{"version":3,"file":"Trinome-eNHhctAu.js","sources":["../../src/modules/Trinome.js"],"sourcesContent":["import FractionEtendue from './FractionEtendue.js'\n\n/**\n * Gère les polynômes du second degré\n *  - Définition depuis la forme développée, canonique ou factorisée\n *  - Calcul du discriminant, des racines, des coordonnées du sommet\n *  - Compatible avec la classe FractionEtendue pour la gestion du calcul exact avec les rationnels\n * @author Rémi Angot\n */\nclass Trinome {\n  /**\n     * Définit un trinôme de la forme ax^2 + bx + c\n     * @param {number | FractionEtendue} a\n     * @param {number | FractionEtendue} b\n     * @param {number | FractionEtendue} c\n     */\n  constructor (a, b, c) {\n    if (typeof a === 'number') this.a = new FractionEtendue(a)\n    else this.a = a\n    if (typeof b === 'number') this.b = new FractionEtendue(b)\n    else this.b = b\n    if (typeof c === 'number') this.c = new FractionEtendue(c)\n    else this.c = c\n  }\n\n  /**\n   * Modifie le polynome pour qu'il soit égal à a(x-x1)(x-x2)\n   * @param {number | FractionEtendue} a\n   * @param {number | FractionEtendue} x1\n   * @param {number | FractionEtendue} x2\n   */\n  defFormeFactorisee (a, x1, x2) {\n    if (a instanceof FractionEtendue === false) a = new FractionEtendue(a)\n    if (x1 instanceof FractionEtendue === false) x1 = new FractionEtendue(x1)\n    if (x2 instanceof FractionEtendue === false) x2 = new FractionEtendue(x2)\n    this.a = a\n    this.b = x1.oppose().sommeFraction(x2.oppose()).produitFraction(a)\n    this.c = x1.produitFraction(x2).produitFraction(a)\n  }\n\n  /**\n   * Modifie le polynome pour qu'il soit égal à k(ax+b)(cx+d)\n   * @param {number | FractionEtendue} k\n   * @param {number | FractionEtendue} a\n   * @param {number | FractionEtendue} b\n   * @param {number | FractionEtendue} c\n   * @param {number | FractionEtendue} d\n   */\n  defFormeFactorisee2 (k, a, b, c, d) {\n    if (k instanceof FractionEtendue === false) k = new FractionEtendue(k)\n    if (a instanceof FractionEtendue === false) a = new FractionEtendue(a)\n    if (b instanceof FractionEtendue === false) b = new FractionEtendue(b)\n    if (c instanceof FractionEtendue === false) c = new FractionEtendue(c)\n    if (d instanceof FractionEtendue === false) d = new FractionEtendue(d)\n    this.a = k.produitFraction(a).produitFraction(c)\n    this.b = k.produitFraction(a).produitFraction(d).sommeFraction(k.produitFraction(b).produitFraction(c))\n    this.c = k.produitFraction(b).produitFraction(d)\n  }\n\n  /**\n   * Modifie le polynome pour qu'il soit égal à a(x - alpha)^2 + beta\n   * @param {number | FractionEtendue} a\n   * @param {number | FractionEtendue} alpha\n   * @param {number | FractionEtendue} beta\n   */\n  defFormeCanonique (a, alpha, beta) {\n    if (a instanceof FractionEtendue === false) a = new FractionEtendue(a)\n    if (alpha instanceof FractionEtendue === false) alpha = new FractionEtendue(alpha)\n    if (beta instanceof FractionEtendue === false) beta = new FractionEtendue(beta)\n    this.a = a\n    this.b = a.produitFraction(alpha).multiplieEntier(-2)\n    this.c = a.produitFraction(alpha).produitFraction(alpha).sommeFraction(beta)\n  }\n\n  /**\n   * Nombre de chiffres après la virgule pour les valeurs approchées (dans les calculs des racines)\n   * @type {number}\n   */\n  precision = 3\n\n  /**\n   * Chaine de caractères de la forme développée ax^2+bx+c\n   * @type {string}\n   */\n  get tex () {\n    let result = ''\n    if (Math.abs(this.a.valeurDecimale) === 1) {\n      if (this.a.s === -1) result += '-'\n      result += 'x^2'\n    } else if (this.a.valeurDecimale === 0) {\n      result += ''\n    } else {\n      result += `${this.a.texFSD}x^2`\n    }\n\n    if (Math.abs(this.b.valeurDecimale) === 1) {\n      result += `${this.b.signeString}x`\n    } else if (this.b.valeurDecimale === 0) {\n      result += ''\n    } else {\n      if (result && this.b.s === 1) result += '+'\n      result += `${this.b.texFSD}x`\n    }\n\n    if (this.c.valeurDecimale === 0) {\n      result += ''\n    } else {\n      if (result && this.c.s === 1) result += '+'\n      result += `${this.c.texFSD}`\n    }\n    return result\n  }\n\n  /**\n   * Discriminant du trinome\n   * @type {FractionEtendue}\n   */\n  get discriminant () {\n    const b2 = this.b.produitFraction(this.b)\n    let ac = this.a.produitFraction(this.c)\n    ac = ac.multiplieEntier(-4)\n    return b2.sommeFraction(ac)\n  }\n\n  /**\n   * Renvoie l'image de x par la fonction définie par le trinome\n   * @param {number | FractionEtendue} x\n   * @returns {FractionEtendue}\n   */\n  image (x) {\n    if (x instanceof FractionEtendue === false) x = new FractionEtendue(x)\n    return this.a.produitFraction(x).produitFraction(x).sommeFraction(this.b.produitFraction(x)).sommeFraction(this.c)\n  }\n\n  /**\n   * Calcul détaillé de l'image d'un nombre\n   * @param {number | FractionEtendue} x\n   * @returns {string}\n   */\n  texCalculImage (x) {\n    if (x instanceof FractionEtendue === false) x = new FractionEtendue(x)\n    let result = ''\n    if (this.a.valeurDecimale === -1) result = '-'\n    else if (this.a.valeurDecimale !== 1) result = `${this.a.texFSD} \\\\times `\n\n    if (x.s === -1 || !x.estEntiere) {\n      result += `\\\\left(${x.texFSD} \\\\right)^2 `\n    } else {\n      result += `${x.texFSD}^2 `\n    }\n\n    if (this.b.valeurDecimale !== 0) {\n      if (this.b.valeurDecimale === 1) result += `${x.simplifie().texFractionSignee} `\n      else if (this.b.valeurDecimale === -1) result += `- ${x.texFSP} `\n      else result += `${this.b.simplifie().texFractionSignee} \\\\times ${x.texFSP} `\n    }\n\n    if (this.c.valeurDecimale !== 0) result += `${this.c.texFractionSignee}`\n\n    result += ` = ${this.image(x).simplifie().texFractionSimplifiee}`\n    return result\n  }\n\n  /**\n   * Calcul sur une ligne du discriminant du polynome\n   * @example\n   * const p = new Trinome(2, 3, 1)\n   * p.texCalculDiscriminantSansResultat\n   * // 3^2-4\\\\times2\\\\times1 = 1\n   * @type {string}\n   * @type {string}\n   */\n  get texCalculDiscriminant () {\n    if (this.b.valeurDecimale === 0) return `-4\\\\times${this.a.texFSP}\\\\times${this.c.texFSP} = ${this.discriminant.texFractionSimplifiee}`\n    else if (this.b.estEntiere && this.b.s === 1) return `${this.b.texFSD}^2-4\\\\times${this.a.texFSP}\\\\times${this.c.texFSP} = ${this.discriminant.texFractionSimplifiee}`\n    return `\\\\left(${this.b.texFSD}\\\\right)^2-4\\\\times${this.a.texFSP}\\\\times${this.c.texFSP} = ${this.discriminant.texFractionSimplifiee}`\n  }\n\n  /**\n   * Calcul sous la forme d'une égalité sans le résultat\n   * @example\n   * const p = new Trinome(2, 3, 1)\n   * p.texCalculDiscriminantSansResultat\n   * // 3^2-4\\\\times2\\\\times1\n   * @type {string}\n   */\n  get texCalculDiscriminantSansResultat () {\n    if (this.b.valeurDecimale === 0) return `-4\\\\times${this.a.texFSP}\\\\times${this.c.texFSP}`\n    else if (this.b.estEntiere && this.b.s === 1) return `${this.b.texFSD}^2-4\\\\times${this.a.texFSP}\\\\times${this.c.texFSP}`\n    return `\\\\left(${this.b.texFSD}\\\\right)^2-4\\\\times${this.a.texFSP}\\\\times${this.c.texFSP}`\n  }\n\n  /**\n   * Calcul détaillée de la première racine avec résultat exact si on peut calculer la racine du discriminant et valeur approchée sinon\n   * @type {string}\n   */\n  get texCalculRacine1 () {\n    if (this.discriminant.s === -1) return ''\n    let result = 'x_1 = '\n    if (this.b.valeurDecimale === 0) result += `\\\\dfrac{-b-\\\\sqrt{\\\\Delta}}{2a}=\\\\dfrac{-\\\\sqrt{${this.discriminant.texFractionSimplifiee}}}{2\\\\times${this.a.s === -1 ? this.a.texFSP : this.a.texFractionSimplifiee}}`\n    else result += `\\\\dfrac{-b-\\\\sqrt{\\\\Delta}}{2a}=\\\\dfrac{${this.b.oppose().texFractionSimplifiee}-\\\\sqrt{${this.discriminant.texFractionSimplifiee}}}{2\\\\times${this.a.s === -1 ? this.a.texFSP : this.a.texFractionSimplifiee}}`\n    if (this.x1 instanceof FractionEtendue) result += `=${this.x1.texFractionSimplifiee}`\n    else result += `\\\\approx${this.x1.toString().replace('.', ',')}`\n    return result\n  }\n\n  /**\n   * Calcul détaillée de la deuxième racine avec résultat exact si on peut calculer la racine du discriminant et valeur approchée sinon\n   * @type {string}\n   */\n  get texCalculRacine2 () {\n    if (this.discriminant.s === -1) return ''\n    let result = 'x_2 = '\n    if (this.b.valeurDecimale === 0) result += `\\\\dfrac{-b+\\\\sqrt{\\\\Delta}}{2a}=\\\\dfrac{\\\\sqrt{${this.discriminant.texFractionSimplifiee}}}{2\\\\times${this.a.s === -1 ? this.a.texFSP : this.a.texFractionSimplifiee}}`\n    else result += `\\\\dfrac{-b+\\\\sqrt{\\\\Delta}}{2a}=\\\\dfrac{${this.b.oppose().texFractionSimplifiee}+\\\\sqrt{${this.discriminant.texFractionSimplifiee}}}{2\\\\times${this.a.s === -1 ? this.a.texFSP : this.a.texFractionSimplifiee}}`\n    if (this.x2 instanceof FractionEtendue) result += `=${this.x2.texFractionSimplifiee}`\n    else result += `\\\\approx${this.x2.toString().replace('.', ',')}`\n    return result\n  }\n\n  /**\n   * Tableau avec 2 étapes pour le développement puis le résultat\n   * @return {string[]} [Étape 1, Étape 2, this.tex]\n   */\n  get arrayTexDevelopperFormeCanonique () {\n    const alpha = this.alpha\n    const beta = this.beta\n    let result1 = ''\n    if (this.a.valeurDecimale === -1) result1 += '-'\n    else if (this.a.valeurDecimale !== 1) result1 += this.a.simplifie().texFSD\n    result1 += `\\\\left(x^2 ${alpha.multiplieEntier(-2).simplifie().texFractionSignee} x ${alpha.produitFraction(alpha).simplifie().texFractionSignee} \\\\right) ${beta.simplifie().texFractionSignee}`\n    let result2 = ''\n    if (this.a.valeurDecimale === -1) result2 += '-x^2'\n    else if (this.a.valeurDecimale !== 1) result2 += `${this.a.simplifie().texFSD} x^2`\n    if (this.b.valeurDecimale === -1) result2 += '-x'\n    else if (this.b.valeurDecimale === 1) result2 += 'x'\n    else result2 += `${this.b.simplifie().texFractionSignee}x ${this.a.produitFraction(alpha).produitFraction(alpha).simplifie().texFractionSignee} ${beta.simplifie().texFractionSignee}`\n\n    return [result1, result2, this.tex]\n  }\n\n  /**\n   * Tableau avec 2 étapes pour le développement puis le résultat\n   *\n   * On considère que a est différent de 1, x1 et x2 sont non nuls\n   */\n  get arrayTexDevelopperFormeFactorisee () {\n    const [a, x1, x2] = [this.a, this.x1, this.x2]\n    const result1 = `${a.simplifie().texFractionSaufUn}\\\\left(x^2 ${x2.oppose().simplifie().texFractionSaufUnSignee}x ${x1.oppose().simplifie().texFractionSaufUnSignee}x ${x1.produitFraction(x2).simplifie().texFractionSignee} \\\\right)`\n    const result2 = `${a.simplifie().texFractionSaufUn}x^2 ${a.produitFraction(x2).oppose().simplifie().texFractionSaufUnSignee}x ${a.produitFraction(x1).oppose().simplifie().texFractionSaufUnSignee}x ${a.produitFraction(x1).produitFraction(x2).simplifie().texFractionSignee}`\n    return [result1, result2, this.tex]\n  }\n\n  /**\n   * Première racine du trinome\n   * @type {FractionEtendue | number}\n   */\n  get x1 () {\n    if (this.discriminant.s === -1) return false\n    const deltaNum = this.discriminant.num\n    const deltaDen = this.discriminant.den\n    let racineDeDelta = new FractionEtendue(1)\n    if (Math.abs((Math.sqrt(deltaNum) - Math.round(Math.sqrt(deltaNum)))) < 0.000001 &&\n     Math.abs(Math.sqrt(deltaDen) - Math.round(Math.sqrt(deltaDen))) < 0.000001) {\n      racineDeDelta = new FractionEtendue(Math.sqrt(deltaNum), Math.sqrt(deltaDen))\n      const unSurDeuxA = this.a.multiplieEntier(2).inverse()\n      return this.b.oppose().sommeFraction(racineDeDelta.oppose()).produitFraction(unSurDeuxA)\n    } else {\n      return Math.round((-this.b.valeurDecimale - Math.sqrt(this.discriminant.valeurDecimale)) / (2 * this.a.valeurDecimale) * (10 ** this.precision)) / (10 ** this.precision)\n    }\n  }\n\n  /**\n   * Deuxième racine du trinome\n   * @type {FractionEtendue | number}\n   */\n  get x2 () {\n    if (this.discriminant.s === -1) return false\n    const deltaNum = this.discriminant.num\n    const deltaDen = this.discriminant.den\n    let racineDeDelta\n    if (Math.abs((Math.sqrt(deltaNum) - Math.round(Math.sqrt(deltaNum)))) < 0.000001 &&\n     Math.abs(Math.sqrt(deltaDen) - Math.round(Math.sqrt(deltaDen))) < 0.000001) {\n      racineDeDelta = new FractionEtendue(Math.sqrt(deltaNum), Math.sqrt(deltaDen))\n      const unSurDeuxA = this.a.multiplieEntier(2).inverse()\n      return this.b.oppose().sommeFraction(racineDeDelta).produitFraction(unSurDeuxA)\n    } else {\n      return Math.round((-this.b.valeurDecimale + Math.sqrt(this.discriminant.valeurDecimale)) / (2 * this.a.valeurDecimale) * (10 ** this.precision)) / (10 ** this.precision)\n    }\n  }\n\n  /**\n   * Écriture LaTeX de la valeur exacte première racine\n   * @type {string}\n   */\n  get texX1 () {\n    if (this.x1 instanceof FractionEtendue) return this.x1.simplifie().texFraction\n    else {\n      const num = this.b.oppose().texFraction + `- \\\\sqrt{${this.discriminant.texFraction}}`\n      const den = 2 * this.a\n      return `\\\\dfrac{${num}}{${den}}`\n    }\n  }\n\n  /**\n   * Écriture LaTeX de la valeur exacte première racine\n   * @type {string}\n   */\n  get texX2 () {\n    if (this.x2 instanceof FractionEtendue) return this.x2.simplifie().texFraction\n    else {\n      const num = this.b.oppose().texFraction + `+ \\\\sqrt{${this.discriminant.texFraction}}`\n      const den = 2 * this.a\n      return `\\\\dfrac{${num}}{${den}}`\n    }\n  }\n\n  /**\n   * a(x-x1)(x-x2)\n   * @type {string}\n   */\n  get texFormeFactorisee () {\n    if (this.x1 instanceof FractionEtendue) {\n      if (this.x1.valeurDecimale === 0) {\n        if (this.a.valeurDecimale === 1) return `x(x${this.x2.oppose().simplifie().texFractionSignee})`\n        else if (this.a.valeurDecimale === -1) return `-x(x${this.x2.oppose().simplifie().texFractionSignee})`\n        else return `${this.a.texFractionSimplifiee}x(x${this.x2.oppose().simplifie().texFractionSignee})`\n      } else if (this.x2.valeurDecimale === 0) {\n        if (this.a.valeurDecimale === 1) return `x(x${this.x1.oppose().simplifie().texFractionSignee})`\n        else if (this.a.valeurDecimale === -1) return `-x(x${this.x1.oppose().simplifie().texFractionSignee})`\n        else return `${this.a.texFractionSimplifiee}x(x${this.x1.oppose().simplifie().texFractionSignee})`\n      }\n      if (this.a.valeurDecimale === 1) return `(x${this.x1.oppose().simplifie().texFractionSignee})(x${this.x2.oppose().simplifie().texFractionSignee})`\n      else if (this.a.valeurDecimale === -1) return `-(x${this.x1.oppose().simplifie().texFractionSignee})(x${this.x2.oppose().simplifie().texFractionSignee})`\n      else return `${this.a.texFractionSimplifiee}(x${this.x1.oppose().simplifie().texFractionSignee})(x${this.x2.oppose().simplifie().texFractionSignee})`\n    } else {\n      if (this.a.valeurDecimale === 1) return '(x-x_1)(x-x_2)'\n      else if (this.a.valeurDecimale === -1) return '-(x-x_1)(x-x_2)'\n      else return `${this.a}(x-x_1)(x-x_2)`\n    }\n  }\n\n  get alpha () {\n    return this.b.diviseFraction(this.a.multiplieEntier(2)).oppose()\n  }\n\n  get beta () {\n    return this.image(this.alpha)\n  }\n\n  get texFormeCanonique () {\n    let result = ''\n    if (this.a.valeurDecimale === -1) result = '-'\n    else if (this.a.valeurDecimale !== 1) result = this.a.texFractionSimplifiee\n    if (this.alpha.valeurDecimale === 0) result += 'x^2'\n    else result += `\\\\left(x ${this.alpha.oppose().simplifie().texFractionSignee}\\\\right)^2`\n    result += ` ${this.beta.simplifie().texFractionSignee}`\n    return result\n  }\n}\n\nexport default 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