files / problems / smale-jacobian-n2 / compute / q2 / certificate.json

611 B · on GitHub

{
  "family": {
    "linear_form": "l=a*x+b*y",
    "map": ["x+c*b*l^d", "y-c*a*l^d"],
    "inverse": ["x-c*b*l^d", "y+c*a*l^d"],
    "degree_condition": "d>=2"
  },
  "exact_cases": [
    {"degree": 2, "a": 1, "b": 1, "c": 1},
    {"degree": 3, "a": 2, "b": -1, "c": 3},
    {"degree": 7, "a": -2, "b": 3, "c": -1},
    {"degree": 125, "a": 1, "b": 2, "c": 1}
  ],
  "classification_steps": [
    "homogeneous determinant degrees force div(H)=0 and det(JH)=0",
    "H=(h_y,-h_x) for a binary homogeneous form h",
    "det(Hess(h))=0",
    "the binary Hessian lemma gives h as a power of one linear form"
  ]
}