files / problems / hilbert16-limit-cycles / compute / q2 / o-iterated-squaring / certs / identity.json
{
"paper": "arXiv:2604.12883v1 Remark 4 / Theorem 2 / \u00a76",
"Phi": "u^2-v^2, 2uv",
"det": "4(u^2+v^2)",
"cauchy_riemann": true,
"identity": "DPhi \u00b7 Y = (det DPhi) (X o Phi)",
"radial": {
"rho2": [
1,
4
],
"identity_ok": true,
"deg_Y": 7,
"bound": 7,
"exact": true,
"Yu_monomials": [
{
"u": 0,
"v": 3,
"num": 2,
"den": 1
},
{
"u": 1,
"v": 2,
"num": 1,
"den": 2
},
{
"u": 2,
"v": 1,
"num": 2,
"den": 1
},
{
"u": 3,
"v": 0,
"num": 1,
"den": 2
},
{
"u": 1,
"v": 6,
"num": -2,
"den": 1
},
{
"u": 3,
"v": 4,
"num": -6,
"den": 1
},
{
"u": 5,
"v": 2,
"num": -6,
"den": 1
},
{
"u": 7,
"v": 0,
"num": -2,
"den": 1
}
],
"Yv_monomials": [
{
"u": 0,
"v": 3,
"num": 1,
"den": 2
},
{
"u": 1,
"v": 2,
"num": -2,
"den": 1
},
{
"u": 2,
"v": 1,
"num": 1,
"den": 2
},
{
"u": 3,
"v": 0,
"num": -2,
"den": 1
},
{
"u": 0,
"v": 7,
"num": -2,
"den": 1
},
{
"u": 2,
"v": 5,
"num": -6,
"den": 1
},
{
"u": 4,
"v": 3,
"num": -6,
"den": 1
},
{
"u": 6,
"v": 1,
"num": -2,
"den": 1
}
]
},
"linear": {
"P": "y",
"Q": "-x",
"identity_ok": true,
"deg_Y": 3,
"bound": 3,
"Yu_closed": "2v(u^2+v^2)",
"Yv_closed": "-2u(u^2+v^2)",
"Yu_monomials": [
{
"u": 0,
"v": 3,
"num": 2,
"den": 1
},
{
"u": 2,
"v": 1,
"num": 2,
"den": 1
}
],
"Yv_monomials": [
{
"u": 1,
"v": 2,
"num": -2,
"den": 1
},
{
"u": 3,
"v": 0,
"num": -2,
"den": 1
}
]
},
"two_step_radial": {
"deg_Y": 15,
"bound": 15,
"identity_ok": true,
"N_formula": "(n+1) 2^k - 1"
},
"chebyshev_T2_one_step": {
"deg_Y": 7,
"bound": 7,
"identity_ok": true
}
}