files / problems / hilbert16-limit-cycles / compute / q1 / e-bezout-bautin / pullback_degree.json
{
"lemma": "deg adj(D\u03a6) X\u2218\u03a6 \u2264 n m + (m-1) for deg \u03a6 \u2264 m, deg X \u2264 n",
"identity": "D\u03a6 \u00b7 Y = (det D\u03a6) (X \u2218 \u03a6)",
"n_examples": 29,
"failures": 0,
"examples": [
{
"name": "chebyshev_n1_m2",
"n": 1,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 1,
"deg_Y": 3,
"bound": 3,
"identity_ok": true,
"ok": true
},
{
"name": "nonsep_um_plus_v_n1_m2",
"n": 1,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 1,
"deg_Y": 3,
"bound": 3,
"identity_ok": true,
"ok": true
},
{
"name": "chebyshev_n2_m2",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true
},
{
"name": "nonsep_um_plus_v_n2_m2",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true
},
{
"name": "chebyshev_n2_m3",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true
},
{
"name": "nonsep_um_plus_v_n2_m3",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true
},
{
"name": "chebyshev_n3_m3",
"n": 3,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 3,
"deg_Y": 11,
"bound": 11,
"identity_ok": true,
"ok": true
},
{
"name": "nonsep_um_plus_v_n3_m3",
"n": 3,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 3,
"deg_Y": 11,
"bound": 11,
"identity_ok": true,
"ok": true
},
{
"name": "random_n2_m2_0",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "-2*u**2 - 2*u*v + 2*u + v**2",
"q": "2*u*v - u - v**2 + 2*v + 2"
},
{
"name": "random_n2_m2_1",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "-u**2 - 2*u*v + u - v + 2",
"q": "-u*v - 2*u + 2*v**2 - 2"
},
{
"name": "random_n2_m2_2",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "-u*v + u - 2*v**2 + 2*v + 1",
"q": "2*u**2 - u*v - 2*u + v**2 - v + 2"
},
{
"name": "random_n2_m2_3",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "2*u*v + v**2 - 2*v",
"q": "2*u**2 + u*v + u - 2*v - 1"
},
{
"name": "random_n2_m2_4",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "u**2 - 2*u*v + 2*u - 2*v - 2",
"q": "2*u**2 - 2*u + 2*v**2 + v + 1"
},
{
"name": "random_n2_m2_5",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "u**2 + 2*u*v - 2*u + 2*v**2 - v + 1",
"q": "-u**2 + 2*u*v + 2*u + v - 1"
},
{
"name": "random_n2_m2_6",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "v**2 + 2*v - 1",
"q": "2*u**2 + u - 2*v + 2"
},
{
"name": "random_n2_m2_7",
"n": 2,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 2,
"deg_Y": 5,
"bound": 5,
"identity_ok": true,
"ok": true,
"p": "2*u**2 + u*v - 2*u - v**2 + 2*v + 2",
"q": "-u**2 + u*v - u - 2*v**2 - 2*v"
},
{
"name": "random_n2_m3_0",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true,
"p": "u**3 + u**2 - 2*u*v**2 - u*v + u + v**3 - v**2 - 2*v + 1",
"q": "-u**3 - u**2*v + 2*u**2 - 2*u*v**2 + u*v - u + 2*v**3 + 2*v**2 - 2"
},
{
"name": "random_n2_m3_1",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true,
"p": "-u**3 - 2*u**2*v - 2*u**2 + u*v**2 + u*v - 2*u + v**3 + 2*v**2 - v + 2",
"q": "2*u**3 - u*v**2 + v**3 - 2"
},
{
"name": "random_n2_m3_2",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true,
"p": "2*u**3 - 2*u**2*v + 2*u*v**2 - u*v + u - v**3 - 2*v**2 - v",
"q": "2*u**3 - u**2*v + u*v**2 + u*v + u + v**3 - 2*v**2 + v + 2"
},
{
"name": "random_n2_m3_3",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true,
"p": "u**2*v + u**2 + 2*u*v**2 - u*v + 2*u + v**3 - v**2 + 2",
"q": "2*u**3 + u**2*v - u**2 + u*v**2 + 2*v**3 - 2*v**2 - 2*v + 2"
},
{
"name": "random_n2_m3_4",
"n": 2,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 2,
"deg_Y": 8,
"bound": 8,
"identity_ok": true,
"ok": true,
"p": "u**2*v + u**2 + 2*u*v**2 + u*v - 2*u + 2*v**3 + 2*v**2 - v",
"q": "2*u**3 - 2*u**2*v - u**2 + 2*u*v**2 + 2*u*v + u - v**3 - 2*v**2 - v"
},
{
"name": "random_n3_m2_0",
"n": 3,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 3,
"deg_Y": 7,
"bound": 7,
"identity_ok": true,
"ok": true,
"p": "2*u**2 - 2*v**2 - 2*v - 2",
"q": "2*u*v + u - v + 1"
},
{
"name": "random_n3_m2_1",
"n": 3,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 3,
"deg_Y": 7,
"bound": 7,
"identity_ok": true,
"ok": true,
"p": "-2*u**2 - u*v + u + 2*v**2 - v",
"q": "2*u*v - u - 2"
},
{
"name": "random_n3_m2_2",
"n": 3,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 3,
"deg_Y": 7,
"bound": 7,
"identity_ok": true,
"ok": true,
"p": "-2*u**2 - u + v**2 + v - 1",
"q": "u**2 - v**2 + 2*v + 2"
},
{
"name": "random_n3_m2_3",
"n": 3,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 3,
"deg_Y": 7,
"bound": 7,
"identity_ok": true,
"ok": true,
"p": "-u**2 + 2*u*v + u + v**2 - 2*v + 1",
"q": "-2*u**2 - 2*u - 2*v**2 - 2*v"
},
{
"name": "random_n3_m2_4",
"n": 3,
"m": 2,
"deg_p": 2,
"deg_q": 2,
"deg_X": 3,
"deg_Y": 7,
"bound": 7,
"identity_ok": true,
"ok": true,
"p": "-2*u**2 - 2*u*v - u + v**2 - 2*v - 2",
"q": "-u**2 + u*v - u - 2*v**2 + 2"
},
{
"name": "random_n3_m3_0",
"n": 3,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 3,
"deg_Y": 11,
"bound": 11,
"identity_ok": true,
"ok": true,
"p": "-2*u**2*v - u*v**2 - u*v - 2*u - 2*v**3 - v**2 - 2*v - 2",
"q": "-2*u**3 + u**2*v + 2*u**2 - 2*u*v + u - v**3 - 2*v**2 + 2*v + 2"
},
{
"name": "random_n3_m3_1",
"n": 3,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 3,
"deg_Y": 11,
"bound": 11,
"identity_ok": true,
"ok": true,
"p": "2*u**2*v - 2*u**2 - 2*u*v**2 - 2*u*v + 2*u + v**3 - 2*v**2 + 2*v + 2",
"q": "2*u**3 + u**2*v - 2*u**2 - 2*u*v**2 + u*v + v**3 + v**2 - 2*v + 2"
},
{
"name": "random_n3_m3_2",
"n": 3,
"m": 3,
"deg_p": 3,
"deg_q": 3,
"deg_X": 3,
"deg_Y": 11,
"bound": 11,
"identity_ok": true,
"ok": true,
"p": "-u**3 + 2*u**2*v - 2*u**2 + u*v**2 - 2*u*v + v**3 + 2*v**2 - v - 2",
"q": "u**2*v - u*v**2 + 2*u"
}
]
}