)=\n",
    "## Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "792264bf-96b3-4cb6-b1cc-6c06e7c62ea4",
   "metadata": {},
   "source": [
    "Julia has numerical arrays bult in, and the basic construction notation is much as in Matlab, with semicolons separating rows.\n",
    "However, not everything is a matrix of real numbers:\n",
    "- Integer values are supported.\n",
    "- There is a distinction between matrices and vectors, with the latter being equivalent to single column matrices.\n",
    "- Single row matrices are still considered as matrices.\n",
    "\n",
    "This all follows common mathematical conventions, and so does multiplication."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b36b3ac5-41f8-40cb-bd89-aa77cc00a835",
   "metadata": {},
   "source": [
    "Vectors (1-index arrays) are created with bracketed, comma separated lists;\n",
    "note the column vector presentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "9d2efee4-f5bb-4fcb-8b57-2a15ad2c7773",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = [1, 2, 3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9f0d29a-6435-4e37-bdeb-15f5314de441",
   "metadata": {},
   "source": [
    "Matrices are created with rows separated by semicolons and elements with a row separated only by spaces:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "58b0288d-73ee-4b22-96d2-e54a61c0b29f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Float64}:\n",
       " 1.0  2.0  3.0\n",
       " 4.0  5.0  6.0"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [ 1.0 2.0 3.0 ; 4.0 5.0 6.0 ]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67d9ff2e-e70a-4c8e-849d-8f317000387c",
   "metadata": {},
   "source": [
    "Note the difference from vector `v` above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "a7dd105d-4fb5-4198-9d52-038815db2cad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 Matrix{Int64}:\n",
       " 1  2  3"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = [ 1 2 3 ]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "184f3b09-5ecf-4ca6-9ef7-2b9ab6ff71c9",
   "metadata": {},
   "source": [
    "On the other hand, a vector can be created as a one-column matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "bd7fff4d-d394-43cf-acb8-00587a0935c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v_as_matrix = [ 1 ; 2 ; 3 ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "06a87fe1-2e4a-48be-b5d0-e92f55ddcb94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v == v_as_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "c3dc4b50-f5cd-4ea9-a790-acc91ab66906",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v == u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "c7ce7f9a-8fa5-4666-8911-af5b1a027077",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Vector{Int64}:\n",
       " 14"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u * v  # like u-transpose times v; the inner product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "4676670e-6160-4b4e-bb29-76493ecf5e44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       " 1  2  3\n",
       " 2  4  6\n",
       " 3  6  9"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outer = v * u  # The outer product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "b4249694-885a-4c6c-b7a0-6d4ffeed93e9",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching *(::Vector{Int64}, ::Vector{Int64})\nThe function `*` exists, but no method is defined for this combination of argument types.\n\n\u001b[0mClosest candidates are:\n\u001b[0m  *(::Any, ::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any...\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4moperators.jl:596\u001b[24m\u001b[39m\n\u001b[0m  *(\u001b[91m::PyCall.PyObject\u001b[39m, ::Any)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:13\u001b[24m\u001b[39m\n\u001b[0m  *(::Any, \u001b[91m::PyCall.PyObject\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:14\u001b[24m\u001b[39m\n\u001b[0m  ...\n",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching *(::Vector{Int64}, ::Vector{Int64})\nThe function `*` exists, but no method is defined for this combination of argument types.\n\n\u001b[0mClosest candidates are:\n\u001b[0m  *(::Any, ::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any...\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4moperators.jl:596\u001b[24m\u001b[39m\n\u001b[0m  *(\u001b[91m::PyCall.PyObject\u001b[39m, ::Any)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:13\u001b[24m\u001b[39m\n\u001b[0m  *(::Any, \u001b[91m::PyCall.PyObject\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:14\u001b[24m\u001b[39m\n\u001b[0m  ...\n",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[118]:1"
     ]
    }
   ],
   "source": [
    "v * v  # vector times vector, a mismatch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf576919-d9ef-458d-ab53-9ea5a795e3dd",
   "metadata": {},
   "source": [
    "A row matrix can be converted to a vector with function `collect`, which we will see again below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "b9f8230a-ed1b-4f33-a161-ccb0c045a77a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "239724fd-a9af-4714-9e8b-9e9b5b469197",
   "metadata": {},
   "source": [
    "(array-indexing-slicing)=\n",
    "### Array indexing and slicing\n",
    "\n",
    "Indices run from 1 (like Matlab, unlike Python), **but** indices are indicated with brackets\n",
    "(like Python, unlike Matlab — which uses parentheses for too many things!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "707b4ef2-0eae-42ad-8ab5-4ce75379ddf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "58a18f37-193d-47aa-a761-e33b70bc0f4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[2,3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48078450-07c1-445f-9f7d-00f3accff62a",
   "metadata": {},
   "source": [
    "**Be careful with single indexing a higher dimensional array.**\n",
    "\n",
    "This treats the elements of the array as if laid out in a singe row (\"flattened\"), rather than selecting a row as in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "d1778165-44e2-44e5-b62f-e7222e965bf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 4.0, 2.0, 5.0, 3.0, 6.0)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1], A[2], A[3], A[4], A[5], A[6]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6b5fddc-2896-46b7-93f6-96152988dba0",
   "metadata": {},
   "source": [
    "Also note the order: the columns are joined end-to-end, not the rows:\n",
    "Julia follows Matlab (and Fortran) in storing arrays in **column-major order**, \n",
    "as opposed to the **row-major order** of Python (and C ,and Java, and in general in languages that count fom zero.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ab01ab7-247b-4a72-ac33-836497199c5e",
   "metadata": {},
   "source": [
    "One can also index expressions directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "b1aea3bf-285a-4556-9a0a-168dfe703925",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(v*u)[2,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "537a68f4-45eb-42e2-9fcf-c6f5e4e0de09",
   "metadata": {},
   "source": [
    "Indexing part of an array can be done with **slicing** which works mostly as in Matlab.\n",
    "\n",
    "The basic form is `first:last`, selecting indices from `first` to `last` *inclusive* (like Matlab, unlike Python)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "182a1c85-b471-45ec-98e5-8600f9bf21e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Int64}:\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[2:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "07cc5d1b-bcf7-4c1c-931f-35591e871734",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 2.0  3.0\n",
       " 5.0  6.0"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1:2,2:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66df6afe-0c87-491b-9542-6467b3f00d11",
   "metadata": {},
   "source": [
    "The final index value can be indicated by `end`, and index arithmetic can be done on this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "5841d0fe-4243-4d1b-a1c2-9eca860eafa9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The last entry in v is 3, the penultimate is 2\n",
      "The last two columns of A are\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 2.0  3.0\n",
       " 5.0  6.0"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "println(\"The last entry in v is \", v[end], \", the penultimate is \", v[end-1])\n",
    "println(\"The last two columns of A are\")\n",
    "A[1:end, end-1:end]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d53376e-0d1c-4271-9920-53783c4694f1",
   "metadata": {},
   "source": [
    "When the slice on an index is all values, one can use `:` instead of `1:end`.\n",
    "So the previous example could also be done as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "3edc2e27-91fd-41eb-a9ad-2d87b67ccb1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 2.0  3.0\n",
       " 5.0  6.0"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:, end-1:end]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d370caf-8522-45f7-a382-0b89a76a2bca",
   "metadata": {},
   "source": [
    "One can also specify an arbitrary collection of indices by giving a bracketed list (a one index array) of indices.\n",
    "\n",
    "For example, The \"corners\" of the outer product `u * v`, flipped vertically, are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "a645f738-9217-46f9-a31a-bef7ea8bc658",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Int64}:\n",
       " 3  9\n",
       " 1  3"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outer[[3,1], [1,3]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44d56dba-2890-49c9-85d5-996d4e12b30a",
   "metadata": {},
   "source": [
    "and we can permute rows like this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "4eb85424-b634-4ed6-9bce-e336a0d4c4f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       " 3  6  9\n",
       " 1  2  3\n",
       " 2  4  6"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outer[[3,1,2],:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "352385d7-a6fa-411d-be98-72b50d360102",
   "metadata": {},
   "source": [
    "A tricky point: slicing to a single row matrix vs slicing to a vector.\n",
    "\n",
    "For some matrix-vector caclulations is is necessary to ensure that an object is a \"1 by n\" row matrix rather than an n-vector (which is an \"n by 1\" column matrix) but unfortunately, **slicing out a single row of matrix returns a vector:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "47cc7211-ae55-4d00-9b8b-4e232341b630",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 1.0\n",
       " 2.0\n",
       " 3.0"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1,:]  # gives a vector, a.k.a. a 1 column matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b60200e-1c65-418b-b11a-f892fb62f813",
   "metadata": {},
   "source": [
    "To keep the slice as a row, indicating the row as `[i]` rather than just `i`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "c8da5200-4694-4028-9cd4-b21402372d59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 Matrix{Float64}:\n",
       " 1.0  2.0  3.0"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[[1],:]  # gives a 1 row matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "960400a3-64a3-4823-b7a8-4d2f709c72e7",
   "metadata": {},
   "source": [
    "So this works as an outer product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "ccc795aa-163f-443d-b60c-8a83e00fad2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Float64}:\n",
       " 3.0   6.0   9.0\n",
       " 4.0   8.0  12.0\n",
       " 5.0  10.0  15.0"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[3, 4, 5] * A[[1],:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c986821-cafb-450c-a275-50102a0717f7",
   "metadata": {},
   "source": [
    "but this fails as a \"vector times vector\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "6accf731-099c-4f03-9cc5-72a1cabf392c",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching *(::Vector{Int64}, ::Vector{Float64})\nThe function `*` exists, but no method is defined for this combination of argument types.\n\n\u001b[0mClosest candidates are:\n\u001b[0m  *(::Any, ::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any...\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4moperators.jl:596\u001b[24m\u001b[39m\n\u001b[0m  *(\u001b[91m::PyCall.PyObject\u001b[39m, ::Any)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:13\u001b[24m\u001b[39m\n\u001b[0m  *(::Any, \u001b[91m::PyCall.PyObject\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:14\u001b[24m\u001b[39m\n\u001b[0m  ...\n",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching *(::Vector{Int64}, ::Vector{Float64})\nThe function `*` exists, but no method is defined for this combination of argument types.\n\n\u001b[0mClosest candidates are:\n\u001b[0m  *(::Any, ::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any...\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[90mBase\u001b[39m \u001b[90m\u001b[4moperators.jl:596\u001b[24m\u001b[39m\n\u001b[0m  *(\u001b[91m::PyCall.PyObject\u001b[39m, ::Any)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:13\u001b[24m\u001b[39m\n\u001b[0m  *(::Any, \u001b[91m::PyCall.PyObject\u001b[39m)\n\u001b[0m\u001b[90m   @\u001b[39m \u001b[32mPyCall\u001b[39m \u001b[90m~/.julia/packages/PyCall/1gn3u/src/\u001b[39m\u001b[90m\u001b[4mpyoperators.jl:14\u001b[24m\u001b[39m\n\u001b[0m  ...\n",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[133]:1"
     ]
    }
   ],
   "source": [
    "[3, 4, 5] * A[1,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "338d15ca-e64b-4e02-a5e2-406d47e550ed",
   "metadata": {},
   "source": [
    "Slicing can also select equally spaced values with syntax `first:step:last`\n",
    "\n",
    "**Warning to Python users:** the order is different (Python uses `first:last:step`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "e2ae01d2-806e-46d5-98bc-65209a4811d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 1.0  3.0\n",
       " 4.0  6.0"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,1:2:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc3ff127-ca6a-4886-ab67-cebac6dd077a",
   "metadata": {},
   "source": [
    "In particular, this allows counting backwards, with step of -1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "38cb7bf9-ba26-4a5f-859c-2f7e731ad380",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Float64}:\n",
       " 3.0  2.0  1.0\n",
       " 6.0  5.0  4.0"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,end:-1:1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfa0ab0e-8c49-4388-8286-a94b7759b508",
   "metadata": {},
   "source": [
    "One big difference from Matlab or Python is some \"orthogonality\":\n",
    "rather than just being a notation used in this context of array indexing,\n",
    "this colon notation is a function (named `:`) whose value is a data type called a **range** that can be used in a variety of contexts, and assigned to variables.\n",
    "\n",
    "One other usage will be seen soon in the notes on [iteration](#iteration).\n",
    "Meanwhile:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "c2561c1e-a7ad-4408-becd-dc05a836d258",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1:2:3"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oddcolumnsorrows = 1:2:3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "7abbf940-11fb-49b7-898a-1643844763be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The odd numbered rows of A are"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 1.0  3.0\n",
       " 4.0  6.0"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"The odd numbered rows of A are\")\n",
    "A[:,oddcolumnsorrows]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "20e403dd-3dd7-4dac-b49c-1c61974d3a91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The odd numbered rows of the outer product 'v u' are"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Int64}:\n",
       " 1  2  3\n",
       " 3  6  9"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"The odd numbered rows of the outer product 'v u' are\")\n",
    "(v*u)[oddcolumnsorrows,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "577c4db6-f5b9-4f41-82d4-4680193e7bb2",
   "metadata": {
    "tags": []
   },
   "source": [
    "(range)=\n",
    "### Function `range`\n",
    "\n",
    "Closely related to this slice syntax is the function `range`, which produces a range value as above, and has several flavors:\n",
    "\n",
    "- `range(start, stop)` returns `start:stop`.\n",
    "\n",
    "- `range(start, stop, length)` returns a range running from `start` to `stop` with `length` values — like `linspace` in both Matlab and Python.\n",
    "\n",
    "- `range(start, stop, step=stepsize)` returns `start:stepsize:stop`. But note that this flexibility requires specifying what the third parameter means by using its name: it is a **keyword parameter**.\n",
    "\n",
    "- More generally, there are four parameters `start`, `stop`, `length` and `step` and you can specify any three (which determines the fourth). However, all other combinations require specifying some or all of them by name, as keyword parameters.\n",
    "\n",
    "Keyword parameters will be discussed in the section [Functions, Part 2](functions2-future), once that section is written!\n",
    "\n",
    "Meanwhile, some examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "896f2e7c-2415-4f92-8ba9-fe2c8b8f7dcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1:11"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(1,11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "9daa263c-ad28-46ee-8f24-87be0d257ccf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0:0.1:2.0"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(1,2,11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "b5353393-74d4-4246-b232-08323bc698cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0:0.1:2.0"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(1, 2, step=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "45e90e90-ad72-4fe6-b8ba-c3d6c9b968f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0:0.1:2.0"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(step=0.1, stop=2, length=11)  # A weird but legal way to do it"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "406bdb86-aaca-4fad-92d3-24d2efc51a58",
   "metadata": {},
   "source": [
    "(tuples)=\n",
    "## Tuples\n",
    "\n",
    "Julia also has tuples, much as in Python.\n",
    "\n",
    "These resemble one index arrays, excpr that\n",
    "- The elements can be anythingm and do not need to be of the same type.\n",
    "- They are **immutable**: leemts can be accessed by indexing, *but cannnot be changed*.\n",
    "\n",
    "Tuples are created as a comma-separated lists, optionally parenthesized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "be2931b5-bf7e-4134-b0e2-b90f67fd077d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('1', \"two\", 3)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuple123 = ('1', \"two\", 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2898bca6-ded6-4e56-a77f-8aa91c474b79",
   "metadata": {},
   "source": [
    "or equivalently"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "f272539a-95a5-4d98-ad27-e969ab081bdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('1', \"two\", 3)"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuple123 = '1', \"two\", 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "fa83e06a-b252-4b2b-acab-d724ab3d9030",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"two\""
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuple123[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52791ef0-0016-43f1-9afa-15602f74c156",
   "metadata": {},
   "source": [
    "but this is not allowed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "be53cb39-e9bf-4b80-acfc-14436d846dce",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching setindex!(::Tuple{Char, String, Int64}, ::Int64, ::Int64)\nThe function `setindex!` exists, but no method is defined for this combination of argument types.",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching setindex!(::Tuple{Char, String, Int64}, ::Int64, ::Int64)\nThe function `setindex!` exists, but no method is defined for this combination of argument types.",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[146]:1"
     ]
    }
   ],
   "source": [
    "tuple123[3] = 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1852f0e1-bf1a-48e6-a2ae-a96ae9fa018d",
   "metadata": {},
   "source": [
    "One very common use of tuples is in functions that return more than one quantity, such as\n",
    "[`row_reduce`](row-reduction) in {ref}`module:NumericalMethods` which returns its results with\n",
    "\n",
    "    return (U, c)\n",
    "Strictly a single quantity is returned, but it is a tuple."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "291931c4-9dfb-475e-8ff9-de1fcd2b2413",
   "metadata": {},
   "source": [
    "(vectorization-and-broadcasting)=\n",
    "## Arithmetic operations on arrays: vectorization and broadcasting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cf30896-0af9-4f35-9959-c6566464ed8f",
   "metadata": {},
   "source": [
    "- With arrays, addition and subtraction and multiplicato or division by numbers work as one would expect with vector matrices and such.\n",
    "\n",
    "- Multiplication of arrays as with `A*b` does matrix-matrix or matrix-vector product (again as with Matlab).\n",
    "\n",
    "- `A/b` and `A\\b` are also matrix and vector friendly; in particular `x = A\\b` means $x = A^{-1}b$ and so solves $A x = b$.\n",
    "\n",
    "- Also copied from Matlab is the \"dot\" or \"pointwise\" versions of operators, but this goes beyond what Matlab does. In the following I use lower case lettters for numbers, upper case for arrays, and illustrate only for 1D arrays though it works in higher dimensions too.\n",
    "\n",
    "- The first case is <a name=\"vectorization\">**vectorization**</a>, creating implicit loops over one or more indices:\n",
    "    - `C = A .* B` computes the product point-wise product, so `C[i] = A[i]*B[i]`.\n",
    "    - `C = a.^B` gives `C[i] = a^B[i]`\n",
    "    - `C = A.^b` gives `C[i] = A[i]^b`\n",
    "    - `C = A.^B` gives `C[i] = A[i]^B[i]`\n",
    "\n",
    "- The second concept is <a name=\"broadcasting\">**broadcasting**</a> where a number is promoted to an appropriate array with that number in each element.\n",
    "\n",
    "- For example `a + B` is an error, but `a .+ B` gives array `C` with `C[i] = a + B[i]`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef2db87f-1a7d-42b8-ad59-e509964a5d98",
   "metadata": {},
   "source": [
    "(condititionals)=\n",
    "## Condititional statements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a65d64d-62a4-430a-a755-cdbcf70f8571",
   "metadata": {},
   "source": [
    "One example probably says it all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "b33a5311-702a-4110-a4c2-b2f0481c7074",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.0"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 11.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "93d6e2f9-bd2f-4806-b280-fc59ba2d62a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is positive\n"
     ]
    }
   ],
   "source": [
    "if x > 0\n",
    "    println(\"x is positive\")\n",
    "elseif x < 0\n",
    "    println(\"x is negative\")\n",
    "else\n",
    "    println(\"x is zero\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14ac0636-3fd8-4d46-80fe-c8f2c1e80bd5",
   "metadata": {},
   "source": [
    "In other words, \"as in Matlab\", again.\n",
    "\n",
    "Note also the use of the Matlab style of using `end` to end blocks of code,\n",
    "which will of course also be seen with loops, function definition and so on.\n",
    "Indentation is optional but \"four spaces per level (no tabs)\" is the usual style.\n",
    "\n",
    "Also note the `println`; more on output to the screen (and to files) later."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90f7c3c4-339b-4a33-9eb7-9047eb26bbb3",
   "metadata": {},
   "source": [
    "(iteration)=\n",
    "## Iteration with `for`, `while`, `break` and `continue`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71aedc84-20c6-467a-bfb4-7c47d1ca6d5b",
   "metadata": {},
   "source": [
    "The title tells much of the story: this is all very much as in Matlab — and as in Python except with `end` statements.\n",
    "\n",
    "The only novelty is the details of the `for` statement, which are roughly the union of the Matlab and Python options.\n",
    "\n",
    "Julia denotes ranges of values with Matlab-style notation:\n",
    "- `a:b` is the values from `a` to `b` by steps of one,\n",
    "- `a:step:b` is the values from `a` to `b` by steps of `step`.\n",
    "\n",
    "This gives the first, Matlab-style `for` loop syntax:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "190f4780-47ee-44ff-994b-d2076e989d5d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12345"
     ]
    }
   ],
   "source": [
    "for i = 1:5\n",
    "    print(i) # no end of lines or spaces\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "cc25e1a6-eca4-4c2f-963d-3546e39d0ad2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3 5 "
     ]
    }
   ],
   "source": [
    "for i = 1:2:5\n",
    "    print(i,\" \")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "4413700d-53c8-4296-bee2-27eba93a93e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 4 3 2 1 "
     ]
    }
   ],
   "source": [
    "for i = 5:-1:1\n",
    "    print(i,\" \")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57ba0909-d471-42d3-b14e-747efda23b57",
   "metadata": {},
   "source": [
    "However, there is a far more flexible syntax for looping over all kinds of lists and even more general collections.\n",
    "The general form is\n",
    "\n",
    "    for item in list\n",
    "        ...\n",
    "    end\n",
    "    \n",
    " but until we see all the sorts of things that the \"list\" can be, just a few examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "cd717ed7-6b42-42f3-a90c-6b68cefb509d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1^2 is 1\n",
      "2^2 is 4\n",
      "3^2 is 9\n",
      "4^2 is 16\n"
     ]
    }
   ],
   "source": [
    "for i in 1:4\n",
    "    println(\"$i^2 is $(i^2)\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "ff7f7238-28fa-49e0-bc43-2b751f92fab9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is 1.0\n",
      "x is 1.3333333333333333\n",
      "x is 3.3166247903554\n"
     ]
    }
   ],
   "source": [
    "for x in [1, 4/3, sqrt(11)]\n",
    "    println(\"x is $x\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7139400-bd31-4d4d-ac91-3b68f4d24d16",
   "metadata": {},
   "source": [
    "A final example using some exotic stuff that will be explained later:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "9b27c6cd-0e9c-4ee9-9c08-ae6c01fc5d71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sin(0.5235987755982988) = 0.49999999999999994\n",
      "cos(0.5235987755982988) = 0.8660254037844387\n",
      "tan(0.5235987755982988) = 0.5773502691896257\n"
     ]
    }
   ],
   "source": [
    "theta = pi/6\n",
    "for f in [sin, cos, tan]\n",
    "    fname = String(Symbol(f))\n",
    "    println(\"$fname($theta) = $(f(theta))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2194f276-bd48-406b-a300-4343b3a7e9f9",
   "metadata": {
    "tags": []
   },
   "source": [
    "(modules)=\n",
    "## Using modules and packages, and some graph plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b130aa2d-83ce-4209-9bef-3fca2022419f",
   "metadata": {
    "tags": []
   },
   "source": [
    "Much like Python, collections of functions (and other stuff like constants) can be created and their contents used.\n",
    "\n",
    "There are several ways to do this; here I describe some but not all, and only for a package that already exists (creating your own comes later):\n",
    "`PyPlot`, which is for plotting, and is very similar to both Matlab's plotting commands and the Python package `matplotlib.pyplot`.\n",
    "(There is a bit more more about [PyPlot](plotting-with-pyplot) below.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1edf99fa-aafb-4cba-af6b-fe397870c765",
   "metadata": {},
   "source": [
    "**Method 1** `import` a module: make the module (or package) available, and access its contents by \"full name\";\n",
    "much like the same statement in Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "a4f021ed-b6c4-4448-9e01-9dc7cbadf9cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import PyPlot\n",
    "x = range(0.0, 2pi, 100)\n",
    "y = sin.(x)\n",
    "PyPlot.plot(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8fc1391-dab2-4504-95c1-53dfe45f3d71",
   "metadata": {},
   "source": [
    "**Notes:**\n",
    "- Function `range` is similar to `linspace` in both Matlab and Python; the usage here is `range(first, last, number_of_points)`, giving that many equally spaced values.\n",
    "- This is our first example of vectorizing a function; it must be `sin.` not just `sin`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9754080-c529-4218-b4e7-208abce23322",
   "metadata": {},
   "source": [
    "**Method 2** `import` specific items from a module, making them available by \"first name\" only;\n",
    "much like `from PyPlot import plot, title` In Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "f2040f85-5624-4a68-9740-a18267d057a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import PyPlot: plot, title\n",
    "x = range(0, 2pi, 100)\n",
    "y = sin.(x)\n",
    "plot(x, y)\n",
    "title(\"y = sin(x)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "326373b0-510b-445d-bd83-14e464a7bebf",
   "metadata": {},
   "source": [
    "**Method 3.** `using` a module, which makes all items available on a first-name basis full; much like a wild import\n",
    "`from PyPlot import *` in Python.\n",
    "\n",
    "But whereas Python style recommends against wild imports, this is common usage in Julia.\n",
    "In this book I will avoid this with user defined modules, to avoid uncertaintly about where an item comes from.\n",
    "\n",
    "(Confession: the above is not quite true: a module can choose to \"export\" only some of its items, but not others;\n",
    "then `using` provides only those exported items on a first-name basis; other items must still be accessed by their full name.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "de1e5264-62ae-4360-b1f3-5316fc3cb42b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using PyPlot\n",
    "x = range(0, 2pi, 100)\n",
    "y = sin.(x)\n",
    "plot(x, y)\n",
    "title(\"y = sin(x)\")\n",
    "xlabel(\"x\")\n",
    "ylabel(\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "829d1eab-8e11-4bab-bda5-3c12ba4a19e9",
   "metadata": {},
   "source": [
    "**Note:** those one character labels still need to be in double quotes;\n",
    "the argument is a string, not a character."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17bdd3c7-5891-4cdb-b745-54526c2edbd2",
   "metadata": {},
   "source": [
    "(functions1)=\n",
    "## Functions, part I"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f33ec9db-a5c1-43e1-a5fc-9aa620afcedb",
   "metadata": {},
   "source": [
    "Julia's function system is quite innovative, powerful, flexible — and therefore rather complicated to describe.\n",
    "So I start with just the simplest cases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "147c7746-1d24-4e3f-8b6f-44cf1ba1f7f4",
   "metadata": {},
   "source": [
    "### One liners\n",
    "\n",
    "A very simple syntax for function that just evaluates a single formula is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "ee591e1f-3efa-4067-8c90-10bfce464587",
   "metadata": {},
   "outputs": [],
   "source": [
    "f(x) = 2x^2 - 6x + 4;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1028ba01-9d29-4455-b22f-a02dd9c679fc",
   "metadata": {},
   "source": [
    "(Multiplication by juxtoposition is nice here!)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "205d745f-01ad-4412-9764-f4463f910b96",
   "metadata": {},
   "source": [
    "Note: semi-colon suppression is used here because the expression defining a function returns a value:\n",
    "some information about the function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24750f63-1562-42f4-a4b4-a08f5d7897f0",
   "metadata": {},
   "source": [
    "This can be used for graphing, but must be vectorized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "c4da711d-2083-46aa-88b8-689df82af5ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L1YyIiDydLANv5CpR1izhjl4mXBvpvqfRm5qaMGfOHNTV1UGrvfTiXjYXi9bWVhQVFaG2thYrV67Ehx9+iC1btmDgwIGdPr+zGYv4+HhUV1dfNpitDAYDMjIyMHnyZKhUjtuCVpZlTPu/nThR1YhXZw7EncPdb1rLWWPlCThWtuF4WY9jZT13Hqu8kjrc8s890PgosPOP10Hr59j8jhwrnU6H8PDwKxYLmz9vq9Vq9OnTBwAwfPhw7Nu3D++88w7ef//9Tp+v0Wig0WguelylUjnkAHHU6/7aHcPjsWj9EXy9vxT3pCc69Gc5kjPGylNwrGzD8bIex8p67jhWK7MtiypOHRSFMK3zZukdMVbWvt5VX5oqy/J5MxLeYPawWCgVEnKKa3G0ol50HCIickHNrSasa1u74s4Rnr12xa/ZVCyef/55bNu2DYWFhcjLy8MLL7yAzZs3Y+7cuY7K55IiAn0xoX8EAODLfVzTgoiILrbhYBnq9UbEh/ohvVeY6DhOY1OxqKiowL333oukpCRMnDgRe/bswYYNGzB58mRH5XNZdw63tM9V2SVoNZoFpyEiIlezou2D5+1p8VAoJMFpnMemayw++ugjR+VwO+OTuiMiUIPKej1+OlyBaW1bqxMREZ0+24jdJ2sgSb8srugtPHv5LwfyUSpwa9vBsiKTp0OIiOgXX7a9L4zt2x0xwX6C0zgXi8VVuKPtdMjWo1Uoq2sWnIaIiFyB0WTu2Mm0/bS5N2GxuAqJ4QEYmRgKswx8ncnt1ImICNh6rAoVOj1C/FWYNDBCdBynY7G4Su1t9KusM9yYjIiI8OU+ywfN2alx0PgoBadxPhaLqzRtcBS6aXxQVNOE3ae4MRkRkTerbtDjx8MVALxr7YpfY7G4Sv5qH8xIiQHANS2IiLzd6v0lMJplpMQHIykqUHQcIVgs7KC9la7PL0ddk3vuvkdERFdHluWOuwTvcMN9pOyFxcIOUuKC0D8qEHqjGWtySkTHISIiAbJOn8Pxygb4qZQdM9neiMXCDiRJwl1tsxZf7C2CjRvGEhGRB1i2twgAcNOQaGh93WuzNHtisbATy9W/Chwpr0dOca3oOERE5ER1zQZ8n2fZyfSukQmC04jFYmEnQf4q3Ni2rPfyvbyIk4jIm6zNKUGLwYykyEAMSwgWHUcoFgs7am+p3xwoRYPeKDgNERE5gyzL+KLtA+VdI+MhSd6z4VhnWCzsaETPEPTuHoCmVhPW5ZSKjkNERE5w4EwdDpfpoPZRYHZqrOg4wrFY2JHlIk7LrMUXbRfxEBGRZ2v/fT89OQrB/mrBacRjsbCzW9PioFYqkFdSh/ySOtFxiIjIgRr0RqzLtcxQ3+3lF222Y7Gws9AANaYMigQALN/HWQsiIk/2TW4pmlpN6NXdsiklsVg4RHtrXZtdiqZWXsRJROSplredBrlrBC/abMdi4QDpvcKQEOqPer0R3x4oEx2HiIgc4FCpDrln6qBSSrh1mPcu4X0hFgsHUCgk3DXyl5U4iYjI8yzbexoAMGVgFMK6aQSncR0sFg5ye1o8fBQSsotqcahUJzoOERHZUaPeiDXZlos2547iRZu/xmLhIN0DNZiaHAXgl1ZLRESeYV2uZSHEXuEBSO8dJjqOS2GxcKC5bRdxrskuRSNX4iQi8hj/2WP5wHj3yARetHkBFgsHSu8dhl7hAefd50xERO7twJla5JdYVtq8NY0XbV6IxcKBJEnCnLZzb//efZrbqRMReYD/7LZclH/j4GiEBnClzQuxWDjYrcPioPZR4GCpDgfOcCVOIiJ3pmsxdMxAz+FFm51isXCwkAB1x3bqy/bw1lMiIne2JrsEzQYT+kV2w/AeIaLjuCQWCydovxVpXW4p6poNgtMQEVFXyLLccRpk7qgevGjzElgsnCCtRwiSIgPRbDBhTXaJ6DhERNQFWafPoaCiHn4qJWYP4/bol8Ji4QS/vohz2Z4iXsRJROSG2k9nz0iJhtZXJTiN62KxcJLZw2Lhp1KioKIe+wrPiY5DREQ2qGlsxbd5lr2f5ozqITiNa2OxcBKtrwozh8YAsNx6SkRE7uOrzGK0Gs0YHBuElLgg0XFcGouFE91zjaXlrs8vQ1W9XnAaIiKyhtks499tK23eew0v2rwSFgsnSo4NwrCEYBhMMlbs462nRETuYMvRKhTXNCPIT4UZKTGi47g8FgsnuzfdMmuxbE8RjCaz4DRERHQln7edvr49LQ5+aqXgNK6PxcLJpiVbloAtrWvBz0cqRcchIqLLKK5pwqYCy+/qudfwok1rsFg4ma9KiTuGxwP4pQUTEZFr+s+eIsgyMLZvOBLDA0THcQssFgLMHZUASQK2HavGyaoG0XGIiKgTLQZTx/Vw96X3FBvGjbBYCBAf6o8JSREALG2YiIhcz/d5ZTjXZEBssB8m9I8QHcdtsFgIck/bRZxfZRajudUkOA0REV2o/XT1nFEJUCp4i6m1WCwEua5vdySE+kPXYsQ3bVvwEhGRa8gvqUN2US1USgl3jogXHcetsFgIolBIuOcay/4hn+0q5P4hREQu5F+7CgFY7uQL76YRG8bNsFgIdHtaPDQ+Chws1SHrNPcPISJyBecaW7E2xzKTfP9o3mJqKxYLgUIC1Jg11LL17qc7C8WGISIiAMDyfcXQG81IjtViWEKI6Dhuh8VCsPtH9wQAbMgvR4WuRWwYIiIvZzSZOzaKvD+9J/cF6QIWC8EGxmgxsmcojGYZ/+GCWUREQv14uBIltc0IDVBzX5AuYrFwAe2zFsv2FkFv5K2nRESifNZ2WvquEfHwVXFfkK5gsXABUwZFIkrri+qGVnyfVyY6DhGRVyoor8euk2ehVEi4h/uCdBmLhQtQKRUdt55+upOnQ4iIRPis7RbTKQMjERPsJzaMG2OxcBF3jUyAWqlAbnEtcoprRcchIvIqdU0GrN5fAuCX09PUNSwWLiK8mwY3pUQD+OUcHxEROcdXWcVoNpjQPyoQoxJDRcdxaywWLuSBtpb87YFSVNXrxYYhIvISJrOMf+1qu8V0NG8xvVosFi5kSFwwhiUEw2CS8Z89vNaCiMgZfj5SiaKaJgT5qToWLaSuY7FwMQ9emwgA+Pdu3npKROQMn+w4BQC4e2QC/NS8xfRqsVi4mBuSoxAd5IvqBj2+zeWtp0REjnS4TIedJyy3mN6XzltM7YHFwsWolArcl94TAPDxjlPc9ZSIyIHaZyumJUfxFlM7YbFwQXePjIevyrLr6d5TNaLjEBF5pOoGPda07WL60JhEwWk8B4uFCwr2V+PWYXEALLMWRERkf8v2FKHVaMbQ+GDuYmpHLBYu6sFrewIANh6qQNHZJrFhiIg8jN5owudtGz+2/74l+2CxcFF9IgIxrl93yPIvy8wSEZF9fHegDFX1ekRqNZg+OFp0HI/CYuHCHmpr0V/uK0aD3ig2DBGRh5BlueM0833pPaFS8q3QnjiaLmxc3+7o3T0A9Xojvs4sFh2HiMgjZJ4+h/wSHTQ+CswZmSA6jsdhsXBhCoXUsWDWJzsLYTLz1lMioqv10TbLbMUtw+IQEqAWnMbzsFi4uFuGxSLYX4XTZ5uQcahCdBwiIrd2+mwjfjhUDuCX081kXywWLs5f7YO5oyxTdR9uOyk4DRGRe/t4+ynIMjA+qTv6RgaKjuORbCoWixYtwogRIxAYGIiIiAjMmjULBQUFjspGbe5P7wm1UoHM0+eQXXROdBwiIrdU29SKLzPPAAB+O7aX4DSey6ZisWXLFsybNw+7d+9GRkYGjEYjpkyZgsbGRkflIwARWl/cPDQGAPDhNi6YRUTUFf/ZU4RmgwkDorUY3TtMdByP5WPLkzds2HDe15988gkiIiKQlZWFcePG2TUYne83YxPxddYZrM8vQ3FNE+JD/UVHIiJyG61GMz7bWQgA+O3YREiSJDaQB7OpWFyorq4OABAaGnrJ5+j1euj1+o6vdTodAMBgMMBgMFzNjz9P+2vZ8zVdSe8wP4zpE4btx8/iw20n8N/T+3f5tTx9rOyJY2Ubjpf1OFbWs8dYrc4uQWW9HpGBGkwd0N1jx92Rx5W1rynJXdw+U5ZlzJw5E+fOncO2bdsu+byFCxfi5ZdfvujxZcuWwd+fn7ptcaRWwpLDSmgUMhammeB/VbWQiMg7yDLwxgElypokzEgwYVIsb93viqamJsyZMwd1dXXQarWXfF6Xi8W8efPw3XffYfv27YiLi7vk8zqbsYiPj0d1dfVlg9nKYDAgIyMDkydPhkqlstvruhJZljHj3V0oqGjAM1P64r/Gdm03Pm8YK3vhWNmG42U9jpX1rnasth8/iwc/y4K/WomtfxiHID/PHW9HHlc6nQ7h4eFXLBZd+sz7xBNPYN26ddi6detlSwUAaDQaaDSaix5XqVQO+Z/JUa/rKn4zthee+foAPt9djN+O6wO1T9fvGPb0sbInjpVtOF7W41hZr6tj9cmuIgDAHcPjEa71jplyRxxX1r6eTe9Ksizj8ccfx6pVq/Dzzz8jMZH71zvbzUNj0D1Qg3JdC749UCo6DhGRSysor8fWo1VQSMDDY/ie5Qw2FYt58+bh3//+N5YtW4bAwECUl5ejvLwczc3NjspHF9D4KPHA6J4AgKVbT6KLZ7KIiLzC+1tPAABuSI7i3XROYlOxWLJkCerq6jB+/HhER0d3/FmxYoWj8lEn7hnVAwFqJY6U12PL0SrRcYiIXFJpbTPW5Vhmdh8Z11twGu9h86mQzv488MADDopHnQnyV+Huth353t/CZb6JiDrz8fZTMJplpPcKQ0p8sOg4XoN7hbiph8YkwkchYdfJs8gtrhUdh4jIpdQ1GfDFXstFm49cx+W7nYnFwk3FBPt1LPO9dCtnLYiIfu3fe06jsdWE/lGBuK5fd9FxvAqLhRv7r3GWFr4+vwyF1dyvhYgIAFoMJnyyoxCAZbaCy3c7F4uFG+sfpcX1Sd1hloEPt3PWgogIsCzfXd2gR0yQL24aEiM6jtdhsXBzj1xnudL5q8wzqG7QX+HZRESezWSW8UHb6eGHx/aCSsm3OWfjiLu5UYmhSIkPht5oxr/adu4jIvJWGYcqcLK6EUF+Ktw1Il50HK/EYuHmJEnCo23XWny26zQa9EbBiYiIxJBlGUu2WBbEuveaHgjQcKdGEVgsPMCUQVHoFR6AumYDvthTJDoOEZEQu05Ybr/X+Chwf9sKxeR8LBYeQKmQ8GjbtRYfbDsJvdEkOBERkfO9u/k4AOCuEfHoHnjx5pfkHCwWHmJWaiyig3xRWa/HyqwS0XGIiJwqp7gWO46fhY9Cwm/HcUEskVgsPITaR4HfjrX8z/TPLSdgNJkFJyIicp73NllmK2YOjUVcCDcbE4nFwoPcNTIeIf4qFNU04bu8MtFxiIic4lhFPTYeqoAkAb8bz9kK0VgsPIi/2gcPXpsIAFiy+QS3VCcir7Bks+VOkCkDI9EnIlBwGmKx8DD3p/fs2FL95yOVouMQETlUcU0T1uZatkZ/bHwfwWkIYLHwOEH+KtxzTQ8AwLubjnPWgog82tKtJ2EyyxjTJ5xbo7sIFgsP9PCYRKh9FNhfVIvdJ2tExyEicoiqej2+zCwGADx2fW/Baagdi4UHitD64va0OACWWQsiIk/04baT0BvNGBofjPReYaLjUBsWCw/16HW94aOQsP14NfYXnRMdh4jIrmoaW/H57tMAgCcm9OHW6C6ExcJDxYf6Y3ZqLADg/346JjgNEZF9fbz9FJpaTRgUo8WE/hGi49CvsFh4sHnX94FCAjYVVCHvTJ3oOEREdlHXbMBnbbs5PzGhL2crXAyLhQfrGR6Am1NiAAD/9zNnLYjIM3y6oxD1eiOSIgMxZWCk6Dh0ARYLD/f4hD6QJGDjoQocLtOJjkNEdFXqWwz4eMcpAJbfbwoFZytcDYuFh+sTEYjpydEAgMW8Q4SI3Nznu0+jrtmAXt0DMH1wtOg41AkWCy/w+ATLanTf55XheGW94DRERF3T1GrEh9vaZiuu7wMlZytcEouFFxgQrcXkgZGQZeDdTSdExyEi6pLl+86gprEVPcL8O64fI9fDYuElnpzQFwCwNqcEhWcbBachIrJNqwn4cHshAOCx8b3ho+Tbl6viv4yXGBwXhAn9I2CWgXc3nRQdh4jIJjsqJFQ1tCIuxA+zU+NEx6HLYLHwIvMnWWYt1h0oQ0Wz4DBERFZqbjXhp1LL29UTE/pA7cO3LlfGfx0vMiQuGJMGWGYtfjjDf3oicg/L9hWj3iAhLsQPtwzjbIWr47uLl5k/qR8AYH+1hBNVvNaCiFxbU6sRS9vuBHnsul5Q8doKl8d/IS+THBuEif27Q4aExbxDhIhc3Oe7TqOm0YAwjYxZQ7luhTtgsfBCT1zfGwDwXX45jlVwXQsick2NeiPe32q52HxqnJmzFW6C/0peaFCMFoNDzJBl4H9/5mqcROSaPt99GjWNrUgI9cPw7rLoOGQlFgsvNS3eDAD49kApjnLWgohcTKPeiKVtsxXzxveCkotsug0WCy8VGwBMGRgBWQb+8eNR0XGIiM7z6c5C1DS2IjE8ADcP4bUV7oTFwos9eX1vSBLwfV458kvqRMchIgIA1DUb8P4Wy8XlT07sw1U23Qz/tbxYUlQgZgyxrLf/VgZnLYjINXy47SR0LUb0jeiGm1NiRcchG7FYeLmnJ/eDUiHh5yOVyDp9TnQcIvJyZxv0+Hi7Zd2K30/pxx1M3RCLhZdLDA/AbW0r2b35Q4HgNETk7ZZsPoHGVhMGxwZh6qAo0XGoC1gsCE9M7AOVUsKuk2ex83i16DhE5KXK61rw+e7TACyzFZLE2Qp3xGJBiAvxx5yRCQCAv20sgCzzfnEicr7Fm45BbzRjRM8QXNevu+g41EUsFgQAmDehD3xVCmQX1eLnI5Wi4xCRlymuacLyvcUAgD9MSeJshRtjsSAAQESgL+4f3RMA8ObGozCbOWtBRM7zjx+PwWiWMbZvOEb1ChMdh64CiwV1eHRcb3TT+OBwmQ7f5pWJjkNEXuJYRT1WZ58BYJmtIPfGYkEdQgLU+K9xvQAAf99YgFajWXAiIvIGf/2hAGYZuGFQFFLig0XHoavEYkHneXhMIsK7aXD6bBNW7CsSHYeIPFzW6RpkHKqAQgL+MJWzFZ6AxYLOE6DxwZMT+wAA3vnpOBr1RsGJiMhTybKM19cfAQDcMTwefSK6CU5E9sBiQRe5a0QCEkL9Uf2rFfCIiOzt5yOV2Fd4DhofBeZP6ic6DtkJiwVdRO2j6JiSfH/rSdQ0tgpORESexmSW8dcNltV+H7i2J6KCfAUnInthsaBO3TQ4GoNitGjQG/HupuOi4xCRh1mTXYKCinpofX3w2HV9RMchO2KxoE4pFBL+dEN/AMDnu07jzLkmwYmIyFPojaaOHZV/N74PgvxVghORPbFY0CWN7RuO0b3D0Goy462N3FadiOzj812nUVLbjEitBg+0LcxHnoPFgi5JkiQ8O80ya7E6pwT5JXWCExGRu6trMuD/fracXn16Uj/4qZWCE5G9sVjQZQ2JC8bNKTGQZeAv3x/mBmVEdFUWbzqGumYD+kV2w+3D40XHIQdgsaAremZqEtRKBXaeOIvNBVWi4xCRmyquacJnOy3boj83fQCUCm405olYLOiK4kP98eC1PQFYZi2MJi71TUS2++sPBWg1mTGmTzjGc1t0j8ViQVZ57Po+CPZX4VhlA77MPCM6DhG5meyic/gmtxSSBDw3vT+3RfdgLBZklSA/FZ6c0BcA8FbGUS71TURWk2UZf/n+MADgltQ4DIoJEpyIHInFgqx2zzU90CPMstT3+1tPio5DRG5i46GKjqW7/zCVS3d7OhYLspraR4Fn2xbNWrr1BMrrWgQnIiJXZzCZ8UbbRmO/HdsL0UF+ghORo7FYkE1uSI5CWo8QtBjM+OsPR0THISIX969dp3GyuhFhAWo8cl0v0XHICVgsyCaSJOHFmwYCAFbtL0FOca3YQETksmoaW/HOj5ZVe/8wNQmBvly62xuwWJDNUuKDccuwWADAK98c5KJZRNSptzOOQtdixIBoLe7gYlhew+ZisXXrVsyYMQMxMTGQJAlr1qxxQCxydX+c2h9+KiX2F9ViXW6p6DhE5GIKyuvxnz2WxbBevGkgF8PyIjYXi8bGRqSkpGDx4sWOyENuIirIF4+N7w0AeGP9ETS3mgQnIiJXIcsy/vztIZhl4IZBUUjvHSY6EjmRj63fMG3aNEybNs0RWcjN/HZcLyzfV4yS2mYs3XoST03qKzoSEbmAnw5XYvvxaqiVCjw/fYDoOORkvMaCusxXpezY/fSfW06grK5ZcCIiEq3VaMZrbYthPTQmEQlh/oITkbPZPGNhK71eD71e3/G1TqcDABgMBhgMBrv9nPbXsudreip7jtXUAeEY3iMYmadrsei7w/j77YOv+jVdCY8r23C8rOepY/XJjkKcqm5EeDc1Hhnbwy5/P08dK0dw5FhZ+5qSfBWX9EuShNWrV2PWrFmXfM7ChQvx8ssvX/T4smXL4O/PJusJihuAv+cpIUPCk4OM6K0VnYiIRNC1Aq/mKKE3Sbi7twnXRPCOMU/S1NSEOXPmoK6uDlrtpX/RO3zG4rnnnsOCBQs6vtbpdIiPj8eUKVMuG8xWBoMBGRkZmDx5MlQq3it9OY4Yq2LNQazILMHGsyFYc8c1HnMFOI8r23C8rOeJY/XHlXnQm8owJFaLhfeNgsJOvwc8cawcxZFj1X7G4UocXiw0Gg00Gs1Fj6tUKoccII56XU9kz7H607SB2HCwEkfK6/HV/lLcm97TLq/rKnhc2YbjZT1PGavMwhqszimDJAF/njUYGo3a7j/DU8bKGRwxVta+ns0XbzY0NCAnJwc5OTkAgFOnTiEnJwdFRUW2vhR5kNAANX4/xbK50N9+KMDZBv0VvoOIPIXJLOPFtQcBAHekxSMlPlhsIBLK5mKRmZmJ1NRUpKamAgAWLFiA1NRUvPjii3YPR+5lzsgEDIjWQtdixJsbC0THISInWba3CIfKdND6+uCPNySJjkOC2Vwsxo8fD1mWL/rz6aefOiAeuRMfpQKvzBwEAFi+rxgHztSKDUREDlfT2Io3f7B8kPj9lCSEdbv41Dd5F65jQXY1omcoZqfGQpaBF9cehNnMq8KJPNmbGwtQ12xA/6hAzB2VIDoOuQAWC7K756b1R4BaiZziWnyVVSw6DhE5yIEztfhir+X6uldmJsNHybcUYrEgB4jQ+mL+JMuFnIvWH0FNY6vgRERkbyazjOdX50GWgVlDYzAyMVR0JHIRLBbkEA9c2xP9owJR22TAorblfYnIc3y+qxD5JToE+vrghRsHio5DLoTFghxCpVTgtdnJAICvss5gX2GN4EREZC+Vuhb8feNRAMAfb+iP7oG8YJN+wWJBDpPWIxR3jYgHALywOg8Gk1lwIiKyhz9/dxj1eiNS4oIwZyQv2KTzsViQQ/3phv4IDVDjaEUDPtp+SnQcIrpK245V4ZvcUigk4LXZgz1m+X6yHxYLcqiQADWea9ta/Z0fj+HMuSbBiYioq1oMJvzPmnwAwH3pPZEcGyQ4EbkiFgtyuNvS4jCyZyiaDSYsXHcIV7GhLhEJtGTzCRSebUJEoKZjCX+iC7FYkMNJkoRXZyfDRyHhx8MV2JBfLjoSEdnoWEU93tt8HADwPzcNRKAvNwOjzrFYkFP0iwzE78b3BgC8uO4g6poMghMRkbXMZhnPrsqDwSRjQv8I3DQkWnQkcmEsFuQ0867vg17dA1BVr8frG7i2BZG7+M/eImSdPocAtRJ/npUMSeIFm3RpLBbkNL4qJRbNHgwA+GJvMXafPCs4ERFdSVldM95YfwQA8MzUJMQG+wlORK6OxYKcalSvMMxp26jouVV5aDGYBCciokuRZRn/s+YgGvRGpCYE4970nqIjkRtgsSCne3Zaf0QEanCquhH/9/Mx0XGI6BLW55fjx8MVUCklvH7LEK5ZQVZhsSCn0/qq8MpMy3Lf7285icNlOsGJiOhCdU0GvLTuIADgd9f1RlJUoOBE5C5YLEiIG5KjcMOgKBjNMp75OpfLfRO5mD9/dwhV9Xr06h6Ax67vIzoOuREWCxLmlZmDEOSnQn6JDku3nhQdh4jabDpSia+zzkCSgL/dNgS+KqXoSORGWCxImAitLxbebNlu+R8/HkVBeb3gRERU12zAc6vyAAAPX5uItB6hghORu2GxIKFmDY3FpAERMJgsp0SMPCVCJNRr3x1Cua4FieEB+P2UJNFxyA2xWJBQkiThtdmDofX1wYEzdVi6jadEiETZXFCJLzMtp0D+etsQ+Kl5CoRsx2JBwkVqffHSjEEAgH9kHMOxCp4SIXI2Xcsvp0AeHJ2IET15CoS6hsWCXMItw2JxfVJ3tJrM+MNXPCVC5GyvfXsYZXUt6BHmj2em8hQIdR2LBbkESZKw6JYhCPT1Qe6ZOry3+YToSERe48dDFViRWWw5BXIrT4HQ1WGxIJcRFeSLV2ZaTon870/HkHemTnAiIs93tkGPZ1cdAAD8ZkwiRvUKE5yI3B2LBbmUWUNjMX2wZeGs+SuyuZcIkQPJsoznV+ehuqEVSZGBvAuE7ILFglyKJEl4bdZgRARqcKKqEW9sOCI6EpHHWrm/BD8ctOwF8tadKVwIi+yCxYJcTkiAGm/cNgQA8MmOQmw/Vi04EZHnKa5pwsK2vUCentwPg2KCBCciT8FiQS7p+qQIzG3bXv2Zr3NR12wQnIjIc5jNMv7wVS4a9EYM7xGCR8b1Fh2JPAiLBbmsF24cgJ5h/iira8F/r8mHLMuiIxF5hKXbTmLPqRr4q5X4+x0p3A6d7IrFglyWv9oHb905FEqFhG9yS7Fyf4noSERu78CZWrz5QwEA4MWbBqJHWIDgRORpWCzIpQ1LCMHTk/oCAF5cm49T1Y2CExG5rwa9EU9+kQ2jWcb0wVG4c0S86EjkgVgsyOX9bnwfXNMrFE2tJjz5RTZajVyVk6grXlp7EIVnmxAT5ItFs4dAkngKhOyPxYJcnlIh4e07hyLYX4W8kjr8fWOB6EhEbmdtTglW7j8DhQT8465UBPmrREciD8ViQW4hOsgPb9xquQX1/a0nse1YleBERO6juKYJ/706HwDw+IS+GJnIDcbIcVgsyG1MHRTVcQvqgi9zUVWvF5yIyPUZTGY8uTwb9W23lj45oY/oSOThWCzIrfz3jQPRN6Ibqur1eHpFDkxm3oJKdDl/3XAE2UW1CPT1wdt3DoWPkr/2ybF4hJFb8VMr8d7cYfBTKbH9eDUW/3xcdCQil5VxqAIfbDsFAPjbbSmID/UXnIi8AYsFuZ2+kYF4dVYyAOAfPx3FzuNc8pvoQsU1Tfj9lzkAgIeuTcQNyVFiA5HXYLEgt3RrWhzuGB4HWQaeXJ6DSl2L6EhELqPVaMbjy/ZD12JESnwwnp3WX3Qk8iIsFuS2Xr45Gf2jAlHdoMeTy7NhNHF9CyIA+Mv3h5F7pg5Bfiq8OycVah/+qifn4dFGbstPrcS7c4chQK3E7pM1+MePx0RHIhLu+7wyfLqzEADw1h0piAvhdRXkXCwW5NZ6d++Gv9wyGACweNNxbDxYLjgRkTjHKurxzFe5AIBHxvXCxAGRghORN2KxILc3c2gsHhjdE4BlfYsTVQ1iAxEJoGsx4JHPs9DYakJ6rzA8MzVJdCTyUiwW5BFeuHEARvYMRYPeiEc+z0KD3ig6EpHTmM0yfv9lLk5WNyImyBeL56RyvQoShkceeQSVUoHFc1MRqdXgeGUDnvkqF7LMxbPIO7y76TgyDlVArVRgyT1pCOumER2JvBiLBXmMiEBfvDc3DSqlhPX55Xh/60nRkYgcblNBJd768SgA4M+zBiElPlhsIPJ6LBbkUdJ6hGDhzYMAWJYy3lxQKTgRkeOcrGrAU19kQ5aBOaMScOeIBNGRiFgsyPPMGZmAO4fHwywDTyzLxvFKXsxJnqeuyYDffJYJXYsRqQnBeGnGQNGRiACwWJAHkiQJr8wahBE9Q1CvN+I3n+1DbVOr6FhEdmM0mfH4F/s7LtZ8/940aHyUomMRAWCxIA+l8VHin/ekITbYD4Vnm/DYf/bDwJU5yUO8+t1hbDtWDT+VEkvvG46IQF/RkYg6sFiQxwrrpsFHDwxHgFqJnSfO4uVvDoqORHTVlu0p6lhZ8+07U5AcGyQ2ENEFWCzIo/WP0uKdu1IhScC/dxfhs7ZfyETuaNeJs3hxbT4A4PeT++GG5GjBiYguxmJBHm/SwEj86QbL7o4vf3MQPx2uEJyIyHbHK+vxyOeZMJplzEiJweMT+oiORNQpFgvyCo+M69Vxp8jjy7Jx4Eyt6EhEVqusb8H9H++DrsWItB4h+NttQyBJkuhYRJ1isSCvIEkSXp2djHH9uqPZYMJDn+5DcU2T6FhEV9SoN+KhT/ehpLYZieEB+OC+4fBV8Q4Qcl0sFuQ1VEoF3ps7DAOitahuaMUDn+zlbajk0owmM574Ihv5JTqEBqjx6YMjEBqgFh2L6LJYLMirdNP44JMHRiA6yBcnqhrxX//KQovBJDoW0UVkWcZL6w7i5yOV0Pgo8OH9w9EjLEB0LKIrYrEgrxMV5ItPHhyBQI0P9hbWYP7yHJjM3LCMXMv//nQc/9lTBEkC3rkrFcMSQkRHIrIKiwV5pf5RWrx/XxrUSgU2HCzH86vyuBsquYzPdhbi7baNxRbOGIQbkqMEJyKyHosFea3RvcPxv3cPhUICVmQW440NBaIjEWFtTgleWmdZzG3+pL64f3RPsYGIbMRiQV7thuRoLLplMADgn1tO4P0tJwQnIm+2qaASv/8yFwBwf3oPPDWxr+BERLZjsSCvd+eIBDw7zbKA1qL1R7BiX5HgROSNsk7X4Hf/zoLRLOPmlBi8NGMQ16ogt8RiQQTg0et645FxvQAAz67Kw9qcEsGJyJvkFtfigY/3ocVgxvik7njz9hQoFCwV5J66VCzee+89JCYmwtfXF2lpadi2bZu9cxE53bPT+uPukQmQZWDBl7n47kCZ6EjkBQ6W6nDvR3tQrzdiZGIo3ps7DGoffuYj92Xz0btixQrMnz8fL7zwArKzszF27FhMmzYNRUWcPib3JkkSXpuVjNvS4mAyy3hqeTZ+PFwpOhZ5sNJG4IFPszqW6v74gRHwV/uIjkV0VWwuFm+99RYefvhh/OY3v8GAAQPwj3/8A/Hx8ViyZIkj8hE5lUIh4Y1bh2DW0BgYzTKeXJGLg+c4JU32d6yyAe8eUqK22YCU+GB88uAIdNOwVJD7s+kobm1tRVZWFp599tnzHp8yZQp27tzZ6ffo9Xro9fqOr3U6HQDAYDDAYDDYmveS2l/Lnq/pqThWV7Zo1kC0Gk34Pr8CHxcoMOxQOSYO5FoCV8JjyzrHKxtw3yeZaDBKGBjdDR/dmwo/JcftUnhcWc+RY2Xta0qyDasClZaWIjY2Fjt27MDo0aM7Hv/LX/6Czz77DAUFF68DsHDhQrz88ssXPb5s2TL4+/tb+6OJnM5kBj49psCBGgWUkowH+pkxJJSLaNHVKWkE3jukRINRQoy/jMcHmhCgEp2K6MqampowZ84c1NXVQavVXvJ5XZp3u/AWKFmWL3lb1HPPPYcFCxZ0fK3T6RAfH48pU6ZcNpitDAYDMjIyMHnyZKhU/L/0cjhW1pvQoscD/9yEnLMKfHrMB3+/bTBuHMyZi0vhsXV5eSV1ePGzLDQYjRgY3Q1zY2sxazrH6kp4XFnPkWPVfsbhSmwqFuHh4VAqlSgvLz/v8crKSkRGRnb6PRqNBhqN5qLHVSqVQw4QR72uJ+JYXVkAgPv6mtEzLhZrcsuw4KsDMJiB24fHi47m0nhsXSyzsAYPfpKFer0RqQnB+PCeVGzflMGxsgHHynqOGCtrX8+mizfVajXS0tKQkZFx3uMZGRnnnRoh8iRKCXjjlmTcPTIBZhl45usD+Hz3adGxyI3sPFGN+z7ei3q9EaMSQ/H5w6Og9eMbJHkmm0+FLFiwAPfeey+GDx+O9PR0LF26FEVFRXj00UcdkY/IJSgUEv4yOxkaHwU+3VmI/1mTj3ONrXhiQh+ujkiXtT6vDE8tz0GryYyxfcOx9N7h8FMreSEieSybi8Wdd96Js2fP4pVXXkFZWRmSk5Px/fffo0ePHo7IR+QyJEnCSzMGopvGB4s3HcdbGUdRVa/HwpsHQclVEqkTn+8+jRfX5kOWgamDIvHOXanwVSlFxyJyqC5dvPnYY4/hscces3cWIpcnSRL+MDUJ3QM1WPjNQXy++zTONurx1h1D+YZBHWRZxtsZR/G/Px8HAMwZlYA/z0xmASWvwHVjibrg/tE9sfjuYVArFfg+rxwPfLIXuhZObRNgNJnx/Oq8jlLx9KR+eG0WSwV5DxYLoi66cUg0Pn3Islri7pM1uPW9nSiuaRIdiwTStRjw8GeZ+GJvMRQS8NrsZDw1qS+vwyGvwmJBdBVG9w7HikeuQZTWF8cqGzDz3R3ILKwRHYsEKK5pwm1LdmLL0Sr4qhRYck8a5o7itWfkfVgsiK7SoJggrJl3LZJjtahpbMWcD/ZgdfYZ0bHIibJO12DWuztwtKIBkVoNvnpkNKYO4kJq5J1YLIjsICrIF18+ko4bBkWh1WTG0yty8bcfjsBs5hLgnm519hncvXQPzja2IjlWi7XzxmBwXJDoWETCsFgQ2Ym/2gfvzR2Gx8b3BgC8u+kEHv5sH2qbWgUnI0doNZqxcN1BPL0iF60mM6YOisSXj6QjKshXdDQioVgsiOxIoZDwxxv64607UqDxUWBTQRVmLN6Og6V1oqORHVXoWjDng934dGchAODx6/tgydw0+Ku57TkRiwWRA9wyLA6rHhuN+FA/FNc045b3dmJlFq+78AR7Tp7Fjf+7HZmnzyFQ44MP7huOP0xNgoK3kxIBYLEgcphBMUH49vGxuD6pO/RGM37/VS6eW3UAza0m0dGoC8xmGUs2n8CcD/egukGPpMhArHtiDCYP7HwDRiJvxWJB5EBB/ip8dP8IzJ/UF5IEfLG3GDMWb8ehUuu2HybXUKFrwb0f78EbG47AZJZxc0oMVs8bjcTwANHRiFwOiwWRgykUEuZP6od/PzwKEYEaHK9swKx3d+CTHacgy7xrxNX9dLgC097Zhh3Hz8JPpcTrtwzGO3cN5fUURJfAYkHkJNf2CceG+eMwaUAEWk1mvPzNITz06T5U6lpER6NONLUa8dLafDz8WSZqGlsxMFqLb54Yg7tGJnAlTaLLYLEgcqLQADU+uG84Xpk5COq2u0Ymv70Vq/af4eyFC9l98iymvbMNn+06DQB46NpErJ43Gn0iuglORuT6OJdH5GSSJOG+9J4YlRiGP3yVi7ySOiz4MhffHijDX2YP5joIAjXqjXhjwxH8q61QRAf54vVbh+C6ft0FJyNyH5yxIBIkKSoQqx8bjWemJkGtVODnI5WY/PYWfLG3iCt2CrD1aBWm/mNrR6m4e2QCNj49jqWCyEacsSASyEepwLzr+2DywEg88/UB5BbX4rlVeVixrxivzkpGciyXhna00tpm/PnbQ1ifXw4AiA32w+u3DsbYviwURF3BGQsiF9AvMhArH03Hf984AAFqJXKKazFj8Xb8z5p81DUZRMfzSK1GM97bfBwT/74F6/PLoVRIePDanvjh6XEsFURXgTMWRC7CR6nAb8b2woyUGPzl+8NYm1OKz3efxvd5ZXhqUl/cPTIBKiU/C1wtWZax8VAF3thwBCerGgEAI3qG4JWZyRgQrRWcjsj9sVgQuZhIrS/euSsVd41IwItr83GssgEvrj2Ij7efwjNT+2P64Cje7thFmYU1WLT+CLJOnwMAhHdT4/npAzA7NZZjSmQnLBZELiq9dxi+f2oslu8twjs/HUPh2SbMW7YfKfHB+OPUJIzuHcY3QysVlNfjzY0FyDhUAQDwVSnwmzG98F/X9YLWVyU4HZFnYbEgcmEqpQL3pvfELcPi8MG2k1i69SRyi2sx98M9SE0IxhMT+uD6pAgWjEs4cKYWi38+jo1thUKpkHDH8HjMn9QXkVre1kvkCCwWRG4gQOOD+ZP6Ye6oHnh303F8sbcI2UW1eOjTTAyM1mLe9X1wQ3IUlNxhE7IsY++pGry7+QS2Hq0CAEgSMC05Cgsm90OfiEDBCYk8G4sFkRvpHqjBwpsH4bHre+Ojbafw792ncahMh3nL9iM22A/3XNMDd46IR2iAWnRUp2sxmLAupxSf7SrEwbZN3pQKCTOHxuCx8b1ZKIichMWCyA1FBPriuekD8LvxvfHJjkL8a1chSmqb8caGI3j7x6O4OSUGc0clYGh8sMefJimsbsQXe4uwIrMYtW235mp8FLg1LQ6PjuuNhDB/wQmJvAuLBZEbC/ZX4+nJ/fC78b3xTa7l03p+iQ5fZ53B11ln0Cs8ALNTYzErNRbxoZ7zBlvT2IpvD5RidXYJsotqOx6PC/HDfek9cHtaPEK8cNaGyBWwWBB5AF+VErcPj8dtaXHILq7F57tOY31+GU5WN+LvGUfx94yjGNEzBFMHRWHSgEj0DA8QHdlmVfV6bDpSiY2HyrG5oArGtmXPFRIwrl933HtND4xPiuB1JkSCsVgQeRBJkjAsIQTDEkLw51nJ2JBfjjXZJdhxohr7Cs9hX+E5vPrdYfSJ6IaJAyJwfVIEhsYHw1elFB39IiazjMNlOmw5WoWMQxXIPVOLX28AmxyrxezUOMxIiUZEIO/wIHIVLBZEHqqbxge3pcXhtrQ4lNe14Lu8Mvx0uAJ7T9XgeGUDjlc24P0tJ6FWKpASH4SRiaEY0TMUQ+KChVz82aA34nCZDntP1WDvqRrsP30O9Xrjec8ZHBuEiQMicOPgaPSN5MWYRK6IxYLIC0QF+eLhMYl4eEwi6poN2Hq0Cj8ersDOE2dRVa/vmM0ATgAAIrUa9I/Son90IPpFBCIuxA+xIX6I0vrC5yqWFTebZVQ36HGmthkl55pxvLIBR8p1OFJej9Nnmy56fqDGByMTQzFxQCQmDojg2hNEboDFgsjLBPmpMCMlBjNSYiDLMgrPNmHfqRrsOVWDrNM1KDzbhAqdHhW6KmxpWweinUICorS+CO2mhtZXhUBfH2h9VQjQ+ECSALPZjMJTCmR9dwStJhm6FgPqW4zQNRtwrsmA8roWtJrMl8wWqdVgWEJIx+zJgGgtr5kgcjMsFkReTJIkJIYHIDE8AHeMiAdgOSVRUF5vmUkoq8eJqgaU1DajrNZSCkrrWlBa13KZV1UA5UWX/q9t5SQ2xA89wgIwIFqLAVGB6B+t9cr1N4g8DYsFEZ2nm8YHaT1CkNYj5LzHzWYZVQ16lNQ2o7ap1TIT0TYb0dRquRbCbDLj+IkT6NO7N/w1Kmj9LLMagb4qBPmpEB3ki6ggX+7SSuTBWCyIyCoKhYRIre9lr3MwGAz43nAM0yf3hUrFzb2IvBE/NhAREZHdsFgQERGR3bBYEBERkd2wWBAREZHdsFgQERGR3bBYEBERkd2wWBAREZHdsFgQERGR3bBYEBERkd2wWBAREZHdsFgQERGR3bBYEBERkd2wWBAREZHdOH13U1mWAQA6nc6ur2swGNDU1ASdTsddFa+AY2U9jpVtOF7W41hZj2NlPUeOVfv7dvv7+KU4vVjU19cDAOLj4539o4mIiOgq1dfXIygo6JL/XZKvVD3szGw2o7S0FIGBgZAkyW6vq9PpEB8fj+LiYmi1Wru9rifiWFmPY2Ubjpf1OFbW41hZz5FjJcsy6uvrERMTA4Xi0ldSOH3GQqFQIC4uzmGvr9VqeeBZiWNlPY6VbThe1uNYWY9jZT1HjdXlZira8eJNIiIishsWCyIiIrIbjykWGo0GL730EjQajegoLo9jZT2OlW04XtbjWFmPY2U9Vxgrp1+8SURERJ7LY2YsiIiISDwWCyIiIrIbFgsiIiKyGxYLIiIishu3KhbvvfceEhMT4evri7S0NGzbtu2yz9+yZQvS0tLg6+uLXr164Z///KeTkopny1ht3rwZkiRd9OfIkSNOTCzG1q1bMWPGDMTExECSJKxZs+aK3+Otx5WtY+XNx9WiRYswYsQIBAYGIiIiArNmzUJBQcEVv88bj62ujJW3HltLlizBkCFDOha/Sk9Px/r16y/7PSKOKbcpFitWrMD8+fPxwgsvIDs7G2PHjsW0adNQVFTU6fNPnTqF6dOnY+zYscjOzsbzzz+PJ598EitXrnRycuezdazaFRQUoKysrONP3759nZRYnMbGRqSkpGDx4sVWPd+bjytbx6qdNx5XW7Zswbx587B7925kZGTAaDRiypQpaGxsvOT3eOux1ZWxaudtx1ZcXBxef/11ZGZmIjMzExMmTMDMmTNx8ODBTp8v7JiS3cTIkSPlRx999LzH+vfvLz/77LOdPv+Pf/yj3L9///Mee+SRR+RrrrnGYRldha1jtWnTJhmAfO7cOSekc10A5NWrV1/2Od58XP2aNWPF4+oXlZWVMgB5y5Ytl3wOjy0La8aKx9YvQkJC5A8//LDT/ybqmHKLGYvW1lZkZWVhypQp5z0+ZcoU7Ny5s9Pv2bVr10XPnzp1KjIzM2EwGByWVbSujFW71NRUREdHY+LEidi0aZMjY7otbz2urgaPK6Curg4AEBoaesnn8NiysGas2nnzsWUymbB8+XI0NjYiPT290+eIOqbcolhUV1fDZDIhMjLyvMcjIyNRXl7e6feUl5d3+nyj0Yjq6mqHZRWtK2MVHR2NpUuXYuXKlVi1ahWSkpIwceJEbN261RmR3Yq3HlddwePKQpZlLFiwAGPGjEFycvIln8djy/qx8uZjKy8vD926dYNGo8Gjjz6K1atXY+DAgZ0+V9Qx5fTdTa/Ghdusy7J82a3XO3t+Z497IlvGKikpCUlJSR1fp6eno7i4GG+++SbGjRvn0JzuyJuPK1vwuLJ4/PHHceDAAWzfvv2Kz/X2Y8vasfLmYyspKQk5OTmora3FypUrcf/992PLli2XLBcijim3mLEIDw+HUqm86BN3ZWXlRW2sXVRUVKfP9/HxQVhYmMOyitaVserMNddcg2PHjtk7ntvz1uPKXrztuHriiSewbt06bNq0CXFxcZd9rrcfW7aMVWe85dhSq9Xo06cPhg8fjkWLFiElJQXvvPNOp88VdUy5RbFQq9VIS0tDRkbGeY9nZGRg9OjRnX5Penr6Rc/fuHEjhg8fDpVK5bCsonVlrDqTnZ2N6Ohoe8dze956XNmLtxxXsizj8ccfx6pVq/Dzzz8jMTHxit/jrcdWV8aqM95ybF1IlmXo9fpO/5uwY8qhl4ba0fLly2WVSiV/9NFH8qFDh+T58+fLAQEBcmFhoSzLsvzss8/K9957b8fzT548Kfv7+8tPP/20fOjQIfmjjz6SVSqV/PXXX4v6KziNrWP19ttvy6tXr5aPHj0q5+fny88++6wMQF65cqWov4LT1NfXy9nZ2XJ2drYMQH7rrbfk7Oxs+fTp07Is87j6NVvHypuPq9/97ndyUFCQvHnzZrmsrKzjT1NTU8dzeGxZdGWsvPXYeu655+StW7fKp06dkg8cOCA///zzskKhkDdu3CjLsuscU25TLGRZlt999125R48eslqtlocNG3be7Uj333+/fN111533/M2bN8upqamyWq2We/bsKS9ZssTJicWxZazeeOMNuXfv3rKvr68cEhIijxkzRv7uu+8EpHa+9tvWLvxz//33y7LM4+rXbB0rbz6uOhsnAPInn3zS8RweWxZdGStvPbYeeuihjt/r3bt3lydOnNhRKmTZdY4pbptOREREduMW11gQERGRe2CxICIiIrthsSAiIiK7YbEgIiIiu2GxICIiIrthsSAiIiK7YbEgIiIiu2GxICIiIrthsSAiIiK7YbEgIiIiu2GxICIiIrthsSAiIiK7+X/FIL4kATzYAQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(0, 3, 100)\n",
    "plot(x, f.(x))\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38f72375-eecb-4512-9027-36372e27bf3a",
   "metadata": {},
   "source": [
    "### Functions defined by a block of code"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "195e71c6-22c5-4a52-9482-c600a77b1793",
   "metadata": {},
   "source": [
    "The more general syntax is `function  ... end`, which for the above example is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "846e2732-557a-45aa-9c35-003b2d8daaef",
   "metadata": {},
   "outputs": [],
   "source": [
    "function f(x)\n",
    "    2x^2 - 6x + 4\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "3c31bc7b-427c-4497-acee-a91d473fa04c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The vertex is at 1.5, giving minimum value -0.5\n"
     ]
    }
   ],
   "source": [
    "a = 2\n",
    "b = -6\n",
    "vertex = -b/(2a)\n",
    "println(\"The vertex is at $vertex, giving minimum value $(f(vertex))\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05503d19-c77f-4d1f-adf3-90767e792cc9",
   "metadata": {},
   "source": [
    "### The keyword `return`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1502c08b-d0c2-4bd6-9535-9a6fbdec1987",
   "metadata": {},
   "source": [
    "This is fine if the output value is always computed on the last line of code,\n",
    "but for more flexibility (and to my mind, better readability) there is the keyword `return`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "4924eb88-7668-4642-aa70-c07cf9967066",
   "metadata": {},
   "outputs": [],
   "source": [
    "function f(x)\n",
    "    return 2x^2 - 6x + 4\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f60faec5-79bb-4859-b29d-9939cb7c1ae5",
   "metadata": {},
   "source": [
    "This time the style is more \"Pythonic\", since the output variables are specifed in the `return` line rather than on the `function` line as Matlab does.\n",
    "This allows different calls of the function to return different type of value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "650afc1e-7b0a-4b36-b1bb-3184a63347e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "function squareroots(x)\n",
    "    if x > 0\n",
    "        return sqrt(x), -sqrt(x)\n",
    "    elseif x == 0\n",
    "        return 0\n",
    "    else\n",
    "        println(\"I can only handle real roots; sorry.\")\n",
    "    end\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "d54aa00b-88bc-49d3-a5ba-e487f6e7dc36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.7320508075688772, -1.7320508075688772)"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "squareroots(3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "4f4ba0e5-8002-4644-b783-9a4866354555",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "squareroots(0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "85310dce-b732-408c-9f51-2b8ac2ce2fcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I can only handle real roots; sorry.\n"
     ]
    }
   ],
   "source": [
    "squareroots(-1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e0ad706-2cda-44ce-8db1-133ec7435b37",
   "metadata": {},
   "source": [
    "(vectorizationoffunctions)=\n",
    "(vectorization-of-functions)=\n",
    "## Vectorization of Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a2122a2-05a9-4631-9ebc-0991998cb871",
   "metadata": {},
   "source": [
    "One innovation in Julia is that the dot notation introduced above for\n",
    "[arithmetic on arrays](vectorization-and-broadcasting) can also be used to vectorize a function; both ones provided by Julia and ones defined in your code.\n",
    "\n",
    "A function `f(x)` whose code expects a number `x` or one `g(x, y)` that expects several numbers can be used on compatable arrays with\n",
    "\n",
    "    Y = f.(X)\n",
    "    Z = g.(X,Y)\n",
    "    \n",
    " The former is thus roughly a short-hand for\n",
    " \n",
    "     for i in length(X)\n",
    "         Y[i] = f(X[i])\n",
    "     end\n",
    "     \n",
    "This is used quite a lot in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "900271fa-0135-4fcb-bcb6-ca1092553a4b",
   "metadata": {},
   "source": [
    "(plotting-with-pyplot)=\n",
    "## Plotting graphs: a bit more about PyPlot\n",
    "\n",
    "There are many graphics packages for Julia; this book uses `PyPlot`.\n",
    "The name is because this is a front end to the Python package `matplotlib.pyplot` and in turn that name reflects the fact that Matplotlib mimics Matlab's plotting tools, so this choice makes it easiest for readers familiar with one of those languages.\n",
    "\n",
    "To install PyPlot, see the notes on [getting PyPlot](pyplot) in {ref}`section:installing-julia-and-packages`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "873e5295-bb4c-4b41-b202-ae3ef33099fd",
   "metadata": {},
   "source": [
    "(lstrings)=\n",
    "### L-Strings for inserting LaTeX mathematical markup\n",
    "\n",
    "Mathematical formulas can be used in the annotations on graphs by the use of **L-strings**:\n",
    "string prefixed with 'L' and containing LaTeX mathematical markup between '$' signs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a433eb0-56e0-4f47-9664-629d82b47748",
   "metadata": {},
   "source": [
    "For now I just illustrate all this with a few examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "ec8bd49d-2da4-4bda-959a-119cc5c1e089",
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "8bef7a14-3ae2-4371-853f-3f828e928863",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(0, 4pi, 100)\n",
    "y = exp.(-x/8) .* cos.(x)\n",
    "\n",
    "figure()\n",
    "title(L\"The decaying oscilation $y = e^{-x/8} \\cos x$\")\n",
    "plot(x, y)\n",
    "xlabel(\"x\")\n",
    "ylabel(\"y\")\n",
    "\n",
    "figure(figsize=[10,6])\n",
    "z = exp.(-x/4) .* sin.(2x)\n",
    "title(\"Adding a faster decay, labels, and wide graph paper\")\n",
    "plot(x, y, label=L\"$e^{-x/8} \\cos x$\")\n",
    "plot(x, z, label=L\"$e^{-x/4} \\sin 2x$\")\n",
    "xlabel(\"x\")\n",
    "ylabel(\"y and z\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14842aea-8e90-4dd9-bfcb-ec4c6d2f4f6b",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "*To Be Continued ...*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.11.4",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}