files / problems / hilbert16-limit-cycles / compute / q1 / c-chebyshev / certs / section6_degree.json

3.8 KB · on GitHub

{
  "paper": "arXiv:2604.12883v1 \u00a76",
  "rho2": [
    1,
    4
  ],
  "T3": "4*t**3 - 3*t",
  "T3_prime": "12*t**2 - 3",
  "X": {
    "P": "-x*(x**2 + y**2 - 1/4) + y",
    "Q": "-x - y*(x**2 + y**2 - 1/4)",
    "deg": 3
  },
  "Y": {
    "u_dot": "T3'(v) * P(T3(u), T3(v))",
    "v_dot": "T3'(u) * Q(T3(u), T3(v))",
    "deg_u": 11,
    "deg_v": 11,
    "deg": 11,
    "monomials_u": [
      {
        "u": 0,
        "v": 1,
        "num": 9,
        "den": 1
      },
      {
        "u": 1,
        "v": 0,
        "num": 9,
        "den": 4
      },
      {
        "u": 0,
        "v": 3,
        "num": -48,
        "den": 1
      },
      {
        "u": 1,
        "v": 2,
        "num": -90,
        "den": 1
      },
      {
        "u": 3,
        "v": 0,
        "num": -84,
        "den": 1
      },
      {
        "u": 0,
        "v": 5,
        "num": 48,
        "den": 1
      },
      {
        "u": 1,
        "v": 4,
        "num": 540,
        "den": 1
      },
      {
        "u": 3,
        "v": 2,
        "num": 444,
        "den": 1
      },
      {
        "u": 5,
        "v": 0,
        "num": 324,
        "den": 1
      },
      {
        "u": 1,
        "v": 6,
        "num": -1008,
        "den": 1
      },
      {
        "u": 3,
        "v": 4,
        "num": -720,
        "den": 1
      },
      {
        "u": 5,
        "v": 2,
        "num": -1296,
        "den": 1
      },
      {
        "u": 7,
        "v": 0,
        "num": -432,
        "den": 1
      },
      {
        "u": 1,
        "v": 8,
        "num": 576,
        "den": 1
      },
      {
        "u": 3,
        "v": 6,
        "num": 1344,
        "den": 1
      },
      {
        "u": 7,
        "v": 2,
        "num": 1728,
        "den": 1
      },
      {
        "u": 9,
        "v": 0,
        "num": 192,
        "den": 1
      },
      {
        "u": 3,
        "v": 8,
        "num": -768,
        "den": 1
      },
      {
        "u": 9,
        "v": 2,
        "num": -768,
        "den": 1
      }
    ],
    "monomials_v": [
      {
        "u": 0,
        "v": 1,
        "num": 9,
        "den": 4
      },
      {
        "u": 1,
        "v": 0,
        "num": -9,
        "den": 1
      },
      {
        "u": 0,
        "v": 3,
        "num": -84,
        "den": 1
      },
      {
        "u": 2,
        "v": 1,
        "num": -90,
        "den": 1
      },
      {
        "u": 3,
        "v": 0,
        "num": 48,
        "den": 1
      },
      {
        "u": 0,
        "v": 5,
        "num": 324,
        "den": 1
      },
      {
        "u": 2,
        "v": 3,
        "num": 444,
        "den": 1
      },
      {
        "u": 4,
        "v": 1,
        "num": 540,
        "den": 1
      },
      {
        "u": 5,
        "v": 0,
        "num": -48,
        "den": 1
      },
      {
        "u": 0,
        "v": 7,
        "num": -432,
        "den": 1
      },
      {
        "u": 2,
        "v": 5,
        "num": -1296,
        "den": 1
      },
      {
        "u": 4,
        "v": 3,
        "num": -720,
        "den": 1
      },
      {
        "u": 6,
        "v": 1,
        "num": -1008,
        "den": 1
      },
      {
        "u": 0,
        "v": 9,
        "num": 192,
        "den": 1
      },
      {
        "u": 2,
        "v": 7,
        "num": 1728,
        "den": 1
      },
      {
        "u": 6,
        "v": 3,
        "num": 1344,
        "den": 1
      },
      {
        "u": 8,
        "v": 1,
        "num": 576,
        "den": 1
      },
      {
        "u": 2,
        "v": 9,
        "num": -768,
        "den": 1
      },
      {
        "u": 8,
        "v": 3,
        "num": -768,
        "den": 1
      }
    ]
  },
  "integer_time_rescale_4X": {
    "P": "-4*x**3 - 4*x*y**2 + x + 4*y",
    "Q": "-4*x**2*y - 4*x - 4*y**3 + y",
    "deg_Y": 11
  },
  "conjugacy": true,
  "expected_deg": 11,
  "H11_from_this_field": 9,
  "beats_HanLi_153": false
}