diff --git "a/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb" "b/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb" index 73d7993..4abd395 100644 --- "a/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb" +++ "b/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb" @@ -1,296 +1,299 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Concept(s)-clé(s) et théorie\n", "\n", "### DÉFINITION 1 :\n", "\n", "Une **équation linéaire** aux inconnues $x_1,\\ldots,x_n$ à coefficients réels est une équation de la forme\n", "\n", "$$a_1x_1+a_2x_2+\\cdots+a_nx_n=b,$$ \n", "où $a_1,a_2,\\ldots,a_n,b\\in \\mathbb{R}.$\n", " \n", "---\n", "### DÉFINITION 2 :\n", "\n", "On appelle **système d'équations linéaires** (ou simplement système linéaire) une famille d'équations linéaires aux inconnues $x_1,\\ldots,x_n$ à coefficients réels de la forme \n", "\n", "$$S=\\left\\{\\begin{array}{ccccccc}\n", "a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n", "a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n", "\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n", "a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m,\n", "\\end{array}\\right. $$\n", "\n", "où $a_{ij},b_i\\in \\mathbb{R}$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j\\leq n.$ \n", "\n", "On dit qu'une suite ordonnée $\\alpha$ de $n$ nombres réels $\\alpha_i$, notée $\\alpha=(\\alpha_1,\\ldots,\\alpha_n)$, est une *solution du système linéaire* $S$ si toutes les égalités du système sont vérifiées lorsque l'on remplace $x_j$ par $\\alpha_j,$ ceci pour tout $1\\leq j\\leq n.$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import Librairie.AL_Fct as al" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### EXEMPLE 1\n", "\n", "Dans ce premier exemple nous nous familiarisons avec les équations et les ensembles de solutions. Soit l'équation\n", "$$ \n", "a_{1}x_{1} + a_{2}x_{2} + \\ldots a_{n}x_{n}=b_1.\n", "$$ \n", "On utilise *la syntaxe suivante pour définir les coefficients* de l'équation \n", "\n", "\n", "\\begin{align*}\n", "A&=[a_1, a_2, \\ldots, a_n]\\\\\n", "b&=[b_1].\n", "\\end{align*}\n", "\n", + "**Remarque**: il ne d'agit pas de la seule manière d'entrer une matrice en Python, mais dans ces Notebooks nous utiliserons cette syntaxe relativement simple.\n", "\n", "---\n", "Dans la case ci-dessous, entrer les coefficients de l'équation \n", "$$3x_1 + 2x_2=7.$$\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Toutes les valeurs sont initialisées à 1\n", "\n", "A = [1,1] \n", "b = [1]\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printEq(A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On utilise *la syntaxe suivante pour entrer une solution* d'une équation\n", "$$\\rm{alpha}=[\\alpha_1, \\alpha_2, \\ldots, \\alpha_n].$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Toutes les valeurs sont initialisées à 1\n", "\n", "alpha = [1, 1] #solution" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "isSol = [al.SolOfEq(alpha, A+b, 1)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 1**\n", "\n", "Enter l'équation $$ \\frac{2}{5}x_1 -4x_2 + x_3 = 8$$ et donner une solution $$\\alpha=(\\alpha_1, \\alpha_2, \\alpha_3).$$\n", "\n", "Vous pouvez aussi adapter le code à l'équation de votre choix." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "\n", "#Par défaut, les valeurs sont fixées à 1\n", "\n", "A = [1, 1, 1] \n", "b =[1]\n", "alpha = [1, 1, 1] #solution " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printEq(A,b)\n", "isSol=[al.SolOfEq(alpha, A+b,1)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### EXEMPLE 2\n", "\n", "Dans cet exercice nous nous familiarisons avec les systèmes d'équations.\n", "\n", "Soit\n", "$$S=\\left\\{\\begin{array}{ccccccc}\n", "a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n", "a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n", "\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n", "a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n", "\\end{array},\\right. $$\n", "\n", "On utilise *la syntaxe suivante pour entrer les coefficients du système*\n", "\n", "\n", "\\begin{align*}\n", "A&=\\quad [\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad]\\\\\n", "b&=\\quad [\\quad b_1, b_2, \\ldots, b_m \\quad]\n", "\\end{align*}\n", "\n", + "**Remarque**: il existe aussi d'autres syntaxes pour entrer une matrice en Python.\n", + "\n", "---\n", "Entrer le système d'équations ci-dessous\n", "\n", "$$\n", "\\left\\{\n", "\\begin{array}{lccc}\n", "x_1 &- & 3 x_2 & = 4\\\\\n", "-x_1 & + & 4 x_2 & = 5\n", "\\end{array}\n", "\\right.\n", "$$\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "\n", "#Par défaut, les valeurs sont fixées à 1\n", "\n", "A = [ [1, 1], [1, 1]] \n", "b=[1, 1] \n", "alpha = [1, 1] #solution" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printSyst(A,b)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.SolOfSyst(alpha, A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 2**\n", " \n", "Entrer le système suivant et trouver une solution du système. \n", "\n", "$$\n", "\\left\\{\\begin{array}{ll}\n", "2x_1 +3 x_2 - x_3&=-6\\\\\n", "-\\dfrac{1}{2}x_1 + x_3&= 3\\\\\n", "x_1 + 3x_2 -x_3 &=0\n", "\\end{array}\\right.\n", "$$\n", "\n", "Vous pouvez aussi adapter le code à l'équation de votre choix." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Par défaut, les valeurs sont fixées à 1\n", "\n", "A = [[1,1,1], [1,1,1], [1,1,1]]\n", "b =[1,1,1]\n", "alpha =[1,1,1] #solution\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printSyst(A,b)\n", "al.SolOfSyst(alpha, A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Passez au notebook du chapitre 1.2: Nombre de solutions d'un système](./1.2.%20Nombre%20de%20solution%20d'un%20système.ipynb)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 } diff --git "a/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solutions d'un syst\303\250me.ipynb" "b/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solutions d'un syst\303\250me.ipynb" index d464c84..2f1f289 100644 --- "a/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solutions d'un syst\303\250me.ipynb" +++ "b/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solutions d'un syst\303\250me.ipynb" @@ -1,595 +1,363 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Concept(s)-clé(s) et théorie\n", "\n", "On considère un système d'équations linéaires aux inconnues $x_1,\\ldots,x_n$\n", "\n", "$$S=\\left\\{\\begin{array}{ccccccc}\n", "a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n", "a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n", "\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n", "a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n", "\\end{array},\\right. $$\n", "\n", "où $a_{ij},b_i\\in \\mathbb{R}$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j\\leq n.$ \n", "\n", "---\n", "Un système d'équations linéaires à coefficients réels satisfait précisément une seule des conditions suivantes.\n", "\n", "1. Le système ne possède aucune solution.\n", "\n", "2. Le système possède une solution unique.\n", "\n", "3. Le système possède une infinité de solutions.\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import Librairie.AL_Fct as al\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import plotly as py\n", - "import plotly.graph_objs as go\n", - "import pandas as pd\n", - "import random\n", - "from IPython.core.magic import register_cell_magic\n", - "from IPython.display import HTML, display\n", - "from ipywidgets import interactive, HBox, VBox, widgets, interact, FloatSlider\n", - "\n", - "py.offline.init_notebook_mode(connected=True)" + "import Corrections.corrections as corrections" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### EXEMPLE 1\n", "\n", "Nous allons travailler avec un système de deux inconnues et deux équations:\n", "\n", "$$\n", "\\begin{cases}\n", "a_{11}x_1 + a_{12}x_2=b_1\\\\\n", "a_{21}x_1 + a_{22}x_2=b_2.\n", "\\end{cases}\n", "$$\n", "\n", - "On rappelle qu'on *la syntaxe suivante pour entrer les coefficients du système*\n", + "On rappelle qu'on utilise *la syntaxe suivante pour entrer les coefficients d'un système*\n", "\n", "\\begin{align*}\n", "A&=\\quad [\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad]\\\\\n", "b&=\\quad [\\quad b_1, b_2, \\ldots, b_m \\quad]\n", "\\end{align*}\n", "\n", "---\n", "Entrer le système ci-dessous - ou n'importe quel système de votre choix. Après avoir étudié les deux droites, entrer une solution du système\n", "\n", "$$\n", "\\begin{cases}\n", "-2x_1 + x_2=2\\\\\n", "2x_1 -2x_2=1.\n", "\\end{cases}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Par défaut, les coefficients sont fixés à 1 et n=2, m=2\n", "\n", "A = [ [-2,1] , [2,-2]]\n", "b = [2,1]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printSyst(A,b)\n", "\n", "al.Plot2DSys(-7,7,15,A,b)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "\n", "alpha=[-2.5, -3]\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "al.SolOfSyst(alpha, A,b)" + "sol=al.SolOfSyst(alpha, A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 1**\n", "\n", "Pour chacun des cas ci-dessous, déterminer la/les solution(s) des systèmes en vous aidant du graphe. \n", "\n", " $$ \n", "a)\\quad \\begin{cases}\n", "\\dfrac{3}{2}x_1 - 2x_2&=0\\\\\n", "-3x_1 + 5 x_2&=3\n", "\\end{cases} \\hspace{1cm} b) \\quad \\begin{cases}\n", "x_1 - x_2&=\\phantom{-}2\\\\\n", "-3x_1 - 2x_2&=-1\\\\\n", "2x_1 + 3x_2&=\\phantom{-}4\n", "\\end{cases}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Par défaut, les coefficients sont fixés à 1 \n", "#Attention d'adapter les valeurs ci-dessous pour a) et b)\n", "\n", "A = [[1, -1], [-3, -2],[2,3]]\n", "b =[2,-1,4]\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printSyst(A,b)\n", "al.Plot2DSys(-7,7,15,A,b)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Entrer une solution du système\n", "alpha=[1,1]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "al.SolOfSyst(alpha, A,b)" + "sol=al.SolOfSyst(alpha, A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 2**\n", "\n", "Pour chacun des cas ci-dessous, déterminer, à l'aide des graphes interactifs, la/les solution(s) des systèmes. \n", "\n", "$$ \n", "a)\\quad \\begin{cases}\n", "x_1 - x_2 + 2x_3 &=0\\\\\n", "-3x_1 &=1\\\\\n", "2x_1 + 5x_2 &=-2\n", "\\end{cases} \\hspace{1cm} b) \\quad \\begin{cases}\n", "x_1 + x_2 -2x_3 &=0\\\\\n", "3x_2 - x_3 &=1\\\\\n", "-2x_1 -2x_2 + 4x_3 &=2\n", "\\end{cases} \\hspace{1cm} c) \\quad \\begin{cases}\n", "x_1 + x_2 -2x_3 &=-1\\\\\n", "3x_2 - x_3 &=1\\\\\n", "-2x_1 -2x_2 + 4x_3 &=2\n", "\\end{cases} \\hspace{1cm}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Par défaut, les coefficients sont fixés à 1 \n", "\n", "A = [[ 1, 1, 1] ,[1, 1, 1] ,[1, 1, 1]]\n", "b= [1, 1, 1]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printSyst(A,b)\n", "al.Plot3DSys(-10,10,100,A,b)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "alpha = [1, 1, 1]\n", "al.SolOfSyst(alpha, A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 3**\n", "\n", - "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètres $h$ et $k$ pour que les systèmes a), b), c) et d) admettent, si possible,\n", + "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètres $l$ et $k$ pour que les systèmes a), b), c) et d) admettent, si possible,\n", "1. aucune solution\n", "2. une unique solution\n", "3. une infinité de solution \n", "\n", "\n", "$$ \n", "a)\\begin{cases}\n", - "x_1 +5 x_2&=h\\\\\n", + "x_1 +5 x_2&=l\\\\\n", "-2x_1 -10 x_2&=18\n", "\\end{cases} \\hspace{1cm} b) \\begin{cases}\n", - "hx_1 + x_2&=3\\\\\n", + "lx_1 + x_2&=3\\\\\n", "-2x_1 - x_2&=-1\n", "\\end{cases}\\hspace{1cm} c) \\begin{cases}\n", - "3x_1 + hx_2&=1\\\\\n", - "x_1 + 3x_2&=h\n", + "3x_1 + lx_2&=1\\\\\n", + "x_1 + 3x_2&=l\n", "\\end{cases}\\hspace{1cm} d) \\begin{cases}\n", - "kx_1 + x_2&=h\\\\\n", + "kx_1 + x_2&=l\\\\\n", "3x_1 -5x_2&=2\n", "\\end{cases}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## CASE a)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "A=[[1, 5], [-2, -10]] # we initialize the problem. The values of h and k must be fixed to one specific value here\n", - "b=[0, 18]\n", - "al.printSyst(A, b) # the system printed below shows the values of h and k inserted here!!\n", - "\n", - "data=[]\n", - "x=np.linspace(-5,5,11)\n", - "m=len(A)\n", - "MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n", - "MatCoeff=np.array(MatCoeff)\n", - "\n", - "for i in range(len(MatCoeff)):\n", - " trace=go.Scatter(x=x, y=(MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='a) Droite %d'%(i+1))\n", - " data.append(trace)\n", - "\n", - "f=go.FigureWidget(data=data,\n", - " layout=go.Layout(xaxis=dict(\n", - " range=[-5, 5]\n", - " ),\n", - " yaxis=dict(\n", - " range=[-10, 10]\n", - " ) )\n", - "\n", - ")\n", - "\n", - "def update_y(h):\n", - " MatCoeff = [[1, 5, h]]\n", - " MatCoeff=np.array(MatCoeff)\n", - " f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n", - " \n", - "freq_slider = interactive(update_y, h=(-15, 15, 1/2)) \n", - "vb = VBox((f, freq_slider))\n", - "vb.layout.align_items = 'center'\n", - "vb" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## CASE b)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "A=[[1, 1], [-2,-1]] # we initialize the problem. The value of h is fixed\n", - "b=[3, -1]\n", - "al.printSyst(A, b) # the system printed below shows the value of h inserted here\n", - "\n", - "m=len(A)\n", - "MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n", - "MatCoeff=np.array(MatCoeff)\n", - "data=[]\n", - "x=np.linspace(-5,5,11)\n", - "MatCoeff=np.array(MatCoeff)\n", - "for i in range(len(MatCoeff)):\n", - " trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='b) Droite %d'%(i+1))\n", - " data.append(trace)\n", - " \n", - "f=go.FigureWidget(data=data,\n", - " layout=go.Layout(xaxis=dict(\n", - " range=[-5, 5]\n", - " ),\n", - " yaxis=dict(\n", - " range=[-10, 10]\n", - " ) )\n", - " \n", - ")\n", - "\n", - "def mat(k):\n", - " h=k\n", - " MatCoeff=[[h,1,3]]\n", - " return MatCoeff\n", - "def update_y(h):\n", - " MatCoeff= mat(h)\n", - " MatCoeff=np.array(MatCoeff)\n", - " f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n", - " \n", - "freq_slider = interactive(update_y, h=(-10, 10, 1/2)) \n", + "$$\n", "\n", - "vb = VBox((f, freq_slider))\n", - "vb.layout.align_items = 'center'\n", - "vb" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## CASE c)" + "**Remarque** pour faire varier les valeurs de $l$ et $k$ vous pouvez utiliser la souris ou cliquer sur le rond (il devient bleu) et utiliser les flèches gauche et droite du clavier." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "A=[[3, 1], [1, 3]] # we initialize the problem. The values of h and k are fixed\n", - "b=[1, 1]\n", - "al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n", - "\n", - "m=len(A)\n", - "MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n", - "MatCoeff=np.array(MatCoeff)\n", - "data=[]\n", - "x=np.linspace(-25,25,101)\n", - "MatCoeff=np.array(MatCoeff)\n", - "for i in range(len(MatCoeff)):\n", - " trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='c) Droite %d'%(i+1))\n", - " data.append(trace)\n", - " \n", - "f=go.FigureWidget(data=data,\n", - " layout=go.Layout(xaxis=dict(\n", - " range=[-25, 25]\n", - " ),\n", - " yaxis=dict(\n", - " range=[-50, 50]\n", - " ) )\n", - " \n", - ")\n", - "\n", - "def mat(h):\n", - " MatCoeff= [[h, 3, 1],[3, 1, h] ]\n", - " return MatCoeff\n", - "\n", - "def update_y(h):\n", - " MatCoeff= mat(h)\n", - " MatCoeff=np.array(MatCoeff)\n", - " f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n", - " f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n", - "\n", - "freq_slider = interactive(update_y, h=(-20, 20, 1)) \n", + "al.bgc('seashell')\n", + "#Entrez a,b,c ou d pour choisir le système voulu\n", + "cas='d'\n", "\n", - "vb = VBox((f, freq_slider))\n", - "vb.layout.align_items = 'center'\n", - "vb" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## CASE d)" + "corrections.Ex3Chapitre1_2(cas)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "A=[[1, 1], [3, -5]] # we initialize the problem. The values of h and k are fixed\n", - "b=[1, 2]\n", - "al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n", - "\n", - "m=len(A)\n", - "MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n", - "MatCoeff=np.array(MatCoeff)\n", - "data=[]\n", - "x=np.linspace(-15,15,101)\n", - "MatCoeff=np.array(MatCoeff)\n", - "for i in range(len(MatCoeff)):\n", - " trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='d) Droite %d'%(i+1))\n", - " data.append(trace)\n", - " \n", - "f=go.FigureWidget(data=data,\n", - " layout=go.Layout(xaxis=dict(\n", - " range=[-15, 15]\n", - " ),\n", - " yaxis=dict(\n", - " range=[-10, 10]\n", - " ) )\n", - " \n", - ")\n", - "\n", - "def update_y(h, k):\n", - " MatCoeff= [[k, 1, h],[2, -5, 5] ]\n", - " MatCoeff=np.array(MatCoeff)\n", - " f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n", - "\n", - " \n", - " f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n", - "\n", - "freq_slider = interactive(update_y, h=(-10, 10, 1/10),k=(-10, 10, 1))\n", - "\n", - "vb = VBox((f, freq_slider))\n", - "vb.layout.align_items = 'center'\n", - "vb" + "#correction\n", + "corrections.corr3Chapitre1_2(cas)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 4**\n", "\n", "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètre $h$ pour que le système admette, si possible,\n", "1. aucune solution\n", "2. une unique solution\n", "3. une infinité de solution \n", "\n", "$$ \n", "\\begin{cases}\n", "hx_1 -2 x_2 &=4\\\\\n", "-2x_1 +h x_2&=-4\\\\\n", "x_1 - x_2 &=h\n", "\\end{cases} \\hspace{1cm}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "np.seterr(divide='ignore', invalid='ignore')\n", - "\n", - "A=[[1, -2], [-2, 1], [1, -1]] # we initialize the problem. The values of h and k are fixed\n", - "b=[4, -4, 0]\n", - "al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n", - "\n", - "m=len(A)\n", - "MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n", - "MatCoeff=np.array(MatCoeff)\n", - "data=[]\n", - "x=np.linspace(-25,25,101)\n", - "MatCoeff=np.array(MatCoeff)\n", - "for i in range(len(MatCoeff)):\n", - " if MatCoeff[i,1] == 0:\n", - " MatCoeff[i,1] += 1e-3\n", - " trace=go.Scatter(x=x, y=(MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='c) Droite %d'%(i+1))\n", - " data.append(trace)\n", - " \n", - "f=go.FigureWidget(data=data,\n", - " layout=go.Layout(xaxis=dict(\n", - " range=[-25, 25]\n", - " ),\n", - " yaxis=dict(\n", - " range=[-100, 100]\n", - " ) )\n", - " \n", - ")\n", - "\n", - "def mat(h):\n", - " MatCoeff= [[h, -2, 4], [-2, h, -4], [1, -1, h]]\n", - " return MatCoeff\n", - "\n", - "def update_y(h):\n", - " MatCoeff= mat(h)\n", - " MatCoeff=np.array(MatCoeff)\n", - " if MatCoeff[0,1] == 0:\n", - " MatCoeff[0,1] += 1e-3\n", - " f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n", - " if MatCoeff[1,1] == 0:\n", - " MatCoeff[1,1] += 1e-3\n", - " f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n", - " if MatCoeff[2,1] == 0:\n", - " MatCoeff[2,1] += 1e-3\n", - " f.data[2].y=(MatCoeff[2,2]-MatCoeff[2,0]*x)/MatCoeff[2,1]\n", - "\n", - "freq_slider = interactive(update_y, h=(-20, 20, 0.5)) \n", - "\n", - "vb = VBox((f, freq_slider))\n", - "vb.layout.align_items = 'center'\n", - "vb" + "corrections.Ex4Chapitre1_2()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "corrections.corr4Chapitre1_2()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Passez au notebook du chapitre 1.3-4: Notation Matricielle](./1.3-4.%20Notation%20Matricielle.ipynb)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 } diff --git a/Chapitre 1 - Systemes equations lineaires/1.3-4. Notation Matricielle.ipynb b/Chapitre 1 - Systemes equations lineaires/1.3-4. Notation Matricielle.ipynb index 3fccc3a..89b0426 100644 --- a/Chapitre 1 - Systemes equations lineaires/1.3-4. Notation Matricielle.ipynb +++ b/Chapitre 1 - Systemes equations lineaires/1.3-4. Notation Matricielle.ipynb @@ -1,431 +1,536 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Concept(s)-clé(s) et théorie\n", "\n", "On considère un système d'équations linéaires aux inconnues $x_1,\\ldots,x_n$\n", "\n", "$$S=\\left\\{\\begin{array}{ccccccc}\n", "a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n", "a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n", "\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n", "a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n", "\\end{array},\\right. $$\n", "\n", "où $a_{ij},b_i\\in \\mathbb{R}$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j\\leq n.$ \n", "\n", "Le système $S$ peut s'écrire sous forme matricielle $A\\overrightarrow{x}=\\overrightarrow{b}$ où la matrice $A$ est appelée *la matrice des coefficients* et $\\overrightarrow{x}$ et $\\overrightarrow{b}$ sont des vecteurs contant les composantes $x_i$ et $b_i$ respectivement. \n", "\n", "Plus précisemment\n", "$$A=\\begin{pmatrix}\n", "a_{11} & a_{12} & \\cdots & a_{1n}\\\\\n", "a_{21} & a_{22} &\\cdots & a_{2n}\\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n", "a_{m1} & a_{m2} & \\cdots & a_{mn}\n", "\\end{pmatrix},\\hskip1em\n", "\\overrightarrow{x}=\\begin{pmatrix}\n", "x_1\\\\\n", "x_2\\\\\n", "\\vdots\\\\\n", "x_n\n", "\\end{pmatrix},\\hskip1em\n", "\\overrightarrow{b}=\n", "\\begin{pmatrix}\n", "b_1\\\\\n", "b_2\\\\\n", "\\vdots\\\\\n", "b_m\n", "\\end{pmatrix}.\n", "$$\n", "\n", "---\n", "\n", "La matrice $A$ est de taille $m\\times n$ où **m correspond au nombre de lignes** et **n au nombre de colonnes**.\n", "Le vecteur $\\overrightarrow{x}$ est de taille $n\\times 1$ et le vecteur $\\overrightarrow{b}$ de taille $m\\times 1$.\n", - "\n" + "\n", + "**Notations**: on utilise $\\mathcal{M}_{m\\times n}(\\mathbb{R})$ pour parler de l'ensemble des matrices de taille $m\\times n$ à coefficients réels. Ainsi $A\\in \\mathcal{M}_{m\\times n}(\\mathbb{R})$, $\\overrightarrow{x}\\in \\mathcal{M}_{n\\times 1}(\\mathbb{R})$ et $\\overrightarrow{b}\\in\\mathcal{M}_{m\\times 1}(\\mathbb{R})$." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import Librairie.AL_Fct as al\n", "import Corrections.corrections as corrections\n", "import numpy as np\n", "import ipywidgets as widgets\n", "import random\n", "\n", "from ipywidgets import interact, interactive, fixed, interact_manual, Layout" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 1**\n", "\n", - "Ci-dessous est générée une matrice $A$ de taille $m\\times n$. Trouver la dimension de la matrice en remplissant les deux champs dans lesquels vous pouvez rentrer une valeur pour $m$ et $n$. \n", + "Ci-dessous est générée une matrice $A$ de taille $m\\times n$. Trouver la dimension de la matrice en remplissant les deux champs pour $m$ et $n$. \n", "\n", "Vérifier en cliquant sur **Run Interact**" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\left(\\begin{array}{ccc} -42 & -63 & -1 \\\\-41 & -57 & -66 \\\\-93 & 37 & 21 \\\\16 & 60 & 23 \\\\68 & -27 & 18 \\\\-90 & 47 & -39 \\\\39 & 65 & 79 \\\\6 & 100 & -69 \\end{array}\\right)$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "50bd4e3f9cbe49009b479be21bcedc6f", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "IntText(value=1, description='m:')" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "47c105b6414349fa87ecb0789090ebe8", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "IntText(value=1, description='n:')" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "640371c77dc548f196d3fd589f9c78c7", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widge…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "A=al.randomA()\n", "al.dimensionA(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Nouvelles notations**\n", "\n", - "Pour rentrer une matrice on utilise *la syntaxe suivante*\n", + "Pour rentrer une matrice nous utilisons *la syntaxe suivante*\n", "$$A=\\quad [\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad].$$\n", "\n", "Comme nous souhaitons différencier les vecteurs colonnes - ceux usuel - des vecteurs lignes, nous les différencions **à partir de maintenant** en utilisant *la syntaxe suivante*\n", "\n", "\n", "\\begin{align*}\n", "\\overrightarrow{b}&=\\begin{pmatrix}b_1 \\\\ b_2 \\\\ \\vdots \\\\ b_m\\end{pmatrix}\n", "&&\\Rightarrow b=\\quad [\\quad [ b_{1} ], \\quad [b_{2}], \\quad \\ldots, \\quad [b_m] \\quad]\\\\\n", "\\overrightarrow{v}&=\\begin{pmatrix} v_1 & v_2 & \\cdots v_n\\end{pmatrix}\n", "&&\\Rightarrow v=\\quad[ \\quad v_1, \\quad v_2, \\quad \\ldots, \\quad v_n \\quad ]\n", "\\end{align*}\n", "\n", "\n", "---\n", "\n", "Entrez les vecteurs et matrices ci-dessous.\n", "$$\n", "\\begin{pmatrix}\n", "1 & -3 \\\\\n", "3 & 5\n", "\\end{pmatrix} \\hskip1em \\begin{pmatrix}\n", "1 \\\\\n", "2 \n", "\\end{pmatrix}\\hskip1em\\begin{pmatrix}\n", "1 \\\\\n", "0.3\\\\\n", "1/4\n", "\\end{pmatrix}\\hskip1em\\begin{pmatrix}\n", "1 &2 &-1\n", "\\end{pmatrix}\\hskip1em\\begin{pmatrix}\n", "1 & 0 & -1\\\\\n", "0 & -1 & 1\\\\\n", "1 & 1 & 0\n", "\\end{pmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "A=[[1]]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printA(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Lorsqu'on travaille avec des systèmes, on s'intéresse à la matrice augmentée - dans laquelle on retrouve la matrice des coefficients $A$ et une colonne additionnelle correspondant au vecteur $\\overrightarrow{b}$ regroupant les termes de droite.\n", + "Lorsqu'on travaille avec des systèmes, on s'intéresse à la matrice augmentée - dans laquelle on retrouve la matrice des coefficients $A$ et une colonne additionnelle correspondant au vecteur $\\overrightarrow{b}$ regroupant les termes de droite (ou termes constants).\n", "\n", "\\begin{align*}\n", "\\text{Notation système} \\quad &\\Leftrightarrow \\quad\\text{Notation matricielle}\\\\\n", "\\begin{cases}\n", "a_{11}x_1 + a_{12}x_2&=b_1\\\\\n", "a_{21}x_1 + a_{22}x_2&=b_2\n", "\\end{cases} \\quad &\\Leftrightarrow \\quad \\left(\\begin{array}{cc|c}\n", "a_{11} & a_{12} & b_1\\\\\n", "a_{21} & a_{22} & b_2\n", "\\end{array}\\right)\n", "\\end{align*}\n", "\n", "\n", "---\n", "Pour entrer les matrices augmentées des systèmes, on utilise la syntaxe suivante\n", "\n", "\n", "\\begin{align*}\n", "A&=\\quad[\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad]\\\\\n", "b&=\\quad[\\quad [b_1], \\quad [b_2], \\ldots, [b_m]\\quad ] \\leftarrow\\text{ceci nous permet de différencier un vecteur colonne d'un vecteur ligne!}\n", "\\end{align*}\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 2**\n", "Entrez les matrices augmentées des systèmes ci-dessous.\n", "\n", "$$\n", "1) \\quad \\begin{cases}\n", "2x_1 -x_2&=3\\\\\n", "x_1 + x_2&=0,\n", "\\end{cases}\\hskip2em\n", "2)\\quad \\begin{cases}\n", "\\dfrac{1}{3}x_1 + x_2 - x_3&=-6\\\\\n", "x_1 + x_3&=2\\\\\n", "-x_1 + \\dfrac{27}{9}x_2- x_3&=-1,\n", "\\end{cases}\\hskip2em\n", "3)\\quad \\begin{cases}\n", "x_1 - 4x_2=7\n", "\\end{cases}\\hskip2em\n", "4) \\begin{cases}\n", "x_1 &=3\\\\\n", "x_2 &= 4\\\\\n", "x_3 &= -1\\\\\n", "x_4&=0\n", "\\end{cases}\\hskip1em\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Entrer la matrice des coeff et le vecteur des termes de droite. Attention aux dimensions!\n", "A=[[1,1], [1,1]]\n", "b=[[1],[1]]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print('Le système est\\n')\n", "\n", "al.printSyst(A,b)\n", "print('\\n')\n", "print(' Son écriture matricielle est\\n')\n", "al.printA(A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Concept(s)-clé(s) et théorie\n", "\n", "Il existe trois type d'opérations que l'on peut effectuer sur les lignes d'un système d'équations linéaires, ou sur la matrice augmentée correspondante, sans changer son ensemble de solution. \n", "\n", "Ces opérations sont appelées *opérations élémentaires* \n", "\n", "\n", - "1. $E_{ij}$ (Échange) Échanger la ligne $i$ avec la ligne $j$. \n", - "2. $E_{i}(\\alpha)$ (Multiplication par un scalaire) Multiplier tous les coefficients de la ligne $i$ par une constante non-nulle $(\\alpha)$.\n", - "3. $E_{ij}(\\alpha)$ (Remplacement) Remplacer la ligne $i$ par la ligne obtenue en lui ajoutant un multiple ($\\alpha$) de la ligne $j$. " + "1. $T_{ij}$ (Échange) Échanger la ligne $i$ avec la ligne $j$. \n", + "2. $D_{i}(\\alpha)$ (Multiplication par un scalaire) Multiplier tous les coefficients de la ligne $i$ par une constante non-nulle $(\\alpha)$.\n", + "3. $L_{ij}(\\alpha)$ (Remplacement) Remplacer la ligne $i$ par la ligne obtenue en lui ajoutant un multiple ($\\alpha$) de la ligne $j$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### EXEMPLE 1 :\n", "\n", "Entrer la matrice (augmentée) correspondante au système ci-dessous et effectuer les trois opérations suivantes sur la matrice de départ. \n", "\n", "1. Échanger la ligne $1$ et la ligne $2$.\n", "2. Multiplier tous les coefficients de la ligne $2$ par $-\\dfrac{1}{2}$.\n", "3. Remplacer la ligne 2 par la ligne obtenue en lui ajoutant 3 fois la ligne $3$. \n", "\n", "Le systèmes est \n", "$$\n", "\\begin{cases}\n", "x_1 -3x_2 + \\dfrac{1}{3}x_3&=0\\\\\n", "x_1 -7 x_3&=2\\\\\n", "-2x_1 + 3x_2 -4x_3&=5\n", "\\end{cases}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.bgc('seashell')\n", "#Entrer la matrice des coeff et le vecteur des termes de droite. Attention aux dimensions!\n", "A=[[1, 1, 1], [1, 1, 1],[1, 1, 1]]\n", "b=[[1],[1],[1]]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "al.printA(A,b)\n", "al.manualOp(A,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 3**\n", "\n", "Parmi les couples de systèmes d'équations linéaires ci-dessous, lesquels ont le même ensemble de solutions? Si c'est le cas, c'est qu'on peut passer d'un système à l'autre en utilisant des opérations élémentaires. Cliquez sur Run Interact pour voir de quelles opérations élémentaires il s'agit.\n", "\n", "\\begin{align*}\n", "&a) \\begin{cases}\n", "2x_1 - 8x_2=2\\\\\n", "x_1 + x_2=3\n", - "\\end{cases} \\quad \\rm{et}\\quad \\begin{cases}\n", + "\\end{cases} \\quad \\rm{et} \\quad \\begin{cases}\n", "x_1 =3-x_2\\\\\n", "-x_1 + 4x_2=-1\n", "\\end{cases}\\\\[2em]\n", "&b) \\begin{cases}\n", "x_1 -x_2=2\\\\\n", "-x_1 + x_2 =-2\n", "\\end{cases} \\quad \\rm{et}\\quad \\begin{cases}\n", "-x_1 + x_2=2\\\\\n", "x_1 -x_2=-2\n", "\\end{cases}\\\\[2em]\n", "&c) \\begin{cases}\n", "\\dfrac{1}{4}x_1 -2x_2+ x_3=5\\\\\n", "x_2-x_3=0\\\\\n", "x_1 + 2x_2-x_3=0\n", "\\end{cases} \\quad \\rm{et}\\quad \\begin{cases}\n", "x_1-8x_2+ 4x_3=20\\\\\n", "x_2-x_3=0\\\\\n", "2x_2-x_3=-4\n", "\\end{cases}\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "corrections.Ex3Chapitre1_3_4()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **EXERCICE 4**\n", "\n", "Parmi les systèmes ci-dessous, lesquels ont le même ensemble de solutions?\n", "\n", "\\begin{align*}\n", "&a) \\quad \\begin{cases}\n", "2x_1 + x_2 &=2\\\\\n", "x_1 + 3x_2 -x_3 &=1\\\\\n", "3x_1 + 4x_2 &=0\n", "\\end{cases}\\hskip2em\n", "&&b)\\quad \\begin{cases}\n", "x_1 + \\dfrac{1}{2}x_2 &=2\\\\\n", "x_2 - \\dfrac{2}{5}x_3 &=1\\\\\n", "x_3 &=0\n", "\\end{cases}\\hskip2em\n", "&&c)\\quad \\begin{cases}\n", "2x_1 + x_2 &=2\\\\\n", "\\dfrac{5}{2}x_2 - x_3 &=0\\\\\n", "x_3 &= -3\n", "\\end{cases}\\hskip2em\n", "&&d) \\quad \\begin{cases}\n", "x_1 + 3x_2 - x_3 &= 1\\\\\n", "2x_1 + x_2 &= 2\\\\\n", "3x_1 + 4x_2 &= 0\\\\\n", "-x_1 -\\frac{1}{2}x_2 &= -1\n", "\\end{cases}\\mbox{}\\\\\n", "\\\\\n", "&e) \\quad \\begin{cases}\n", "2x_1 + x_2 &= 2\\\\\n", "3x_1 + 4x_3 &= 0\\\\\n", "x_1 + 3x_2 - x_3 &= 1\n", "\\end{cases}\\hskip2em\n", "&&f) \\quad \\begin{cases}\n", "2x_1 + x_2 &= 2\\\\\n", "3x_1 + 4x_2 &= 0\\\\\n", "3x_1 + 4x_3 &= 0\\\\\n", "x_1 + 3x_2 - x_3 &= 1\\hskip2em\n", "\\end{cases}\n", "&&g) \\quad \\begin{cases}\n", "x_1 + \\dfrac{1}{2}x_2 &= 1\\\\\n", "\\dfrac{5}{2}x_2 - x_3 &= 1\\\\\n", "\\dfrac{3}{2}x_1 + 2x_2 &= 0\n", "\\end{cases}\\hskip2em\n", "&&h) \\quad \\begin{cases}\n", "x_1 + 3x_2 - x_3 &= 1\\\\\n", "-\\dfrac{5}{2}x_2 + x_3 &= 0\\\\\n", "\\dfrac{3}{4}x_1 + x_2 &= 0\\\\\n", "\\end{cases}\\hskip2em\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "corrections.Ex4Chapitre1_3_4() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Passez au notebook du chapitre 1.5-1.6: Matrices Echelonnées](./1.5-1.6.%20Matrices%20Echelonnées.ipynb)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.4" + "version": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 } diff --git "a/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" "b/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" index 7b7b4de..6233a1a 100644 --- "a/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" +++ "b/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" @@ -1,65572 +1,64698 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Concept(s)-clé(s) et théorie\n", "\n", "Soit $ V $ un ensemble non-vide muni d'une opération binaire $+$ et d'une action sur les nombres réels $\\cdot$, c'est-à-dire que pour tout $u,v\\in V$, il existe un unique élément $u+v\\in V$ et pour tout $u\\in V$, $\\lambda\\in \\mathbb{R}$, il existe un unique élément $\\lambda\\cdot u\\in V$. On dira que $V$ est un $\\mathbb{R}$-espace vectoriel si les huit axiomes suivants sont satisfaits, pour tous $u,v,w\\in V$ et $\\lambda, \\mu\\in \\mathbb{R}$.\n", "\n", "\n", "1. $u+ v=v+ u$\n", "2. $(u+ v) + w = u + (v+ w)$\n", "3. $\\lambda\\cdot( u + v)= \\lambda \\cdot u + \\lambda \\cdot v$\n", "4. $(\\lambda + \\mu)\\cdot v=\\lambda \\dot v + \\mu\\cdot v$\n", "5. $\\lambda \\cdot (\\mu\\cdot v)=(\\lambda \\mu)\\cdot v$\n", "6. $1\\cdot u=u$\n", "7. Il existe un élément neutre pour la loi $+$, i.e. un élément $e\\in V$ tel que $e+ u=u$ pour tout $u\\in V$.\n", "8. Pour tout $u\\in V$, il existe un unique inverse par rapport à la loi $+$, i.e. un élément $u' \\in V$ tel que $u+ u'=e$. \n", "\n", "Remarques: \n", "1. On écrit $\\lambda v$ au lieu de $\\lambda \\cdot v$. \n", "2. Les éléments de $V$ sont appelés des vecteurs (même si on ne les écrit pas $\\overrightarrow v$) et les éléments de $\\mathbb{R}$ des scalaires.\n", "\n", "Commentaire: on parle de $\\mathbb{R}$-espace vectoriel car les scalaires appartiennent à $\\mathbb{R}$. Dans certains cas, par traités ici, les scalaires peuvent appartenir à un autre ensemble, comme par exemple êtres des nombres complexes (dans $\\mathbb{C}$). Dans ce cas on parlerait de $\\mathbb{C}$- espace vectoriel. \n" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 97, "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - " \n", - " " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import AL_Fct as al\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import plotly\n", "import plotly.graph_objs as go\n", "import pandas as pd\n", "import random\n", "from IPython.core.magic import register_cell_magic\n", "from IPython.display import HTML, display" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "line": { "color": "teal", "width": 3 }, "mode": "lines", "name": "Vecteur u", "type": "scatter", - "uid": 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", 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PJjUrY0i5jCGlauMY6n23ZwxXY28t/pylM4agfsZQBUofTGpWxpByGUNK1aYx1PfmWK7G3lX8OZuSMQT1M4YqUPpgUrMyhpTLGFKqNoyhgU0b81dj33ll7H7uydg18FHx52xaxhDUzxiqQOmDSc3KGFIuY0ippuoY6unZE7s3PBr7b104wtXYLxd/ziZnDEH9jKEKlD6Y1KyMIeUyhpRqqo2h3h07Y8+j9+evxl57b/TteKf4c54MGUNQP2OoAqUPJjUrY0i5jCGlmipjqP/1V2PvyqXp7wdaelHs3vBI9OzaXfw5T6aMIaifMVSB0geTmpUxpFzGkFKd1GNo4OMYeOHp2H/XVemrsVd0t/pq7IlmDEH9jKEKlD6Y1KyMIeUyhpTqZBxDve/1xuD6h+LAzV3p7wf6ze3R9+abxZ/zZM8YgvoZQxUofTCpWRlDymUMKdXJNIb6tm6LPauXp18Kt6QzBh9f6WrsCjOGoH7GUAVKH0xqVsaQchlDSnUyjKGBzS/Gvnuvy1yNfUXsfv7J2NX/YfHnnGoZQ1A/Y6gCpQ8mNStjSLmMIaVq6hg6fDX2uth/2yWZq7FvcjV2zRlDUD9jqAKlDyY1K2NIuYwhpWraGOp9+93DV2Nff276auxH7o2+t94u/pxtyBiC+hlDFSh9MKlZGUPKZQwpVVPG0IhXYy+7KHY/vdbV2JOcMQT1M4YqUPpgUrMyhpTLGFKqomNo9yejX4390nPFP0dtzRiC+hlDFSh9MKlZGUPKZQwpVYkxdPRq7Fvmj3A19hvFPzdtzxiC+hlDFSh9MKlZGUPKZQwp1WSOob5t22PPw3dlrsbuiMHHVkbvzg+Kf050OGMI6mcMVaD0waRmZQwplzGkVJMxhgY2vxj77rs+fzX2c+tjV9+B4p8LHZsxBPUzhipQ+mBSszKGlMsYUqq6xlBP797Y/cxj+auxf70k+l/dXPzjVz5jCOpnDFWg9MGkZmUMKZcxpFRVj6Hed96LwXUPxIc3nJe+GnvtPdH32x3FP26NnjEE9TOGKlD6YFKzMoaUyxhSqqrGUP+W12LvqmWZq7EXHL4a+4OB4h+vxp4xBPUzhipQ+mBSszKGlMsYUqqJjqGBF5+JfXdfnbkae7GrsU/ijCGonzFUgdIHk5qVMaRcxpBSncgY6n2/LwafXB0Hbrkg/f1Aq25zNfYUyBiC+hlDFSh9MKlZGUPKZQwp1XjGUN/232avxv7wxrmHr8Z+53fFPyZVkzEE9TOGKlD6YFKzMoaUyxhSqrGMof6XX4p9992Qvhr7jstj97NPuBp7CmYMQf1aO4aWrVgT06bPHvXnLexeHqecOvO4hip9MKlZGUPKZQwpVW4M9fTt+/3V2Jfmr8Z+ZVPx51d9GUNQv9aNobXrNx4dNGMdQzNmdY34c0ofTGpWxpByGUNKNXwM/eFq7PPTV2OvWeFq7JZkDEH9WjeGjhjPV4aMIY0nY0i5jCGlOjKG+t94PfauvDV9NfbSC2PwyYej53f9xZ9Xk5cxBPUzhkYx/GVyqbcpfTCpWRlDymUMKdWeTc/G1yuvy1+N/eKzxZ9RZTKGoH7G0DjNmNV13FeKPvn8K+lon37+lT8XSnbwq6/ji4NfF38Ole/TvXvj843r4ss7LoqDN58fh5bOjS9vOv9onz9yZ3y6c3vx51TZvvr6UHz+ZbPODJhqjKFxOvI9R0Pt++gL6Wj7P/4iDh3y50LH98Xv/1JT+jlUrgM7346P190Tn9147tE+X3JeHFp6fnx2S2d8/OSq2P/BB8WfU83oy4Nfx8efHSz+HEODqcYYGqfUGCr9JWs1Ky+TUy4vk2tv/S9vyl6N/eGdl8VXrz8TPb37iz+nmpWXyUH9jKFhhr8MbvjPmTZ9dszp7D7mx0ofTGpWxpByGUPt6vDV2I/H/tsvS38/0P03Rv/Lm8b1H11VuzKGoH6tG0NDr9Y+0sLu5Uf//fAxNGNW1zE/d/gQivCXXh2bMaRcxlA76n3n/Rh8dJSrsbe/dfTnG0PKZQxB/Vo3hupQ+mBSszKGlMsYmtr1v7ElfzX2LRf8/mrsvuPfzhhSJmMI6mcMVaD0waRmZQwplzE0NRt48dnYt2Jx+qVwd18TAxufGfHtjSHlMoagfsZQBUofTGpWxpByGUNTp57f9cfgkw/HgaUXJkfQ3pW3Rv+W18f0vowh5TKGoH7GUAVKH0xqVsaQchlDJ39929+KPWtWpG+Fu+H8GHz0gejd+f643qcxpFzGENTPGKpA6YNJzcoYUi5j6OSt/5VNsffXS5IjaP9tl8buZx6Pnr59J/a+jSFlMoagfsZQBUofTGpWxpByGUMnVz29+2P3s0/E/jsuT38/0H03RP8rmyb86xhDymUMQf2MoQqUPpjUrIwh5TKGTo563/ldDD62Mj68cW76auzVd0Xf9t9W9usZQ8plDEH9jKEKlD6Y1KyMIeUyhppd/xtbYu+q20a4Gnt18mrsCf+6xpAyGUNQP2OoAqUPJjUrY0i5jKFmNvDSc/mrse+6OgZeHPlq7IlmDCmXMQT1M4YqUPpgUrMyhpTLGGpOPb/rj8Gn1sSBZQvSV2OvWhb9W16blGcxhpTLGIL6GUMVKH0wqVkZQ8plDJWv77c78ldjX39eDK57IHrfeW9Sn8kYUi5jCOpnDFWg9MGkZmUMKZcxVK4Rr8a+/dLY/cxj0dO7t8yzGUPKZAxB/YyhCpQ+mNSsjCHlMoYmub4DI1+Nff8N0f/yS8Wf0xhSLmMI6mcMVaD0waRmZQwplzE0OfXu/CAGH1sZB5Z0pK/Gfviu6Nu2vfhzHskYUi5jCOpnDFWg9MGkZmUMKZcxVG99b74Re39ze+Zq7PkxuP6h6H2/+quxJ5oxpFzGENTPGKpA6YNJzcoYUi5jqJ4OX43dnX4p3N1Xx8DGDbFr9yfFnzOXMaRcxhDUzxiqQOmDSc3KGFIuY6i6ej4YiN1Pr81fjb1y6aRdjT3RjCHlMoagfsZQBUofTGpWxpByGUMTr++tt2PPI/dmrsY+N/as+3X0vv1u8eccT8aQchlDUD9jqAKlDyY1K2NIuYyhE6//1c2x94Gb0ldj33ZJ0auxJ/yxGUPKZAxB/YyhCpQ+mNSsjCHlMobGWf+Hsfv5J2P/nVekvx/o3utiYPOL5Z9zghlDymUMQf2MoQqUPpjUrIwh5TKGxlbvzg9i8PGVceCmzvTV2KuXN+pq7IlmDCmXMQT1M4YqUPpgUrMyhpTLGBq5vjffzF+NfXPX4aux3+st/pxVZwwplzEE9TOGKlD6YFKzMoaUyxhKN7Dp+dh3T/pq7P13XRUDLzzd6KuxJ5oxpFzGENTPGKpA6YNJzcoYUi5j6A/17Np9+GrspRflr8Z+/dXizzkZGUPKZQxB/YyhCpQ+mNSsjCHlMobGcDX2o/dH746dxZ9zMjOGlMsYgvoZQxUofTCpWRlDytXmMdT/2sux94Gb0y+Fu3Vh7N7waPT07Cn+nEU+N8aQMhlDUD9jqAKlDyY1K2NIuVo3ho5ejX1l/mrsTRvLP2fhjCHlMoagfsZQBUofTGpWxpBytWUM9b67KwYfXxUHlmSuxn7ozujbuq34czYlY0i5jCGonzFUgdIHk5qVMaRcU30M9W3dGnt/c0f+auwnfhO97/YUf86mZQwplzEE9TOGKlD6YFKzMoaUa6qOoYFNL8S+FZmrsZcvOnw19sDHxZ+zqRlDymUMQf2MoQqUPpjUrIwh5ZpKY6inZzB2b3g0Diy7OH019oO3RP9rrxR/zpMhY0i5jCGonzFUgdIHk5qVMaRcU2EM9e14J/Y8cl/6auzrzmnl1dgTzRhSLmMI6mcMVaD0waRmZQwp18k8hvpfeyV7NfaBZRcfvhp712Dx5zwZM4aUyxiC+hlDFSh9MKlZGUPKddKNoYGPYuD5p2L/8kXpq7HvudbV2BVkDCmXMQT1M4YqUPpgUrMyhpTrZBlDve/2HL4a+6Z5+aux39xa/DmnSsaQchlDUD9jqAKlDyY1K2NIuZo+hvre3Bp7Hroz/VK4m+bF4OOrovc9V2NXnTGkXMYQ1M8YqkDpg0nNyhhSrqaOoYFNG2PfPdemr8a+88oYeP6p2DXwUfHnnKoZQ8plDEH9jKEKlD6Y1KyMIeVq0hjq2XX4auz9ty5MX439wM3R/9rLxZ+zDRlDymUMQf2MoQqUPpjUrIwh5WrCGOrdsTP2PHp//mrstfdG3453in+u2pQxpFzGENTPGKpA6YNJzcoYUq6SY6j/tVdi74O35K/GfvqR6Nm1u/jnqI0ZQ8plDEH9jKEKlD6Y1KyMIeWa9DE08HEMvPB0/mrsFd0xsOmF4p+XtmcMKZcxBPUzhipQ+mBSszKGlGuyxlDve70x+MRv4sDNXenvB/rNHdH35pvFPx86nDGkXMYQ1M8YqkDpg0nNyhhSrrrHUN/WbfmrsZd0xuATq6L33V3FPw86NmNIuYwhqJ8xVIHSB5OalTGkXHWNoYHNL8a+e6/LXo29+/knY1f/h8U/fqUzhpTLGIL6GUMVKH0wqVkZQ8pV5Rjq6dkTuzesy1+N/aCrsU+WjCHlMoagfsZQBUofTGpWxpByVTGGet9+9/DV2Nefm74a+5F7o++tt4t/rBp7xpByGUNQP2OoAqUPJjUrY0i5JjKG+l9/NfauXJq5Gvui2P30Wldjn6QZQ8plDEH9jKEKlD6Y1KyMIeUa9xja/cnhq7HvumqEq7GfL/5xaWIZQ8plDEH9jKEKlD6Y1KyMIeUa6xjqfa83Btc/FAdumZ+5Gvt2V2NPoYwh5TKGoH7GUAVKH0xqVsaQco02hvq2bY89D9+VuRq7IwYfXxm9Oz8o/nGo2owh5TKGoH7G0BgtW7Empk2fnfx3pQ8mNStjSLlyY2hg84ux777rM1djX+Fq7CmeMaRcxhDUzxgaxdr1G+OUU2fGKafONIY0powh3fvqtmQPb98Rq7a+Ffe+ui3uf+nVeOLB5fHKNb+KNxaeGTsuO+vYl8L9ekn0v7q5+Mei+jOGlMsYgvoZQ2PkK0Maa8aQrnj6hfijjo5k/8evfhZ/ddZ34rzv/nF0/Mf/d7TNC75/+GrstfdE3293FP8YNHkZQ8plDEH9jKExMoY01owh7Rr8NP7i1juOGUH/19k/in+e9e1jBtCRVsz97uGrsT8YKP7cmvyMIeUyhqB+xtAYjTSGvvjya+kPHfzanwtF/4efxP9z7XXx//7s9Djj+99MjqDTfvCtOO3yedH/4SfFn1fl+vLg13HokDNDx/f1oUNx8KtDxZ9jaDDVGENjNNIYGjzwufSHPvw8Dh3y56LNvbb9rei+7uI4/wd/mRxB08+cHv/nf54V/+XyK+Ltgf3Fn1dl2/fRF/HV14eKP4ea1xcHv44PPzlY/DmGBlONMTRGXianseZlcu1tzdNPxcIFP0sOoF+d9o3487P+Jf73c34Rf9TREf/rggVx08ZXiz+zyudlcsrlZXJQP2NojIwhjTVjqH0tf+Du6Drnu8kR1HHWt+Pfun4R/8v55x3zPUQd654q/txqRsaQchlDUD9jaBRDr9Y+0sLu5cf8nNIHk5qVMdSOtr3fH9fffFV0nPX3yRE0/7zvxYqV9x39+f/3Nd1Hh9A/3n1fsedW8zKGlMsYgvoZQxUofTCpWRlDU7unN22Oy6+cGx2nfSM5gi695Jex7tlnj3u7rbv2xf+24KL4L1dcEVt37Sv+cag5GUPKZQxB/YyhCpQ+mNSsjKGp2QOPrI4LO89MvxTuh9+MxddfGq9se3vE93HkP7pa+mNRszKGlMsYgvoZQxUofTCpWRlDU6tld90SnT//TnIEzfvFv8StK24d8/v65LODse/jL4t/TGpWxpByGUNQP2OoAqUPJjUrY+jkb/O2HXHNtQtj7vf/KjmCLuz6cax6dM24368xpFTGkHIZQ1A/Y6gCpQ8mNStj6OTtkQ1Px8KLz04OoLmn/2lcsagzntl84tdhGztnyp4AABi5SURBVENKZQwplzEE9TOGKlD6YFKzMoZOvu5edW/MP+e05AjqPOvbceOy7njr/d0T/nWMIaUyhpTLGIL6GUMVKH0wqVkZQydH29/vjxtuuSY6zvp2+mrsc06LFQ/eW+mvaQwplTGkXMYQ1M8YqkDpg0nNyhhqdhs2vxJXXtkRHd/7k+QIWnjx2fHohg21/NrGkFIZQ8plDEH9jKEKlD6Y1KyMoWb24NrVsSB3Nfasv4nF1y6Ml7fuqPUZjCGlMoaUyxiC+hlDFSh9MKlZGUPNatldS2Ne7mrsn38nlt21dNKexRhSKmNIuYwhqJ8xVIHSB5OalTFUvs1bd8TiaxdGx6y/SY6gBZ1nxoNrV0/6cxlDSmUMKZcxBPUzhipQ+mBSszKGyvXI0/mrsTu+9ydx5ZUdsWHTy8WezxhSKmNIuYwhqJ8xVIHSB5OalTE0+d39YP5q7I6zvh033HJNbH+/v/hzGkNKZQwplzEE9TOGKlD6YFKzMoYmp7fe3x03LuuOzhGuxr57VbVXY080Y0ipjCHlMoagfsZQBUofTGpWxlC9PbP51bhiUWfMPf1P01djX/SLeGTD08WfM5UxpFTGkHIZQ1A/Y6gCpQ8mNStjqJ5WPbomLuz6cXIAzf3+X8U11y6MzdvqvRp7ohlDSmUMKZcxBPUzhipQ+mBSszKGqu3WFbfGvF/8S3IEdf78O7HsrluKP+NYM4aUyhhSLmMI6mcMVaD0waRmZQxNvFe2vR2Lr780On74zeQIurDzzHjgkdXFn3O8GUNKZQwplzEE9TOGKlD6YFKzMoZOvHXPPhuXXvLL9K1wp30jLr9ybjy9aXPx5zzRjCGlMoaUyxiC+hlDFSh9MKlZGUPjb8XK++KC80/PXI3993H9zVfFtgZcjT3RjCGlMoaUyxiC+hlDFSh9MKlZGUNja8cHe2LJsu7o/Mk/JEdQ1znfjbseuLv4c1aZMaRUxpByGUNQP2OoAqUPJjUrY2jknt38aiy6al7MPePP0ldjL/hZrH3qyeLPWUfGkFIZQ8plDEH9jKEKlD6Y1KyMoXSr1q2NBfPPSr8U7gd/Fdd0XxSb3nyr+HPWmTGkVMaQchlDUD9jqAKlDyY1K2Po2G6757aYd/a/pq/G/tk/x9I7b4oPdn9S/DknI2NIqYwh5TKGoH7GUAVKH0xqVsbQp/Hq9ndi8Q2XRces9NXYCzpnxa/XPlT8OSc7Y0ipjCHlMoagfsZQBUofTGpWbR5Djz33XP5q7O99Iy6/4vx46sWXij9nqYwhpTKGlMsYgvoZQxUofTCpWbVxDK1YdX9ccN73Mldj/11cf8vVsfXd3uLPWTpjSKmMIeUyhqB+xlAFSh9MalZtGUNv9+yNJbddF52zp6evxv7Vf8TyX99V/DmblDGkVMaQchlDUD9jqAKlDyY1q6k+hp57dUssunp+/mrsi34ea55cX/w5m5gxpFTGkHIZQ1A/Y6gCpQ8mNaupOoZ+88S6uOiCnyQH0Nwf/FVcvXhBvLRle/HnbHLGkFIZQ8plDEH9jKEKlD6Y1Kym2hi6/Z7bouvsfxvxauz3Bz4u/pwnQ8aQUhlDymUMQf2MoQqUPpjUrKbCGHrtrffi2hsvj7ln/k1yBF3Q8cO4/+FVxZ/zZMsYUipjSLmMIaifMVSB0geTmtXJPIYee/a5uOyyX6VvhTttWlx++XnxZIuvxp5oxpBSGUPKZQxB/YyhCpQ+mNSsTsYxdO/qB2P+3DPSI+jH/z2uu2lRbN3ZU/w5T/aMIaUyhpTLGIL6GUMVKH0wqVmdLGPonZ69cdNt10fHT/8pfTX2L/897nQ1dqUZQ0plDCmXMQT1M4YqUPpgUrNq+hh6/vU3Y9HiC2Lu6X+evhr7wjmxZv0TxZ9zKmYMKZUxpFzGENTPGKpA6YNJzaqpY+ihJ9bFRfMzV2N//y/jqsUXxotbthV/zqmcMaRUxpByGUNQP2OoAqUPJjWrpo2hO+67I+adPTN9Nfac/xE337Ek3us7UPw525AxpFTGkHIZQ1A/Y6gCpQ8mNasmjKHXd7z/+6uxv5UcQRfO/UHcv3pl8c9V2zKGlMoYUi5jCOpnDFWg9MGkZlVyDD3+/PNx2aWZq7G/+8dx2eXnxvoXNhb/HLU1Y0ipjCHlMoagfsZQBUofTGpWJcbQvQ89GBec//309wP96G/juhuviDfe/qD456btGUNKZQwplzEE9TOGKlD6YFKzmqwx9G7f/rjpthuiM3c19n/+z7jj/uXFPx/6Q8aQUhlDymUMQf2MoQqUPpjUrOoeQy9s2RqLrp4fc8/4i+QIuvjCn8bqJx4r/nnQ8RlDSmUMKZcxBPUzhipQ+mBSs6prDK1+4rG46MKfpl8Kd8ZfxFXXXBAvvL61+MevfMaQUhlDymUMQf2MoQqUPpjUrKoeQ3fcvzx7NXbHT/8pbr79xni3b3/xj1ujZwwplTGkXMYQ1M8YqkDpg0nNqoox9MbbH8R1N14RHT/62+zV2Pe5GvukyxhSKmNIuYwhqJ8xVIHSB5Oa1UTG0PqNL8Zll58bHd/94+QIuuyyc+KJF14o/jHqxDKGlMoYUi5jCOpnDFWg9MGkZnUiY+j+1Svjwo4fpr8f6MxvxbVLrogt77ga+2TPGFIqY0i5jCGonzFUgdIHk5rVWMfQe30H4uY7lkTnnP+RHEHzzp4Zd9x7e/GPR9VlDCmVMaRcxhDUzxiqQOmDSc1qtDG08fWtcdXiC2Pu9/8yOYIumv+TeOiJdcU/DlWfMaRUxpByGUNQv1aOoRmzuuKUU2fGKafOjBmzukb8uQu7lx/9uUMbqvTBpGaVG0MPr38iFl44J/1SuNP/PBYtviBeeP3N4s+v+jKGlMoYUi5jCOrXujE0p7P7mAE0Y1ZXzOnszv78hd3LRx1MpQ8mNavhY+jO+5dH1y//PX019ux/jJtuuz7e6dlb/LlVf8aQUhlDymUMQf1aN4amTZ8da9dvPPrPa9dvjGnTZ2d/vjGk8daz59MY3Lsnrl9yZXT8+L8nR9D888+Iex96oPizanIzhpTKGFIuYwjq16oxtGX7zjjl1JmxZfvOEX9sqOEvk0sNp9IHk5rT+o0vxuWXnxsdp03LXI39q3js2eeKP6fKZAwplTGkXMYQ1M8YGmUMDTdjVtdxXyn66utDanmPrl8dF88/MzmAOs/8Vixdtih6BvqKP6fKdujQofj6UPnnUPM65H9LlOjQoYivG/AcQ4Opxhga5xhau37jcRco9O37TC1s155PYunyJdH5s39OjqCuX86MO+67vfhzqjl9+vlXceCTg8WfQ81q8MDn8dVXh4o/h5rX519+Ffs+/rL4cwwNpppWjaGI8X/P0HCpMVT6S9aa3F7asj2uWrwgOnJXY1/wk9iw8aniz6nm5WVySuVlcsrlZXJQv9aNodFukxv+MrjhQ2na9NnH3T5X+mDS5LTmyfWxcMHP0ldjn/Hnsejqrnju1S1j/o+uqn0ZQ0plDCmXMQT1a90Yihj5vzM0fAwN/bmnnDozeQ136YNJ9bb813dlr8bunD09ltx+fbw95GpsY0i5jCGlMoaUyxiC+rVyDFWt9MGk6tv6Xl9cf8vV0XHW32Wuxj497ll1f/JtjSHlMoaUyhhSLmMI6mcMVaD0waTqeurFl+LyK87PXo196aW/iseeG/lqbGNIuYwhpTKGlMsYgvoZQxUofTBp4v167UOxoHNWcgB1zPpmdN9wWbz2251jel/GkHIZQ0plDCmXMQT1M4YqUPpg0on1u4GPY+mdN0Xnz2ckR9C8s/81br/ntnG/X2NIuYwhpTKGlMsYgvoZQxUofTBpfL305ltxTfdFMTdzNfaC+WfFqnVrT/j9G0PKZQwplTGkXMYQ1M8YqkDpg0lja+Srsf8sFl01L557+bUJ/zrGkHIZQ0plDCmXMQT1M4YqUPpg0sgtf+Du6Drnu+mrsX/yD7FkWXfs+N1gZb+eMaRcxpBSGUPKZQxB/YyhCpQ+mHR8297ri+tvvio6fvL3yRF0wXnfixUr76vl1zaGlMsYUipjSLmMIaifMVSB0geT/tBTL22Ky6+cGx2nfSN9NfYlv4x1zzxT6zMYQ8plDCmVMaRcxhDUzxiqQOmDSZ/GA2tXx4J5Z6avxj7zW7H4+kvjlW1vT8qzGEPKZQwplTGkXMYQ1M8YqkDpg6nNLbt7acz7Wfpq7K6z/zVuXXHrpD+TMaRcxpBSGUPKZQxB/YyhCpQ+mNrW5m074pprL465P/jr9NXYXT+OVY+uKfZ8xpByGUNKZQwplzEE9TOGKlD6YGpLj2x4OhYu+Hn6auzT/zSuvGpePLP51eLPaQwplzGkVMaQchlDUD9jqAKlD6ap3t2r7o3555yW/n6gn/xD3Lh0cbz1/u7iz3kkY0i5jCGlMoaUyxiC+hlDFSh9ME3Ftr/fHzfcck10nJW+Gnt+jVdjTzRjSLmMIaUyhpTLGIL6GUMVKH0wTaU2bH4lrryyIzq+9yfJEXTJwv+MRzdsKP6cI2UMKZcxpFTGkHIZQ1A/Y6gCpQ+mqdCDa1fHgnk/Sr8U7offjMXXXRIvT9LV2BPNGFIuY0ipjCHlMoagfsZQBUofTCdzy+5aGvN+/p3kCJr38+/ErXcvK/6M480YUi5jSKmMIeUyhqB+xlAFSh9MJ1svb9sRi69dGB25q7E7z4yVjzxc/DlPNGNIuYwhpTKGlMsYgvoZQxUofTCdLD2yYUMsvPjs9EvhvvcnceWVHbFh08vFn3OiGUPKZQwplTGkXMYQ1M8YqkDpg6nprXjw3ph/7vfSI+jHfx833HJNbH+/v/hzVpUxpFzGkFIZQ8plDEH9jKEKlD6Ymthv3xuIG5d1R+dZ305fjX3OaXH3ynuLP2cdGUPKZQwplTGkXMYQ1M8YqkDpg6lJbXjp5bhyUWfMPf1PkyNo4UW/iEc2PF38OevMGFIuY0ipjCHlMoagfsZQBUofTE1o5SMP56/G/sFfxzXXLozNW98q/pyTkTGkXMaQUhlDymUMQf2MoQqUPphKduvdy2LeL/4lezX2srtuKf6Mk50xpFzGkFIZQ8plDEH9jKEKlD6YJrtXtr0di6+7JDp++M301djzfhQPPLK6+HOWyhhSLmNIqYwh5TKGoH7GUAVKH0yT1bpnn41LFv5n9mrsK66cG09v2lz8OUtnDCmXMaRUxpByGUNQP2OoAqUPprpbsfK+mH9e5mrss/4+brjl6tg2ha7GnmjGkHIZQ0plDCmXMQT1M4YqUPpgqqMdH+yJJcu6o2OEq7HveuDu4s/ZxIwh5TKGlMoYUi5jCOpnDFWg9MFUZc9ufjUWXd01wtXYP4+1U/xq7IlmDCmXMaRUxpByGUNQP2OoAqUPpipatW5tLOj6cXIAzf3BX8c1114cm95sx9XYE80YUi5jSKmMIeUyhqB+xlAFSh9ME+m2e26LrrP/NXM19oxYdvfS+KABz3kyZQwplzGkVMaQchlDUD9jqAKlD6bx9ur2d2LxDZdFx6zM1dids+KBtauLP+fJmjGkXMaQUhlDymUMQf2MoQqUPpjG2mPPPhuXXvLLzNXY34jLrzg/nnrxpeLPebJnDCmXMaRUxpByGUNQP2OoAqUPptFaser+uCB7NfbfxfW3XB1b3+0t/pxTJWNIuYwhpTKGlMsYgvoZQxUofTClevuDPXHTbddF50//MTmCun71H7H813cVf86pmDGkXMaQUhlDymUMQf2MoQqUPpiG9twrr8eiq+bF3DP+LHs19pr1TxR/zqmcMaRcxpBSGUPKZQxB/YyhCpQ+mHYNHr4a+6ILfpK+Gvv7fxlXL14QL23ZXvw525AxpFzGkFIZQ8plDEH9jKEKlDyUbr/ntug6+9+SI6jzZ/8cS++8Kd7v/6j44dmmjCHlMoaUyhhSLmMI6mcMVWCyD6LX3novum+4LOb+6FvJEXRhxw/j/odXFT8w25oxpFzGkFIZQ8plDEH9jKEKTNYB9Nizz8Wll/4qfSvcadPi8svPiyddjV08Y0i5jCGlMoaUyxiC+hlDFaj74Ll39YMx//zTs1djX3fToti6s6f4AanDGUPKZQwplTGkXMYQ1M8YqkAdh807PXvjptuuj87Z09NXY//y3+NOV2M3MmNIuYwhpTKGlMsYgvoZQxWo8pB5/vU3Y9HVXTH39D9PX4294Geuxm54xpByGUNKZQwplzEE9TOGKlDF4fLQE+uyV2N3fP8v46rFC+LFN1yNfTJkDCmXMaRUxpByGUNQP2OoAhM5VO64746Yd/bM7NXYt9yxJN7v+7D44aexZwwplzGkVMaQchlDUD9jqALjPUhe3/F+XLvk8pg762/SV2PP/YGrsU/ijCHlMoaUyhhSLmMI6mcMVWCsB8jjzz8fl+Wuxv7uH8dll58b61/YWPyg08QyhpTLGFIqY0i5jCGonzFUgdEOjvtWPxgXnP/95Aia+6O/jetuvCLeePuD4gecqskYUi5jSKmMIeUyhqB+xlAFUofFzt59cfNtN0TnT/8pfTX2f/7PuOP+5cUPNVWfMaRcxpBSGUPKZQxB/YyhMZgxqytOOXVmnHLqzJgxq+u4fz/0kHjh9Tdj0dXzY+4Zf5EcQRdf+NNY/cRjxQ8z1ZcxpFzGkFIZQ8plDEH9jKFRzOnsPmYAzZjVFXM6u4/5ObsGP42HHl8XF1340/RL4c74i7jqmgvihdfeLH6Iqf6MIeUyhpTKGFIuYwjqZwyNYtr02bF2/caj/7x2/caYNn320X9e+dDd2auxO376T3Hz7TfGu337ix9emryMIeUyhpTKGFIuYwjqZwyNYMv2nXHKqTNjy/ad2R9LvhSu84fxm3UPxYefHlQL++jTgxERxZ9DzevLg1/HZ19+Xfw51Kw+/uxgfH3ImaHjO/jVofj0i6+KP8fQYKoxhkYwpjF0xp8dvRr7mkXnxWtbXynzsAAAwLgYQyMYyxi6654lseSWRfFub1/x/2+NmpGvDCmXrwwpla8MKZevDEH9jKFRjPY9QxG+N0TH5nuGlMv3DCmV7xlSLt8zBPUzhkYx1tvkpCMZQ8plDCmVMaRcxhDUzxgag/H8d4YkY0i5jCGlMoaUyxiC+hlDFSh9MKlZGUPKZQwplTGkXMYQ1M8YqkDpg0nNyhhSLmNIqYwh5TKGoH7GUAVKH0xqVsaQchlDSmUMKZcxBPUzhipQ+mBSszKGlMsYUipjSLmMIaifMVSB0geTmpUxpFzGkFIZQ8plDEH9jKEKlD6Y1KyMIeUyhpTKGFIuYwjqZwxVoPTBpGZlDCmXMaRUxpByGUNQP2OoAqUPJjUrY0i5jCGlMoaUyxiC+hlDFSh9MKlZGUPKZQwplTGkXMYQ1M8YAgAAWskYAgAAWskYAgAAWskYAgAAWskYOkEzZnXFKafOjFNOnRkzZnWVfhwm2Xh+/xd2Lz/6c4dG+yxbsSamTZ9d+jEoZKy//84M5nR2H/N77+8ZUB9j6ATM6ew+5mCaMasr5nR2F3wiJtN4f/8Xdi/3P2Qtt3b9xqN/qTGG2me8v//ODIb/OZk2fXYs7F5e6GlgajOGTsC06bNj7fqNR/957fqN/oLTIuP9/fcXG47wlaF2G89XhpwZDOXPBNTHGBqnLdt3ximnzowt23eO+GNMTSfy+z/8JS/+MtxexlC7nejL5PyZYcasLl8ZgpoYQ+NkDLVbFb//M2Z1+f/wtZQx1G4n+vvvzGi3I+MYqIcxNE7GULtV8ft/5PsHaB9jqN1O9PffmdFey1as8fcLqJkxdAJ8z1C7TfT3319s2ssYajdjiPHwFSGYHMbQCXCbXLuN9vs//CUtqVuB/HlpJ2Oo3XK//84MhvPSSJg8xtAJ8t8ZareRfv+H/4/Y0J97yqkz/aWmhYZerXwk3wzdHqP9/jszGOrIS69TDX1VAlANYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGglYwgAAGil/x8eH8B7GMzzaQAAAABJRU5ErkJggg==", + "image/png": 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\n", + "
\n", " \n", "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#what they seee\n", "u=[[1],[1]]\n", "v=[[2],[4]]\n", "lam=2\n", "\n", "#Initial settings, change to np.array\n", "o=[[0],[0]]\n", "\n", "u=np.array(u)\n", "v=np.array(v)\n", "data = []\n", "t = np.linspace(-5, 5, 51)\n", "s = np.linspace(0, 1, 10)\n", "peak = go.Scatter(x=u[0], y=u[1], marker=dict(symbol=6, size=12, color='teal'), showlegend=False)\n", "peak2 = go.Scatter(x=v[0], y=v[1], marker=dict(symbol=6, size=12, color='slateblue'), showlegend=False)\n", "vector = go.Scatter(x=o[0] + s * u[0], y=o[1] + s * u[1], mode='lines',\n", "line=dict(width=3, color='teal'), name='Vecteur u')\n", "vector2 = go.Scatter(x=o[0] + s * v[0], y=o[1] + s * v[1], mode='lines',\n", "line=dict(width=3, color='slateblue'), name='Vecteur v')\n", "zero = go.Scatter(x=t*0, y=t*0, name='Origine', marker=dict(symbol=6, size=12, color='black'),\n", " showlegend=False)\n", "data.append(vector)\n", "data.append(vector2)\n", "data.append(zero)\n", "data.append(peak)\n", "data.append(peak2)\n", "\n", "#règle du parrallelogramme\n", "trace1= go.Scatter(x=u[0] + s * v[0], y=u[1] + s * v[1], mode='lines',\n", "line=dict(width=1, color='slateblue', dash='dash'), name='\"v\"')\n", "trace2= go.Scatter(x=v[0] + s * u[0], y=v[1] + s * u[1], mode='lines',\n", "line=dict(width=1, color='teal', dash='dash'), name='\"u\"')\n", "w=u+v\n", "sumUV=go.Scatter(x=o[0] + s *w[0], y=o[1] + s * w[1], mode='lines',\n", "line=dict(width=1, color='orangered', dash='dash'), name='u+v',hoverinfo='none')\n", "peakUV = go.Scatter(x=w[0], y=w[1], marker=dict(symbol=6, size=12, color='orangered'), showlegend=False)\n", "\n", "data.append(trace1)\n", "data.append(trace2)\n", "\n", "data.append(sumUV)\n", "data.append(peakUV)\n", "\n", "fig = go.FigureWidget(data=data)\n", "plotly.offline.iplot(fig)\n", "\n", "#multiplication par lambda\n", "data=[]\n", "peak = go.Scatter(x=u[0], y=u[1], marker=dict(symbol=6, size=12, color='teal'), opacity=1,showlegend=False)\n", "data.append(peak)\n", "vector = go.Scatter(x=o[0] + s * u[0], y=o[1] + s * u[1], mode='lines',\n", "line=dict(width=3, color='teal'), opacity=1,name='Vecteur u')\n", "data.append(vector)\n", "peak2 = go.Scatter(x=lam*u[0], y=lam*u[1], marker=dict(symbol=6, size=12, color='orangered'),opacity=0.5, showlegend=False)\n", "data.append(peak2)\n", "vector2 = go.Scatter(x=o[0] + lam*s * u[0], y=o[1] + lam*s * u[1], mode='lines',\n", "line=dict(width=3, color='orangered'), opacity=0.5,name='Vecteur \\lambda u')\n", "data.append(vector2)\n", "\n", "fig = go.FigureWidget(data=data)\n", "plotly.offline.iplot(fig)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Soit $\\mathbb{R}^n$ l'espace définit par \n", + "**Exemples**\n", + "\n", + "1. Soit $\\mathbb{R}^n$ l'espace définit par \n", "\n", "$$\n", - "\\mathbb{R}^n =\\left\\{\\(x_1,x_2, \\ldots, x_n) \\mid x_1, \\ldots, x_n\\in \\mathbb{R}\\right\\}.\n", + "\\mathbb{R}^n =\\left\\{(x_1,x_2, \\ldots, x_n) \\mid x_1, \\ldots, x_n\\in \\mathbb{R}\\right\\}.\n", "$$\n", "Alors $\\mathbb{R}^n$ muni de la lois d'addition $+$ et de multiplication par un scalaire $\\cdot$ définies ci-dessous est un $\\mathbb{R}$-espace vectoriel. Les éléments de $\\mathbb{R}^n$, noté $\\overrightarrow{x}$ et appelé des vecteurs, possèdes $n$ composantes $x_1, \\ldots, x_n$ \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "L'espace vectoriel des polynômes est " + "2. Soit $\\mathbb{P}(\\mathbb{R})$ l'ensemble des fonctions polynômiales à coefficients réels de $\\mathbb{R}$ dans $\\mathbb{R}$. Soit $p\\in \\mathbb{P}(\\mathbb{R})$, alors il existe $n\\in\\mathbb{N}$ et $a_0,a_1, \\ldots, a_n\\in \\mathbb{R}$ (les coefficients) tels que \n", + "$$\n", + "p(x)=a_0 + a_1x+ a_2x^2+ \\cdots + a_nx^n, x\\in \\mathbb{R}.\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pour rentrer un polyôme, il suffit de lister les coefficients $a_0,a_1,\\ldots, a_n$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Pour rentrer un polyôme ou une fonction, utilisez la syntaxe suivante\n", + "**Exercice**\n", + "Soit les polynômes ci-dessous. Donner les degrés et les racines des polynômes (c'est-à-dire les valeurs réelles $x$ pour lesquelles $p(x)=0$).\n", "\n", - "$\n", - "p(t)=a_\n", - "$" + "\\begin{align*}\n", + "&a) p(x)&=1+x & &b) p(x)=x^2 & &c) p(x)=-2 + x^2 + \\dfrac{1}{2}x^5\n", + "\\end{lign*}" ] }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 162, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "Le polynôme entré est\n", + "True\n", + "ici\n" + ] + }, { "data": { "text/latex": [ - "$\\displaystyle 1 + 2 t + 3 t^{2}$" + "$\\displaystyle 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - "plotlyServerURL": "https://plot.ly" - }, - "data": [ - { - "type": "scatter", - "x": [ - -3, - -2, - -1, - 0, - 1, - 2 - ], - "y": [ - 22, - 9, - 2, - 1, - 6, - 17 - ] - } - ], - "layout": { - "autosize": true, - "template": { - "data": { - "bar": [ - { - 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" - ] - }, - "metadata": {}, - "output_type": "display_data" + "ename": "ValueError", + "evalue": "\n Invalid value of type 'builtins.int' received for the 'y' property of scatter\n Received value: 1\n\n The 'y' property is an array that may be specified as a tuple,\n list, numpy array, or pandas Series", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 32\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\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;36m0.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 33\u001b[0m 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\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_set_prop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprop\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\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 3991\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3992\u001b[0m \u001b[0;31m# Make sure properties dict is initialized\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/plotly/basedatatypes.py\u001b[0m in \u001b[0;36m_set_prop\u001b[0;34m(self, prop, val)\u001b[0m\n\u001b[1;32m 4306\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4307\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4308\u001b[0;31m \u001b[0;32mraise\u001b[0m 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\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mraise_invalid_val\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\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 392\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 393\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/_plotly_utils/basevalidators.py\u001b[0m in \u001b[0;36mraise_invalid_val\u001b[0;34m(self, v, inds)\u001b[0m\n\u001b[1;32m 283\u001b[0m \u001b[0mtyp\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtype_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\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 284\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrepr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\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--> 285\u001b[0;31m \u001b[0mvalid_clr_desc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdescription\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[1;32m 286\u001b[0m )\n\u001b[1;32m 287\u001b[0m )\n", + "\u001b[0;31mValueError\u001b[0m: \n Invalid value of type 'builtins.int' received for the 'y' property of scatter\n Received value: 1\n\n The 'y' property is an array that may be specified as a tuple,\n list, numpy array, or pandas Series" + ] } ], "source": [ "import plotly.graph_objects as go\n", "import numpy as np\n", "import sympy as sp\n", "from sympy.printing.latex import LatexPrinter\n", "from IPython.display import display, Latex, Math\n", "sp.init_printing()\n", "\n", "\n", "#define coeff\n", - "coeff=[1,2,3]\n", + "coeff=[1,0,0]\n", + "\n", "\n", + "#hidden\n", "l=len(coeff)\n", - "t=sp.Symbol('t')\n", + "x=sp.Symbol('x')\n", "poly= 0 \n", "\n", - "poly=sp.Add(*[coeff[i]*t**i for i in range(l)], evaluate=False)\n", - "s=LatexPrinter(dict(order='none'))\n", - "display(Math(s._print_Add(poly)))\n", + "poly=sp.Add(*[coeff[i]*x**i for i in range(l)], evaluate=False)\n", + "print(poly)\n", + "\n", + "#if all zero of if only one coeff!=0, then s_print_Add is strange\n", + "count=len([i for i in coeff if i!=0])\n", + "print('Le polynôme entré est')\n", + "print(str(count)=='1')\n", + "if str(count)=='0' or str(count)=='1':\n", + " print('ici')\n", + " display(Math(sp.latex(poly)))\n", + "else:\n", + " s=LatexPrinter(dict(order='none'))\n", + " display(Math(s._print_Add(poly)))\n", + "\n", + "t = np.arange(-10,10,0.5)\n", "\n", - "x = np.arange(-3,3)\n", - "exp=sp.lambdify(t,poly)\n", - "fig = go.Figure(data=go.Scatter(x=x, y=exp(x)))\n", - "fig.show()" + "fig = go.Figure(data=go.Scatter(x=t, y=exp(t)))\n", + "fig.show()\n", + "\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "line": { "color": "black", "width": 1 }, "mode": "lines", "name": "axe Ox", "type": "scatter3d", "x": [ [ -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5 ], [ -4.898989898989899, -4.898989898989899, -4.898989898989899, -4.898989898989899, -4.898989898989899, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xL=-5\n", "xR=5\n", "p=100\n", "\n", "\n", "s = np.linspace(xL, xR, p)\n", "t = np.linspace(xL, xR, p)\n", "tGrid, sGrid = np.meshgrid(s, t)\n", "data = []\n", "\n", "x = sGrid\n", "y = tGrid\n", "surface = go.Surface(x=x, y=y, z=0*y,\n", " showscale=False, showlegend=True, colorscale='teal', opacity=.5, name='Plan')\n", "\n", "axeX=go.Scatter3d(x=x, y=x,z=0*x, mode='lines',\n", "line=dict(width=1, color='black'), name='axe Ox')\n", "\n", "data.append(axeX)\n", "\n", "data.append(surface)\n", "layout = go.Layout(legend=dict(orientation=\"h\"),\n", " autosize=True,\n", " width=800,\n", " height=800,\n", " scene=go.layout.Scene(\n", " xaxis=dict(\n", " gridcolor='rgb(255, 255, 255)',\n", " zerolinecolor='rgb(255, 255, 255)',\n", " showbackground=True,\n", " backgroundcolor='rgb(230, 230,230)'\n", " ),\n", " yaxis=dict(\n", " gridcolor='rgb(255, 255, 255)',\n", " zerolinecolor='rgb(255, 255, 255)',\n", " showbackground=True,\n", " backgroundcolor='rgb(230, 230,230)'\n", " ),\n", " zaxis=dict(\n", " gridcolor='rgb(255, 255, 255)',\n", " zerolinecolor='rgb(255, 255, 255)',\n", " showbackground=True,\n", " backgroundcolor='rgb(230, 230,230)'\n", " )\n", " ))\n", "fig = go.Figure(data=data, layout=layout)\n", "plotly.offline.iplot(fig)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }