{
  "oracle": "SymPy 1.14.0",
  "seed": 20261007,
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      "family": "fractions",
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      "family": "fractions",
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      "family": "fractions",
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      "family": "fractions",
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      "family": "fractions",
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      "family": "fractions",
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      "family": "premier_degre",
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      "family": "premier_degre",
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      "family": "premier_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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      "family": "second_degre",
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    {
      "family": "second_degre",
      "input": "-2*x^2 + 6*x - 27=0",
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        "symbolic": []
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      "family": "second_degre",
      "input": "-2*x^2 - 2*x - 21=0",
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      "family": "second_degre",
      "input": "-5*x^2 - 4*x + 26=0",
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          "-2/5 + sqrt(134)/5"
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    {
      "family": "second_degre",
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          "7 + sqrt(57)"
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    {
      "family": "second_degre",
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        "solutions": [],
        "symbolic": []
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      "family": "second_degre",
      "input": "-2*x^2 - 14*x - 30=0",
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        "solutions": [],
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    {
      "family": "second_degre",
      "input": "3*x^2 + 17*x - 2=0",
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        "solutions": [
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        "symbolic": [
          "-sqrt(313)/6 - 17/6",
          "-17/6 + sqrt(313)/6"
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    {
      "family": "second_degre",
      "input": "x^2 - 11*x - 24=0",
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        "solutions": [
          -1.8654599313281177,
          12.865459931328118
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        "symbolic": [
          "11/2 - sqrt(217)/2",
          "11/2 + sqrt(217)/2"
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    {
      "family": "second_degre",
      "input": "-2*x^2 - 3*x - 30=0",
      "expected": {
        "solutions": [],
        "symbolic": []
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    },
    {
      "family": "second_degre",
      "input": "-5*x^2 + 8*x + 3=0",
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        "solutions": [
          -0.3135528725660044,
          1.9135528725660045
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        "symbolic": [
          "4/5 - sqrt(31)/5",
          "4/5 + sqrt(31)/5"
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    },
    {
      "family": "second_degre",
      "input": "7*x^2 - 3*x - 13=0",
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        "solutions": [
          -1.1652291368448546,
          1.5938005654162832
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        "symbolic": [
          "3/14 - sqrt(373)/14",
          "3/14 + sqrt(373)/14"
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    {
      "family": "second_degre",
      "input": "7*x^2 + 3*x - 14=0",
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        "solutions": [
          -1.6446417424643418,
          1.2160703138929132
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        "symbolic": [
          "-sqrt(401)/14 - 3/14",
          "-3/14 + sqrt(401)/14"
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    },
    {
      "family": "second_degre",
      "input": "-5*x^2 + 18*x - 30=0",
      "expected": {
        "solutions": [],
        "symbolic": []
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    },
    {
      "family": "second_degre",
      "input": "7*x^2 + 10*x + 25=0",
      "expected": {
        "solutions": [],
        "symbolic": []
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    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^4 + 34*x^3/3 + 61*x^2/3 - 26*x/3 - 24=0",
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        "solutions": [
          -9.0,
          -2.0,
          -1.3333333333333333,
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        "symbolic": [
          "-9",
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          "-4/3",
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    {
      "family": "produits_et_degres_superieurs",
      "input": "x^4 + 11*x^3/6 - 103*x^2/6 - 95*x/3 + 28=0",
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        "solutions": [
          -3.5,
          -3.0,
          0.6666666666666666,
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        "symbolic": [
          "-7/2",
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    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 10*x^2 - 3*x + 108=0",
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        "solutions": [
          -3.0,
          4.0,
          9.0
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        "symbolic": [
          "-3",
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    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^5 + 5*x^4/2 - 43*x^3/9 - 145*x^2/18 + 28*x/3=0",
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        "solutions": [
          -2.6666666666666665,
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          1.0,
          1.5
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        "symbolic": [
          "-8/3",
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          "1",
          "3/2"
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    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^4 + 11*x^3/2 + 10*x^2 + 194*x/27 + 16/9=0",
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        "solutions": [
          -2.6666666666666665,
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          -0.6666666666666666
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        "symbolic": [
          "-8/3",
          "-3/2",
          "-2/3"
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    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^5 + 22*x^4 + 1451*x^3/9 + 3838*x^2/9 + 640*x/3 - 384=0",
      "expected": {
        "solutions": [
          -9.0,
          -8.0,
          -3.0,
          -2.6666666666666665,
          0.6666666666666666
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        "symbolic": [
          "-9",
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          "-8/3",
          "2/3"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 + 11*x^2 + 19*x + 9=0",
      "expected": {
        "solutions": [
          -9.0,
          -1.0
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        "symbolic": [
          "-9",
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      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 7*x^2/3 - 2*x=0",
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        "solutions": [
          -0.6666666666666666,
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          3.0
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        "symbolic": [
          "-2/3",
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          "3"
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      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 5*x^2/6 - 17*x + 63/2=0",
      "expected": {
        "solutions": [
          -4.5,
          2.3333333333333335,
          3.0
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        "symbolic": [
          "-9/2",
          "7/3",
          "3"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 5*x^2 - 64*x/9 + 20/3=0",
      "expected": {
        "solutions": [
          -1.6666666666666667,
          0.6666666666666666,
          6.0
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        "symbolic": [
          "-5/3",
          "2/3",
          "6"
        ]
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    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^4 + 20*x^3/3 + 45*x^2/4 - 5*x/12 - 7/2=0",
      "expected": {
        "solutions": [
          -3.5,
          -3.0,
          -0.6666666666666666,
          0.5
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        "symbolic": [
          "-7/2",
          "-3",
          "-2/3",
          "1/2"
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    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^5 - 2*x^4 - 9*x^3 + 65*x^2/4 + 275*x/16 - 375/16=0",
      "expected": {
        "solutions": [
          -2.5,
          -1.5,
          1.0,
          2.5
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        "symbolic": [
          "-5/2",
          "-3/2",
          "1",
          "5/2"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^5 + 13*x^4/6 + 7*x^3/6 - x^2/6 - x/6=0",
      "expected": {
        "solutions": [
          -1.0,
          -0.5,
          0.0,
          0.3333333333333333
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        "symbolic": [
          "-1",
          "-1/2",
          "0",
          "1/3"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 29*x^2/3 + 24*x - 12=0",
      "expected": {
        "solutions": [
          0.6666666666666666,
          3.0,
          6.0
        ],
        "symbolic": [
          "2/3",
          "3",
          "6"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 43*x^2/3 + 60*x - 224/3=0",
      "expected": {
        "solutions": [
          2.3333333333333335,
          4.0,
          8.0
        ],
        "symbolic": [
          "7/3",
          "4",
          "8"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^5 - 7*x^4/3 - 65*x^3 - 15*x^2 + 504*x + 324=0",
      "expected": {
        "solutions": [
          -6.0,
          -3.0,
          -0.6666666666666666,
          3.0,
          9.0
        ],
        "symbolic": [
          "-6",
          "-3",
          "-2/3",
          "3",
          "9"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 7*x^2/2 + 67*x/18 - 10/9=0",
      "expected": {
        "solutions": [
          0.5,
          1.3333333333333333,
          1.6666666666666667
        ],
        "symbolic": [
          "1/2",
          "4/3",
          "5/3"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^5 + x^4/6 - 19*x^3/4 - 7*x^2/8 + 97*x/24 - 5/4=0",
      "expected": {
        "solutions": [
          -1.6666666666666667,
          -1.5,
          0.5,
          2.0
        ],
        "symbolic": [
          "-5/3",
          "-3/2",
          "1/2",
          "2"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^4 + 7*x^3 + 17*x^2/4 - 71*x/2 - 18=0",
      "expected": {
        "solutions": [
          -4.5,
          -4.0,
          -0.5,
          2.0
        ],
        "symbolic": [
          "-9/2",
          "-4",
          "-1/2",
          "2"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 2*x^2/3 - 127*x/12 + 14=0",
      "expected": {
        "solutions": [
          -3.5,
          1.5,
          2.6666666666666665
        ],
        "symbolic": [
          "-7/2",
          "3/2",
          "8/3"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 3*x^2/2 - 27*x/2=0",
      "expected": {
        "solutions": [
          -3.0,
          0.0,
          4.5
        ],
        "symbolic": [
          "-3",
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          "9/2"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 13*x/9 + 4/9=0",
      "expected": {
        "solutions": [
          -1.3333333333333333,
          0.3333333333333333,
          1.0
        ],
        "symbolic": [
          "-4/3",
          "1/3",
          "1"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 3*x^2/2 - 107*x/2 - 126=0",
      "expected": {
        "solutions": [
          -4.0,
          -3.5,
          9.0
        ],
        "symbolic": [
          "-4",
          "-7/2",
          "9"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 + 17*x^2/2 + 47*x/2 + 21=0",
      "expected": {
        "solutions": [
          -3.5,
          -3.0,
          -2.0
        ],
        "symbolic": [
          "-7/2",
          "-3",
          "-2"
        ]
      }
    },
    {
      "family": "produits_et_degres_superieurs",
      "input": "x^3 - 6*x^2 - x + 30=0",
      "expected": {
        "solutions": [
          -2.0,
          3.0,
          5.0
        ],
        "symbolic": [
          "-2",
          "3",
          "5"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 5)/(x - 5)=3",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 2)/(x - 1)=-4",
      "expected": {
        "solutions": [
          1.2
        ],
        "symbolic": [
          "6/5"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 5)/(x - 5)=6",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 5)/(x + 4)=-5",
      "expected": {
        "solutions": [
          -4.166666666666667
        ],
        "symbolic": [
          "-25/6"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 6)/(x - 3)=8",
      "expected": {
        "solutions": [
          2.5714285714285716
        ],
        "symbolic": [
          "18/7"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 7)/(x - 5)=-7",
      "expected": {
        "solutions": [
          5.25
        ],
        "symbolic": [
          "21/4"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 5)/(x + 7)=3",
      "expected": {
        "solutions": [
          -13.0
        ],
        "symbolic": [
          "-13"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 3)/(x - 6)=-6",
      "expected": {
        "solutions": [
          5.571428571428571
        ],
        "symbolic": [
          "39/7"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 4)/(x - 6)=-1",
      "expected": {
        "solutions": [
          1.0
        ],
        "symbolic": [
          "1"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 7)/(x - 5)=6",
      "expected": {
        "solutions": [
          7.4
        ],
        "symbolic": [
          "37/5"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 3)/(x + 3)=6",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 2)/(x - 6)=7",
      "expected": {
        "solutions": [
          7.333333333333333
        ],
        "symbolic": [
          "22/3"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 3)/(x + 2)=-1",
      "expected": {
        "solutions": [
          0.5
        ],
        "symbolic": [
          "1/2"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 8)/(x + 3)=-7",
      "expected": {
        "solutions": [
          -1.625
        ],
        "symbolic": [
          "-13/8"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 8)/(x + 3)=8",
      "expected": {
        "solutions": [
          -4.571428571428571
        ],
        "symbolic": [
          "-32/7"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 3)/(x + 7)=3",
      "expected": {
        "solutions": [
          -9.0
        ],
        "symbolic": [
          "-9"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 2)/(x - 6)=2",
      "expected": {
        "solutions": [
          10.0
        ],
        "symbolic": [
          "10"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 8)/(x + 5)=5",
      "expected": {
        "solutions": [
          -8.25
        ],
        "symbolic": [
          "-33/4"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "x/(x - 6)=-2",
      "expected": {
        "solutions": [
          4.0
        ],
        "symbolic": [
          "4"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 6)/(x + 1)=4",
      "expected": {
        "solutions": [
          0.6666666666666666
        ],
        "symbolic": [
          "2/3"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 1)/(x - 6)=-6",
      "expected": {
        "solutions": [
          5.285714285714286
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        "symbolic": [
          "37/7"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 3)/(x - 5)=3",
      "expected": {
        "solutions": [
          9.0
        ],
        "symbolic": [
          "9"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 5)/(x + 6)=-5",
      "expected": {
        "solutions": [
          -5.833333333333333
        ],
        "symbolic": [
          "-35/6"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 5)/(x - 6)=2",
      "expected": {
        "solutions": [
          7.0
        ],
        "symbolic": [
          "7"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 8)/(x + 1)=6",
      "expected": {
        "solutions": [
          0.4
        ],
        "symbolic": [
          "2/5"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 3)/(x + 7)=-2",
      "expected": {
        "solutions": [
          -5.666666666666667
        ],
        "symbolic": [
          "-17/3"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 5)/(x - 5)=5",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x - 4)/(x + 8)=4",
      "expected": {
        "solutions": [
          -12.0
        ],
        "symbolic": [
          "-12"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 2)/(x - 3)=7",
      "expected": {
        "solutions": [
          3.8333333333333335
        ],
        "symbolic": [
          "23/6"
        ]
      }
    },
    {
      "family": "equations_rationnelles",
      "input": "(x + 8)/(x + 1)=-7",
      "expected": {
        "solutions": [
          -1.875
        ],
        "symbolic": [
          "-15/8"
        ]
      }
    },
    {
      "family": "systemes",
      "input": "-3*x - 5*y=13;4*x - 3*y=14",
      "expected": {
        "solution": {
          "x": "31/29",
          "y": "-94/29"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-6*x - 5*y=-13;2*x + 8*y=14",
      "expected": {
        "solution": {
          "x": "17/19",
          "y": "29/19"
        }
      }
    },
    {
      "family": "systemes",
      "input": "7*x + 8*y=2;6*x - 5*y=5",
      "expected": {
        "solution": {
          "x": "50/83",
          "y": "-23/83"
        }
      }
    },
    {
      "family": "systemes",
      "input": "6*x - 2*y=-14;-x + 7*y=-12",
      "expected": {
        "solution": {
          "x": "-61/20",
          "y": "-43/20"
        }
      }
    },
    {
      "family": "systemes",
      "input": "6*x - y=-10;2*x - 4*y=-12",
      "expected": {
        "solution": {
          "x": "-14/11",
          "y": "26/11"
        }
      }
    },
    {
      "family": "systemes",
      "input": "5*x + 8*y=3;3*x + y=-3",
      "expected": {
        "solution": {
          "x": "-27/19",
          "y": "24/19"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-3*x - 3*y=-6;-5*x + 7*y=1",
      "expected": {
        "solution": {
          "x": "13/12",
          "y": "11/12"
        }
      }
    },
    {
      "family": "systemes",
      "input": "5*x=8;-3*x - 2*y=11",
      "expected": {
        "solution": {
          "x": "8/5",
          "y": "-79/10"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-x + 2*y=-11;-8*x - 3*y=-11",
      "expected": {
        "solution": {
          "x": "55/19",
          "y": "-77/19"
        }
      }
    },
    {
      "family": "systemes",
      "input": "8*x + 7*y=-15;4*x - 7*y=-9",
      "expected": {
        "solution": {
          "x": "-2",
          "y": "1/7"
        }
      }
    },
    {
      "family": "systemes",
      "input": "4*x - y=4;-8*x=11",
      "expected": {
        "solution": {
          "x": "-11/8",
          "y": "-19/2"
        }
      }
    },
    {
      "family": "systemes",
      "input": "3*x + 3*y=2;2*x + 5*y=10",
      "expected": {
        "solution": {
          "x": "-20/9",
          "y": "26/9"
        }
      }
    },
    {
      "family": "systemes",
      "input": "6*x - 8*y=-5;-5*x + y=12",
      "expected": {
        "solution": {
          "x": "-91/34",
          "y": "-47/34"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-6*x + 7*y=-13;2*x + 2*y=0",
      "expected": {
        "solution": {
          "x": "1",
          "y": "-1"
        }
      }
    },
    {
      "family": "systemes",
      "input": "x - 5*y=-3;8*x + 8*y=10",
      "expected": {
        "solution": {
          "x": "13/24",
          "y": "17/24"
        }
      }
    },
    {
      "family": "systemes",
      "input": "4*x + 7*y=-7;-3*x - y=-7",
      "expected": {
        "solution": {
          "x": "56/17",
          "y": "-49/17"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-5*x + 3*y=-6;5*x + 2*y=2",
      "expected": {
        "solution": {
          "x": "18/25",
          "y": "-4/5"
        }
      }
    },
    {
      "family": "systemes",
      "input": "3*x - 6*y=4;-x - 3*y=3",
      "expected": {
        "solution": {
          "x": "-2/5",
          "y": "-13/15"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-2*x + 4*y=4;-6*x=-15",
      "expected": {
        "solution": {
          "x": "5/2",
          "y": "9/4"
        }
      }
    },
    {
      "family": "systemes",
      "input": "8*x + 6*y=-12;3*x - 5*y=-1",
      "expected": {
        "solution": {
          "x": "-33/29",
          "y": "-14/29"
        }
      }
    },
    {
      "family": "systemes",
      "input": "7*x + 7*y=8;-7*x - 2*y=-2",
      "expected": {
        "solution": {
          "x": "-2/35",
          "y": "6/5"
        }
      }
    },
    {
      "family": "systemes",
      "input": "7*x - 7*y=-11;6*x + 6*y=-4",
      "expected": {
        "solution": {
          "x": "-47/42",
          "y": "19/42"
        }
      }
    },
    {
      "family": "systemes",
      "input": "6*x - 2*y=-6;-2*x + 2*y=1",
      "expected": {
        "solution": {
          "x": "-5/4",
          "y": "-3/4"
        }
      }
    },
    {
      "family": "systemes",
      "input": "2*x - 2*y=3;-2*x - 7*y=-15",
      "expected": {
        "solution": {
          "x": "17/6",
          "y": "4/3"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-2*x + 4*y=-15;-2*x - 5*y=-6",
      "expected": {
        "solution": {
          "x": "11/2",
          "y": "-1"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-5*x - y=-2;4*x + 3*y=15",
      "expected": {
        "solution": {
          "x": "-9/11",
          "y": "67/11"
        }
      }
    },
    {
      "family": "systemes",
      "input": "x + 4*y=-5;-5*x - 6*y=13",
      "expected": {
        "solution": {
          "x": "-11/7",
          "y": "-6/7"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-4*x + 3*y=-14;8*x - 7*y=3",
      "expected": {
        "solution": {
          "x": "89/4",
          "y": "25"
        }
      }
    },
    {
      "family": "systemes",
      "input": "4*x - 3*y=-6;-7*x - 4*y=0",
      "expected": {
        "solution": {
          "x": "-24/37",
          "y": "42/37"
        }
      }
    },
    {
      "family": "systemes",
      "input": "2*x - 2*y=2;-5*x - y=-15",
      "expected": {
        "solution": {
          "x": "8/3",
          "y": "5/3"
        }
      }
    },
    {
      "family": "systemes",
      "input": "7*x + 5*y=11;7*x=14",
      "expected": {
        "solution": {
          "x": "2",
          "y": "-3/5"
        }
      }
    },
    {
      "family": "systemes",
      "input": "2*x - 7*y=7;4*x=14",
      "expected": {
        "solution": {
          "x": "7/2",
          "y": "0"
        }
      }
    },
    {
      "family": "systemes",
      "input": "-6*x + 4*y=1;-2*x - 4*y=12",
      "expected": {
        "solution": {
          "x": "-13/8",
          "y": "-35/16"
        }
      }
    },
    {
      "family": "inequations",
      "input": "((x - 7)*(x + 7))/(1)<0",
      "expected": {
        "intervals": [
          {
            "lo": -7.0,
            "hi": 7.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 7)/(x)<=0",
      "expected": {
        "intervals": [
          {
            "lo": 0.0,
            "hi": 7.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 4)/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 4.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 2)*(x + 2))/(x - 1)>=0",
      "expected": {
        "intervals": [
          {
            "lo": -2.0,
            "hi": 1.0,
            "lc": true,
            "hc": false
          },
          {
            "lo": 2.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 4)/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -4.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 8)/(x + 1)<0",
      "expected": {
        "intervals": [
          {
            "lo": -8.0,
            "hi": -1.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 9)*(x + 9))/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -9.0,
            "hi": 9.0,
            "lc": true,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 5)/(x - 5)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -5.0,
            "lc": false,
            "hc": true
          },
          {
            "lo": 5.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 1)/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 1.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x^2)/(x + 2)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -2.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 0.0,
            "hi": 0.0,
            "lc": true,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 9)/(1)>0",
      "expected": {
        "intervals": [
          {
            "lo": -9.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 7)/(x - 4)>0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 4.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 7.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 8)*(x + 8))/(1)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -8.0,
            "lc": false,
            "hc": true
          },
          {
            "lo": 8.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 7)/(x + 6)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -7.0,
            "hi": -6.0,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 4)/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -4.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 4)*(x + 4))/(x - 7)>0",
      "expected": {
        "intervals": [
          {
            "lo": -4.0,
            "hi": 4.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 7.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 4)/(1)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 4.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 5)/(x - 8)<0",
      "expected": {
        "intervals": [
          {
            "lo": -5.0,
            "hi": 8.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 7)*(x + 7))/(1)>0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -7.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 7.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 5)/(x - 4)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -5.0,
            "lc": false,
            "hc": true
          },
          {
            "lo": 4.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 8)/(1)>=0",
      "expected": {
        "intervals": [
          {
            "lo": 8.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 4)*(x + 4))/(x - 1)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -4.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 1.0,
            "hi": 4.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 7)/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -7.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 1)/(x)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 0.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 1.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 6)*(x + 6))/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -6.0,
            "hi": 6.0,
            "lc": true,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 7)/(x + 9)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -9.0,
            "hi": 7.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 1)/(1)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -1.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 2)*(x + 2))/(x - 7)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -2.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 2.0,
            "hi": 7.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 8)/(1)>=0",
      "expected": {
        "intervals": [
          {
            "lo": 8.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 7)/(x - 2)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -7.0,
            "lc": false,
            "hc": true
          },
          {
            "lo": 2.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 4)*(x + 4))/(1)<0",
      "expected": {
        "intervals": [
          {
            "lo": -4.0,
            "hi": 4.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 9)/(x + 2)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -2.0,
            "hi": 9.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 2)/(1)>=0",
      "expected": {
        "intervals": [
          {
            "lo": -2.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 1)*(x + 1))/(x - 4)>=0",
      "expected": {
        "intervals": [
          {
            "lo": -1.0,
            "hi": 1.0,
            "lc": true,
            "hc": true
          },
          {
            "lo": 4.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 6)/(1)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 6.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 2)/(x + 8)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -8.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": -2.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 7)*(x + 7))/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -7.0,
            "hi": 7.0,
            "lc": true,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 6)/(x)<0",
      "expected": {
        "intervals": [
          {
            "lo": 0.0,
            "hi": 6.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 6)/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -6.0,
            "lc": false,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 3)*(x + 3))/(x - 4)>0",
      "expected": {
        "intervals": [
          {
            "lo": -3.0,
            "hi": 3.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 4.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 6)/(1)>=0",
      "expected": {
        "intervals": [
          {
            "lo": -6.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 1)/(x + 6)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -6.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": -1.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 9)*(x + 9))/(1)<=0",
      "expected": {
        "intervals": [
          {
            "lo": -9.0,
            "hi": 9.0,
            "lc": true,
            "hc": true
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 7)/(x + 9)>0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -9.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": -7.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x + 7)/(1)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -7.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "((x - 7)*(x + 7))/(x - 5)<0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -7.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 5.0,
            "hi": 7.0,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 6)/(1)>0",
      "expected": {
        "intervals": [
          {
            "lo": 6.0,
            "hi": null,
            "lc": false,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "inequations",
      "input": "(x - 7)/(x)>=0",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": 0.0,
            "lc": false,
            "hc": false
          },
          {
            "lo": 7.0,
            "hi": null,
            "lc": true,
            "hc": false
          }
        ]
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x + 8)=-5",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x - 5)=1",
      "expected": {
        "solutions": [
          6.0
        ],
        "symbolic": [
          "6"
        ]
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x - 5)=-4",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x + 12)=-4",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x + 8)=6",
      "expected": {
        "solutions": [
          28.0
        ],
        "symbolic": [
          "28"
        ]
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x - 10)=-1",
      "expected": {
        "solutions": [],
        "symbolic": []
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x - 9)=2",
      "expected": {
        "solutions": [
          13.0
        ],
        "symbolic": [
          "13"
        ]
      }
    },
    {
      "family": "racines_isolees",
      "input": "sqrt(x + 12)=2",
      "expected": {
        "solutions": [
          -8.0
        ],
        "symbolic": [
          "-8"
        ]
      }
    },
    {
      "family": "racines_isolees",
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        "symbolic": [
          "3"
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    {
      "family": "exponentielles",
      "input": "3^x=81",
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        "solutions": [
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        "symbolic": [
          "4"
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    },
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      "family": "exponentielles",
      "input": "5^x=1/25",
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        "solutions": [
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        "symbolic": [
          "-2"
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    },
    {
      "family": "exponentielles",
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        "solutions": [
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        "symbolic": [
          "log(3)/log(2)"
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    },
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      "family": "exponentielles",
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        "solutions": [
          -3.0
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        "symbolic": [
          "-log(8)/log(2)"
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    },
    {
      "family": "logarithmes",
      "input": "ln(x - 1)=0",
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        "solutions": [
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        "symbolic": [
          "2"
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    },
    {
      "family": "logarithmes",
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        "solutions": [
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        "symbolic": [
          "1 + E"
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    },
    {
      "family": "logarithmes",
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        "symbolic": [
          "1 + exp(2)"
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    {
      "family": "logarithmes",
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        "symbolic": [
          "exp(-1) + 1"
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    },
    {
      "family": "doubles_inegalites",
      "input": "-6<2*x + 2<6",
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            "lo": "-4",
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    {
      "family": "doubles_inegalites",
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        "intervalSymbolic": [
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            "lo": "2/5",
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    },
    {
      "family": "doubles_inegalites",
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      "family": "doubles_inegalites",
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      "family": "doubles_inegalites",
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    {
      "family": "doubles_inegalites",
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    {
      "family": "doubles_inegalites",
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    {
      "family": "doubles_inegalites",
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            "lo": 2.8,
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            "lo": "14/5",
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    {
      "family": "doubles_inegalites",
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      "family": "doubles_inegalites",
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            "lo": -1.5,
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            "lo": "-3/2",
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    {
      "family": "doubles_inegalites",
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            "lo": null,
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    {
      "family": "doubles_inegalites",
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    {
      "family": "doubles_inegalites",
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            "lo": null,
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    {
      "family": "doubles_inegalites",
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    {
      "family": "doubles_inegalites",
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            "lo": "-3",
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    },
    {
      "family": "doubles_inegalites",
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        "intervalSymbolic": [
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            "lo": null,
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    },
    {
      "family": "doubles_inegalites",
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            "lo": 3.5,
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        "intervalSymbolic": [
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            "lo": "7/2",
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    },
    {
      "family": "doubles_inegalites",
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        "intervalSymbolic": []
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    },
    {
      "family": "doubles_inegalites",
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    },
    {
      "family": "doubles_inegalites",
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            "lo": 1.5,
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        "intervalSymbolic": [
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            "lo": "3/2",
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    },
    {
      "family": "doubles_inegalites",
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            "lo": 1.2,
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        "intervalSymbolic": [
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            "lo": "6/5",
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    },
    {
      "family": "doubles_inegalites",
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            "lo": -2.0,
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            "lo": "-2",
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    {
      "family": "doubles_inegalites",
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            "lo": -1.0,
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        "intervalSymbolic": [
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            "lo": "-1",
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    },
    {
      "family": "doubles_inegalites",
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            "lo": null,
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    },
    {
      "family": "doubles_inegalites",
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            "lo": -5.0,
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            "lo": "-5",
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    },
    {
      "family": "doubles_inegalites",
      "input": "2>2 - x>=3",
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        "intervals": [],
        "intervalSymbolic": []
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    },
    {
      "family": "doubles_inegalites",
      "input": "0<x - 4<-6",
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        "intervalSymbolic": []
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    },
    {
      "family": "doubles_inegalites",
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            "lo": 8.0,
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        "intervalSymbolic": [
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            "lo": "8",
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    },
    {
      "family": "doubles_inegalites",
      "input": "8<=-5*x - 6>=-5",
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        "intervals": [
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            "lo": null,
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        "intervalSymbolic": [
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            "lo": null,
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    },
    {
      "family": "doubles_inegalites",
      "input": "7>x - 2>=-6",
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            "lo": -4.0,
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        "intervalSymbolic": [
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            "lo": "-4",
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    },
    {
      "family": "doubles_inegalites",
      "input": "-3<4*x + 4>=5",
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            "lo": 0.25,
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        "intervalSymbolic": [
          {
            "lo": "1/4",
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    },
    {
      "family": "doubles_inegalites",
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            "lo": -2.2,
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        "intervalSymbolic": [
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            "lo": "-11/5",
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    },
    {
      "family": "inequations_valeur_absolue",
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            "lo": "4",
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    },
    {
      "family": "inequations_valeur_absolue",
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            "lo": null,
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    },
    {
      "family": "inequations_valeur_absolue",
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          {
            "lo": "-8/9",
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      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "3*abs(2*x - 1)+3<6",
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            "lo": 0.0,
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        "intervalSymbolic": [
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            "lo": "0",
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    },
    {
      "family": "inequations_valeur_absolue",
      "input": "-2*abs(2*x + 3)+0<1",
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    },
    {
      "family": "inequations_valeur_absolue",
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        "intervalSymbolic": []
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    },
    {
      "family": "inequations_valeur_absolue",
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            "lo": -4.333333333333333,
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            "lo": "-13/3",
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      }
    },
    {
      "family": "inequations_valeur_absolue",
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    },
    {
      "family": "inequations_valeur_absolue",
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            "lo": -6.0,
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            "lo": "-6",
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      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "3*abs(2*x - 5)+-1<=5",
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        "intervals": [
          {
            "lo": 1.5,
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        "intervalSymbolic": [
          {
            "lo": "3/2",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(2*x - 3)+2<5",
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        "intervals": [
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            "lo": 0.0,
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        "intervalSymbolic": [
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            "lo": "0",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(3 - x)+-2>=-2",
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        "intervals": [
          {
            "lo": null,
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        ],
        "intervalSymbolic": [
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    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(2*x - 2)+-2<=2",
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        "intervals": [
          {
            "lo": -1.0,
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        "intervalSymbolic": [
          {
            "lo": "-1",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(x - 5)+-3>=3",
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        "intervals": [
          {
            "lo": null,
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            "hc": true
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          {
            "lo": 11.0,
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        ],
        "intervalSymbolic": [
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            "lo": "11",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(-x - 3)+0<=5",
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        "intervals": [
          {
            "lo": -8.0,
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            "hc": true
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        ],
        "intervalSymbolic": [
          {
            "lo": "-8",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(x + 5)+1<=-1",
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        "intervalSymbolic": []
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    },
    {
      "family": "inequations_valeur_absolue",
      "input": "-2*abs(-x - 3)+2>=-2",
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        "intervals": [
          {
            "lo": -5.0,
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            "hc": true
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        ],
        "intervalSymbolic": [
          {
            "lo": "-5",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "1*abs(2 - x)+3<=3",
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        "intervals": [
          {
            "lo": 2.0,
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            "hc": true
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        ],
        "intervalSymbolic": [
          {
            "lo": "2",
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        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "-2*abs(x - 5)+2>-2",
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        "intervals": [
          {
            "lo": 3.0,
            "hi": 7.0,
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            "hc": false
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        ],
        "intervalSymbolic": [
          {
            "lo": "3",
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          }
        ]
      }
    },
    {
      "family": "inequations_valeur_absolue",
      "input": "3*abs(-x - 2)+-3>-2",
      "expected": {
        "intervals": [
          {
            "lo": null,
            "hi": -2.3333333333333335,
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          {
            "lo": -1.6666666666666667,
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        ],
        "intervalSymbolic": [
          {
            "lo": null,
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          {
            "lo": "-5/3",
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      "family": "inequations_valeur_absolue",
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        "symbolic": [
          "0"
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    },
    {
      "family": "exposants_racines",
      "input": "x^(-1/4)=0",
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    },
    {
      "family": "exposants_racines",
      "input": "x^(1/4)=1",
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        "symbolic": [
          "1"
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    },
    {
      "family": "exposants_racines",
      "input": "x^(-1/4)=1",
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        "symbolic": [
          "1"
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    },
    {
      "family": "exposants_racines",
      "input": "x^(1/4)=3",
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        "symbolic": [
          "81"
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    },
    {
      "family": "exposants_racines",
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        "symbolic": [
          "1/81"
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    },
    {
      "family": "exposants_racines",
      "input": "x^(1/5)=-2",
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        "symbolic": [
          "-32"
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    },
    {
      "family": "exposants_racines",
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        "symbolic": [
          "-1/32"
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    {
      "family": "exposants_racines",
      "input": "x^(1/5)=0",
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        "solutions": [
          0.0
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        "symbolic": [
          "0"
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    },
    {
      "family": "exposants_racines",
      "input": "x^(-1/5)=0",
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    },
    {
      "family": "exposants_racines",
      "input": "x^(1/5)=1",
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        "symbolic": [
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    {
      "family": "exposants_racines",
      "input": "x^(-1/5)=1",
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          "1"
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    },
    {
      "family": "exposants_racines",
      "input": "x^(1/5)=3",
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        "symbolic": [
          "243"
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    },
    {
      "family": "exposants_racines",
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    },
    {
      "family": "difference_racines_proches",
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        "symbolic": [
          "999998000001/4000000"
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    },
    {
      "family": "difference_racines_proches",
      "input": "-sqrt(x) + sqrt(x + 1)=1/10000000",
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        "symbolic": [
          "9999999999999800000000000001/400000000000000"
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    {
      "family": "difference_racines_proches",
      "input": "-sqrt(x) + sqrt(x + 1)=1/10000000000000",
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        "symbolic": [
          "9999999999999999999999999800000000000000000000000001/400000000000000000000000000"
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    },
    {
      "family": "difference_racines_proches",
      "input": "-sqrt(x) + sqrt(x + 1)=1/100000000000000000000",
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        "solutions": [
          2.5e+39
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        "symbolic": [
          "99999999999999999999999999999999999999980000000000000000000000000000000000000001/40000000000000000000000000000000000000000"
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    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x + 3)^2)=x + 3",
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        "intervals": [
          {
            "lo": -3.0,
            "hi": null,
            "lc": true,
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            "lo": "-3",
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    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x + 3)^2)=-(x + 3)",
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          {
            "lo": null,
            "hi": -3.0,
            "lc": false,
            "hc": true
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        "intervalSymbolic": [
          {
            "lo": null,
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    },
    {
      "family": "identites_et_domaines",
      "input": "ln(x + 3)=ln(x + 3)",
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        "intervals": [
          {
            "lo": -3.0,
            "hi": null,
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            "hc": false
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        "intervalSymbolic": [
          {
            "lo": "-3",
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "0*sqrt(x + 3)=0",
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        "intervals": [
          {
            "lo": -3.0,
            "hi": null,
            "lc": true,
            "hc": false
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        "intervalSymbolic": [
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x)^2)=x",
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          {
            "lo": 0.0,
            "hi": null,
            "lc": true,
            "hc": false
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        "intervalSymbolic": [
          {
            "lo": "0",
            "hi": null
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        ]
      }
    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x)^2)=-(x)",
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        "intervals": [
          {
            "lo": null,
            "hi": 0.0,
            "lc": false,
            "hc": true
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        ],
        "intervalSymbolic": [
          {
            "lo": null,
            "hi": "0"
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "ln(x)=ln(x)",
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        "intervals": [
          {
            "lo": 0.0,
            "hi": null,
            "lc": false,
            "hc": false
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        ],
        "intervalSymbolic": [
          {
            "lo": "0",
            "hi": null
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        ]
      }
    },
    {
      "family": "identites_et_domaines",
      "input": "0*sqrt(x)=0",
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        "intervals": [
          {
            "lo": 0.0,
            "hi": null,
            "lc": true,
            "hc": false
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        "intervalSymbolic": [
          {
            "lo": "0",
            "hi": null
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        ]
      }
    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x - 2)^2)=x - 2",
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        "intervals": [
          {
            "lo": 2.0,
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            "hc": false
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        "intervalSymbolic": [
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            "lo": "2",
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x - 2)^2)=-(x - 2)",
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          {
            "lo": null,
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            "lc": false,
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        "intervalSymbolic": [
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            "lo": null,
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "ln(x - 2)=ln(x - 2)",
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        "intervals": [
          {
            "lo": 2.0,
            "hi": null,
            "lc": false,
            "hc": false
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        ],
        "intervalSymbolic": [
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            "lo": "2",
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "0*sqrt(x - 2)=0",
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          {
            "lo": 2.0,
            "hi": null,
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            "hc": false
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        ],
        "intervalSymbolic": [
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            "lo": "2",
            "hi": null
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x - 5)^2)=x - 5",
      "expected": {
        "intervals": [
          {
            "lo": 5.0,
            "hi": null,
            "lc": true,
            "hc": false
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        ],
        "intervalSymbolic": [
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            "lo": "5",
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        ]
      }
    },
    {
      "family": "identites_et_domaines",
      "input": "sqrt((x - 5)^2)=-(x - 5)",
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          {
            "lo": null,
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        ],
        "intervalSymbolic": [
          {
            "lo": null,
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        ]
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    },
    {
      "family": "identites_et_domaines",
      "input": "ln(x - 5)=ln(x - 5)",
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        "intervals": [
          {
            "lo": 5.0,
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        "intervalSymbolic": [
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            "lo": "5",
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    },
    {
      "family": "identites_et_domaines",
      "input": "0*sqrt(x - 5)=0",
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            "lo": 5.0,
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        "intervalSymbolic": [
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            "lo": "5",
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        ]
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    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1-1e-12)",
      "expected": {
        "value": -1.0000000000005e-12
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1+1e-12)",
      "expected": {
        "value": 9.999999999995e-13
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1-1e-16)",
      "expected": {
        "value": -1.0000000000000001e-16
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1+1e-16)",
      "expected": {
        "value": 1e-16
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1-1e-20)",
      "expected": {
        "value": -1e-20
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1+1e-20)",
      "expected": {
        "value": 1e-20
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1-1e-30)",
      "expected": {
        "value": -1e-30
      }
    },
    {
      "family": "logarithmes_proches_de_un",
      "input": "ln(1+1e-30)",
      "expected": {
        "value": 1e-30
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  ],
  "version": "5.0",
  "date": "2026-10-08",
  "summary": {
    "oracle": "SymPy 1.14.0",
    "total": 576,
    "passed": 576,
    "families": {
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      "premier_degre": 35,
      "second_degre": 40,
      "produits_et_degres_superieurs": 25,
      "equations_rationnelles": 30,
      "systemes": 33,
      "inequations": 48,
      "racines_isolees": 20,
      "racines_candidats_extraneens": 15,
      "valeurs_absolues": 20,
      "puissances": 30,
      "coefficients_irrationnels": 12,
      "exponentielles": 5,
      "logarithmes": 4,
      "doubles_inegalites": 32,
      "inequations_valeur_absolue": 36,
      "inequations_absolues_rationnelles": 16,
      "bornes_irrationnelles": 16,
      "bornes_et_domaines": 7,
      "deux_racines_somme": 20,
      "deux_racines_difference": 20,
      "deux_racines_coefficients": 4,
      "deux_racines_egalite": 6,
      "deux_logarithmes": 6,
      "deux_valeurs_absolues": 6,
      "exposants_racines": 32,
      "difference_racines_proches": 4,
      "identites_et_domaines": 16,
      "logarithmes_proches_de_un": 8
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    "failures": []
  }
}