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finite monoid group completion
From a supplied complete1..5element associative commutative monoid table withidentityelement0,construct its Grothendieck group of formal differences. Pair(a,b) is equivalent(c,d) iff some sourceelementt gives(a+d)+t=(c+b)+t. Return every equivalenceclass with all orderedsourcepairs,leastpair representatives,pair-to-class matrix,complete groupaddition,inverses and canonicalsource map a->[a,0]. Classes ordered byleastpair;members lexicographic. Canonicalidentity class0. Noncancellative sources.
POST https://datenvertrag.halowerk.com/v1/finite-monoid-group-completionEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| table | Siehe Schema | Ja | |
| claimed_value | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"table": {
"anyOf": [
{
"type": "array",
"maxItems": 5,
"items": {
"type": "array",
"maxItems": 5,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 4
},
"minItems": 1
},
"minItems": 1
},
{
"type": "null"
}
]
},
"claimed_value": {
"anyOf": [
{
"type": "object",
"properties": {
"source_size": {
"type": "integer",
"minimum": 1,
"maximum": 5
},
"group_size": {
"type": "integer",
"minimum": 1,
"maximum": 25
},
"identity": {
"const": 0
},
"classes": {
"type": "array",
"maxItems": 25,
"items": {
"type": "array",
"maxItems": 25,
"items": {
"type": "array",
"maxItems": 2,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 4
},
"minItems": 2
}
}
},
"representatives": {
"type": "array",
"maxItems": 25,
"items": {
"type": "array",
"maxItems": 2,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 4
},
"minItems": 2
}
},
"pair_classes": {
"type": "array",
"maxItems": 5,
"items": {
"type": "array",
"maxItems": 5,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 24
}
}
},
"addition": {
"type": "array",
"maxItems": 25,
"items": {
"type": "array",
"maxItems": 25,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 24
}
}
},
"inverse": {
"type": "array",
"maxItems": 25,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 24
}
},
"monoid_map": {
"type": "array",
"maxItems": 5,
"items": {
"type": "integer",
"minimum": 0,
"maximum": 24
}
}
},
"required": [
"source_size",
"group_size",
"identity",
"classes",
"representatives",
"pair_classes",
"addition",
"inverse",
"monoid_map"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"table",
"claimed_value"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"table": [
[
0,
1
],
[
1,
0
]
],
"claimed_value": {
"source_size": 2,
"group_size": 2,
"identity": 0,
"classes": [
[
[
0,
0
],
[
1,
1
]
],
[
[
0,
1
],
[
1,
0
]
]
],
"representatives": [
[
0,
0
],
[
0,
1
]
],
"pair_classes": [
[
0,
1
],
[
1,
0
]
],
"addition": [
[
0,
1
],
[
1,
0
]
],
"inverse": [
0,
1
],
"monoid_map": [
0,
1
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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