files / problems / hilbert16-limit-cycles / compute / q1 / d-restricted-upper / certs / identities.json
{
"claim": "polar identities for the radial cubic; Hamiltonian dH/dt = 0; Lotka-Volterra weighted Dulac and Delta=0 reduction",
"cramer": {
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},
{
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{
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],
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{
"b": 1,
"c": 1,
"coeff": "1"
}
],
"variables": [
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"e",
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],
"x_coeff_times_Delta": [],
"y_coeff_times_Delta": []
},
"hamiltonian": {
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},
{
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},
{
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{
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{
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{
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{
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{
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{
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{
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}
],
"Hx": [
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{
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{
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{
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],
"Hy": [
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{
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{
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{
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{
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}
],
"dHdt": [],
"variables": [
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"a02",
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]
},
"lotka_volterra": {
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{
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{
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{
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{
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{
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{
"alpha": 1,
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"x": 1
}
],
"variables": [
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"a",
"b",
"c",
"d",
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"alpha",
"beta"
],
"weighted_div_over_B": [
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},
{
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]
},
"parallel": {
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},
{
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}
],
"right": [
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"lam": 1
}
],
"variables": [
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]
},
"polar": {
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{
"coeff": "1",
"y": 1
},
{
"coeff": "1",
"rho": 2,
"x": 1
},
{
"coeff": "-1",
"x": 1,
"y": 2
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{
"coeff": "-1",
"x": 3
}
],
"Q": [
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"y": 1
},
{
"coeff": "-1",
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{
"coeff": "-1",
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{
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],
"angular_left": [
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],
"angular_right": [
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"radial_left": [
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],
"radial_right": [
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},
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}
],
"variables": [
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},
"radial_speed": {
"factored": [
{
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"r": 1,
"rho": 2
},
{
"coeff": "-1",
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}
],
"r_times_rho2_minus_r2": [
{
"coeff": "1",
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"rho": 2
},
{
"coeff": "-1",
"r": 3
}
],
"variables": [
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]
},
"schema": "hilbert16-d-restricted-upper/v1"
}