{
  "ring": "Q(i,A^(1/2))[epsilon,zeta]/(epsilon^2-1,zeta^2-1)",
  "identity": "1-W(v)=G+(W(2h)-1)U+(W(2s)-A^4)V",
  "h": [
    -1,
    -1,
    1,
    1
  ],
  "s": [
    -1,
    0,
    0,
    1
  ],
  "v": [
    -4,
    0,
    4,
    0
  ],
  "tetrahedron_left_multipliers": [
    [
      1,
      1,
      1,
      4,
      1
    ],
    [
      2,
      2,
      0,
      4,
      -1
    ],
    [
      1,
      1,
      0,
      4,
      -1
    ],
    [
      1,
      0,
      2,
      4,
      1
    ],
    [
      2,
      1,
      1,
      4,
      -1
    ],
    [
      2,
      0,
      1,
      4,
      1
    ],
    [
      1,
      0,
      1,
      0,
      -1
    ],
    [
      2,
      1,
      0,
      0,
      1
    ]
  ],
  "G": [
    {
      "root": [
        -2,
        0,
        2,
        0
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        2,
        2
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        4,
        -2
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        4,
        0
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        -2,
        2,
        0
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        -2,
        4,
        -2
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        -2,
        4,
        0
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        -2,
        6,
        -2
      ],
      "A_degree": "6",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        4,
        -2
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        4,
        -2
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    }
  ],
  "U_squared": [
    {
      "root": [
        2,
        0,
        0,
        -2
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -4
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -2
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        4,
        -4
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    }
  ],
  "V_squared": [
    {
      "root": [
        -2,
        0,
        4,
        -2
      ],
      "A_degree": "-4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        2,
        -2
      ],
      "A_degree": "-4",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        4,
        -2
      ],
      "A_degree": "-4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        0,
        -2
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -4
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -2
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        4,
        -4
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    }
  ],
  "U_central": [
    {
      "root": [
        1,
        -1,
        1,
        -1
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        1,
        -1,
        3,
        -3
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        1,
        -1,
        3,
        -1
      ],
      "A_degree": "3",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        1,
        -1,
        5,
        -3
      ],
      "A_degree": "5",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        0,
        -2
      ],
      "A_degree": "4",
      "central_mask": 1,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -4
      ],
      "A_degree": "2",
      "central_mask": 1,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -2
      ],
      "A_degree": "2",
      "central_mask": 1,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        4,
        -4
      ],
      "A_degree": "4",
      "central_mask": 1,
      "coefficient": [
        1,
        0
      ]
    }
  ],
  "V_central": [
    {
      "root": [
        -3,
        0,
        4,
        -1
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        4,
        -2
      ],
      "A_degree": "-2",
      "central_mask": 2,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        -1,
        0,
        2,
        -1
      ],
      "A_degree": "-3",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        -1,
        0,
        2,
        1
      ],
      "A_degree": "1",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -1,
        0,
        4,
        -1
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        2,
        -2
      ],
      "A_degree": "-2",
      "central_mask": 2,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        2,
        0
      ],
      "A_degree": "2",
      "central_mask": 2,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        4,
        -2
      ],
      "A_degree": "-2",
      "central_mask": 2,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        1,
        0,
        0,
        -1
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        1,
        0,
        2,
        -3
      ],
      "A_degree": "-1",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        1,
        0,
        2,
        -1
      ],
      "A_degree": "-1",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        1,
        0,
        4,
        -3
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        0,
        -2
      ],
      "A_degree": "2",
      "central_mask": 2,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -4
      ],
      "A_degree": "0",
      "central_mask": 2,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        2,
        -2
      ],
      "A_degree": "0",
      "central_mask": 2,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        2,
        0,
        4,
        -4
      ],
      "A_degree": "2",
      "central_mask": 2,
      "coefficient": [
        1,
        0
      ]
    }
  ],
  "reverse_U_squared": [
    {
      "root": [
        0,
        -2,
        -2,
        4
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        -2,
        2
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        0,
        0,
        -2,
        4
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
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        0
      ]
    },
    {
      "root": [
        0,
        0,
        0,
        2
      ],
      "A_degree": "4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        2,
        -2,
        -2,
        2
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        4,
        0,
        -4,
        0
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    }
  ],
  "reverse_V_squared": [
    {
      "root": [
        -2,
        -4,
        0,
        6
      ],
      "A_degree": "-4",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        -2,
        0,
        4
      ],
      "A_degree": "-4",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        -2,
        -2,
        0,
        6
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        -2,
        2,
        4
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        -2,
        4
      ],
      "A_degree": "-2",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        -2,
        6
      ],
      "A_degree": "2",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        0,
        2
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        1,
        0
      ]
    },
    {
      "root": [
        -2,
        0,
        0,
        4
      ],
      "A_degree": "0",
      "central_mask": 0,
      "coefficient": [
        -1,
        0
      ]
    }
  ]
}