HALOWERKDatenvertragswerk
ramanujan gcd class projection
For an original period vector length1..12 with integers-16..16 at positions0..n-1, project onto the subspace constant on gcd(position,n) classes. Return every positive divisor q of n in ascending order,phi(q),the whole integer Ramanujan-sum basis row c_q(j), exact reduced rational expansion coefficients, projected vector and residual x-projection, with is_gcd_even iff residualzero. Position0 represents the source period endpoint n. This unshifted divisor basis has dimension tau(n), NOT a.
POST https://datenvertrag.halowerk.com/v1/ramanujan-gcd-class-projectionEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| signal | Siehe Schema | Ja | |
| claimed_transform | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"additionalProperties": false,
"required": [
"signal",
"claimed_transform"
],
"properties": {
"signal": {
"anyOf": [
{
"type": "array",
"maxItems": 12,
"items": {
"type": "integer",
"minimum": -16,
"maximum": 16
},
"minItems": 1
},
{
"type": "null"
}
]
},
"claimed_transform": {
"anyOf": [
{
"type": "object",
"additionalProperties": false,
"required": [
"coefficients",
"projected",
"residual"
],
"properties": {
"coefficients": {
"type": "array",
"maxItems": 12,
"items": {
"type": "object",
"additionalProperties": false,
"required": [
"num",
"den"
],
"properties": {
"num": {
"type": "integer",
"minimum": -100000,
"maximum": 100000
},
"den": {
"type": "integer",
"minimum": 1,
"maximum": 100000
}
}
}
},
"projected": {
"type": "array",
"maxItems": 12,
"items": {
"type": "object",
"additionalProperties": false,
"required": [
"num",
"den"
],
"properties": {
"num": {
"type": "integer",
"minimum": -100000,
"maximum": 100000
},
"den": {
"type": "integer",
"minimum": 1,
"maximum": 100000
}
}
}
},
"residual": {
"type": "array",
"maxItems": 12,
"items": {
"type": "object",
"additionalProperties": false,
"required": [
"num",
"den"
],
"properties": {
"num": {
"type": "integer",
"minimum": -100000,
"maximum": 100000
},
"den": {
"type": "integer",
"minimum": 1,
"maximum": 100000
}
}
}
}
}
},
{
"type": "null"
}
]
}
}
}Veröffentlichtes Eingabebeispiel
{
"signal": [
2,
-1,
5,
3,
0,
4
],
"claimed_transform": {
"coefficients": [
{
"num": 13,
"den": 6
},
{
"num": 1,
"den": 6
},
{
"num": 1,
"den": 6
},
{
"num": -1,
"den": 3
}
],
"projected": [
{
"num": 2,
"den": 1
},
{
"num": 3,
"den": 2
},
{
"num": 5,
"den": 2
},
{
"num": 3,
"den": 1
},
{
"num": 5,
"den": 2
},
{
"num": 3,
"den": 2
}
],
"residual": [
{
"num": 0,
"den": 1
},
{
"num": -5,
"den": 2
},
{
"num": 5,
"den": 2
},
{
"num": 0,
"den": 1
},
{
"num": -5,
"den": 2
},
{
"num": 5,
"den": 2
}
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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