"homogeneous" meaning in All languages combined

See homogeneous on Wiktionary

Adjective [English]

IPA: /ˌhɒ.mə(ʊ)ˈd͡ʒiː.nɪəs/ [UK], /ˌhəʊ.mə(ʊ)ˈd͡ʒiː.nɪəs/ [UK], /ˌhoʊ.moʊˈd͡ʒiː.njəs/ [US], /ˌhoʊ.məˈd͡ʒiː.njəs/ [US], /ˌhoʊ.moʊˈd͡ʒɛ.njəs/ [US], /həˈmɑ.d͡ʒə.nəs/ [US] Audio: En-uk-homogeneous.ogg Forms: homogenous [alternative]
Etymology: From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix). Etymology templates: {{der|en|ML.|homogeneus}} Medieval Latin homogeneus, {{der|en|grc|ὁμογενής||of the same race, family or kind}} Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”) Head templates: {{en-adj|-}} homogeneous (not comparable)
  1. Of the same kind; alike, similar. Tags: not-comparable Translations (of the same kind; alike, similar): homogeen (Afrikaans), homogjen (Albanian), միատարր (miatarr) (Armenian), համասեռ (hamaseṙ) (Armenian), еднороден (ednoroden) (Bulgarian), homogeni (Catalan), 同質 /同质 (tóngzhí, tóngzhì) (Chinese Mandarin), stejnorodý (Czech), homogenní (Czech), homogeen (Dutch), samanlainen (Finnish), homogeeninen (Finnish), homogène (French), homoxéneo (Galician), homogen (German), gleichartig (German), ομογενής (omogenís) (Greek), ομοιογενής (omoiogenís) (Greek), homogén (Hungarian), einsleitur (Icelandic), einleitur (Icelandic), eingerður (Icelandic), samkynja (Icelandic), samleitur (Icelandic), aonchineálach (Irish), omogeneo (Italian), 均質 (kinshitsu) (alt: きんしつ) (Japanese), 同質 (dōshitsu) (alt: どうしつ) (Japanese), гомогендік (gomogendık) (Kazakh), біртекті (bırtektı) (Kazakh), еднообразен (ednoobrazen) (Macedonian), еднороден (ednoroden) (Macedonian), хомоген (homogen) (Macedonian), cocheintagh (Manx), homogen (Norwegian Bokmål), homogen (Norwegian Nynorsk), jednorodny (Polish), jednolity (Polish), homogêneo (Portuguese), homogéneo (Portuguese), omogen (Romanian), одноро́дный (odnoródnyj) (Russian), гомоге́нный (gomogénnyj) (Russian), единообра́зный (jedinoobráznyj) (Russian), homogéneo (Spanish), homogen (Swedish), enhetlig (Swedish), tulad-uriin (Tagalog), సజాతి (sajāti) (Telugu)
    Sense id: en-homogeneous-en-adj-rBYmedCj Disambiguation of 'of the same kind; alike, similar': 38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0
  2. Having the same composition throughout; of uniform make-up. Tags: not-comparable Translations (having the same composition throughout): համասեռ (hamaseṙ) (Armenian), еднороден (ednoroden) (Bulgarian), хомогенен (homogenen) (Bulgarian), homogeni (Catalan), tasa-aineinen (Finnish), homogeeninen (Finnish), homogène (French), omogeneo (Italian), еднороден (ednoroden) (Macedonian), еднообразен (ednoobrazen) (Macedonian), хомоген (homogen) (Macedonian), kanorite (Maori), هملوناء (Persian), homogêneo (Portuguese), homogéneo (Spanish), homogen (Swedish), tulad-uriin (Tagalog)
    Sense id: en-homogeneous-en-adj-6oN~FP6g Disambiguation of 'having the same composition throughout': 9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1
  3. (chemistry) In the same state of matter. Tags: not-comparable
    Sense id: en-homogeneous-en-adj-1v2Brlrf Categories (other): Chemistry Topics: chemistry, natural-sciences, physical-sciences
  4. (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.). Tags: not-comparable
    Sense id: en-homogeneous-en-adj-pg-jzEKx Categories (other): Mathematics Topics: mathematics, sciences
  5. (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
    Of polynomials, functions, equations, systems of equations, or linear maps:
    (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-6x8KOypq Categories (other): Algebra, Mathematics, English terms prefixed with homo-, Pages with 1 entry, Systems theory Disambiguation of English terms prefixed with homo-: 2 3 4 4 11 12 6 4 6 9 5 6 5 5 6 7 4 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Systems theory: 1 2 1 3 16 16 16 2 7 7 7 2 2 3 7 7 3 Topics: algebra, mathematics, sciences
  6. (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
    Of polynomials, functions, equations, systems of equations, or linear maps:
    (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj--KhrxETj Categories (other): Linear algebra, Mathematics, English terms prefixed with homo-, Pages with 1 entry, Systems theory Disambiguation of English terms prefixed with homo-: 2 3 4 4 11 12 6 4 6 9 5 6 5 5 6 7 4 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Systems theory: 1 2 1 3 16 16 16 2 7 7 7 2 2 3 7 7 3 Topics: linear-algebra, mathematics, sciences
  7. (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
    Of polynomials, functions, equations, systems of equations, or linear maps:
    (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-vmGi20zg Categories (other): Mathematical analysis, Mathematics, Pages with 1 entry, Systems theory Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Systems theory: 1 2 1 3 16 16 16 2 7 7 7 2 2 3 7 7 3 Topics: mathematical-analysis, mathematics, sciences
  8. The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;. Tags: not-comparable
    Sense id: en-homogeneous-en-adj-NRlnDRwH
  9. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
    (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-gAQ5SM9E Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Terms with Norwegian Nynorsk translations Disambiguation of English entries with incorrect language header: 0 2 3 3 9 9 9 3 10 10 10 4 2 4 10 9 3 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Pages with entries: 0 2 2 3 9 9 9 3 11 11 11 3 2 3 11 10 3 Disambiguation of Terms with Norwegian Nynorsk translations: 0 1 2 2 9 9 9 3 10 10 10 3 2 3 10 12 4
  10. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
    (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj--vq~tX75 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Terms with Norwegian Nynorsk translations Disambiguation of English entries with incorrect language header: 0 2 3 3 9 9 9 3 10 10 10 4 2 4 10 9 3 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Pages with entries: 0 2 2 3 9 9 9 3 11 11 11 3 2 3 11 10 3 Disambiguation of Terms with Norwegian Nynorsk translations: 0 1 2 2 9 9 9 3 10 10 10 3 2 3 10 12 4
  11. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
    (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-3QKIWMZI Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Terms with Norwegian Nynorsk translations Disambiguation of English entries with incorrect language header: 0 2 3 3 9 9 9 3 10 10 10 4 2 4 10 9 3 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Pages with entries: 0 2 2 3 9 9 9 3 11 11 11 3 2 3 11 10 3 Disambiguation of Terms with Norwegian Nynorsk translations: 0 1 2 2 9 9 9 3 10 10 10 3 2 3 10 12 4
  12. In abstract algebra and geometry:
    (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-x7YC8KG4 Categories (other): Algebra
  13. In abstract algebra and geometry:
    (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-XvwXesgq
  14. In abstract algebra and geometry:
    (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-No2MKDN5 Categories (other): Geometry Topics: geometry, mathematics, sciences
  15. In abstract algebra and geometry:
    (geometry) Of or relating to homogeneous coordinates.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-U6d14Ipd Categories (other): Geometry, English entries with incorrect language header, Pages with 1 entry, Pages with entries, Terms with Norwegian Nynorsk translations Disambiguation of English entries with incorrect language header: 0 2 3 3 9 9 9 3 10 10 10 4 2 4 10 9 3 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Pages with entries: 0 2 2 3 9 9 9 3 11 11 11 3 2 3 11 10 3 Disambiguation of Terms with Norwegian Nynorsk translations: 0 1 2 2 9 9 9 3 10 10 10 3 2 3 10 12 4 Topics: geometry, mathematics, sciences
  16. In miscellaneous other senses:
    (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-3tyMqrt- Categories (other): Probability theory, English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Afrikaans translations, Terms with Albanian translations, Terms with Arabic translations, Terms with Armenian translations, Terms with Bulgarian translations, Terms with Catalan translations, Terms with Czech translations, Terms with Dutch translations, Terms with Finnish translations, Terms with French translations, Terms with Galician translations, Terms with German translations, Terms with Greek translations, Terms with Hungarian translations, Terms with Icelandic translations, Terms with Irish translations, Terms with Italian translations, Terms with Japanese translations, Terms with Kazakh translations, Terms with Macedonian translations, Terms with Mandarin translations, Terms with Manx translations, Terms with Maori translations, Terms with Norwegian Bokmål translations, Terms with Norwegian Nynorsk translations, Terms with Persian translations, Terms with Polish translations, Terms with Portuguese translations, Terms with Romanian translations, Terms with Russian translations, Terms with Spanish translations, Terms with Swedish translations, Terms with Tagalog translations, Terms with Telugu translations, Terms with Urdu translations Disambiguation of English entries with incorrect language header: 0 2 3 3 9 9 9 3 10 10 10 4 2 4 10 9 3 Disambiguation of Entries with translation boxes: 0 2 2 2 7 7 10 2 8 8 8 6 2 6 8 19 3 Disambiguation of Pages with 1 entry: 1 1 3 2 9 10 9 4 10 10 10 4 2 3 10 9 4 Disambiguation of Pages with entries: 0 2 2 3 9 9 9 3 11 11 11 3 2 3 11 10 3 Disambiguation of Terms with Afrikaans translations: 1 2 3 3 7 7 8 3 8 9 8 5 3 5 9 13 5 Disambiguation of Terms with Albanian translations: 1 2 3 3 7 7 8 3 8 9 8 5 3 5 9 13 5 Disambiguation of Terms with Arabic translations: 1 2 3 4 7 7 9 3 7 8 7 5 4 5 8 12 5 Disambiguation of Terms with Armenian translations: 1 2 3 3 7 7 8 3 8 9 8 5 3 5 9 13 5 Disambiguation of Terms with Bulgarian translations: 1 3 3 3 7 7 9 3 8 9 8 5 3 5 9 13 4 Disambiguation of Terms with Catalan translations: 1 2 3 3 7 7 8 3 8 8 8 5 3 5 8 13 5 Disambiguation of Terms with Czech translations: 1 2 3 3 7 7 9 3 8 9 8 6 3 5 8 13 5 Disambiguation of Terms with Dutch translations: 0 2 3 3 7 8 10 3 8 8 8 5 3 5 9 14 4 Disambiguation of Terms with Finnish translations: 1 2 3 3 7 7 9 3 8 8 8 6 3 5 9 13 4 Disambiguation of Terms with French translations: 0 3 3 3 7 7 8 3 8 9 8 5 3 5 9 15 4 Disambiguation of Terms with Galician translations: 1 2 3 3 7 7 8 3 8 8 8 5 3 6 9 14 4 Disambiguation of Terms with German translations: 1 2 3 3 7 7 8 3 8 8 8 6 3 5 8 16 4 Disambiguation of Terms with Greek translations: 1 3 7 6 7 7 8 3 6 8 6 8 3 6 7 11 4 Disambiguation of Terms with Hungarian translations: 1 3 6 5 7 7 7 3 6 9 6 8 3 6 7 11 4 Disambiguation of Terms with Icelandic translations: 1 2 3 3 7 7 9 3 8 8 8 5 3 5 9 13 5 Disambiguation of Terms with Irish translations: 1 2 3 3 7 7 8 4 8 8 8 5 3 5 8 13 5 Disambiguation of Terms with Italian translations: 1 3 3 4 7 7 8 3 8 8 8 5 3 5 8 14 4 Disambiguation of Terms with Japanese translations: 1 2 3 3 7 7 9 3 8 9 8 5 3 5 8 13 5 Disambiguation of Terms with Kazakh translations: 1 2 3 3 7 7 8 3 8 9 8 5 3 5 9 13 5 Disambiguation of Terms with Macedonian translations: 1 2 3 3 7 7 8 3 8 10 8 5 3 5 9 13 4 Disambiguation of Terms with Mandarin translations: 1 3 5 4 7 7 8 3 8 8 8 7 3 5 8 12 4 Disambiguation of Terms with Manx translations: 1 2 3 3 7 7 8 3 8 8 8 5 3 5 9 13 5 Disambiguation of Terms with Maori translations: 1 2 3 3 7 7 8 3 8 8 8 5 3 5 9 13 5 Disambiguation of Terms with Norwegian Bokmål translations: 1 3 3 3 7 7 8 3 8 8 8 6 3 5 9 13 4 Disambiguation of Terms with Norwegian Nynorsk translations: 0 1 2 2 9 9 9 3 10 10 10 3 2 3 10 12 4 Disambiguation of Terms with Persian translations: 1 2 3 3 7 7 8 3 8 9 8 5 3 5 9 13 5 Disambiguation of Terms with Polish translations: 1 3 3 3 7 7 9 3 8 8 8 6 3 5 9 13 4 Disambiguation of Terms with Portuguese translations: 1 2 3 3 7 7 8 3 8 9 8 5 3 5 8 14 5 Disambiguation of Terms with Romanian translations: 1 2 3 3 7 7 9 3 8 8 8 5 3 5 9 13 4 Disambiguation of Terms with Russian translations: 0 2 2 3 7 7 10 2 8 9 8 7 3 4 9 14 3 Disambiguation of Terms with Spanish translations: 0 2 2 3 8 8 9 3 9 9 9 4 3 5 9 13 3 Disambiguation of Terms with Swedish translations: 1 2 3 3 7 7 8 3 8 8 8 5 3 5 9 13 5 Disambiguation of Terms with Tagalog translations: 1 2 3 3 7 7 8 3 8 8 8 6 3 5 9 13 5 Disambiguation of Terms with Telugu translations: 0 2 2 3 7 8 9 3 8 9 8 5 3 5 9 14 5 Disambiguation of Terms with Urdu translations: 1 2 3 3 7 7 8 3 8 8 8 5 3 5 9 13 5 Topics: mathematics, probability-theory, sciences
  17. In miscellaneous other senses:
    (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
    Tags: not-comparable
    Sense id: en-homogeneous-en-adj-wwS6Tg4L Categories (other): Set theory Topics: mathematics, order-theory, sciences, set-theory
The following are not (yet) sense-disambiguated
Synonyms: homogeneous, invariable, of a piece [idiomatic], onefold, samely [dialectal], uniform, uniformal [obsolete], unmixed, unvaried, unvarying Hyponyms: connatural, monolithic [figuratively], monotone, steady, unalloyed Related terms: homogeneity, homogenesis, homogenise, homogenize, homogeny

Alternative forms

{
  "antonyms": [
    {
      "word": "heterogeneous"
    },
    {
      "word": "inhomogeneous"
    }
  ],
  "derived": [
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "bihomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "dishomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous broadening"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous catalysis"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous coordinate"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous equilibrium"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous function"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous ideal"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneously"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous mixture"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneousness"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous number"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous polynomial"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous radiation"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous society"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous space"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous system"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneous width"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "inhomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "nonhomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "prehomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "quasihomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "subhomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "superhomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "time-homogeneous Markovian type"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "ultrahomogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "unhomogeneous"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "ML.",
        "3": "homogeneus"
      },
      "expansion": "Medieval Latin homogeneus",
      "name": "der"
    },
    {
      "args": {
        "1": "en",
        "2": "grc",
        "3": "ὁμογενής",
        "4": "",
        "5": "of the same race, family or kind"
      },
      "expansion": "Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”)",
      "name": "der"
    }
  ],
  "etymology_text": "From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).",
  "forms": [
    {
      "form": "homogenous",
      "tags": [
        "alternative"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "homogeneous (not comparable)",
      "name": "en-adj"
    }
  ],
  "hyponyms": [
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "connatural"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "tags": [
        "figuratively"
      ],
      "word": "monolithic"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "monotone"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "steady"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "unalloyed"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeneity"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogenesis"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogenise"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogenize"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "word": "homogeny"
    }
  ],
  "senses": [
    {
      "glosses": [
        "Of the same kind; alike, similar."
      ],
      "id": "en-homogeneous-en-adj-rBYmedCj",
      "links": [
        [
          "alike",
          "alike"
        ],
        [
          "similar",
          "similar"
        ]
      ],
      "tags": [
        "not-comparable"
      ],
      "translations": [
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "af",
          "lang": "Afrikaans",
          "sense": "of the same kind; alike, similar",
          "word": "homogeen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "sq",
          "lang": "Albanian",
          "sense": "of the same kind; alike, similar",
          "word": "homogjen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "hy",
          "lang": "Armenian",
          "roman": "miatarr",
          "sense": "of the same kind; alike, similar",
          "word": "միատարր"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "hy",
          "lang": "Armenian",
          "roman": "hamaseṙ",
          "sense": "of the same kind; alike, similar",
          "word": "համասեռ"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "bg",
          "lang": "Bulgarian",
          "roman": "ednoroden",
          "sense": "of the same kind; alike, similar",
          "word": "еднороден"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "ca",
          "lang": "Catalan",
          "sense": "of the same kind; alike, similar",
          "word": "homogeni"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "tóngzhí, tóngzhì",
          "sense": "of the same kind; alike, similar",
          "word": "同質 /同质"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "cs",
          "lang": "Czech",
          "sense": "of the same kind; alike, similar",
          "word": "stejnorodý"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "cs",
          "lang": "Czech",
          "sense": "of the same kind; alike, similar",
          "word": "homogenní"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "nl",
          "lang": "Dutch",
          "sense": "of the same kind; alike, similar",
          "word": "homogeen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "fi",
          "lang": "Finnish",
          "sense": "of the same kind; alike, similar",
          "word": "samanlainen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "fi",
          "lang": "Finnish",
          "sense": "of the same kind; alike, similar",
          "word": "homogeeninen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "fr",
          "lang": "French",
          "sense": "of the same kind; alike, similar",
          "word": "homogène"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "gl",
          "lang": "Galician",
          "sense": "of the same kind; alike, similar",
          "word": "homoxéneo"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "de",
          "lang": "German",
          "sense": "of the same kind; alike, similar",
          "word": "homogen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "de",
          "lang": "German",
          "sense": "of the same kind; alike, similar",
          "word": "gleichartig"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "el",
          "lang": "Greek",
          "roman": "omogenís",
          "sense": "of the same kind; alike, similar",
          "word": "ομογενής"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "el",
          "lang": "Greek",
          "roman": "omoiogenís",
          "sense": "of the same kind; alike, similar",
          "word": "ομοιογενής"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "hu",
          "lang": "Hungarian",
          "sense": "of the same kind; alike, similar",
          "word": "homogén"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "is",
          "lang": "Icelandic",
          "sense": "of the same kind; alike, similar",
          "word": "einsleitur"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "is",
          "lang": "Icelandic",
          "sense": "of the same kind; alike, similar",
          "word": "einleitur"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "is",
          "lang": "Icelandic",
          "sense": "of the same kind; alike, similar",
          "word": "eingerður"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "is",
          "lang": "Icelandic",
          "sense": "of the same kind; alike, similar",
          "word": "samkynja"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "is",
          "lang": "Icelandic",
          "sense": "of the same kind; alike, similar",
          "word": "samleitur"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "ga",
          "lang": "Irish",
          "sense": "of the same kind; alike, similar",
          "word": "aonchineálach"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "it",
          "lang": "Italian",
          "sense": "of the same kind; alike, similar",
          "word": "omogeneo"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "alt": "きんしつ",
          "code": "ja",
          "lang": "Japanese",
          "roman": "kinshitsu",
          "sense": "of the same kind; alike, similar",
          "word": "均質"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "alt": "どうしつ",
          "code": "ja",
          "lang": "Japanese",
          "roman": "dōshitsu",
          "sense": "of the same kind; alike, similar",
          "word": "同質"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "kk",
          "lang": "Kazakh",
          "roman": "gomogendık",
          "sense": "of the same kind; alike, similar",
          "word": "гомогендік"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "kk",
          "lang": "Kazakh",
          "roman": "bırtektı",
          "sense": "of the same kind; alike, similar",
          "word": "біртекті"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "mk",
          "lang": "Macedonian",
          "roman": "ednoobrazen",
          "sense": "of the same kind; alike, similar",
          "word": "еднообразен"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "mk",
          "lang": "Macedonian",
          "roman": "ednoroden",
          "sense": "of the same kind; alike, similar",
          "word": "еднороден"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "mk",
          "lang": "Macedonian",
          "roman": "homogen",
          "sense": "of the same kind; alike, similar",
          "word": "хомоген"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "gv",
          "lang": "Manx",
          "sense": "of the same kind; alike, similar",
          "word": "cocheintagh"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "nb",
          "lang": "Norwegian Bokmål",
          "sense": "of the same kind; alike, similar",
          "word": "homogen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "nn",
          "lang": "Norwegian Nynorsk",
          "sense": "of the same kind; alike, similar",
          "word": "homogen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "pl",
          "lang": "Polish",
          "sense": "of the same kind; alike, similar",
          "word": "jednorodny"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "pl",
          "lang": "Polish",
          "sense": "of the same kind; alike, similar",
          "word": "jednolity"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "of the same kind; alike, similar",
          "word": "homogêneo"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "of the same kind; alike, similar",
          "word": "homogéneo"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "ro",
          "lang": "Romanian",
          "sense": "of the same kind; alike, similar",
          "word": "omogen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "ru",
          "lang": "Russian",
          "roman": "odnoródnyj",
          "sense": "of the same kind; alike, similar",
          "word": "одноро́дный"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "ru",
          "lang": "Russian",
          "roman": "gomogénnyj",
          "sense": "of the same kind; alike, similar",
          "word": "гомоге́нный"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "ru",
          "lang": "Russian",
          "roman": "jedinoobráznyj",
          "sense": "of the same kind; alike, similar",
          "word": "единообра́зный"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "es",
          "lang": "Spanish",
          "sense": "of the same kind; alike, similar",
          "word": "homogéneo"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "sv",
          "lang": "Swedish",
          "sense": "of the same kind; alike, similar",
          "word": "homogen"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "sv",
          "lang": "Swedish",
          "sense": "of the same kind; alike, similar",
          "word": "enhetlig"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "tl",
          "lang": "Tagalog",
          "sense": "of the same kind; alike, similar",
          "word": "tulad-uriin"
        },
        {
          "_dis1": "38 8 9 6 6 6 6 1 4 1 0 0 0 10 0 1 0",
          "code": "te",
          "lang": "Telugu",
          "roman": "sajāti",
          "sense": "of the same kind; alike, similar",
          "word": "సజాతి"
        }
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          "ref": "1946, Bertrand Russell, History of Western Philosophy, I.25:",
          "text": "Their citizens were not of homogeneous origin, but were from all parts of Greece.",
          "type": "quote"
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          "ref": "2013 October 14, Jirapornchai Suksaeree, Laksana Charoenchai, Chaowalit Monton, Tun Chusut, Apirak Sakunpak, Wiwat Pichayakorn and Prapaporn Boonme, “Preparation of a Pseudolatex-Membrane for Ketoprofen Transdermal Drug Delivery Systems”, in Industrial & Engineering Chemistry Research, volume 52, number 45, →DOI:",
          "text": "All pseudolatex formulations were homogeneous and smooth in texture and elegant in appearance.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Having the same composition throughout; of uniform make-up."
      ],
      "id": "en-homogeneous-en-adj-6oN~FP6g",
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      "tags": [
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      "translations": [
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "hy",
          "lang": "Armenian",
          "roman": "hamaseṙ",
          "sense": "having the same composition throughout",
          "word": "համասեռ"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "bg",
          "lang": "Bulgarian",
          "roman": "ednoroden",
          "sense": "having the same composition throughout",
          "word": "еднороден"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "bg",
          "lang": "Bulgarian",
          "roman": "homogenen",
          "sense": "having the same composition throughout",
          "word": "хомогенен"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "ca",
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          "sense": "having the same composition throughout",
          "word": "homogeni"
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          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
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          "lang": "Finnish",
          "sense": "having the same composition throughout",
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        },
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          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "fi",
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          "sense": "having the same composition throughout",
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        },
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          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
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          "lang": "French",
          "sense": "having the same composition throughout",
          "word": "homogène"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "it",
          "lang": "Italian",
          "sense": "having the same composition throughout",
          "word": "omogeneo"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "mk",
          "lang": "Macedonian",
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          "sense": "having the same composition throughout",
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        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
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          "lang": "Macedonian",
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          "sense": "having the same composition throughout",
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        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "mk",
          "lang": "Macedonian",
          "roman": "homogen",
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        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "mi",
          "lang": "Maori",
          "sense": "having the same composition throughout",
          "word": "kanorite"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "fa",
          "lang": "Persian",
          "sense": "having the same composition throughout",
          "word": "هملوناء"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "having the same composition throughout",
          "word": "homogêneo"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "es",
          "lang": "Spanish",
          "sense": "having the same composition throughout",
          "word": "homogéneo"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "sv",
          "lang": "Swedish",
          "sense": "having the same composition throughout",
          "word": "homogen"
        },
        {
          "_dis1": "9 27 10 8 8 8 8 1 5 2 0 1 1 11 0 1 1",
          "code": "tl",
          "lang": "Tagalog",
          "sense": "having the same composition throughout",
          "word": "tulad-uriin"
        }
      ]
    },
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          "name": "Chemistry",
          "orig": "en:Chemistry",
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      "glosses": [
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          "chemistry"
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          "state of matter"
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      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "chemistry",
        "natural-sciences",
        "physical-sciences"
      ]
    },
    {
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        {
          "kind": "other",
          "langcode": "en",
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          "orig": "en:Mathematics",
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        }
      ],
      "glosses": [
        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.)."
      ],
      "id": "en-homogeneous-en-adj-pg-jzEKx",
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      "raw_glosses": [
        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.)."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
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      ]
    },
    {
      "categories": [
        {
          "kind": "other",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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      ],
      "examples": [
        {
          "text": "The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials"
        }
      ],
      "glosses": [
        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "Such that all its nonzero terms have the same degree."
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      "id": "en-homogeneous-en-adj-6x8KOypq",
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      "raw_glosses": [
        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "(algebra, of a polynomial) Such that all its nonzero terms have the same degree."
      ],
      "raw_tags": [
        "of a polynomial"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
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        "mathematics",
        "sciences"
      ]
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      "glosses": [
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        "Of polynomials, functions, equations, systems of equations, or linear maps:",
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        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
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        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ("
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        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "(mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ("
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        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
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          "first-order"
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          "differential equation"
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        "(of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other."
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      "glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "Having its degree-zero term equal to zero; admitting the trivial solution."
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        "(of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution."
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        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
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        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "(of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives."
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      "glosses": [
        "In abstract algebra and geometry:",
        "Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
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          "ring theory"
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          "monoid"
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        "(ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
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        "Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
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        [
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        [
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          "linear"
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        [
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          "map"
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        [
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          "vector spaces"
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        [
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          "grading"
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        [
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          "commutative"
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          "monoid"
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        "(of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
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          "orig": "en:Geometry",
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      "glosses": [
        "In abstract algebra and geometry:",
        "Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
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        [
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        [
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          "geometry"
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        [
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          "space"
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        [
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          "group action"
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          "point"
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        [
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          "transitively"
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        [
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          "automorphism"
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        [
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          "faithful"
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      "raw_glosses": [
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        "(geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
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        "mathematics",
        "sciences"
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          "name": "Terms with Polish translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "1 2 3 3 7 7 8 3 8 9 8 5 3 5 8 14 5",
          "kind": "other",
          "name": "Terms with Portuguese translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "1 2 3 3 7 7 9 3 8 8 8 5 3 5 9 13 4",
          "kind": "other",
          "name": "Terms with Romanian translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "0 2 2 3 7 7 10 2 8 9 8 7 3 4 9 14 3",
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "0 2 2 3 8 8 9 3 9 9 9 4 3 5 9 13 3",
          "kind": "other",
          "name": "Terms with Spanish translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "1 2 3 3 7 7 8 3 8 8 8 5 3 5 9 13 5",
          "kind": "other",
          "name": "Terms with Swedish translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "1 2 3 3 7 7 8 3 8 8 8 6 3 5 9 13 5",
          "kind": "other",
          "name": "Terms with Tagalog translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "0 2 2 3 7 8 9 3 8 9 8 5 3 5 9 14 5",
          "kind": "other",
          "name": "Terms with Telugu translations",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "1 2 3 3 7 7 8 3 8 8 8 5 3 5 9 13 5",
          "kind": "other",
          "name": "Terms with Urdu translations",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "In miscellaneous other senses:",
        "Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
      ],
      "id": "en-homogeneous-en-adj-3tyMqrt-",
      "links": [
        [
          "probability theory",
          "probability theory"
        ],
        [
          "Fourier analysis",
          "Fourier analysis"
        ],
        [
          "distribution",
          "distribution"
        ],
        [
          "Euclidean",
          "Euclidean"
        ],
        [
          "test function",
          "test function"
        ]
      ],
      "qualifier": "Fourier analysis",
      "raw_glosses": [
        "In miscellaneous other senses:",
        "(probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
      ],
      "raw_tags": [
        "of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "other",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "In miscellaneous other senses:",
        "Holding between a set and itself; being an endorelation."
      ],
      "id": "en-homogeneous-en-adj-wwS6Tg4L",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "order theory",
          "order theory"
        ],
        [
          "relation",
          "relation"
        ],
        [
          "set",
          "set"
        ],
        [
          "endorelation",
          "endorelation"
        ]
      ],
      "raw_glosses": [
        "In miscellaneous other senses:",
        "(set theory, order theory, of a relation) Holding between a set and itself; being an endorelation."
      ],
      "raw_tags": [
        "of a relation"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˌhɒ.mə(ʊ)ˈd͡ʒiː.nɪəs/",
      "tags": [
        "UK"
      ]
    },
    {
      "ipa": "/ˌhəʊ.mə(ʊ)ˈd͡ʒiː.nɪəs/",
      "tags": [
        "UK"
      ]
    },
    {
      "ipa": "/ˌhoʊ.moʊˈd͡ʒiː.njəs/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/ˌhoʊ.məˈd͡ʒiː.njəs/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/ˌhoʊ.moʊˈd͡ʒɛ.njəs/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/həˈmɑ.d͡ʒə.nəs/",
      "tags": [
        "US"
      ]
    },
    {
      "audio": "En-uk-homogeneous.ogg",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/4/41/En-uk-homogeneous.ogg/En-uk-homogeneous.ogg.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/4/41/En-uk-homogeneous.ogg"
    }
  ],
  "synonyms": [
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "homogeneous"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "invariable"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "tags": [
        "idiomatic"
      ],
      "word": "of a piece"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "onefold"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "tags": [
        "dialectal"
      ],
      "word": "samely"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "uniform"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "tags": [
        "obsolete"
      ],
      "word": "uniformal"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "unmixed"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "unvaried"
    },
    {
      "_dis1": "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
      "source": "Thesaurus:homogeneous",
      "word": "unvarying"
    }
  ],
  "word": "homogeneous"
}
{
  "antonyms": [
    {
      "word": "heterogeneous"
    },
    {
      "word": "inhomogeneous"
    }
  ],
  "categories": [
    "English adjectives",
    "English entries with incorrect language header",
    "English lemmas",
    "English terms derived from Ancient Greek",
    "English terms derived from Medieval Latin",
    "English terms prefixed with homo-",
    "English uncomparable adjectives",
    "Entries with translation boxes",
    "Pages with 1 entry",
    "Pages with entries",
    "Requests for review of Arabic translations",
    "Requests for review of Urdu translations",
    "Terms with Afrikaans translations",
    "Terms with Albanian translations",
    "Terms with Arabic translations",
    "Terms with Armenian translations",
    "Terms with Bulgarian translations",
    "Terms with Catalan translations",
    "Terms with Czech translations",
    "Terms with Dutch translations",
    "Terms with Finnish translations",
    "Terms with French translations",
    "Terms with Galician translations",
    "Terms with German translations",
    "Terms with Greek translations",
    "Terms with Hungarian translations",
    "Terms with Icelandic translations",
    "Terms with Irish translations",
    "Terms with Italian translations",
    "Terms with Japanese translations",
    "Terms with Kazakh translations",
    "Terms with Macedonian translations",
    "Terms with Mandarin translations",
    "Terms with Manx translations",
    "Terms with Maori translations",
    "Terms with Norwegian Bokmål translations",
    "Terms with Norwegian Nynorsk translations",
    "Terms with Persian translations",
    "Terms with Polish translations",
    "Terms with Portuguese translations",
    "Terms with Romanian translations",
    "Terms with Russian translations",
    "Terms with Spanish translations",
    "Terms with Swedish translations",
    "Terms with Tagalog translations",
    "Terms with Telugu translations",
    "Terms with Urdu translations",
    "en:Systems theory"
  ],
  "derived": [
    {
      "word": "bihomogeneous"
    },
    {
      "word": "dishomogeneous"
    },
    {
      "word": "homogeneous broadening"
    },
    {
      "word": "homogeneous catalysis"
    },
    {
      "word": "homogeneous coordinate"
    },
    {
      "word": "homogeneous equilibrium"
    },
    {
      "word": "homogeneous function"
    },
    {
      "word": "homogeneous ideal"
    },
    {
      "word": "homogeneously"
    },
    {
      "word": "homogeneous mixture"
    },
    {
      "word": "homogeneousness"
    },
    {
      "word": "homogeneous number"
    },
    {
      "word": "homogeneous polynomial"
    },
    {
      "word": "homogeneous radiation"
    },
    {
      "word": "homogeneous society"
    },
    {
      "word": "homogeneous space"
    },
    {
      "word": "homogeneous system"
    },
    {
      "word": "homogeneous width"
    },
    {
      "word": "inhomogeneous"
    },
    {
      "word": "nonhomogeneous"
    },
    {
      "word": "prehomogeneous"
    },
    {
      "word": "quasihomogeneous"
    },
    {
      "word": "subhomogeneous"
    },
    {
      "word": "superhomogeneous"
    },
    {
      "word": "time-homogeneous Markovian type"
    },
    {
      "word": "ultrahomogeneous"
    },
    {
      "word": "unhomogeneous"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "ML.",
        "3": "homogeneus"
      },
      "expansion": "Medieval Latin homogeneus",
      "name": "der"
    },
    {
      "args": {
        "1": "en",
        "2": "grc",
        "3": "ὁμογενής",
        "4": "",
        "5": "of the same race, family or kind"
      },
      "expansion": "Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”)",
      "name": "der"
    }
  ],
  "etymology_text": "From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).",
  "forms": [
    {
      "form": "homogenous",
      "tags": [
        "alternative"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "homogeneous (not comparable)",
      "name": "en-adj"
    }
  ],
  "hyponyms": [
    {
      "source": "Thesaurus:homogeneous",
      "word": "connatural"
    },
    {
      "source": "Thesaurus:homogeneous",
      "tags": [
        "figuratively"
      ],
      "word": "monolithic"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "monotone"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "steady"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "unalloyed"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "word": "homogeneity"
    },
    {
      "word": "homogenesis"
    },
    {
      "word": "homogenise"
    },
    {
      "word": "homogenize"
    },
    {
      "word": "homogeny"
    }
  ],
  "senses": [
    {
      "glosses": [
        "Of the same kind; alike, similar."
      ],
      "links": [
        [
          "alike",
          "alike"
        ],
        [
          "similar",
          "similar"
        ]
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "Quotation templates to be cleaned"
      ],
      "examples": [
        {
          "bold_text_offsets": [
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              27,
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          ],
          "ref": "1946, Bertrand Russell, History of Western Philosophy, I.25:",
          "text": "Their citizens were not of homogeneous origin, but were from all parts of Greece.",
          "type": "quote"
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        {
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          "ref": "2013 October 14, Jirapornchai Suksaeree, Laksana Charoenchai, Chaowalit Monton, Tun Chusut, Apirak Sakunpak, Wiwat Pichayakorn and Prapaporn Boonme, “Preparation of a Pseudolatex-Membrane for Ketoprofen Transdermal Drug Delivery Systems”, in Industrial & Engineering Chemistry Research, volume 52, number 45, →DOI:",
          "text": "All pseudolatex formulations were homogeneous and smooth in texture and elegant in appearance.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Having the same composition throughout; of uniform make-up."
      ],
      "links": [
        [
          "composition",
          "composition"
        ],
        [
          "uniform",
          "uniform"
        ]
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "categories": [
        "en:Chemistry"
      ],
      "glosses": [
        "In the same state of matter."
      ],
      "links": [
        [
          "chemistry",
          "chemistry"
        ],
        [
          "state of matter",
          "state of matter"
        ]
      ],
      "raw_glosses": [
        "(chemistry) In the same state of matter."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "chemistry",
        "natural-sciences",
        "physical-sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "uniform",
          "uniform"
        ],
        [
          "scalable",
          "scalable"
        ],
        [
          "determined",
          "determined"
        ]
      ],
      "raw_glosses": [
        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.)."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Algebra",
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials"
        }
      ],
      "glosses": [
        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "Such that all its nonzero terms have the same degree."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "uniform",
          "uniform"
        ],
        [
          "scalable",
          "scalable"
        ],
        [
          "determined",
          "determined"
        ],
        [
          "polynomial",
          "polynomial#English"
        ],
        [
          "function",
          "function#English"
        ],
        [
          "equation",
          "equation#English"
        ],
        [
          "system",
          "system#English"
        ],
        [
          "linear",
          "linear#English"
        ],
        [
          "map",
          "map#English"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
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          "polynomial"
        ],
        [
          "terms",
          "terms"
        ],
        [
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          "degree"
        ]
      ],
      "raw_glosses": [
        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "(algebra, of a polynomial) Such that all its nonzero terms have the same degree."
      ],
      "raw_tags": [
        "of a polynomial"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Linear algebra",
        "en:Mathematics"
      ],
      "glosses": [
        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "Such that all the constant terms are zero."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
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        [
          "uniform",
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        [
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        [
          "determined",
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        [
          "polynomial",
          "polynomial#English"
        ],
        [
          "function",
          "function#English"
        ],
        [
          "equation",
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        ],
        [
          "system",
          "system#English"
        ],
        [
          "linear",
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        ],
        [
          "map",
          "map#English"
        ],
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "system",
          "system"
        ],
        [
          "linear equation",
          "linear equation"
        ],
        [
          "constant",
          "constant"
        ]
      ],
      "qualifier": "by specialization",
      "raw_glosses": [
        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "(linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero."
      ],
      "raw_tags": [
        "of a system of linear equations"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematical analysis",
        "en:Mathematics"
      ],
      "glosses": [
        "In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ("
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "uniform",
          "uniform"
        ],
        [
          "scalable",
          "scalable"
        ],
        [
          "determined",
          "determined"
        ],
        [
          "polynomial",
          "polynomial#English"
        ],
        [
          "function",
          "function#English"
        ],
        [
          "equation",
          "equation#English"
        ],
        [
          "system",
          "system#English"
        ],
        [
          "linear",
          "linear#English"
        ],
        [
          "map",
          "map#English"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "function",
          "function"
        ],
        [
          "scalar",
          "scalar"
        ],
        [
          "partial function",
          "partial function"
        ],
        [
          "vector spaces",
          "vector spaces"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "linear cone",
          "linear cone"
        ]
      ],
      "qualifier": "generalizing the case of polynomial functions",
      "raw_glosses": [
        "(mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).",
        "Of polynomials, functions, equations, systems of equations, or linear maps:",
        "(mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ("
      ],
      "raw_tags": [
        "of a function f"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with usage examples"
      ],
      "glosses": [
        "The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;."
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other."
      ],
      "links": [
        [
          "ordinary differential equation",
          "ordinary differential equation#English"
        ],
        [
          "first-order",
          "first-order"
        ],
        [
          "differential equation",
          "differential equation"
        ]
      ],
      "raw_glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "(of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other."
      ],
      "raw_tags": [
        "of a first-order differential equation"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "Having its degree-zero term equal to zero; admitting the trivial solution."
      ],
      "links": [
        [
          "ordinary differential equation",
          "ordinary differential equation#English"
        ],
        [
          "linear",
          "linear"
        ],
        [
          "trivial",
          "trivial"
        ]
      ],
      "raw_glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "(of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution."
      ],
      "raw_tags": [
        "of a linear differential equation"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "Homogeneous as a function of the dependent variable and its derivatives."
      ],
      "links": [
        [
          "ordinary differential equation",
          "ordinary differential equation#English"
        ]
      ],
      "raw_glosses": [
        "In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):",
        "(of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives."
      ],
      "raw_tags": [
        "of a general differential equation"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "categories": [
        "en:Algebra"
      ],
      "glosses": [
        "In abstract algebra and geometry:",
        "Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
      ],
      "links": [
        [
          "abstract algebra",
          "abstract algebra#English"
        ],
        [
          "geometry",
          "geometry#English"
        ],
        [
          "ring theory",
          "ring theory"
        ],
        [
          "element",
          "element"
        ],
        [
          "graded ring",
          "graded ring"
        ],
        [
          "summand",
          "summand"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "commutative",
          "commutative"
        ],
        [
          "monoid",
          "monoid"
        ]
      ],
      "qualifier": "ring theory",
      "raw_glosses": [
        "In abstract algebra and geometry:",
        "(ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)"
      ],
      "raw_tags": [
        "of an element of a graded ring"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "glosses": [
        "In abstract algebra and geometry:",
        "Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
      ],
      "links": [
        [
          "abstract algebra",
          "abstract algebra#English"
        ],
        [
          "geometry",
          "geometry#English"
        ],
        [
          "linear",
          "linear"
        ],
        [
          "map",
          "map"
        ],
        [
          "vector spaces",
          "vector spaces"
        ],
        [
          "graded",
          "grading"
        ],
        [
          "commutative",
          "commutative"
        ],
        [
          "monoid",
          "monoid"
        ],
        [
          "respect",
          "respect"
        ]
      ],
      "raw_glosses": [
        "In abstract algebra and geometry:",
        "(of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I."
      ],
      "raw_tags": [
        "of a linear map f between vector spaces graded by a commutative monoid I"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "categories": [
        "en:Geometry"
      ],
      "glosses": [
        "In abstract algebra and geometry:",
        "Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
      ],
      "links": [
        [
          "abstract algebra",
          "abstract algebra#English"
        ],
        [
          "geometry",
          "geometry#English"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "space",
          "space"
        ],
        [
          "equip",
          "equip"
        ],
        [
          "group action",
          "group action"
        ],
        [
          "point",
          "point"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "transitively",
          "transitively"
        ],
        [
          "automorphism",
          "automorphism"
        ],
        [
          "faithful",
          "faithful"
        ]
      ],
      "raw_glosses": [
        "In abstract algebra and geometry:",
        "(geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful)."
      ],
      "raw_tags": [
        "of a space equipped with a group action"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Geometry"
      ],
      "glosses": [
        "In abstract algebra and geometry:",
        "Of or relating to homogeneous coordinates."
      ],
      "links": [
        [
          "abstract algebra",
          "abstract algebra#English"
        ],
        [
          "geometry",
          "geometry#English"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "homogeneous coordinate",
          "homogeneous coordinate"
        ]
      ],
      "raw_glosses": [
        "In abstract algebra and geometry:",
        "(geometry) Of or relating to homogeneous coordinates."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Probability theory"
      ],
      "glosses": [
        "In miscellaneous other senses:",
        "Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
      ],
      "links": [
        [
          "probability theory",
          "probability theory"
        ],
        [
          "Fourier analysis",
          "Fourier analysis"
        ],
        [
          "distribution",
          "distribution"
        ],
        [
          "Euclidean",
          "Euclidean"
        ],
        [
          "test function",
          "test function"
        ]
      ],
      "qualifier": "Fourier analysis",
      "raw_glosses": [
        "In miscellaneous other senses:",
        "(probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m."
      ],
      "raw_tags": [
        "of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Set theory"
      ],
      "glosses": [
        "In miscellaneous other senses:",
        "Holding between a set and itself; being an endorelation."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "order theory",
          "order theory"
        ],
        [
          "relation",
          "relation"
        ],
        [
          "set",
          "set"
        ],
        [
          "endorelation",
          "endorelation"
        ]
      ],
      "raw_glosses": [
        "In miscellaneous other senses:",
        "(set theory, order theory, of a relation) Holding between a set and itself; being an endorelation."
      ],
      "raw_tags": [
        "of a relation"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
        "set-theory"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˌhɒ.mə(ʊ)ˈd͡ʒiː.nɪəs/",
      "tags": [
        "UK"
      ]
    },
    {
      "ipa": "/ˌhəʊ.mə(ʊ)ˈd͡ʒiː.nɪəs/",
      "tags": [
        "UK"
      ]
    },
    {
      "ipa": "/ˌhoʊ.moʊˈd͡ʒiː.njəs/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/ˌhoʊ.məˈd͡ʒiː.njəs/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/ˌhoʊ.moʊˈd͡ʒɛ.njəs/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/həˈmɑ.d͡ʒə.nəs/",
      "tags": [
        "US"
      ]
    },
    {
      "audio": "En-uk-homogeneous.ogg",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/4/41/En-uk-homogeneous.ogg/En-uk-homogeneous.ogg.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/4/41/En-uk-homogeneous.ogg"
    }
  ],
  "synonyms": [
    {
      "source": "Thesaurus:homogeneous",
      "word": "homogeneous"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "invariable"
    },
    {
      "source": "Thesaurus:homogeneous",
      "tags": [
        "idiomatic"
      ],
      "word": "of a piece"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "onefold"
    },
    {
      "source": "Thesaurus:homogeneous",
      "tags": [
        "dialectal"
      ],
      "word": "samely"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "uniform"
    },
    {
      "source": "Thesaurus:homogeneous",
      "tags": [
        "obsolete"
      ],
      "word": "uniformal"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "unmixed"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "unvaried"
    },
    {
      "source": "Thesaurus:homogeneous",
      "word": "unvarying"
    }
  ],
  "translations": [
    {
      "code": "af",
      "lang": "Afrikaans",
      "sense": "of the same kind; alike, similar",
      "word": "homogeen"
    },
    {
      "code": "sq",
      "lang": "Albanian",
      "sense": "of the same kind; alike, similar",
      "word": "homogjen"
    },
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "miatarr",
      "sense": "of the same kind; alike, similar",
      "word": "միատարր"
    },
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "hamaseṙ",
      "sense": "of the same kind; alike, similar",
      "word": "համասեռ"
    },
    {
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "ednoroden",
      "sense": "of the same kind; alike, similar",
      "word": "еднороден"
    },
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "of the same kind; alike, similar",
      "word": "homogeni"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "tóngzhí, tóngzhì",
      "sense": "of the same kind; alike, similar",
      "word": "同質 /同质"
    },
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "of the same kind; alike, similar",
      "word": "stejnorodý"
    },
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "of the same kind; alike, similar",
      "word": "homogenní"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "of the same kind; alike, similar",
      "word": "homogeen"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "of the same kind; alike, similar",
      "word": "samanlainen"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "of the same kind; alike, similar",
      "word": "homogeeninen"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "of the same kind; alike, similar",
      "word": "homogène"
    },
    {
      "code": "gl",
      "lang": "Galician",
      "sense": "of the same kind; alike, similar",
      "word": "homoxéneo"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "of the same kind; alike, similar",
      "word": "homogen"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "of the same kind; alike, similar",
      "word": "gleichartig"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "omogenís",
      "sense": "of the same kind; alike, similar",
      "word": "ομογενής"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "omoiogenís",
      "sense": "of the same kind; alike, similar",
      "word": "ομοιογενής"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "of the same kind; alike, similar",
      "word": "homogén"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "of the same kind; alike, similar",
      "word": "einsleitur"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "of the same kind; alike, similar",
      "word": "einleitur"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "of the same kind; alike, similar",
      "word": "eingerður"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "of the same kind; alike, similar",
      "word": "samkynja"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "of the same kind; alike, similar",
      "word": "samleitur"
    },
    {
      "code": "ga",
      "lang": "Irish",
      "sense": "of the same kind; alike, similar",
      "word": "aonchineálach"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "of the same kind; alike, similar",
      "word": "omogeneo"
    },
    {
      "alt": "きんしつ",
      "code": "ja",
      "lang": "Japanese",
      "roman": "kinshitsu",
      "sense": "of the same kind; alike, similar",
      "word": "均質"
    },
    {
      "alt": "どうしつ",
      "code": "ja",
      "lang": "Japanese",
      "roman": "dōshitsu",
      "sense": "of the same kind; alike, similar",
      "word": "同質"
    },
    {
      "code": "kk",
      "lang": "Kazakh",
      "roman": "gomogendık",
      "sense": "of the same kind; alike, similar",
      "word": "гомогендік"
    },
    {
      "code": "kk",
      "lang": "Kazakh",
      "roman": "bırtektı",
      "sense": "of the same kind; alike, similar",
      "word": "біртекті"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "ednoobrazen",
      "sense": "of the same kind; alike, similar",
      "word": "еднообразен"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "ednoroden",
      "sense": "of the same kind; alike, similar",
      "word": "еднороден"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "homogen",
      "sense": "of the same kind; alike, similar",
      "word": "хомоген"
    },
    {
      "code": "gv",
      "lang": "Manx",
      "sense": "of the same kind; alike, similar",
      "word": "cocheintagh"
    },
    {
      "code": "nb",
      "lang": "Norwegian Bokmål",
      "sense": "of the same kind; alike, similar",
      "word": "homogen"
    },
    {
      "code": "nn",
      "lang": "Norwegian Nynorsk",
      "sense": "of the same kind; alike, similar",
      "word": "homogen"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "of the same kind; alike, similar",
      "word": "jednorodny"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "of the same kind; alike, similar",
      "word": "jednolity"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "of the same kind; alike, similar",
      "word": "homogêneo"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "of the same kind; alike, similar",
      "word": "homogéneo"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "of the same kind; alike, similar",
      "word": "omogen"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "odnoródnyj",
      "sense": "of the same kind; alike, similar",
      "word": "одноро́дный"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "gomogénnyj",
      "sense": "of the same kind; alike, similar",
      "word": "гомоге́нный"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "jedinoobráznyj",
      "sense": "of the same kind; alike, similar",
      "word": "единообра́зный"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "of the same kind; alike, similar",
      "word": "homogéneo"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "of the same kind; alike, similar",
      "word": "homogen"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "of the same kind; alike, similar",
      "word": "enhetlig"
    },
    {
      "code": "tl",
      "lang": "Tagalog",
      "sense": "of the same kind; alike, similar",
      "word": "tulad-uriin"
    },
    {
      "code": "te",
      "lang": "Telugu",
      "roman": "sajāti",
      "sense": "of the same kind; alike, similar",
      "word": "సజాతి"
    },
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "hamaseṙ",
      "sense": "having the same composition throughout",
      "word": "համասեռ"
    },
    {
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "ednoroden",
      "sense": "having the same composition throughout",
      "word": "еднороден"
    },
    {
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "homogenen",
      "sense": "having the same composition throughout",
      "word": "хомогенен"
    },
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "having the same composition throughout",
      "word": "homogeni"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "having the same composition throughout",
      "word": "tasa-aineinen"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "having the same composition throughout",
      "word": "homogeeninen"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "having the same composition throughout",
      "word": "homogène"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "having the same composition throughout",
      "word": "omogeneo"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "ednoroden",
      "sense": "having the same composition throughout",
      "word": "еднороден"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "ednoobrazen",
      "sense": "having the same composition throughout",
      "word": "еднообразен"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "homogen",
      "sense": "having the same composition throughout",
      "word": "хомоген"
    },
    {
      "code": "mi",
      "lang": "Maori",
      "sense": "having the same composition throughout",
      "word": "kanorite"
    },
    {
      "code": "fa",
      "lang": "Persian",
      "sense": "having the same composition throughout",
      "word": "هملوناء"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "having the same composition throughout",
      "word": "homogêneo"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "having the same composition throughout",
      "word": "homogéneo"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "having the same composition throughout",
      "word": "homogen"
    },
    {
      "code": "tl",
      "lang": "Tagalog",
      "sense": "having the same composition throughout",
      "word": "tulad-uriin"
    }
  ],
  "word": "homogeneous"
}

Download raw JSONL data for homogeneous meaning in All languages combined (27.9kB)

{
  "called_from": "page/1412",
  "msg": "gloss may contain unhandled list items: The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.",
  "path": [
    "homogeneous"
  ],
  "section": "English",
  "subsection": "adjective",
  "title": "homogeneous",
  "trace": ""
}

{
  "called_from": "extractor.en.page.sense_template_fn/1415",
  "msg": "Example template is used for gloss text",
  "path": [
    "homogeneous",
    "Template:ux",
    "TEMPLATE_FN"
  ],
  "section": "English",
  "subsection": "adjective",
  "title": "homogeneous",
  "trace": ""
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-13 from the enwiktionary dump dated 2025-05-01 using wiktextract (9a214a4 and 1b6da77). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.