{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Devoir 1\n",
    "\n",
    "En utilisant SymPy ou Mathematica mais un seul des deux, répondre aux questions suivantes.\n",
    "\n",
    "Écrire vos réponses dans le fichier `Devoir-1-<MATRICULE>-<NOM>.ipynb` ou `Devoir-1-<MATRICULE>-<NOM>.nb` selon que vous utilisiez SymPy ou Mathematica téléchargeable sur la page web du cours. Inclure la démarche, les réponses aux questions et les justifications. Envoyer votre fichier avant le **jeudi 24 mars à 23h59** par courriel à l'adresse `slabbe@ulg.ac.be` en remplaçant `<MATRICULE>` par votre numéro de matricule et `<NOM>` par votre nom.\n",
    "\n",
    "Pour écrire du texte entre les cellules et justifier une réponse, utiliser\n",
    "`Format > Style > Text` en Mathematica, et `Cell > Cell Type >\n",
    "Markdown` en SymPy et Jupyter.\n",
    "\n",
    "Le plagiat sera détecté et entraînera une note de zéro pour les personnes\n",
    "impliquées."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1\n",
    "Le [Théorème de\n",
    "Gauss--Wantzel](https://fr.wikipedia.org/wiki/Théorème_de_Gauss-Wantzel) dit qu'un polygone régulier à $n$ côtés est\n",
    "constructible avec la règle et le compas si et seulement si $n$ est le produit\n",
    "d'une puissance de $2$ et de nombres premiers de Fermat distincts dont les seuls\n",
    "connus sont 3, 5, 17, 257 et 65537."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Est-ce qu'un polygone régulier à 6 côtés est constructible?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2: 1, 3: 1}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import factorint\n",
    "factorint(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse:** OUI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Est-ce qu'un polygone régulier à 24480 côtés est constructible?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2: 5, 3: 2, 5: 1, 17: 1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factorint(24480)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse:** NON"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Est-ce qu'un polygone régulier à 88305875025920 côtés est constructible?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{2: 20, 5: 1, 257: 1, 65537: 1}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factorint(88305875025920)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse:** OUI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Question 2\n",
    "Résoudre l'équation $x^3-3x^2-5=0$ et donner une valeur numérique approchée des\n",
    "solutions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import init_printing\n",
    "init_printing(use_latex='mathjax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ 1 + \\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{3 \\sqrt{5}}{2} + \\frac{7}{2}} + \\frac{1}{\\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{3 \\sqrt{5}}{2} + \\frac{7}{2}}}, \\quad 1 + \\frac{1}{\\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{3 \\sqrt{5}}{2} + \\frac{7}{2}}} + \\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{3 \\sqrt{5}}{2} + \\frac{7}{2}}, \\quad \\frac{1}{\\sqrt[3]{\\frac{3 \\sqrt{5}}{2} + \\frac{7}{2}}} + 1 + \\sqrt[3]{\\frac{3 \\sqrt{5}}{2} + \\frac{7}{2}}\\right ]$$"
      ],
      "text/plain": [
       "⎡                     __________                                              \n",
       "⎢    ⎛  1   √3⋅ⅈ⎞    ╱ 3⋅√5   7                 1                             \n",
       "⎢1 + ⎜- ─ - ────⎟⋅3 ╱  ──── + ─  + ───────────────────────────, 1 + ──────────\n",
       "⎢    ⎝  2    2  ⎠ ╲╱    2     2                     __________                \n",
       "⎢                                  ⎛  1   √3⋅ⅈ⎞    ╱ 3⋅√5   7       ⎛  1   √3⋅\n",
       "⎢                                  ⎜- ─ - ────⎟⋅3 ╱  ──── + ─       ⎜- ─ + ───\n",
       "⎣                                  ⎝  2    2  ⎠ ╲╱    2     2       ⎝  2    2 \n",
       "\n",
       "                                     __________                           ____\n",
       "   1                ⎛  1   √3⋅ⅈ⎞    ╱ 3⋅√5   7         1                 ╱ 3⋅√\n",
       "───────────────── + ⎜- ─ + ────⎟⋅3 ╱  ──── + ─ , ────────────── + 1 + 3 ╱  ───\n",
       "       __________   ⎝  2    2  ⎠ ╲╱    2     2       __________       ╲╱    2 \n",
       "ⅈ⎞    ╱ 3⋅√5   7                                    ╱ 3⋅√5   7                \n",
       "─⎟⋅3 ╱  ──── + ─                                 3 ╱  ──── + ─                \n",
       " ⎠ ╲╱    2     2                                 ╲╱    2     2                \n",
       "\n",
       "______⎤\n",
       "5   7 ⎥\n",
       "─ + ─ ⎥\n",
       "    2 ⎥\n",
       "      ⎥\n",
       "      ⎥\n",
       "      ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import solve,N\n",
    "from sympy.abc import x\n",
    "racines = solve(x**3-3*x**2-5)\n",
    "racines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.212994378680811 - 1.18914510810655*I\n",
      "-0.212994378680811 + 1.18914510810655*I\n",
      "3.42598875736162\n"
     ]
    }
   ],
   "source": [
    "for racine in racines:\n",
    "    print racine.n()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Question 3\n",
    "Tracer la [surface de Dini](https://en.wikipedia.org/wiki/Dini's_surface)\n",
    "dont les équations paramétriques sont:\n",
    "\\begin{align*}\n",
    "    x&=a\\cos\\left(u\\right)\\sin\\left(v\\right)\\\\\n",
    "    y&=a\\sin\\left(u\\right)\\sin\\left(v\\right)\\\\\n",
    "    z&=a\\left(\\cos\\left(v\\right)+\\ln\\left(\\tan\\left(\\frac{v}{2}\\right)\\right)\\right)+bu \n",
    "\\end{align*}\n",
    "pour $a=1$, $b=1$ sur les intervalles $0\\leq u \\leq 5\\pi$ et $0.01 \\leq v\\leq\n",
    "1$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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4cNttjL3qVUy+8pW4nneF7/a1YSv54vUtMwfHTRRF12198fC5Xa/Xd2wJ8G7yopPuoOPX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ZAoZfGqMVqtoY1AW4Hvjse2BaTxXHBmoWtwUmBmsfYXa+rDRMAnSXc0Gn0ke3ThY0K6JzsYHoSp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\nU8888wx79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jF//nxuvfVWnnjiCZ9WZ5aUlDB//nzsdjv33XcfRUVFDu/v2bOHKVOmKF0l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\nDvtK7L1+xgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8b9a3ea950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f8b9a92b790>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from sympy.plotting import plot3d_parametric_surface\n",
    "from sympy import cos,sin,tan,log,pi\n",
    "from sympy.abc import u,v\n",
    "plot3d_parametric_surface(cos(u)*sin(v), sin(u)*sin(v),cos(v)+log(tan(v/2))+u, (u,0,5*pi), (v,0.01,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4\n",
    "Soit $p(x)=- x^{4} + 28 x^{3} - 221 x^{2} + 350 x + 600$ un polynôme. Trouver\n",
    "l'ensemble des valeurs de $x$ telles que $p(x)$ atteint un optimum local et dire s'il s'agit d'un minimum ou un maximum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- x^{4} + 28 x^{3} - 221 x^{2} + 350 x + 600$$"
      ],
      "text/plain": [
       "   4       3        2              \n",
       "- x  + 28⋅x  - 221⋅x  + 350⋅x + 600"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.abc import x\n",
    "p = -x**4+28*x**3-221*x**2+350*x+600\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ 7, \\quad - \\frac{\\sqrt{146}}{2} + 7, \\quad \\frac{\\sqrt{146}}{2} + 7\\right ]$$"
      ],
      "text/plain": [
       "⎡     √146      √146    ⎤\n",
       "⎢7, - ──── + 7, ──── + 7⎥\n",
       "⎣      2         2      ⎦"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import diff,solve\n",
    "p_optimum = solve(diff(p, x), x)\n",
    "p_optimum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ 7.0, \\quad 0.958477013202714, \\quad 13.0415229867973\\right ]$$"
      ],
      "text/plain": [
       "[7.0, 0.958477013202714, 13.0415229867973]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import N\n",
    "map(N, p_optimum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left ( - \\frac{\\sqrt{146}}{2} + 7, \\quad -292.0\\right ), \\quad \\left ( 7, \\quad 146.0\\right ), \\quad \\left ( \\frac{\\sqrt{146}}{2} + 7, \\quad -292.0\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡⎛  √146            ⎞              ⎛√146            ⎞⎤\n",
       "⎢⎜- ──── + 7, -292.0⎟, (7, 146.0), ⎜──── + 7, -292.0⎟⎥\n",
       "⎣⎝   2              ⎠              ⎝ 2              ⎠⎦"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_xx = diff(p, x, x)\n",
    "[(a, p_xx.subs(x, a).n()) for a in sorted(p_optimum)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse:** p atteint des maximum en x=0.95 et x=13.04, car la dérivée seconde est négative en ces points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse:** p atteint un minimum en x=7, car la dérivée seconde est positive en ce point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculer l'aire de la région $A=\\{(x,y):0\\leq y\\leq p(x)\\}$ bornée supérieurement par le polynôme $p(x)$ et\n",
    "inférieurement par l'abscisse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XInzx6qtwxx2mq/Bc166wdavpKpxLgtpDFd0edu8vrCotTW+aI8LL/v2wYQMMH266Es91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\nsLn/B2T4f+MjGUhrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8b9884b050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f8b9886f510>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import plot\n",
    "plot(p, (x,-5, 20), ylim=(-1000,1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ -1, \\quad 4, \\quad 10, \\quad 15\\right ]$$"
      ],
      "text/plain": [
       "[-1, 4, 10, 15]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_racines = solve(p, x)\n",
    "p_racines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{14500}{3}$$"
      ],
      "text/plain": [
       "14500/3"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import integrate\n",
    "aire = integrate(p, (x,-1,4)) + integrate(p, (x,10, 15))\n",
    "aire"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$4833.33333333333$$"
      ],
      "text/plain": [
       "4833.33333333333"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aire.n()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5\n",
    "On considère la fonction $f(x)=x^{x\\over 1-x}$ pour tout réel $x>0$. Donner le\n",
    "domaine de définition de $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import oo\n",
    "from sympy.abc import x\n",
    "f = x**(x/(1-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( 1, \\quad \\mathrm{NaN}, \\quad \\mathrm{NaN}\\right )$$"
      ],
      "text/plain": [
       "(1, nan, nan)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(x,0), f.subs(x,1), f.subs(x,oo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Réponse:** le domaine est $[0, 1[\\cup]1,\\infty[$ si on accepte que $0^0=1$ est bien défini."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculer les limites de la fonction $f$ aux bornes des intervalles qui composent le domaine de $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import limit\n",
    "limit(f, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$e^{-1}$$"
      ],
      "text/plain": [
       " -1\n",
       "ℯ  "
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(f, x, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$0$$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(f, x, oo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expliquez comment prolonger $f$ par continuité aux points $x=0$ et $x=1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Réponse:** par le résultat des calculs des limites."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 6\n",
    "On considère les vecteurs\n",
    "$v_1=(-8, 1, -10, 1, 6)$,\n",
    "$v_2=(-6, -10, 2, 10, -3)$,\n",
    "$v_3=(-2, 8, 10, 1, 10)$,\n",
    "$v_4=(-14, -9, -8, 11, 3)$,\n",
    "$v_5=(-2, -3, 5, -8, -6)$.\n",
    "Donner une base du sous espace vectoriel engendré par $v_1$, $v_2$, $v_3$, $v_4$\n",
    "et $v_5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v1=(-8, 1, -10, 1, 6)\n",
    "v2=(-6, -10, 2, 10, -3)\n",
    "v3=(-2, 8, 10, 1, 10)\n",
    "v4=(-14, -9, -8, 11, 3)\n",
    "v5=(-2, -3, 5, -8, -6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}-8 & 1 & -10 & 1 & 6\\\\-6 & -10 & 2 & 10 & -3\\\\-2 & 8 & 10 & 1 & 10\\\\-14 & -9 & -8 & 11 & 3\\\\-2 & -3 & 5 & -8 & -6\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-8    1   -10  1   6 ⎤\n",
       "⎢                     ⎥\n",
       "⎢-6   -10   2   10  -3⎥\n",
       "⎢                     ⎥\n",
       "⎢-2    8   10   1   10⎥\n",
       "⎢                     ⎥\n",
       "⎢-14  -9   -8   11  3 ⎥\n",
       "⎢                     ⎥\n",
       "⎣-2   -3    5   -8  -6⎦"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "M = Matrix([v1, v2, v3, v4, v5])\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & - \\frac{11373}{21334}\\\\0 & 1 & 0 & 0 & \\frac{11541}{10667}\\\\0 & 0 & 1 & 0 & - \\frac{200}{10667}\\\\0 & 0 & 0 & 1 & \\frac{4969}{10667}\\\\0 & 0 & 0 & 0 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡            -11373 ⎤\n",
       "⎢1  0  0  0  ───────⎥\n",
       "⎢             21334 ⎥\n",
       "⎢                   ⎥\n",
       "⎢             11541 ⎥\n",
       "⎢0  1  0  0   ───── ⎥\n",
       "⎢             10667 ⎥\n",
       "⎢                   ⎥\n",
       "⎢             -200  ⎥\n",
       "⎢0  0  1  0   ───── ⎥\n",
       "⎢             10667 ⎥\n",
       "⎢                   ⎥\n",
       "⎢              4969 ⎥\n",
       "⎢0  0  0  1   ───── ⎥\n",
       "⎢             10667 ⎥\n",
       "⎢                   ⎥\n",
       "⎣0  0  0  0     0   ⎦"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mreduite, pivots = M.rref()\n",
    "Mreduite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le vecteur $w=(0, -6, -1, -8, 10)$ est-il dans ce sous-espace vectoriel?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}1 & 0 & 0 & 1 & 0 & 0\\\\0 & 1 & 0 & 1 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right], \\quad \\left [ 0, \\quad 1, \\quad 2, \\quad 4, \\quad 5\\right ]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡1  0  0  1  0  0⎤, [0, 1, 2, 4, 5]⎞\n",
       "⎜⎢                ⎥                 ⎟\n",
       "⎜⎢0  1  0  1  0  0⎥                 ⎟\n",
       "⎜⎢                ⎥                 ⎟\n",
       "⎜⎢0  0  1  0  0  0⎥                 ⎟\n",
       "⎜⎢                ⎥                 ⎟\n",
       "⎜⎢0  0  0  0  1  0⎥                 ⎟\n",
       "⎜⎢                ⎥                 ⎟\n",
       "⎝⎣0  0  0  0  0  1⎦                 ⎠"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = (0, -6, -1, -8, 10)\n",
    "M = Matrix([v1, v2, v3, v4, v5, w])\n",
    "M.transpose().rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Réponse:** NON, le système est incompatible"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si oui, l'exprimer  comme combinaison linéaire des vecteurs de la base."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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