{
  "ring": "Q(i,A^(1/2))",
  "identity": "P_native=L0*f0+L1*f1+(W(2h)-1)*U",
  "h": [
    1,
    1,
    -1,
    -1
  ],
  "a": [
    1,
    0,
    0,
    -1
  ],
  "P_native": [
    {
      "root": [
        -4,
        0,
        0,
        4
      ],
      "A_degree": "-4",
      "coefficient": -1
    },
    {
      "root": [
        -2,
        0,
        2,
        2
      ],
      "A_degree": "-2",
      "coefficient": -1
    },
    {
      "root": [
        -2,
        2,
        -2,
        2
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        0,
        0
      ],
      "A_degree": "-8",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        0,
        0
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "-4",
      "coefficient": -1
    },
    {
      "root": [
        0,
        2,
        0,
        2
      ],
      "A_degree": "-10",
      "coefficient": 1
    },
    {
      "root": [
        0,
        2,
        0,
        2
      ],
      "A_degree": "-6",
      "coefficient": 1
    },
    {
      "root": [
        2,
        -2,
        2,
        -2
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        2,
        0,
        0,
        -2
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        2,
        0,
        2,
        -2
      ],
      "A_degree": "-6",
      "coefficient": -1
    },
    {
      "root": [
        2,
        0,
        2,
        0
      ],
      "A_degree": "-10",
      "coefficient": 1
    },
    {
      "root": [
        2,
        0,
        2,
        0
      ],
      "A_degree": "-6",
      "coefficient": 1
    },
    {
      "root": [
        2,
        2,
        2,
        2
      ],
      "A_degree": "-12",
      "coefficient": 1
    }
  ],
  "L0": [
    {
      "root": [
        0,
        0,
        2,
        4
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        2,
        0,
        0,
        0
      ],
      "A_degree": "-8",
      "coefficient": 1
    }
  ],
  "L1": [
    {
      "root": [
        -2,
        0,
        2,
        2
      ],
      "A_degree": "-2",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        2,
        2
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        2,
        0,
        2,
        -2
      ],
      "A_degree": "-6",
      "coefficient": 1
    }
  ],
  "U": [
    {
      "root": [
        -4,
        0,
        0,
        4
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        -2,
        -2,
        2,
        2
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        -2,
        0,
        2,
        4
      ],
      "A_degree": "-6",
      "coefficient": 1
    },
    {
      "root": [
        -2,
        0,
        2,
        4
      ],
      "A_degree": "-2",
      "coefficient": 1
    },
    {
      "root": [
        0,
        -2,
        2,
        0
      ],
      "A_degree": "-4",
      "coefficient": 1
    },
    {
      "root": [
        0,
        -2,
        2,
        2
      ],
      "A_degree": "-6",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        4,
        4
      ],
      "A_degree": "-4",
      "coefficient": 1
    }
  ],
  "f0": [
    {
      "root": [
        -2,
        0,
        0,
        0
      ],
      "A_degree": "0",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        0,
        0
      ],
      "A_degree": "0",
      "coefficient": -1
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "0",
      "coefficient": 1
    }
  ],
  "f1": [
    {
      "root": [
        0,
        -2,
        0,
        0
      ],
      "A_degree": "0",
      "coefficient": 1
    },
    {
      "root": [
        0,
        0,
        0,
        0
      ],
      "A_degree": "0",
      "coefficient": -1
    },
    {
      "root": [
        0,
        0,
        0,
        2
      ],
      "A_degree": "0",
      "coefficient": 1
    }
  ],
  "E2": [
    {
      "root": [
        0,
        0,
        0,
        0
      ],
      "A_degree": "0",
      "coefficient": -1
    },
    {
      "root": [
        2,
        2,
        -2,
        -2
      ],
      "A_degree": "0",
      "coefficient": 1
    }
  ],
  "filled_bracket": [
    {
      "root": [
        0,
        0,
        0,
        0
      ],
      "A_degree": "-4",
      "coefficient": 1
    }
  ]
}