HALOWERKDatenvertragswerk
finite group class sum algebra
For a complete valid1..6element finite group Cayleytable on labels0..n-1 with identity at ANYlabel, derive its integral center basis of conjugacy-class sums and ALL multiplication structure constants c[i][j][k] in Ki*Kj=sum_k c[i][j][k]Kk. Classes/members are ordered by numeric leastlabel/ascendinglabel. Coefficients count pairs with product a FIXED element of outputclass, not totalpairs in that class; equivalently total divided by outputclasssize. Return full classes, coefficientcube,.
POST https://datenvertrag.halowerk.com/v1/finite-group-class-sum-algebraEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| table | Siehe Schema | Ja | |
| claimed_algebra | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"additionalProperties": false,
"required": [
"table",
"claimed_algebra"
],
"properties": {
"table": {
"anyOf": [
{
"type": "array",
"maxItems": 6,
"items": {
"type": "array",
"maxItems": 6,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 5
},
"minItems": 1
},
"minItems": 1
},
{
"type": "null"
}
]
},
"claimed_algebra": {
"anyOf": [
{
"type": "object",
"additionalProperties": false,
"required": [
"classes",
"structure_constants",
"unit_class",
"inversion_classes"
],
"properties": {
"classes": {
"type": "array",
"maxItems": 6,
"items": {
"type": "array",
"maxItems": 6,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 5
}
}
},
"structure_constants": {
"type": "array",
"maxItems": 6,
"items": {
"type": "array",
"maxItems": 6,
"items": {
"type": "array",
"maxItems": 6,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 36
}
}
}
},
"unit_class": {
"type": "integer",
"minimum": 0,
"maximum": 5
},
"inversion_classes": {
"type": "array",
"maxItems": 6,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 5
}
}
}
},
{
"type": "null"
}
]
}
}
}Veröffentlichtes Eingabebeispiel
{
"table": [
[
0,
1,
2,
3,
4,
5
],
[
1,
0,
4,
5,
2,
3
],
[
2,
3,
0,
1,
5,
4
],
[
3,
2,
5,
4,
0,
1
],
[
4,
5,
1,
0,
3,
2
],
[
5,
4,
3,
2,
1,
0
]
],
"claimed_algebra": {
"classes": [
[
0
],
[
1,
2,
5
],
[
3,
4
]
],
"structure_constants": [
[
[
1,
0,
0
],
[
0,
1,
0
],
[
0,
0,
1
]
],
[
[
0,
1,
0
],
[
3,
0,
3
],
[
0,
2,
0
]
],
[
[
0,
0,
1
],
[
0,
2,
0
],
[
2,
0,
1
]
]
],
"unit_class": 0,
"inversion_classes": [
0,
1,
2
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
Weitere Endpunkte dieses Hubs
- Datenvertragswerk0,003 USDC
adjacency cospectral graph family
POSThttps://datenvertrag.halowerk.com/v1/adjacency-cospectral-graph-familyGiven n1..5 and a monic degree-n integer polynomial det(xI-A), return EVERY labelled simple undirected graph on vertices0..n-1 having exactly that adjacency characteristic polynomial over integers. Coefficients are descending degree order,
- Datenvertragswerk0,003 USDC
adjacent swap permutation tour
POSThttps://datenvertrag.halowerk.com/v1/adjacent-swap-permutation-tourFor 0 to 5 labels starting at zero, construct the whole Steinhaus-Johnson-Trotter permutation tour from identity. Each transition swaps the largest mobile value with its adjacent smaller neighbor, then reverses directions of greater values.
- Datenvertragswerk0,003 USDC
aligned record cut audit
POSThttps://datenvertrag.halowerk.com/v1/aligned-record-cut-auditA stream-runtime fixture maintainer checks which record IDs belong to a supplied aligned checkpoint cut and which same-channel post-barrier records must stay buffered until all input barriers arrive. One aligned local checkpoint;record iden