{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Commandes utiles pour le bloc-notes ARCHES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Déclaration de vecteurs à composantes formelles\n",
    "# SR signifie Symbolic Ring pour manipuler des composantes symboliques et non seulement numériques (RR, Real Ring)\n",
    "# Exécuter (Run sous cocalc)\n",
    "var('u_1 u_2 u_3 v_1 v_2 v_3'); u = vector(SR,3,[u_1,u_2,u_3] ); v = vector(SR,3,[v_1,v_2,v_3] );\n",
    "show('u = ',u, '  v = ',v);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ATTENTION à la convention Python: COMPLETER LES ... avant d'exécuter (Run)\n",
    "show('u_1 =', u[0]);\n",
    "show('u_2 =', u[...]);\n",
    "show('u_3 =', u[...]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Produit scalaire (uv variable contenant le produit scalaire de u par v)\n",
    "uv = u*v; show('Produit scalaire u.v =',uv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Produit vectoriel (uxv variable contenant \"u vectoriel v\")\n",
    "uxv = u.cross_product(v); show('Produit vectoriel uxv =',uxv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercice (COMPLETER)\n",
    "vxu = ...; show(uxv+vxu) # Logique?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercice (COMPLETER: u.uxv variable contenant le produit scalaire de u par uxv)\n",
    "u.uxv = ...; show('u.uxv =',u.uxv);\n",
    "u.uxv = u.uxv.simplify_full(); show('u.uxv =',u.uxv);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Substitution. \n",
    "# On effectue la substitution de 2 composantes du vecteur u par des valeurs numériques définissant un nouveau vecteur U\n",
    "var('x')\n",
    "U = u.subs(u_1=x,u_2=3); show('U = ',U);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Graphe de fonctions\n",
    "var('theta');\n",
    "f = sin(theta); g = cos(theta);\n",
    "plot([f,g],theta,0,2*pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercice: tracer la fonction sin(x)*log(x) entre 0 et 5\n",
    "..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Définition d'une équation différentielle de fonction inconnue u\n",
    "function('u')(x);\n",
    "ED = derivative(u(x),x) + x*exp(x) == 0; show('Equa. Diff : ',ED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Résolution d'une équation différentielle (...)\n",
    "Sol_u = desolve(ED,u(x),[0,10],ivar=x); u_sol = Sol_u; show('u(x) = ',u_sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pour des informations sur desolve...\n",
    "desolve?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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