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two square lattice shell inventory

For an integer norm from 0 to 1024, return every ordered signed integer pair (x,y) satisfying x*x+y*y=norm, sorted by x then y. Partition points by sign changes and coordinate exchange, with canonical nonnegative representative a<=b; return each full orbit, coordinate gcd and primitive flag(gcd=1), and total/primitive point counts. Zero has exactly point(0,0), gcd0 and nonprimitive flag. A norm with no representation has a known empty shell. Compare the entire ordered canonical signed point.

POST https://datenvertrag.halowerk.com/v1/two-square-lattice-shell-inventory

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
normSiehe SchemaJa
claimed_pointsSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "$schema": "http://json-schema.org/draft-07/schema#",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "norm",
    "claimed_points"
  ],
  "properties": {
    "norm": {
      "anyOf": [
        {
          "type": "integer",
          "minimum": 0,
          "maximum": 1024
        },
        {
          "type": "null"
        }
      ]
    },
    "claimed_points": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 24,
          "items": {
            "type": "array",
            "minItems": 2,
            "maxItems": 2,
            "items": {
              "type": "integer",
              "minimum": -32,
              "maximum": 32
            }
          }
        },
        {
          "type": "null"
        }
      ]
    }
  }
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "norm": 325,
  "claimed_points": [
    [
      -18,
      -1
    ],
    [
      -18,
      1
    ],
    [
      -17,
      -6
    ],
    [
      -17,
      6
    ],
    [
      -15,
      -10
    ],
    [
      -15,
      10
    ],
    [
      -10,
      -15
    ],
    [
      -10,
      15
    ],
    [
      -6,
      -17
    ],
    [
      -6,
      17
    ],
    [
      -1,
      -18
    ],
    [
      -1,
      18
    ],
    [
      1,
      -18
    ],
    [
      1,
      18
    ],
    [
      6,
      -17
    ],
    [
      6,
      17
    ],
    [
      10,
      -15
    ],
    [
      10,
      15
    ],
    [
      15,
      -10
    ],
    [
      15,
      10
    ],
    [
      17,
      -6
    ],
    [
      17,
      6
    ],
    [
      18,
      -1
    ],
    [
      18,
      1
    ]
  ]
}

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

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