HALOWERKTechnische Prüfungen & Formate
F B NIGHT FINITE STRUCTURES / padic newton polygon root valuations
A p-adic algebra conformance agent needs the exact valuation multiset of all roots over an algebraicclosure ofQ_p for a complete supplied polynomial. No coefficientfactorization,realroots or one fieldroot lift.
POST https://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/padic-newton-polygon-root-valuationsEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| artifact | object | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"additionalProperties": false,
"required": [
"artifact"
],
"properties": {
"artifact": {
"type": "object",
"additionalProperties": false,
"required": [
"newton"
],
"properties": {
"newton": {
"type": "object",
"additionalProperties": false,
"required": [
"prime",
"coefficients",
"claim"
],
"properties": {
"prime": {
"type": "integer",
"minimum": 2,
"maximum": 101
},
"coefficients": {
"type": "array",
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
},
"maxItems": 17,
"minItems": 1
},
"claim": {
"type": "object",
"additionalProperties": false,
"required": [
"degree",
"zero_roots",
"polygon_vertices",
"nonzero_root_valuations"
],
"properties": {
"degree": {
"type": "integer",
"minimum": 0,
"maximum": 16
},
"zero_roots": {
"type": "integer",
"minimum": 0,
"maximum": 16
},
"polygon_vertices": {
"type": "array",
"items": {
"type": "object",
"additionalProperties": false,
"required": [
"degree",
"valuation"
],
"properties": {
"degree": {
"type": "integer",
"minimum": 0,
"maximum": 16
},
"valuation": {
"type": "integer",
"minimum": 0,
"maximum": 30
}
}
},
"maxItems": 17,
"minItems": 0
},
"nonzero_root_valuations": {
"type": "array",
"items": {
"type": "object",
"additionalProperties": false,
"required": [
"numerator",
"denominator",
"multiplicity"
],
"properties": {
"numerator": {
"type": "integer",
"minimum": -30,
"maximum": 30
},
"denominator": {
"type": "integer",
"minimum": 1,
"maximum": 16
},
"multiplicity": {
"type": "integer",
"minimum": 1,
"maximum": 16
}
}
},
"maxItems": 16,
"minItems": 0
}
}
}
}
}
}
}
}
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