files / problems / hilbert16-limit-cycles / compute / q3 / pp-christopher-lloyd / certs / preimages.json

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{
  "cl_circle_point": {
    "target": [
      5,
      2,
      2,
      1
    ],
    "real_regular": 4,
    "bezout_m2": 4,
    "attains_m2": true,
    "note": "four sign combinations of (\u00b1sqrt(5/2), \u00b1sqrt(2))"
  },
  "cl_half_half": {
    "target": [
      1,
      2,
      1,
      2
    ],
    "real_regular": 4,
    "bezout_m2": 4,
    "attains_m2": true
  },
  "chebyshev_T2_half_half": {
    "target": [
      1,
      2,
      1,
      2
    ],
    "real_regular": 4,
    "attains_m2": true,
    "t2_equation": "2t^2-3/2=0",
    "disc": 12
  },
  "holomorphic_half_0": {
    "target": [
      1,
      2,
      0,
      1
    ],
    "real_regular": 2,
    "attains_m2": false
  },
  "polar_z_to_z2": [
    {
      "target": [
        1,
        2,
        0,
        1
      ],
      "count": 2
    },
    {
      "target": [
        1,
        2,
        1,
        2
      ],
      "count": 2
    },
    {
      "target": [
        5,
        2,
        2,
        1
      ],
      "count": 2
    }
  ],
  "oval": {
    "equation": "(u^2-2)^2+(v^2-2)^2=1/4",
    "u2_min": [
      3,
      2
    ],
    "u2_max": [
      5,
      2
    ],
    "components": 4,
    "uv_nonzero": true,
    "jac_nonzero": true
  },
  "untranslated_hits_axes": true,
  "translated_first_quadrant": true,
  "honesty": {
    "separable_square_is_4_to_1_off_axes": true,
    "holomorphic_square_is_2_to_1": true,
    "four_sign_combinations": true
  }
}