HALOWERKDatenvertragswerk
gaussian euclidean trace audit
Reconstruct the entire exact Euclidean division trace for two Gaussian integers, including every quotient/remainder/norm, canonical first-quadrant gcd and unit-rotated Bezout coefficients. Coordinates -128..128; componentwise nearest quotient with half ties toward positive infinity; nonzero canonical gcd real>0,imag>=0, deterministic zero-zero convention. Compare the whole supplied claimed artifact, independent of object-key order. Missing operands produce unknown; missing claim keeps the.
POST https://datenvertrag.halowerk.com/v1/gaussian-euclidean-trace-auditEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| a | Siehe Schema | Ja | |
| b | Siehe Schema | Ja | |
| claimed_value | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"a": {
"anyOf": [
{
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -128,
"maximum": 128
}
},
{
"type": "null"
}
]
},
"b": {
"anyOf": [
{
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -128,
"maximum": 128
}
},
{
"type": "null"
}
]
},
"claimed_value": {
"anyOf": [
{
"type": "object",
"properties": {
"gcd": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"bezout_a": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"bezout_b": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"normalizing_unit": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1,
"maximum": 1
}
},
"trace": {
"type": "array",
"maxItems": 32,
"items": {
"type": "object",
"properties": {
"dividend": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"divisor": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"quotient": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"remainder": {
"type": "array",
"minItems": 2,
"maxItems": 2,
"items": {
"type": "integer",
"minimum": -1000000000,
"maximum": 1000000000
}
},
"divisor_norm": {
"type": "integer",
"minimum": 1,
"maximum": 32768
},
"remainder_norm": {
"type": "integer",
"minimum": 0,
"maximum": 32767
}
},
"required": [
"dividend",
"divisor",
"quotient",
"remainder",
"divisor_norm",
"remainder_norm"
],
"additionalProperties": false
}
}
},
"required": [
"gcd",
"bezout_a",
"bezout_b",
"normalizing_unit",
"trace"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"a",
"b",
"claimed_value"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"a": [
3,
2
],
"b": [
1,
1
],
"claimed_value": {
"gcd": [
1,
0
],
"bezout_a": [
0,
1
],
"bezout_b": [
0,
-3
],
"normalizing_unit": [
0,
1
],
"trace": [
{
"dividend": [
3,
2
],
"divisor": [
1,
1
],
"quotient": [
3,
0
],
"remainder": [
0,
-1
],
"divisor_norm": 2,
"remainder_norm": 1
},
{
"dividend": [
1,
1
],
"divisor": [
0,
-1
],
"quotient": [
-1,
1
],
"remainder": [
0,
0
],
"divisor_norm": 1,
"remainder_norm": 0
}
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-05, 03:23 UTC.
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