{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "39a632f2",
   "metadata": {},
   "source": [
    "<i>École Polytechnique de Montréal</i>\n",
    "<br>\n",
    "<i>Cours MTH2210A : Calcul scientifique pour ingénieurs</i>\n",
    "<br>\n",
    "<i>Session d'hiver 2023</i>\n",
    "\n",
    "<h1><center>Laboratoire 2</center></h1>\n",
    "\n",
    "| Nom et prénoms    | Nom et prénoms |\n",
    "|-------------------|---------------------|\n",
    "| Matricule 9999999 | Matricule 0000000   |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "501b57da",
   "metadata": {},
   "source": [
    "# Initialisation du notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31a1c6b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Réinitialisation complète de l'environnement\n",
    "%reset -f\n",
    "\n",
    "# Import des bibliothèques requises\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "421fe283",
   "metadata": {},
   "source": [
    "# Exercice 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cacc054b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# a)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b5de2ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# b)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99870e71",
   "metadata": {},
   "source": [
    "Commentaire éventuel."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f46e872a",
   "metadata": {},
   "source": [
    "# Exercice 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50ee6fff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# a)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d66c5c0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# b)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48d9f8ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# c)\n",
    "\n",
    "# La version Python de l'algorithme de Horner proposé dans le sujet est disponible via la fonction ci-dessous.\n",
    "# argument d'entrée:  n, le degré du polynôme\n",
    "# argument de sortie: y, la valeur de P_n(alpha^2)\n",
    "def hhorner(n):\n",
    "    alphacarre =  0.006694380022903415749574948586\n",
    "    a = np.zeros(n+1)\n",
    "    for i in range(len(a)):\n",
    "        a[i] = np.math.factorial(2*i+1)/((2*i+3)*(2*i+5)*np.math.factorial(i)**2*2**(2*i-2))\n",
    "    y = a[-1]\n",
    "    for i in range(len(a)-2,-1,-1):\n",
    "        y = a[i] + alphacarre*y\n",
    "    return y\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8425571",
   "metadata": {},
   "source": [
    "d) Discussion."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ebe28fc",
   "metadata": {},
   "source": [
    "# Exercice 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01c7daf3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# a) - code\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fde1c749",
   "metadata": {},
   "outputs": [],
   "source": [
    "# a) - tableau\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d73f694a",
   "metadata": {},
   "source": [
    "a) - Commentaire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f2709962",
   "metadata": {},
   "outputs": [],
   "source": [
    "# b) - code\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12ca340a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# b) - tableau\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "934af01e",
   "metadata": {},
   "source": [
    "b) - Commentaire."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}