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quadratic surd periodic continued fraction
For the POSITIVE square-root branch value x=(sqrt(d)+p)/q with nonsquare integer d2..31, integer p−2..2 and positive q1..3, reconstruct its canonical regular continued fraction by floor then reciprocal fractionalpart. Return the shortest preperiod, primitive repeating period, period_length, and EVERY rational convergent for the finite digit list preperiod followed by exactly one period. This list need not begin with an integerpart outside the cycle: sqrt(2)+1 is purely periodic [overline2],.
POST https://datenvertrag.halowerk.com/v1/quadratic-surd-periodic-continued-fractionEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| d | Siehe Schema | Ja | |
| p | Siehe Schema | Ja | |
| q | Siehe Schema | Ja | |
| claim | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"d": {
"anyOf": [
{
"type": "integer",
"minimum": 2,
"maximum": 31
},
{
"type": "null"
}
]
},
"p": {
"anyOf": [
{
"type": "integer",
"minimum": -2,
"maximum": 2
},
{
"type": "null"
}
]
},
"q": {
"anyOf": [
{
"type": "integer",
"minimum": 1,
"maximum": 3
},
{
"type": "null"
}
]
},
"claim": {
"anyOf": [
{
"type": "object",
"properties": {
"preperiod": {
"type": "array",
"items": {
"type": "integer",
"minimum": -2,
"maximum": 64
},
"minItems": 0,
"maxItems": 64
},
"period": {
"type": "array",
"items": {
"type": "integer",
"minimum": 1,
"maximum": 64
},
"minItems": 1,
"maxItems": 64
},
"period_length": {
"type": "integer",
"minimum": 0,
"maximum": 64
},
"convergents": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "string",
"minLength": 1,
"maxLength": 64,
"pattern": "^-?[0-9]+$"
},
"minItems": 2,
"maxItems": 2
},
"minItems": 1,
"maxItems": 128
}
},
"required": [
"preperiod",
"period",
"period_length",
"convergents"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"d",
"p",
"q",
"claim"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"d": 2,
"p": 0,
"q": 1,
"claim": {
"preperiod": [
1
],
"period": [
2
],
"period_length": 1,
"convergents": [
[
"1",
"1"
],
[
"3",
"2"
]
]
}
}Ergebnis & Dokumentation
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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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