files / problems / hilbert16-limit-cycles / compute / q3 / ff-two-well / certs / identities.json

6.1 KB · on GitHub

{
  "figure_eight": {
    "I0_den": 15,
    "I0_num": 4,
    "anti15": [
      {
        "coeff": "-10",
        "t": 3
      },
      {
        "coeff": "12",
        "t": 5
      }
    ],
    "deriv_diff": [],
    "integrand": [
      {
        "coeff": "-2",
        "t": 2
      },
      {
        "coeff": "4",
        "t": 4
      }
    ],
    "variables": [
      "t"
    ]
  },
  "jets": {
    "L1_minus": {
      "den": 1,
      "num": 1,
      "s_power": 1
    },
    "L1_plus": {
      "den": 1,
      "num": 1,
      "s_power": 1
    },
    "minus": {
      "a02": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a03": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a11": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a12": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a20": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a21": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a30": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b02": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b03": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b11": {
        "den": 1,
        "num": 1,
        "s_power": 1
      },
      "b12": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b20": {
        "den": 2,
        "num": -3,
        "s_power": 0
      },
      "b21": {
        "den": 2,
        "num": -1,
        "s_power": 1
      },
      "b30": {
        "den": 2,
        "num": 1,
        "s_power": 0
      }
    },
    "plus": {
      "a02": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a03": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a11": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a12": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a20": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a21": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "a30": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b02": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b03": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b11": {
        "den": 1,
        "num": -1,
        "s_power": 1
      },
      "b12": {
        "den": 1,
        "num": 0,
        "s_power": 0
      },
      "b20": {
        "den": 2,
        "num": 3,
        "s_power": 0
      },
      "b21": {
        "den": 2,
        "num": -1,
        "s_power": 1
      },
      "b30": {
        "den": 2,
        "num": 1,
        "s_power": 0
      }
    }
  },
  "perturbed": {
    "P": [
      {
        "coeff": "1",
        "y": 1
      }
    ],
    "Q": [
      {
        "coeff": "1",
        "mu": 1,
        "y": 1
      },
      {
        "coeff": "1",
        "x": 1
      },
      {
        "coeff": "-1",
        "mu": 1,
        "x": 2,
        "y": 1
      },
      {
        "coeff": "-1",
        "x": 3
      }
    ],
    "claimed4": [
      {
        "coeff": "4",
        "mu": 1,
        "y": 2
      },
      {
        "coeff": "-4",
        "mu": 1,
        "x": 2,
        "y": 2
      }
    ],
    "dH4": [
      {
        "coeff": "4",
        "mu": 1,
        "y": 2
      },
      {
        "coeff": "-4",
        "mu": 1,
        "x": 2,
        "y": 2
      }
    ],
    "trace": [
      {
        "coeff": "1",
        "mu": 1
      },
      {
        "coeff": "-1",
        "mu": 1,
        "x": 2
      }
    ],
    "variables": [
      "x",
      "y",
      "mu"
    ]
  },
  "schema": "hilbert16-ff-two-well-identities/v1",
  "translate_minus": {
    "Q": [
      {
        "X": 1,
        "coeff": "-2"
      },
      {
        "X": 1,
        "Y": 1,
        "coeff": "2",
        "mu": 1
      },
      {
        "X": 2,
        "coeff": "3"
      },
      {
        "X": 2,
        "Y": 1,
        "coeff": "-1",
        "mu": 1
      },
      {
        "X": 3,
        "coeff": "-1"
      }
    ],
    "claimed": [
      {
        "X": 1,
        "coeff": "-2"
      },
      {
        "X": 1,
        "Y": 1,
        "coeff": "2",
        "mu": 1
      },
      {
        "X": 2,
        "coeff": "3"
      },
      {
        "X": 2,
        "Y": 1,
        "coeff": "-1",
        "mu": 1
      },
      {
        "X": 3,
        "coeff": "-1"
      }
    ],
    "diff": [],
    "variables": [
      "X",
      "Y",
      "mu"
    ]
  },
  "translate_plus": {
    "Q": [
      {
        "X": 1,
        "coeff": "-2"
      },
      {
        "X": 1,
        "Y": 1,
        "coeff": "-2",
        "mu": 1
      },
      {
        "X": 2,
        "coeff": "-3"
      },
      {
        "X": 2,
        "Y": 1,
        "coeff": "-1",
        "mu": 1
      },
      {
        "X": 3,
        "coeff": "-1"
      }
    ],
    "claimed": [
      {
        "X": 1,
        "coeff": "-2"
      },
      {
        "X": 1,
        "Y": 1,
        "coeff": "-2",
        "mu": 1
      },
      {
        "X": 2,
        "coeff": "-3"
      },
      {
        "X": 2,
        "Y": 1,
        "coeff": "-1",
        "mu": 1
      },
      {
        "X": 3,
        "coeff": "-1"
      }
    ],
    "diff": [],
    "variables": [
      "X",
      "Y",
      "mu"
    ]
  },
  "unperturbed": {
    "H4": [
      {
        "coeff": "2",
        "y": 2
      },
      {
        "coeff": "-2",
        "x": 2
      },
      {
        "coeff": "1",
        "x": 4
      }
    ],
    "P": [
      {
        "coeff": "1",
        "y": 1
      }
    ],
    "Q": [
      {
        "coeff": "1",
        "x": 1
      },
      {
        "coeff": "-1",
        "x": 3
      }
    ],
    "Q_factored": [
      {
        "coeff": "1",
        "x": 1
      },
      {
        "coeff": "-1",
        "x": 3
      }
    ],
    "dH4": [],
    "det": [
      {
        "coeff": "-1"
      },
      {
        "coeff": "3",
        "x": 2
      }
    ],
    "div": [],
    "variables": [
      "x",
      "y"
    ]
  }
}