Zum Inhalt
HALOWERK

Datenvertragswerk

binary polynomial composition split inventory

For a canonical coefficient vector overF2 of degree<=8, enumerate ALL formal polynomial identities f(x)=g(h(x)) with both component degrees>1 and normalized monicinner h(0)=0. Coefficients are constant-first, canonical leading1; zero is[]. Output complete outer/inner coefficientpairs sorted by innerdegree,innerbitmask,outerbitmask, plus count and degree(-1forzero). Include inseparable/wild-characteristic cases; no derivativeinvertibility assumption. This is formal coefficientidentity, not.

POST https://datenvertrag.halowerk.com/v1/binary-polynomial-composition-split-inventory

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
polynomialSiehe SchemaJa
claimSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "$schema": "http://json-schema.org/draft-07/schema#",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "polynomial",
    "claim"
  ],
  "properties": {
    "polynomial": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 9,
          "items": {
            "type": "integer",
            "minimum": 0,
            "maximum": 1
          }
        },
        {
          "type": "null"
        }
      ]
    },
    "claim": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 16,
          "items": {
            "type": "object",
            "additionalProperties": false,
            "required": [
              "outer",
              "inner"
            ],
            "properties": {
              "outer": {
                "type": "array",
                "maxItems": 5,
                "items": {
                  "type": "integer",
                  "minimum": 0,
                  "maximum": 1
                },
                "minItems": 3
              },
              "inner": {
                "type": "array",
                "maxItems": 5,
                "items": {
                  "type": "integer",
                  "minimum": 0,
                  "maximum": 1
                },
                "minItems": 3
              }
            }
          }
        },
        {
          "type": "null"
        }
      ]
    }
  }
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "polynomial": [
    0,
    0,
    1,
    0,
    0,
    0,
    0,
    0,
    1
  ],
  "claim": [
    {
      "outer": [
        0,
        1,
        0,
        0,
        1
      ],
      "inner": [
        0,
        0,
        1
      ]
    },
    {
      "outer": [
        0,
        0,
        1,
        0,
        1
      ],
      "inner": [
        0,
        1,
        1
      ]
    },
    {
      "outer": [
        0,
        0,
        1
      ],
      "inner": [
        0,
        1,
        0,
        0,
        1
      ]
    },
    {
      "outer": [
        0,
        1,
        1
      ],
      "inner": [
        0,
        0,
        1,
        0,
        1
      ]
    }
  ]
}

Ergebnis & Dokumentation

Maschinenlesbare Dokumentation dieses Hubs

Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.

Weitere Endpunkte dieses Hubs

Alle Endpunkte dieses Hubs →