{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fba39ca9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Calculators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a0ea050",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "**CS1302 Introduction to Computer Programming**\n",
    "___"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9dc57835",
   "metadata": {
    "hide_input": false,
    "init_cell": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "from math import cos, exp, log, pi, sin, tan\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact\n",
    "\n",
    "# interactive plot with ipympl\n",
    "%matplotlib widget  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa709cfa",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The following code is a Python one-liner that creates a calculator.\n",
    "\n",
    "- Evaluate the cell with `Ctrl+Enter`.\n",
    "- Enter `1+1` and see the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "38cbdc21",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-c12a7640cdb0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "print(eval(input()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a5b58e2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{tip}\n",
    "\n",
    "Try some calculations below using this calculator:  \n",
    "\n",
    "1. $2^3$ by entering `2**3`;\n",
    "1. $\\frac23$ by entering `2/3`;\n",
    "1. $\\left\\lceil\\frac32\\right\\rceil$ by entering `3//2`;\n",
    "1. $3\\mod 2$ by entering `3%2`;\n",
    "1. $\\sqrt{2}$ by entering `2**0.5`; and\n",
    "1. $\\sin(\\pi/6)$ by entering `sin(pi/6)`;\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f1684fb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For this lab, you will create more powerful and dedicated calculators.   \n",
    "We will first show you a demo. Then, it will be your turn to create the calculators."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be618dd2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Hypotenuse Calculator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c33f846",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{prf:proposition} \n",
    "\n",
    "By the Pythagoras theorem, given a right-angled triangle,\n",
    "\n",
    "![Right-angled triangle](images/pythagoras.dio.svg)\n",
    "\n",
    "the length of the hypotenuse is\n",
    "\n",
    "$$\n",
    "c = \\sqrt{a^2 + b^2}\n",
    "$$ (hypotenuse)\n",
    "\n",
    "where $a$ and $b$ are the lengths of the other sides of the triangle.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f68ce08c",
   "metadata": {},
   "source": [
    "We can define the following function to calculate the length `c` of the hypotenuse when given the lengths `a` and `b` of the other sides:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a4c49ba",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def length_of_hypotenuse(a, b):\n",
    "    c = (a**2 + b**2)**(0.5)  # Pythagoras\n",
    "    return c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47e70e31",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{important}\n",
    "\n",
    "You need not understand how a function is defined, but\n",
    "\n",
    "- you should know how to *write the formula {eq}`hypotenuse` as a Python expression* using the exponentiation operator `**`, and\n",
    "- *assign the variable* `c` the value of the expression (Line 2) using the assignment operator `=`.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e60a2e0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For example, you may be asked to write Line 2, while Line 1 and 3 are given to you:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8223241f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Exercise** Complete the function below to return the length `c` of the hypotenuse given the lengths `a` and `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "78599baa",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "07e9bf0ce74ed11e07ad5f772a79f6b8",
     "grade": false,
     "grade_id": "length_of_hypotenuse",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def length_of_hypotenuse(a, b):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f65bc9ca",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{caution}\n",
    "\n",
    "- Complete the above exercise to get the credit even though the answer was already revealed as a demo. Instead of copy-and-paste the answer, type it yourself.\n",
    "- Note that indentation affects the execution of Python code. In particular, the assignment statement must be indented to indicate that it is part of the *body* of the function. \n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bb1d1ce",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We will use `ipywidgets` to let user interact with the calculator more easily:\n",
    "\n",
    "- After running the cell, move the sliders to change the values of `a` and `b`. \n",
    "- Observer that the value of `c` is updated immediately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ee2083ef",
   "metadata": {
    "code_folding": [],
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "67d41aa368a14567b022235dd07db487",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description='a', max=10), IntSlider(value=4, description='b', max=10)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# hypotenuse calculator\n",
    "@interact(a=(0, 10, 1), b=(0, 10, 1))\n",
    "def calculate_hypotenuse(a=3, b=4):\n",
    "    print(\"c: {:.2f}\".format(length_of_hypotenuse(a, b)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fa3dfd5",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{important}\n",
    "\n",
    "You need not know how to write widgets, but you should know how to *format a floating point number* (Line 3).\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4efbc9a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "You can check your code with a few cases listed in the test cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fa4c77eb",
   "metadata": {
    "code_folding": [],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "f52b93d815cfd306fae374ec4d8a58c4",
     "grade": true,
     "grade_id": "test-length_of_hypotenuse",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-2287d5f2e161>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mtest_length_of_hypotenuse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0mtest_length_of_hypotenuse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0mtest_length_of_hypotenuse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m7\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8.06225774829855\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-6-2287d5f2e161>\u001b[0m in \u001b[0;36mtest_length_of_hypotenuse\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_length_of_hypotenuse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mc_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlength_of_hypotenuse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mcorrect\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcorrect\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-4-0aab5c1b1d83>\u001b[0m in \u001b[0;36mlength_of_hypotenuse\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mlength_of_hypotenuse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_length_of_hypotenuse(a, b, c):\n",
    "    c_ = length_of_hypotenuse(a, b)\n",
    "    correct = math.isclose(c, c_)\n",
    "    if not correct:\n",
    "        print(f\"For a={a} and b={b}, c should be {c}, not {c_}.\")\n",
    "    assert correct\n",
    "\n",
    "\n",
    "test_length_of_hypotenuse(3, 4, 5)\n",
    "test_length_of_hypotenuse(0, 0, 0)\n",
    "test_length_of_hypotenuse(4, 7, 8.06225774829855)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75945024",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Quadratic equation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f76d65e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Graphical calculator for parabola"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0714184",
   "metadata": {},
   "source": [
    "![Parabola calculator](images/parabola.dio.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb95df8e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "````{prf:definition} Parabola\n",
    "\n",
    "\n",
    "The collection of points $(x,y)$ satisfying the following equation forms a *parabola*:\n",
    "\n",
    "$$\n",
    "y=ax^2+bx+c\n",
    "$$ (parabola)\n",
    "\n",
    "where $a$, $b$, and $c$ are real numbers called the *coefficients*.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fee847f7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Exercise** Given the variables `x`, `a`, `b`, and `c` store the $x$-coordinate and the coefficients $a$, $b$, and $c$ respectively, assign `y` the corresponding $y$-coordinate of the parabola {eq}`parabola`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8379397a",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "2c86fa4ce83bcbe0906f9b64b5c1a032",
     "grade": false,
     "grade_id": "get_y",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def get_y(x, a, b, c):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06cc970e",
   "metadata": {},
   "source": [
    "To test your code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "899ca6e8",
   "metadata": {
    "code_folding": [],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "4d00403723b0578d72ce900068e343fa",
     "grade": true,
     "grade_id": "test-get_y",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-7d60c79d95e3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mtest_get_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0mtest_get_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0mtest_get_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-8-7d60c79d95e3>\u001b[0m in \u001b[0;36mtest_get_y\u001b[0;34m(y, x, a, b, c)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_get_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0my_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mcorrect\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcorrect\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-7-768f4a0c40f7>\u001b[0m in \u001b[0;36mget_y\u001b[0;34m(x, a, b, c)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_get_y(y, x, a, b, c):\n",
    "    y_ = get_y(x, a, b, c)\n",
    "    correct = math.isclose(y, y_)\n",
    "    if not correct:\n",
    "        print(f\"With (x, a, b, c)={x,a,b,c}, y should be {y} not {y_}.\")\n",
    "    assert correct\n",
    "\n",
    "\n",
    "test_get_y(0, 0, 0, 0, 0)\n",
    "test_get_y(1, 0, 1, 2, 1)\n",
    "test_get_y(2, 0, 2, 1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a3c105d1",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "0adfafae7b0307eb4e3a7be0bd936147",
     "grade": true,
     "grade_id": "htest-get_y",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86482b78",
   "metadata": {},
   "source": [
    "To run the graphical calculator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "09cf534e",
   "metadata": {
    "code_folding": [],
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8bab6b6b93b9409d87306be3fd94b1c6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-840962895d60>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_ylim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mymin\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymax\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mget_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0minteract\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-7-768f4a0c40f7>\u001b[0m in \u001b[0;36mget_y\u001b[0;34m(x, a, b, c)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# graphical calculator for parabola\n",
    "fig, ax = plt.subplots()\n",
    "xmin, xmax, ymin, ymax, resolution = -10, 10, -10, 10, 50\n",
    "x = np.linspace(xmin, xmax, resolution)\n",
    "ax.set_title(r'$y=ax^2+bx+c$')\n",
    "ax.set_xlabel(r'$x$')\n",
    "ax.set_ylabel(r'$y$')\n",
    "ax.set_xlim([xmin, xmax])\n",
    "ax.set_ylim([ymin, ymax])\n",
    "ax.grid()\n",
    "p, = ax.plot(x, get_y(x, 0, 0, 0))\n",
    "\n",
    "@interact(a=(-10, 10, 1), b=(-10, 10, 1), c=(-10, 10, 1))\n",
    "def plot_parabola(a, b, c):\n",
    "    p.set_ydata(get_y(x, a, b, c))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91104b1c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Quadratic equation solver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "426f4459",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "![quadratic equtaion solver](images/quadratic.dio.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47cb1719",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "````{prf:proposition} \n",
    "\n",
    "For the quadratic equation\n",
    "\n",
    "$$\n",
    "ax^2+bx+c=0,\n",
    "$$ (quadratic)\n",
    "the *roots* (solutions for $x$) are give by\n",
    "\n",
    "$$\n",
    "\\frac{-b-\\sqrt{b^2-4ac}}{2a},\\frac{-b+\\sqrt{b^2-4ac}}{2a}.\n",
    "$$ (quadratic_roots)\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94036e56",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Exercise** Assign to `root1` and `root2` the values of the first and second roots above respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "14f40e38",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ac8d52d2f7328a894d73bce80d19dafc",
     "grade": false,
     "grade_id": "get_roots",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def get_roots(a, b, c):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return root1, root2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29ad0dc2",
   "metadata": {},
   "source": [
    "To test your code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8cac790c",
   "metadata": {
    "code_folding": [],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "cd703af7ee4d214a1588e34c86a832eb",
     "grade": true,
     "grade_id": "test-get_roots",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-0022c65c9ae1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      7\u001b[0m                       sorted(roots_, key=mysort)).all()\n\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-12-0022c65c9ae1>\u001b[0m in \u001b[0;36mtest_get_roots\u001b[0;34m(roots, a, b, c)\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmysort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimag\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0mroots_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     assert np.isclose(sorted(roots, key=mysort), \n\u001b[1;32m      7\u001b[0m                       sorted(roots_, key=mysort)).all()\n",
      "\u001b[0;32m<ipython-input-11-b9b79580546a>\u001b[0m in \u001b[0;36mget_roots\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mroot1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mroot2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_get_roots(roots, a, b, c):\n",
    "    def mysort(c):\n",
    "        return c.real, c.imag\n",
    "    roots_ = get_roots(a, b, c)\n",
    "    assert np.isclose(sorted(roots, key=mysort), \n",
    "                      sorted(roots_, key=mysort)).all()\n",
    "\n",
    "test_get_roots((-1.0, 0.0), 1, 1, 0)\n",
    "test_get_roots((-1.0, -1.0), 1, 2, 1)\n",
    "test_get_roots((-2.0, -1.0), 1, 3, 2)\n",
    "test_get_roots([(-0.5-0.5j), (-0.5+0.5j)], 2, 2, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c586eb41",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "79a531007ec3cae77b0a47be0ba9710c",
     "grade": true,
     "grade_id": "htest-get_roots",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "014dc4c8",
   "metadata": {},
   "source": [
    "To run the calculator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c16dedb9",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "92cf8c4182774febb4f418b2bb76734a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='a', max=10, min=-10), IntSlider(value=2, description='b'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# quadratic equations solver\n",
    "@interact(a=(-10,10,1),b=(-10,10,1),c=(-10,10,1))\n",
    "def quadratic_equation_solver(a=1,b=2,c=1):\n",
    "    print('Roots: {}, {}'.format(*get_roots(a,b,c)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46de304d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Number conversion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fb12606",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Byte-to-Decimal calculator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffca5af9",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "![byte-to-decimal](images/byte-to-decimal.dio.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8348f05b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Denote a binary number stored in a byte ($8$ bits) as\n",
    "\n",
    "$$ \n",
    "b_7\\circ b_6\\circ b_5\\circ b_4\\circ b_3\\circ b_2\\circ b_1\\circ b_0, \n",
    "$$\n",
    "where $\\circ$ concatenates $b_i$'s together into a binary string."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75b1f37c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The binary string can be converted to a decimal number by the formula\n",
    "\n",
    "$$ \n",
    "b_7\\cdot 2^7 + b_6\\cdot 2^6 + b_5\\cdot 2^5 + b_4\\cdot 2^4 + b_3\\cdot 2^3 + b_2\\cdot 2^2 + b_1\\cdot 2^1 + b_0\\cdot 2^0. \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0385199",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "E.g., the binary string `'11111111'` is the largest integer represented by a byte:\n",
    "\n",
    "$$\n",
    "2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0=255=2^8-1.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "720abf1a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Exercise** Assign to `decimal` the *integer* value represented by the binary sequence `b7,b6,b5,b4,b3,b2,b1,b0` of *characters* `'0'` or `'1'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "55176120",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "9e002976b002de6304164af3ad806f43",
     "grade": false,
     "grade_id": "byte_to_decimal",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0):\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "    -----------\n",
    "    b7, ..., b0 are single characters either '0' or '1'.\n",
    "    \"\"\"\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1161699",
   "metadata": {},
   "source": [
    "To test your code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "68ad4c32",
   "metadata": {
    "code_folding": [],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "030e6a4746ee213dd7febd09db3d7680",
     "grade": true,
     "grade_id": "test-byte_to_decimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-223820389b58>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mtest_byte_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m38\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mtest_byte_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mtest_byte_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m22\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'1'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'0'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-16-223820389b58>\u001b[0m in \u001b[0;36mtest_byte_to_decimal\u001b[0;34m(decimal, b7, b6, b5, b4, b3, b2, b1, b0)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_byte_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb7\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb6\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mdecimal_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbyte_to_decimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb7\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb6\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mdecimal\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mdecimal_\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-15-55517ebc7c72>\u001b[0m in \u001b[0;36mbyte_to_decimal\u001b[0;34m(b7, b6, b5, b4, b3, b2, b1, b0)\u001b[0m\n\u001b[1;32m      6\u001b[0m     \"\"\"\n\u001b[1;32m      7\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mdecimal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_byte_to_decimal(decimal, b7, b6, b5, b4, b3, b2, b1, b0):\n",
    "    decimal_ = byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0)\n",
    "    assert decimal == decimal_ and isinstance(decimal_, int)\n",
    "\n",
    "\n",
    "test_byte_to_decimal(38, '0', '0', '1', '0', '0', '1', '1', '0')\n",
    "test_byte_to_decimal(20, '0', '0', '0', '1', '0', '1', '0', '0')\n",
    "test_byte_to_decimal(22, '0', '0', '0', '1', '0', '1', '1', '0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f6e74482",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "368a00935ff0f11755434b00e27eeaff",
     "grade": true,
     "grade_id": "htest-byte_to_decimal",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9f3ea98",
   "metadata": {},
   "source": [
    "To run the calculator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8a9dff58",
   "metadata": {
    "code_folding": [
     0
    ],
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d7a49ffe8d894cf680689b23aec54892",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='b7', options=('0', '1'), value='0'), Dropdown(description='b6', op…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# byte-to-decimal calculator\n",
    "bit = ['0', '1']\n",
    "\n",
    "\n",
    "@interact(b7=bit, b6=bit, b5=bit, b4=bit, b3=bit, b2=bit, b1=bit, b0=bit)\n",
    "def convert_byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0):\n",
    "    print('decimal:', byte_to_decimal(b7, b6, b5, b4, b3, b2, b1, b0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53688fd0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Decimal-to-Byte calculator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "982580c3",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "![decimal-to-byte](images/decimal-to-byte.dio.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee8a9ba",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Exercise** Assign to `byte` a *string of 8 bits* that represents the value of `decimal`, a non-negative decimal integer from $0$ to $2^8-1=255$.  \n",
    "*Hint: Use `//` and `%`.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b2807701",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "9de8a3c79ad6c5af5db8a55ce33675e4",
     "grade": false,
     "grade_id": "decimal_to_byte",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def decimal_to_byte(decimal):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return byte"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38f3bf24",
   "metadata": {},
   "source": [
    "To test your code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d4dd94eb",
   "metadata": {
    "code_folding": [],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "216c2407ac5231bc82b9d61a1ec8a628",
     "grade": true,
     "grade_id": "test-decimal_to_byte",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-20-4df66bcfcee3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mtest_decimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'01100111'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m103\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mtest_decimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'00000011'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mtest_decimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'00011100'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m28\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-20-4df66bcfcee3>\u001b[0m in \u001b[0;36mtest_decimal_to_byte\u001b[0;34m(byte, decimal)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtest_decimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbyte\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mbyte_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdecimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mbyte\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mbyte_\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbyte\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbyte\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-19-c7fe89c8fa86>\u001b[0m in \u001b[0;36mdecimal_to_byte\u001b[0;34m(decimal)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdecimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mbyte\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_decimal_to_byte(byte,decimal):\n",
    "    byte_ = decimal_to_byte(decimal)\n",
    "    assert byte == byte_ and isinstance(byte, str) and len(byte) == 8\n",
    "\n",
    "\n",
    "test_decimal_to_byte('01100111', 103)\n",
    "test_decimal_to_byte('00000011', 3)\n",
    "test_decimal_to_byte('00011100', 28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e28f47f1",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "7f8a949776449868af9155c44585aa19",
     "grade": true,
     "grade_id": "htest-decimal_to_byte",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19014332",
   "metadata": {},
   "source": [
    "To run the calculator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0f2a1a1f",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7456fba641674fe08b9c9d961ab299f3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='decimal', max=255), Output()), _dom_classes=('widget-int…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# decimal-to-byte calculator\n",
    "@interact(decimal=(0,255,1))\n",
    "def convert_decimal_to_byte(decimal=0):\n",
    "    print('byte:', decimal_to_byte(decimal))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1843627",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Symbolic calculator (optional)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f54da48",
   "metadata": {},
   "source": [
    "Can we do complicated arithmetics with Python. What about Calculus?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db966349",
   "metadata": {},
   "source": [
    "$$\n",
    "\\int \\tan(x)\\, dx = \\color{red}{?}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c175588",
   "metadata": {},
   "source": [
    "Solution: <https://gamma.sympy.org/input/?i=integrate(tan(x))>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11c61b15",
   "metadata": {},
   "source": [
    "````{tip}\n",
    "\n",
    "- Take a look at the different panels to learn about the solution: `Steps`, `Plot`, and `Derivative`.\n",
    "- Try different [random examples](https://gamma.sympy.org/).\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "886d2271",
   "metadata": {},
   "source": [
    "**How does SymPy Gamma work?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66fffa0c",
   "metadata": {},
   "source": [
    "[SymPy Gamma](https://gamma.sympy.org/) is a web application running [SymPy](https://docs.sympy.org/latest/index.html), which is a python library for symbolic computation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a701a2c5",
   "metadata": {},
   "source": [
    "**How to use SymPy?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1c70fde",
   "metadata": {},
   "source": [
    "To import the library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7c6adba0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0349255",
   "metadata": {},
   "source": [
    "We need to define a symbolic variable and assign it to a python variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8433bbaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x$"
      ],
      "text/plain": [
       "x"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sp.symbols('x')\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53cc6015",
   "metadata": {},
   "source": [
    "The SymPy expression for $\\tan(x)$ is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "10425d88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\tan{\\left(x \\right)}$"
      ],
      "text/plain": [
       "tan(x)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = sp.tan(x)\n",
    "f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16fc6416",
   "metadata": {},
   "source": [
    "To compute the integration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "271c6bfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\log{\\left(\\cos{\\left(x \\right)} \\right)}$"
      ],
      "text/plain": [
       "-log(cos(x))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_f = sp.integrate(f)\n",
    "int_f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d2bca9",
   "metadata": {},
   "source": [
    "To compute the derivative:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "95e972ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sin{\\left(x \\right)}}{\\cos{\\left(x \\right)}}$"
      ],
      "text/plain": [
       "sin(x)/cos(x)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_int_f = sp.diff(int_f)\n",
    "diff_int_f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b2eb608",
   "metadata": {},
   "source": [
    "The answer can be simplified as expected:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "fcd2f622",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\tan{\\left(x \\right)}$"
      ],
      "text/plain": [
       "tan(x)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
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    }
   ],
   "source": [
    "diff_int_f.simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94093cdb",
   "metadata": {},
   "source": [
    "To plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "08135102",
   "metadata": {},
   "outputs": [
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   "source": [
    "p = sp.plot(f, int_f, (x, -sp.pi/4, sp.pi/4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc702fa0",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "Try to compute the following in SymPy and in jupyter notebook:\n",
    "\n",
    "- $\\frac{d}{dx} x^x$\n",
    "- $\\frac{d}{dx} \\frac{1}{\\sqrt{1 - x^2}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "346cb1db",
   "metadata": {},
   "source": [
    "````{hint}\n",
    "\n",
    "Use `sp.sqrt` or `**(sp.S(1)/2)` for square root instead of `**0.5`. See [SymPy gotchas](https://docs.sympy.org/latest/gotchas.html).\n",
    "\n",
    "````"
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          "\u001b[0;32m<ipython-input-14-ee28e42f9be2>\u001b[0m in \u001b[0;36mquadratic_equation_solver\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0minteract\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mquadratic_equation_solver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Roots: {}, {}'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
          "\u001b[0;32m<ipython-input-11-b9b79580546a>\u001b[0m in \u001b[0;36mget_roots\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mroot1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mroot2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
          "\u001b[0;31mNotImplementedError\u001b[0m: "
         ]
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       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_58620797c8f749f2abc28ed5995454d6",
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          "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
          "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
          "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipywidgets/widgets/interaction.py\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    254\u001b[0m                     \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_interact_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    255\u001b[0m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mwidget\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_kwarg\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 256\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    257\u001b[0m                 \u001b[0mshow_inline_matplotlib_plots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    258\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mauto_display\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
          "\u001b[0;32m<ipython-input-22-b4d5e32d5362>\u001b[0m in \u001b[0;36mconvert_decimal_to_byte\u001b[0;34m(decimal)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0minteract\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m255\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mconvert_decimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'byte:'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdecimal_to_byte\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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