{
  "version": "5.0",
  "date": "2026-10-08",
  "count": 242,
  "cases": [
    [
      "Addition exacte de décimaux",
      "0.1+0.2",
      {
        "exact": "3/10"
      }
    ],
    [
      "Virgules françaises",
      "1,5 + 2,25",
      {
        "exact": "15/4"
      }
    ],
    [
      "Addition de fractions",
      "1/3+1/6",
      {
        "exact": "1/2"
      }
    ],
    [
      "Soustraction de fractions",
      "3/4-1/6",
      {
        "exact": "7/12"
      }
    ],
    [
      "Multiplication de fractions",
      "(2/3)*(9/4)",
      {
        "exact": "3/2"
      }
    ],
    [
      "Division de fractions",
      "(2/3)/(4/9)",
      {
        "exact": "3/2"
      }
    ],
    [
      "Priorité des produits",
      "2+3*4",
      {
        "exact": "14"
      }
    ],
    [
      "Parenthèses",
      "(2+3)*4",
      {
        "exact": "20"
      }
    ],
    [
      "Signe moins et carré",
      "-2^2",
      {
        "exact": "-4"
      }
    ],
    [
      "Carré d’un négatif",
      "(-2)^2",
      {
        "exact": "4"
      }
    ],
    [
      "Puissances à droite",
      "2^3^2",
      {
        "exact": "512"
      }
    ],
    [
      "Puissance négative",
      "2^-3",
      {
        "exact": "1/8"
      }
    ],
    [
      "Pourcentage d’un total",
      "15%*80",
      {
        "exact": "12"
      }
    ],
    [
      "Hausse de 10 %",
      "200*(1+10%)",
      {
        "exact": "220"
      }
    ],
    [
      "Pourcentage comme fraction",
      "200+10%",
      {
        "exact": "2001/10"
      }
    ],
    [
      "Racine carrée exacte",
      "sqrt(81)",
      {
        "exact": "9"
      }
    ],
    [
      "Racine cubique exacte",
      "cbrt(-27)",
      {
        "exact": "-3"
      }
    ],
    [
      "Racine approchée",
      "sqrt(2)",
      {
        "value": 1.4142135623730951
      }
    ],
    [
      "Sinus en degrés",
      "sin(30)",
      {
        "value": 0.5
      }
    ],
    [
      "Sinus en radians",
      "sin(pi/2)",
      {
        "value": 1
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Logarithme décimal",
      "log(100)",
      {
        "value": 2,
        "exact": "2"
      }
    ],
    [
      "Valeur absolue",
      "abs(-5/2)",
      {
        "exact": "5/2"
      }
    ],
    [
      "Factorielle",
      "5!",
      {
        "exact": "120"
      }
    ],
    [
      "Factorielle de zéro",
      "0!",
      {
        "exact": "1"
      }
    ],
    [
      "Notation scientifique",
      "1e-3*1e3",
      {
        "exact": "1"
      }
    ],
    [
      "Premier degré avec parenthèses",
      "2(x+3)=18",
      {
        "solutions": [
          6
        ]
      }
    ],
    [
      "Inconnue des deux côtés",
      "3x+2=x+10",
      {
        "solutions": [
          4
        ]
      }
    ],
    [
      "Équation à fractions",
      "x/3+1/2=5/6",
      {
        "solutions": [
          1
        ]
      }
    ],
    [
      "Solution fractionnaire",
      "3x=1",
      {
        "exactSolutions": [
          "1/3"
        ]
      }
    ],
    [
      "Décimaux exacts dans une équation",
      "0.1x=0.3",
      {
        "solutions": [
          3
        ]
      }
    ],
    [
      "Petits coefficients non nuls",
      "0.0000000000001x=0.0000000000002",
      {
        "solutions": [
          2
        ]
      }
    ],
    [
      "Deux solutions quadratiques",
      "x²-5x+6=0",
      {
        "solutions": [
          2,
          3
        ]
      }
    ],
    [
      "Racine double",
      "(x-2)^2=0",
      {
        "solutions": [
          2
        ]
      }
    ],
    [
      "Racines irrationnelles",
      "x^2=2",
      {
        "solutions": [
          -1.4142135623730951,
          1.4142135623730951
        ]
      }
    ],
    [
      "Coefficient dominant négatif",
      "-x^2+x+1=0",
      {
        "solutions": [
          -0.6180339887498949,
          1.618033988749895
        ]
      }
    ],
    [
      "Discriminant négatif",
      "x^2+1=0",
      {
        "answer": "Aucune solution réelle"
      }
    ],
    [
      "Identité",
      "2(x+1)=2x+2",
      {
        "answer": "Tous les nombres réels"
      }
    ],
    [
      "Contradiction",
      "2x+1=2x+3",
      {
        "answer": "Aucune solution réelle"
      }
    ],
    [
      "Égalité numérique vraie",
      "2+2=4",
      {
        "answer": "Égalité vraie"
      }
    ],
    [
      "Fraction algébrique",
      "1/(x-1)=2",
      {
        "solutions": [
          1.5
        ],
        "domain": "x ≠ 1"
      }
    ],
    [
      "Annulation d’un facteur",
      "(x^2-1)/(x-1)=0",
      {
        "solutions": [
          -1
        ],
        "domain": "x ≠ 1"
      }
    ],
    [
      "Identité avec exclusion",
      "x/x=1",
      {
        "answer": "Tous les réels du domaine",
        "domain": "x ≠ 0"
      }
    ],
    [
      "Racine interdite",
      "x^2/x=0",
      {
        "answer": "Aucune solution réelle",
        "domain": "x ≠ 0"
      }
    ],
    [
      "Aucune solution rationnelle",
      "1/x=0",
      {
        "answer": "Aucune solution réelle"
      }
    ],
    [
      "Puissance négative en x",
      "x^-1=2",
      {
        "solutions": [
          0.5
        ],
        "domain": "x ≠ 0"
      }
    ],
    [
      "Dénominateur imbriqué",
      "1/(1/x)=2",
      {
        "solutions": [
          2
        ],
        "domain": "x ≠ 0"
      }
    ],
    [
      "Développement",
      "2(x+3)-x",
      {
        "answer": "x + 6"
      }
    ],
    [
      "Produit de parenthèses",
      "(x+1)(x-1)",
      {
        "answer": "x² − 1"
      }
    ],
    [
      "Simplification avec restriction",
      "(x^2-1)/(x-1)",
      {
        "answer": "x + 1",
        "domain": "x ≠ 1"
      }
    ],
    [
      "Puissance nulle et domaine",
      "x^0=1",
      {
        "answer": "Tous les réels du domaine",
        "domain": "x ≠ 0"
      }
    ],
    [
      "Zéro au dénominateur",
      "1/0",
      {
        "error": true
      }
    ],
    [
      "Dénominateur identiquement nul",
      "1/(x-x)=0",
      {
        "error": true
      }
    ],
    [
      "Racine négative",
      "sqrt(-1)",
      {
        "error": true
      }
    ],
    [
      "Logarithme de zéro",
      "ln(0)",
      {
        "error": true
      }
    ],
    [
      "Tangente singulière",
      "tan(90)",
      {
        "error": true
      }
    ],
    [
      "Puissance indéfinie",
      "0^0",
      {
        "error": true
      }
    ],
    [
      "Puissance cubique",
      "x^3=1",
      {
        "solutions": [
          1
        ]
      }
    ],
    [
      "Racine isolable",
      "sqrt(x)=2",
      {
        "solutions": [
          4
        ]
      }
    ],
    [
      "Plusieurs inconnues",
      "x+y=2",
      {
        "error": true
      }
    ],
    [
      "Égalités multiples",
      "x=1=2",
      {
        "error": true
      }
    ],
    [
      "Parenthèse manquante",
      "2(x+1",
      {
        "error": true
      }
    ],
    [
      "Deux nombres sans opérateur",
      "2 3",
      {
        "error": true
      }
    ],
    [
      "Saisie non mathématique",
      "alert(1)",
      {
        "error": true
      }
    ],
    [
      "Imbrication excessive",
      "((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",
      {
        "error": true
      }
    ],
    [
      "Exposant trop grand",
      "2^101",
      {
        "error": true
      }
    ],
    [
      "Sinus nul en degrés",
      "1/sin(180)",
      {
        "error": true
      }
    ],
    [
      "Cosinus nul en degrés",
      "1/cos(90)",
      {
        "error": true
      }
    ],
    [
      "Sinus nul en radians",
      "1/sin(pi)",
      {
        "error": true
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Cosinus nul en radians",
      "1/cos(pi/2)",
      {
        "error": true
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Cube négatif fractionnaire",
      "(-8)^(1/3)",
      {
        "exact": "-2"
      }
    ],
    [
      "Racine négative extrêmement petite",
      "sqrt(-(1e-90)^4)",
      {
        "error": true
      }
    ],
    [
      "Double factorielle ambiguë",
      "3!!",
      {
        "error": true
      }
    ],
    [
      "Factorielle répétée",
      "(3!)!",
      {
        "exact": "720"
      }
    ],
    [
      "Égalité numérique fausse",
      "2+2=5",
      {
        "answer": "Égalité fausse"
      }
    ],
    [
      "Autre inconnue",
      "2y+3=7",
      {
        "answer": "y = 2"
      }
    ],
    [
      "Produit nul cubique",
      "(x-1)(x-2)(x-3)=0",
      {
        "solutions": [
          1,
          2,
          3
        ]
      }
    ],
    [
      "Polynôme cubique développé",
      "x^3-6x^2+11x-6=0",
      {
        "solutions": [
          1,
          2,
          3
        ]
      }
    ],
    [
      "Puissance paire",
      "x^4=16",
      {
        "solutions": [
          -2,
          2
        ]
      }
    ],
    [
      "Puissance paire sans réel",
      "x^4=-16",
      {
        "solutions": []
      }
    ],
    [
      "Puissance impaire négative",
      "x^3=-8",
      {
        "solutions": [
          -2
        ]
      }
    ],
    [
      "Puissance composée",
      "(2x+1)^3=8",
      {
        "solutions": [
          0.5
        ]
      }
    ],
    [
      "Degré 5 factorisable",
      "x^5-x=0",
      {
        "solutions": [
          -1,
          0,
          1
        ]
      }
    ],
    [
      "Facteur exclu au degré 4",
      "(x^4-16)/(x-2)=0",
      {
        "solutions": [
          -2
        ]
      }
    ],
    [
      "Polynôme non entièrement résolu",
      "x^3+x+1=0",
      {
        "error": true
      }
    ],
    [
      "Racine et parenthèse",
      "sqrt(x+1)=3",
      {
        "solutions": [
          8
        ]
      }
    ],
    [
      "Racine égale à un négatif",
      "sqrt(x+1)=-3",
      {
        "solutions": []
      }
    ],
    [
      "Candidat introduit par le carré",
      "sqrt(x+1)=x-1",
      {
        "solutions": [
          3
        ]
      }
    ],
    [
      "Racine carrée composée",
      "sqrt(x^2-1)=0",
      {
        "solutions": [
          -1,
          1
        ]
      }
    ],
    [
      "Racine cubique avec inconnue",
      "cbrt(x)=-2",
      {
        "solutions": [
          -8
        ]
      }
    ],
    [
      "Valeur absolue composée",
      "abs(2x-1)=3",
      {
        "solutions": [
          -1,
          2
        ]
      }
    ],
    [
      "Valeur absolue négative",
      "abs(x)=-1",
      {
        "solutions": []
      }
    ],
    [
      "Valeur absolue rationnelle",
      "abs(1/(x-1))=2",
      {
        "solutions": [
          0.5,
          1.5
        ]
      }
    ],
    [
      "Exposant inconnu",
      "2^x=8",
      {
        "solutions": [
          3
        ]
      }
    ],
    [
      "Exponentielle exacte",
      "exp(x)=2",
      {
        "exactSolutions": [
          "ln(2)"
        ],
        "solutions": [
          0.6931471805599453
        ]
      }
    ],
    [
      "Logarithme naturel",
      "ln(x-1)=0",
      {
        "solutions": [
          2
        ]
      }
    ],
    [
      "Logarithme décimal",
      "log(x)=2",
      {
        "solutions": [
          100
        ]
      }
    ],
    [
      "Coefficient irrationnel",
      "sqrt(2)*x=4",
      {
        "solutions": [
          2.8284271247461903
        ]
      }
    ],
    [
      "Inéquation linéaire",
      "-2x<4",
      {
        "answer": "S = ]-2 ; +∞["
      }
    ],
    [
      "Inéquation large",
      "x^2<=4",
      {
        "answer": "S = [-2 ; 2]"
      }
    ],
    [
      "Inéquation stricte",
      "x^2<4",
      {
        "answer": "S = ]-2 ; 2["
      }
    ],
    [
      "Solution isolée",
      "x^2<=0",
      {
        "answer": "S = {0}"
      }
    ],
    [
      "Inéquation impossible",
      "x^2<0",
      {
        "answer": "S = ∅"
      }
    ],
    [
      "Réels sauf zéro",
      "x^2>0",
      {
        "answer": "S = ]−∞ ; 0[ ∪ ]0 ; +∞["
      }
    ],
    [
      "Identité avec trou",
      "x/x>=1",
      {
        "answer": "S = ]−∞ ; 0[ ∪ ]0 ; +∞["
      }
    ],
    [
      "Signe du quotient",
      "(x-1)/(x+2)>0",
      {
        "answer": "S = ]−∞ ; -2[ ∪ ]1 ; +∞["
      }
    ],
    [
      "Borne interdite après simplification",
      "(x^2-1)/(x-1)>=0",
      {
        "answer": "S = [-1 ; 1[ ∪ ]1 ; +∞["
      }
    ],
    [
      "Système unique",
      "x+y=3;x-y=1",
      {
        "solution": {
          "x": "2",
          "y": "1"
        }
      }
    ],
    [
      "Système fractionnaire",
      "x/2+y=2;x-y=1",
      {
        "solution": {
          "x": "2",
          "y": "1"
        }
      }
    ],
    [
      "Système incompatible",
      "x+y=3;2x+2y=7",
      {
        "answer": "Aucune solution"
      }
    ],
    [
      "Système indéterminé",
      "x+y=3;2x+2y=6",
      {
        "answer": "x = 3 - (1)*t ; y = t"
      }
    ],
    [
      "Système nul",
      "x+y=x+y;2x+2y=2x+2y",
      {
        "answer": "Tous les couples réels"
      }
    ],
    [
      "Système non linéaire refusé",
      "x*y=3;x-y=1",
      {
        "error": true
      }
    ],
    [
      "Trois inconnues refusées",
      "x+y+z=3;x-y=1",
      {
        "error": true
      }
    ],
    [
      "Équation trigonométrique refusée",
      "sin(x)=0",
      {
        "error": true
      }
    ],
    [
      "Double inégalité stricte",
      "0<x<1",
      {
        "answer": "S = ]0 ; 1["
      }
    ],
    [
      "Logarithme préservé",
      "ln(2)",
      {
        "exact": "ln(2)"
      }
    ],
    [
      "Radical simplifié",
      "sqrt(8)",
      {
        "exact": "2*sqrt(2)"
      }
    ],
    [
      "Identité remarquable factorisée",
      "x^2-9",
      {
        "answer": "(-3+x)*(3+x)"
      },
      {
        "action": "factoriser"
      }
    ],
    [
      "Factorisation rationnelle contrôlée",
      "x^3-43*x^2/3+60*x-224/3=0",
      {
        "solutions": [
          2.3333333333333335,
          4,
          8
        ]
      }
    ],
    [
      "Paramètre distinct des inconnues",
      "t+x=3;2t+2x=6",
      {
        "answer": "t = 3 - (1)*s ; x = s"
      }
    ],
    [
      "Dénominateur radical exactement nul",
      "1/(sqrt(2)^2-2)",
      {
        "error": true
      }
    ],
    [
      "Somme d’angles exactement singulière",
      "1/sin(pi+pi)",
      {
        "error": true
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Fausse égalité masquée par l’arrondi",
      "sqrt(2)^2=2.0000000000001",
      {
        "answer": "Égalité fausse"
      }
    ],
    [
      "Un petit sinus ne vaut pas zéro",
      "sin(1e-20)=0",
      {
        "answer": "Égalité fausse (contrôle numérique)"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Petit sinus conservé",
      "sin(1e-20)",
      {
        "value": 1e-20
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Identité exacte avec radical",
      "sqrt(2)*sqrt(2)=2",
      {
        "answer": "Égalité vraie"
      }
    ],
    [
      "Très petits décimaux exacts",
      "1e-100-1e-100=0",
      {
        "answer": "Égalité vraie"
      }
    ],
    [
      "Différence de constantes trop proches",
      "1/(sqrt(2)-1.4142135623730951)",
      {
        "error": true
      }
    ],
    [
      "Exponentielle sous la précision numérique",
      "exp(-1000)",
      {
        "error": true
      }
    ],
    [
      "Un calcul exact après un refus",
      "sqrt(8)/sqrt(2)",
      {
        "exact": "2"
      }
    ],
    [
      "Carré sous une racine",
      "sqrt(x^2)",
      {
        "answer": "abs(x)"
      }
    ],
    [
      "Carré d’un polynôme sous une racine",
      "sqrt((x+1)^2)",
      {
        "answer": "abs(x + 1)"
      }
    ],
    [
      "Regrouper les coefficients radicaux",
      "sqrt(2)*x+sqrt(8)*x",
      {
        "answer": "(3*sqrt(2))*x"
      }
    ],
    [
      "Exposant négatif en caractères typographiques",
      "x⁻²=4",
      {
        "solutions": [
          -0.5,
          0.5
        ]
      }
    ],
    [
      "Barres de valeur absolue",
      "|2x-1|=3",
      {
        "solutions": [
          -1,
          2
        ]
      }
    ],
    [
      "Barre non refermée",
      "|x+1",
      {
        "error": true
      }
    ],
    [
      "Double inégalité à bornes différentes",
      "3<=2x+2<6",
      {
        "answer": "S = [1/2 ; 2["
      }
    ],
    [
      "Double inégalité décroissante",
      "3>x>=-2",
      {
        "answer": "S = [-2 ; 3["
      }
    ],
    [
      "Intersection vide",
      "3<x<1",
      {
        "answer": "S = ∅"
      }
    ],
    [
      "Intersection réduite à un point",
      "2<=x<=2",
      {
        "answer": "S = {2}"
      }
    ],
    [
      "Double inégalité avec quotient",
      "1/(x-1)<0<x+3",
      {
        "answer": "S = ]-3 ; 1["
      }
    ],
    [
      "Encadrement de valeur absolue",
      "abs(x-2)<=3",
      {
        "answer": "S = [-1 ; 5]"
      }
    ],
    [
      "Valeur absolue extérieure stricte",
      "|2x-1|>3",
      {
        "answer": "S = ]−∞ ; -1[ ∪ ]2 ; +∞["
      }
    ],
    [
      "Coefficient négatif devant la valeur absolue",
      "-2abs(x+1)<=-4",
      {
        "answer": "S = ]−∞ ; -3] ∪ [1 ; +∞["
      }
    ],
    [
      "Valeur absolue strictement négative",
      "abs(x)<0",
      {
        "answer": "S = ∅"
      }
    ],
    [
      "Valeur absolue nulle",
      "abs(x)<=0",
      {
        "answer": "S = {0}"
      }
    ],
    [
      "Valeur absolue positive ou nulle",
      "abs(x)>=0",
      {
        "answer": "S = ]−∞ ; +∞["
      }
    ],
    [
      "Inégalité absolue inversée",
      "2>abs(x)",
      {
        "answer": "S = ]-2 ; 2["
      }
    ],
    [
      "Valeur absolue et dénominateur interdit",
      "abs(1/(x-1))<=2",
      {
        "answer": "S = ]−∞ ; 1/2] ∪ [3/2 ; +∞["
      }
    ],
    [
      "Seuil négatif conserve le domaine",
      "abs(1/(x-1))>=-2",
      {
        "answer": "S = ]−∞ ; 1[ ∪ ]1 ; +∞["
      }
    ],
    [
      "Valeur absolue avec autre inconnue",
      "abs(t-2)<=3",
      {
        "answer": "S = [-1 ; 5]",
        "variable": "t"
      }
    ],
    [
      "Le partage conserve les deux équations",
      "x+y=3;x-y=1",
      {
        "rawInput": "x+y=3;x-y=1",
        "action": "auto"
      }
    ],
    [
      "Système diagonal",
      "x=2;y=1",
      {
        "solution": {
          "x": "2",
          "y": "1"
        }
      }
    ],
    [
      "Système avec inconnues inversées",
      "y=2;x=1",
      {
        "solution": {
          "x": "1",
          "y": "2"
        }
      }
    ],
    [
      "Trois inégalités refusées explicitement",
      "0<x<2<3",
      {
        "error": true
      }
    ],
    [
      "Deux valeurs absolues non isolables",
      "abs(x)+abs(x-1)<3",
      {
        "error": true
      }
    ],
    [
      "Pas de notation exécutable",
      "alert(1)",
      {
        "error": true
      }
    ],
    [
      "Parenthèses autour de l’exposant négatif",
      "2⁻³",
      {
        "exact": "1/8"
      }
    ],
    [
      "Degrés explicites",
      "sin(30°)",
      {
        "exact": "1/2"
      }
    ],
    [
      "Degrés explicites en radians",
      "sin(30°)",
      {
        "exact": "1/2"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Angles mixtes explicites",
      "sin(30°)+sin(pi/2)",
      {
        "exact": "3/2"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Argument composé en degrés",
      "cos((30+30)°)",
      {
        "exact": "1/2"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Tangente avec unité",
      "tan(45°)",
      {
        "exact": "1"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Unité hors fonction refusée",
      "30°",
      {
        "error": true
      }
    ],
    [
      "Unité après fonction refusée",
      "sin(30)°",
      {
        "error": true
      }
    ],
    [
      "Préfixe résoudre",
      "résoudre 2x=4",
      {
        "exactSolutions": [
          "2"
        ]
      }
    ],
    [
      "Préfixe calculer",
      "calculer 1/3+1/6",
      {
        "exact": "1/2"
      }
    ],
    [
      "Préfixe simplifier",
      "simplifier (x+2)^2",
      {
        "kind": "simplify"
      }
    ],
    [
      "Inégalité numérique vraie",
      "1<2",
      {
        "kind": "comparison",
        "truth": true
      }
    ],
    [
      "Inégalité numérique fausse",
      "2<1",
      {
        "kind": "comparison",
        "truth": false
      }
    ],
    [
      "Inégalité numérique large",
      "2<=2",
      {
        "kind": "comparison",
        "truth": true
      }
    ],
    [
      "Comparaison irrationnelle",
      "sqrt(2)<2",
      {
        "truth": true
      }
    ],
    [
      "Comparaison exacte très proche",
      "1<1.00000000000000000000001",
      {
        "truth": true
      }
    ],
    [
      "Double comparaison vraie",
      "1<2<3",
      {
        "kind": "comparison",
        "truth": true
      }
    ],
    [
      "Double comparaison fausse",
      "1<2>3",
      {
        "kind": "comparison",
        "truth": false
      }
    ],
    [
      "Double comparaison décroissante",
      "3>2>1",
      {
        "kind": "comparison",
        "truth": true
      }
    ],
    [
      "Double comparaison avec inconnue",
      "0<1<x",
      {
        "answer": "S = ]1 ; +∞["
      }
    ],
    [
      "Condition constante impossible",
      "1<0<x",
      {
        "answer": "S = ∅"
      }
    ],
    [
      "Somme de deux racines",
      "sqrt(x+1)+sqrt(x-1)=2",
      {
        "exactSolutions": [
          "5/4"
        ]
      }
    ],
    [
      "Différence de deux racines",
      "sqrt(x+1)-sqrt(x-1)=1",
      {
        "exactSolutions": [
          "5/4"
        ]
      }
    ],
    [
      "Somme de racines négative impossible",
      "sqrt(x+1)+sqrt(x-1)=-2",
      {
        "exactSolutions": []
      }
    ],
    [
      "Somme de racines nulle impossible",
      "sqrt(x+1)+sqrt(x-1)=0",
      {
        "exactSolutions": []
      }
    ],
    [
      "Différence de racines nulle impossible",
      "sqrt(x+1)-sqrt(x-1)=0",
      {
        "exactSolutions": []
      }
    ],
    [
      "Deux racines : faux candidat rejeté",
      "sqrt(x+1)+sqrt(x-1)=1",
      {
        "exactSolutions": []
      }
    ],
    [
      "Différence de racines : signe interdit",
      "sqrt(x+1)-sqrt(x-1)=-1",
      {
        "exactSolutions": []
      }
    ],
    [
      "Deux racines et membres inversés",
      "2=sqrt(x+1)+sqrt(x-1)",
      {
        "exactSolutions": [
          "5/4"
        ]
      }
    ],
    [
      "Radicandes identiques",
      "sqrt(x+1)+sqrt(x+1)=2",
      {
        "exactSolutions": [
          "0"
        ]
      }
    ],
    [
      "Identité avec domaine résolue",
      "sqrt(x)-sqrt(x)=0",
      {
        "answer": "S = [0 ; +∞["
      }
    ],
    [
      "Cubic non factorisé : motif juste",
      "x^3-x-1=0",
      {
        "error": true,
        "errorContains": "factorisation"
      }
    ],
    [
      "Carré isolé sans division inutile",
      "x^2=4",
      {
        "exactSolutions": [
          "-2",
          "2"
        ],
        "noStep": "divis.*par 1(?:\\D|$)"
      }
    ],
    [
      "Premier degré sans division inutile",
      "x+2=4",
      {
        "exactSolutions": [
          "2"
        ],
        "noStep": "divis.*par 1(?:\\D|$)"
      }
    ],
    [
      "Méthode premier degré",
      "3(x-2)=x+4",
      {
        "exactSolutions": [
          "5"
        ]
      }
    ],
    [
      "Méthode signes quotient",
      "(x-1)/(x+2)>=0",
      {
        "answer": "S = ]−∞ ; -2[ ∪ [1 ; +∞["
      }
    ],
    [
      "Différence écrite avec opposé",
      "-sqrt(x-1)+sqrt(x+1)=1",
      {
        "exactSolutions": [
          "5/4"
        ]
      }
    ],
    [
      "Opposé en second terme",
      "sqrt(x+1)+(-sqrt(x-1))=1",
      {
        "exactSolutions": [
          "5/4"
        ]
      }
    ],
    [
      "LaTeX fractions",
      "\\frac{1}{3}+\\frac{1}{6}",
      {
        "exact": "1/2"
      }
    ],
    [
      "LaTeX équation",
      "\\frac{x+1}{2}=3",
      {
        "exactSolutions": [
          "5"
        ]
      }
    ],
    [
      "LaTeX fraction imbriquée",
      "\\frac{\\frac{1}{2}}{\\frac{3}{4}}",
      {
        "exact": "2/3"
      }
    ],
    [
      "LaTeX racine",
      "\\sqrt{x+1}=2",
      {
        "exactSolutions": [
          "3"
        ]
      }
    ],
    [
      "LaTeX racine cubique",
      "\\sqrt[3]{-8}",
      {
        "exact": "-2"
      }
    ],
    [
      "LaTeX puissance",
      "x^{2}-5x+6=0",
      {
        "exactSolutions": [
          "2",
          "3"
        ]
      }
    ],
    [
      "LaTeX signe inférieur",
      "x \\leq 3",
      {
        "answer": "S = ]−∞ ; 3]"
      }
    ],
    [
      "LaTeX unité degré",
      "\\sin(30^{\\circ})",
      {
        "exact": "1/2"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "LaTeX dollars",
      "$$\\frac{2}{3}$$",
      {
        "exact": "2/3"
      }
    ],
    [
      "LaTeX délimiteurs",
      "\\(\\frac{2}{3}\\)",
      {
        "exact": "2/3"
      }
    ],
    [
      "LaTeX commande non ignorée",
      "\\input{evil}",
      {
        "error": true,
        "errorContains": "non prise en charge"
      }
    ],
    [
      "LaTeX intégrale refusée",
      "\\int{x}",
      {
        "error": true,
        "errorContains": "non prise en charge"
      }
    ],
    [
      "LaTeX matrice refusée",
      "\\begin{matrix}1\\end{matrix}",
      {
        "error": true
      }
    ],
    [
      "LaTeX accolade manquante",
      "\\frac{1}{2",
      {
        "error": true,
        "errorContains": "accolade"
      }
    ],
    [
      "LaTeX arguments manquants",
      "\\frac12",
      {
        "error": true
      }
    ],
    [
      "LaTeX indice non reconnu",
      "\\sqrt[0]{2}",
      {
        "error": true
      }
    ],
    [
      "Préfixe avec deux-points",
      "résoudre:2x=4",
      {
        "exactSolutions": [
          "2"
        ]
      }
    ],
    [
      "Égalité entre deux racines",
      "sqrt(x+3)=sqrt(2x+1)",
      {
        "exactSolutions": [
          "2"
        ]
      }
    ],
    [
      "Racines : candidat hors domaine",
      "sqrt(x+1)=sqrt(2x+3)",
      {
        "exactSolutions": []
      }
    ],
    [
      "Racines : décalage exact non nul",
      "sqrt(x)=sqrt(x+1e-13)",
      {
        "exactSolutions": []
      }
    ],
    [
      "Égalité entre valeurs absolues",
      "abs(x)=abs(2x-3)",
      {
        "exactSolutions": [
          "1",
          "3"
        ]
      }
    ],
    [
      "Égalité entre logarithmes",
      "ln(x+2)=ln(2x)",
      {
        "exactSolutions": [
          "2"
        ]
      }
    ],
    [
      "Égalité exponentielle",
      "exp(2x)=exp(x+1)",
      {
        "exactSolutions": [
          "1"
        ]
      }
    ],
    [
      "Racine sous forme de puissance",
      "x^(1/2)=2",
      {
        "exactSolutions": [
          "4"
        ],
        "domain": "x ≥ 0"
      }
    ],
    [
      "Racine cubique sous forme de puissance",
      "x^(1/3)=-2",
      {
        "exactSolutions": [
          "-8"
        ]
      }
    ],
    [
      "Racine inverse positive",
      "x^(-1/2)=2",
      {
        "exactSolutions": [
          "1/4"
        ],
        "domain": "x > 0"
      }
    ],
    [
      "Racine inverse impaire",
      "x^(-1/3)=-2",
      {
        "exactSolutions": [
          "-1/8"
        ]
      }
    ],
    [
      "Racine inverse non nulle",
      "x^(-1/3)=0",
      {
        "exactSolutions": []
      }
    ],
    [
      "Identité carrée avec signe",
      "sqrt(x^2)=x",
      {
        "answer": "S = [0 ; +∞["
      }
    ],
    [
      "Identité carrée avec signe négatif",
      "sqrt(x^2)=-x",
      {
        "answer": "S = ]−∞ ; 0]"
      }
    ],
    [
      "Carré de racine : domaine conservé",
      "sqrt(x)^2=x",
      {
        "answer": "S = [0 ; +∞["
      }
    ],
    [
      "Identité logarithmique",
      "ln(x-1)=ln(x-1)",
      {
        "answer": "S = ]1 ; +∞["
      }
    ],
    [
      "Identité sans domaine réel",
      "sqrt(-x^2-1)=sqrt(-x^2-1)",
      {
        "answer": "S = ∅"
      }
    ],
    [
      "Facteur nul et domaine",
      "0*sqrt(x)=0",
      {
        "answer": "S = [0 ; +∞["
      }
    ],
    [
      "Identité absolue",
      "abs(x)=abs(-x)",
      {
        "answer": "S = ]−∞ ; +∞["
      }
    ],
    [
      "Identité avec dénominateur interdit",
      "sqrt(1/(x-1))=sqrt(1/(x-1))",
      {
        "answer": "S = ]1 ; +∞["
      }
    ],
    [
      "Logarithme naturel proche de 1",
      "ln(1+1e-20)",
      {
        "value": 1e-20
      }
    ],
    [
      "Logarithme décimal proche de 1",
      "log(1+1e-20)",
      {
        "value": 4.342944819032518e-21
      }
    ],
    [
      "Logarithme négatif proche de 1",
      "ln(1-1e-20)",
      {
        "value": -1e-20
      }
    ],
    [
      "Réciproque trigonométrique instable refusée",
      "1/sin(pi+1e-17)",
      {
        "error": true,
        "errorContains": "précision"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Cosinus proche de zéro refusé",
      "cos(pi/2+1e-17)",
      {
        "error": true,
        "errorContains": "précision"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Petit sinus valide",
      "sin(1e-20)",
      {
        "value": 1e-20
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Zéro trigonométrique exact conservé",
      "sin(pi+pi)",
      {
        "exact": "0"
      },
      {
        "angle": "rad"
      }
    ],
    [
      "Différence de racines exactes, 10^-3",
      "sqrt(x+1)-sqrt(x)=1e-3",
      {
        "exactSolutions": [
          "999998000001/4000000"
        ]
      }
    ],
    [
      "Différence de racines exactes, 10^-7",
      "sqrt(x+1)-sqrt(x)=1e-7",
      {
        "exactSolutions": [
          "9999999999999800000000000001/400000000000000"
        ]
      }
    ],
    [
      "Différence de racines exactes, 10^-13",
      "sqrt(x+1)-sqrt(x)=1e-13",
      {
        "exactSolutions": [
          "9999999999999999999999999800000000000000000000000001/400000000000000000000000000"
        ]
      }
    ],
    [
      "Différence de racines exactes, 10^-20",
      "sqrt(x+1)-sqrt(x)=1e-20",
      {
        "exactSolutions": [
          "99999999999999999999999999999999999999980000000000000000000000000000000000000001/40000000000000000000000000000000000000000"
        ]
      }
    ]
  ]
}