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   "source": [
    "# Parametric question\n",
    "\n",
    "On this page an example is given for parametric questions, in which an equation is checked on equivalence with the correct answer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
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   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "import numpy as np\n",
    "from sympy import pi, latex\n",
    "from sympy.printing.mathml import mathml\n",
    "\n",
    "import operator\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display, Latex, display_jpeg, Math, Markdown\n",
    "sp.init_printing(use_latex=True) \n",
    "\n",
    "check_equation = lambda eq1, eq2: sp.simplify(eq1-eq2) == 0\n",
    "\n",
    "def check_answer(variable_name, expected, comparison = operator.eq):\n",
    "    output = widgets.Output()\n",
    "    button = widgets.Button(description=\"Check answer\")\n",
    "    def _inner_check(button):\n",
    "        with output:\n",
    "            if comparison(globals()[variable_name], expected):\n",
    "                output.outputs = [{'name': 'stdout', 'text': 'Correct!',\n",
    "                                   'output_type': 'stream'}]\n",
    "            else:\n",
    "                output.outputs = [{'name': 'stdout', 'text': 'Incorrect!',\n",
    "                                   'output_type': 'stream'}]\n",
    "    button.on_click(_inner_check)\n",
    "    display(button, output)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises on Taylor expansion\n",
    "\n",
    "This page shows some exercises on calculation Taylor expansion. If you reload this page, you'll get new values.\n",
    "\n",
    "### Exercise 1\n",
    "\n",
    "Calculate the taylor series expension of:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "tags": [
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   "source": [
    "x, y = sp.symbols('x, y')\n",
    "a_1 = sp.Integer(np.random.randint(2,6))\n",
    "b_1 = sp.Integer(np.random.randint(-10,10))\n",
    "c_1 = sp.Integer(np.random.randint(-5,5))\n",
    "eq1_original = a_1 * x**2 + b_1*x\n",
    "eq1_correct = sp.series(eq1_original,x,c_1)\n",
    "eq1_answer = 0\n",
    "display(eq1_original)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "around:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "display(sp.Eq(x,c_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fill in your answer and run the cell before clicking 'Check answer'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "auto-execute-page",
     "disable-download-page"
    ]
   },
   "outputs": [],
   "source": [
    "eq1_answer = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "check_answer(\"eq1_answer\",eq1_correct, check_equation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "\n",
    "Calculate the taylor series expension of:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "a_2 = sp.Integer(np.random.randint(1,7))\n",
    "c_2 = sp.Integer(np.random.randint(-5,5))\n",
    "eq2_original = a_2*sp.tan(x)\n",
    "display(eq2_original)\n",
    "eq2_correct = sp.series(eq2_original,x,c_2*sp.pi,3).removeO()\n",
    "#display(eq2_correct)\n",
    "eq2_answer = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "around:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "display(sp.Eq(x,c_2*sp.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "discard any $O(x^3)$ terms.\n",
    "\n",
    "Fill in your answer and run the cell before clicking 'Check answer'. Furthermore, use `pi` for $\\pi$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq2_answer = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "check_answer(\"eq2_answer\",eq2_correct, check_equation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3\n",
    "\n",
    "Calculate the taylor series expension of:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "a_3 = sp.Integer(np.random.randint(1,10))\n",
    "c_3 = sp.Integer(np.random.randint(-1,1))\n",
    "eq3_original = a_3 / (1 - x)\n",
    "display(eq3_original)\n",
    "eq3_correct = sp.series(eq3_original,x,c_3,3).removeO()\n",
    "#display(eq3_correct)\n",
    "eq3_answer = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "around:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "display(sp.Eq(x,c_3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "discard any $O(x^3)$ terms.\n",
    "\n",
    "Fill in your answer and run the cell before clicking 'Check answer':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq3_answer ="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-remove-input-init"
    ]
   },
   "outputs": [],
   "source": [
    "check_answer(\"eq3_answer\",eq3_correct, check_equation)"
   ]
  }
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