@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q743418 rdfs:label "مثمان"@ar,
        "актаніён"@be-tarask,
        "octonió"@ca,
        "oktonion"@cs,
        "Кэли алгебри"@cv,
        "Oktave"@de,
        "οκτόνιο"@el,
        "octonion"@en,
        "octonion"@en-ca,
        "octonion"@en-gb,
        "okopnombro"@eo,
        "octonión"@es,
        "oktonioi"@eu,
        "اکتنیون"@fa,
        "octonion"@fr,
        "octonión"@gl,
        "אוקטוניונים"@he,
        "októniók"@hu,
        "octonion"@ia,
        "oktonion"@id,
        "ottetto"@it,
        "八元数"@ja,
        "팔원수"@ko,
        "numerus octonus"@la,
        "八元數"@lzh,
        "oktonion"@nb,
        "octonion"@nl,
        "oktawy Cayleya"@pl,
        "octoniões"@pt,
        "octônios"@pt-br,
        "octonion"@ro,
        "Алгебра Кэли"@ru,
        "oktonion"@sl,
        "oktonion"@sv,
        "ออกโทเนียน"@th,
        "октоніони"@uk,
        "octonion"@vi,
        "八元數"@yue,
        "八元数"@zh ;
    schema1:dateModified "2026-05-26T04:26:52+00:00"^^xsd:dateTime ;
    schema1:description "non-commutative, non-associative algebra of numbers with eight real components"@en,
        "nekomuta, neasocieca sistemo de nombroj kun ok realnombraj komponantoj"@eo,
        "extensión no asociativa de los números reales"@es,
        "algèbre non commutative et non associative de nombres avec huit composantes réelles"@fr,
        "extensión non asociativa dos cuaternións"@gl,
        "מונח מתמטי"@he,
        "estensione non associativa dei quaternioni"@it,
        "struktura algebraiczna rozszerzająca kwaterniony; ośmiowymiarowa przestrzeń kartezjańska (ℝ⁸) z mnożeniem i dzieleniem wektorów"@pl,
        "álgebra não associativa não comutativa de números com oito componentes reais"@pt,
        "álgebra não associativa não comutativa de números com oito componentes reais"@pt-br,
        "система гиперкомплексных чисел"@ru,
        "四元数的一个非结合推广"@zh ;
    schema1:version 2497650042 ;
    wikibase:identifiers 15 ;
    wikibase:sitelinks 36 ;
    wikibase:statements 38 ;
    skos:altLabel "أوكتونيون"@ar,
        "المثمان"@ar,
        "اوكتونيون"@ar,
        "عدد ثماني مركب"@ar,
        "актава Кэйлея"@be-tarask,
        "Cayley-Zahl"@de,
        "Cayley-Zahlen"@de,
        "Cayleyzahl"@de,
        "Cayleyzahlen"@de,
        "Oktonionen"@de,
        "Cayley number"@en,
        "Cayley numbers"@en,
        "octave"@en,
        "octaves"@en,
        "octonions"@en,
        "nombro de Cayley"@eo,
        "oktoniono"@eo,
        "octonion"@es,
        "nombres de Cayley"@fr,
        "octave"@fr,
        "octaves"@fr,
        "octaves de Cayley"@fr,
        "octonions"@fr,
        "Numeri di Cayley"@it,
        "Numero di Cayley"@it,
        "ottetti"@it,
        "ottetti di Cayley"@it,
        "ottonione"@it,
        "ottonioni"@it,
        "liczby Cayleya"@pl,
        "oktoniony"@pl,
        "8元数"@zh,
        "8元數"@zh,
        "八元數"@zh ;
    p:P10376 wds:Q743418-c3502535-4d3b-ae70-cc2a-df854db92c7e ;
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    p:P7235 wds:Q743418-2fdc688d-442a-bffd-568b-94b77ef2e0b6,
        wds:Q743418-e4791195-4aa8-5ace-4e66-1715c5a8b38c ;
    p:P8189 wds:Q743418-CDD55727-871E-48D6-92E8-E82673D8ADF4 ;
    p:P8885 wds:Q743418-86f0582b-4d69-a74d-0c2c-faac07fc5c1b ;
    p:P910 wds:Q743418-2F62D871-29EE-4CAC-98EA-6E10A8CC7735 ;
    wdtn:P2163 <http://id.worldcat.org/fast/849971> ;
    wdtn:P227 <https://d-nb.info/gnd/4745179-8> ;
    wdtn:P244 <http://id.loc.gov/authorities/names/sh2002008702> ;
    wdtn:P268 <http://data.bnf.fr/ark:/12148/cb15608111r#about> ;
    wdtn:P269 <http://www.idref.fr/122706331/id> ;
    wdtn:P6366 <https://makg.org/entity/2779181008> ;
    wdt:P10376 "mathematics/octonions" ;
    wdt:P13591 "concept/55f53b31-2e07-4558-b872-9767f8de88cc" ;
    wdt:P1482 <https://math.stackexchange.com/tags/octonions>,
        <https://mathoverflow.net/tags/octonions> ;
    wdt:P155 wd:Q173853 ;
    wdt:P156 wd:Q79188 ;
    wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/Octonionstar123.png> ;
    wdt:P2163 "849971" ;
    wdt:P227 "4745179-8" ;
    wdt:P244 "sh2002008702" ;
    wdt:P2534 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mrow data-mjx-texclass=\"ORD\"><mi>𝕆</mi></mrow></mtd><mtd><mo stretchy=\"false\">=</mo><mo fence=\"false\" stretchy=\"false\">{</mo><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>0</mn></mrow></msub><mo stretchy=\"false\">+</mo><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msub><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msub><mo stretchy=\"false\">+</mo><mo stretchy=\"false\">&#x22EF;</mo><mo stretchy=\"false\">+</mo><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>7</mn></mrow></msub><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mn>7</mn></mrow></msub><mspace width=\"0.278em\"></mspace><mo stretchy=\"false\">&#x2223;</mo><mspace width=\"0.278em\"></mspace><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>0</mn></mrow></msub><mo>,</mo><mo stretchy=\"false\">&#x2026;</mo><mo>,</mo><msub><mi>a</mi><mrow data-mjx-texclass=\"ORD\"><mn>7</mn></mrow></msub><mo stretchy=\"false\">&#x2208;</mo><mrow data-mjx-texclass=\"ORD\"><mi>ℝ</mi></mrow><mo fence=\"false\" stretchy=\"false\">}</mo></mtd></mtr><mtr><mtd><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>i</mi></mrow></msub><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>j</mi></mrow></msub></mtd><mtd><mo stretchy=\"false\">=</mo><mo stretchy=\"false\">&#x2212;</mo><msub><mi>&#x03B4;</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i</mi><mi>j</mi></mrow></mrow></msub><mo stretchy=\"false\">+</mo><msub><mi>c</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i</mi><mi>j</mi><mi>k</mi></mrow></mrow></msub><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>c</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i</mi><mi>j</mi><mi>k</mi></mrow></mrow></msub></mtd><mtd><mo stretchy=\"false\">=</mo><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">{</mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left left\"><mtr><mtd><mn>1</mn></mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>even perm. of&#xA0;</mtext></mrow><mn>1</mn><mn>2</mn><mn>3</mn><mo>,</mo><mn>1</mn><mn>4</mn><mn>5</mn><mo>,</mo><mn>1</mn><mn>7</mn><mn>6</mn><mo>,</mo><mn>2</mn><mn>4</mn><mn>6</mn><mo>,</mo><mn>2</mn><mn>5</mn><mn>7</mn><mo>,</mo><mn>3</mn><mn>4</mn><mn>7</mn><mo>,</mo><mn>3</mn><mn>6</mn><mn>5</mn></mtd></mtr><mtr><mtd><mo stretchy=\"false\">&#x2212;</mo><mn>1</mn></mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>odd perm. of&#xA0;</mtext></mrow><mn>1</mn><mn>2</mn><mn>3</mn><mo>,</mo><mn>1</mn><mn>4</mn><mn>5</mn><mo>,</mo><mn>1</mn><mn>7</mn><mn>6</mn><mo>,</mo><mn>2</mn><mn>4</mn><mn>6</mn><mo>,</mo><mn>2</mn><mn>5</mn><mn>7</mn><mo>,</mo><mn>3</mn><mn>4</mn><mn>7</mn><mo>,</mo><mn>3</mn><mn>6</mn><mn>5</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>otherwise</mtext></mrow></mtd></mtr></mtable><mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" data-mjx-texclass=\"CLOSE\"></mo></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P268 "15608111r" ;
    wdt:P269 "122706331" ;
    wdt:P279 wd:Q837414 ;
    wdt:P2812 "CayleyNumber",
        "Octonion" ;
    wdt:P31 wd:Q2165111,
        wd:Q2835924 ;
    wdt:P361 wd:Q2835924 ;
    wdt:P373 "Octonions" ;
    wdt:P4215 "octonion" ;
    wdt:P527 wd:Q173853 ;
    wdt:P5555 <http://commons.wikimedia.org/wiki/Special:FilePath/Octonion-Multiplication-Table.png> ;
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    wdt:P61 wd:Q940427 ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "2779181008" ;
    wdt:P646 "/m/0dkps" ;
    wdt:P6781 "Definition:Octonion" ;
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        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>i</mi></mrow></msub></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P8189 "987007558916605171" ;
    wdt:P8885 "팔원수" ;
    wdt:P910 wd:Q10179671 .