See homogeneous on Wiktionary
{
"antonyms": [
{
"word": "heterogeneous"
},
{
"word": "inhomogeneous"
}
],
"derived": [
{
"_dis1": "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",
"word": "dishomogeneous"
},
{
"_dis1": "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",
"word": "homogeneous catalysis"
},
{
"_dis1": "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",
"word": "homogeneous equilibrium"
},
{
"_dis1": "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",
"word": "homogeneous ideal"
},
{
"_dis1": "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",
"word": "homogeneous mixture"
},
{
"_dis1": "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",
"word": "homogeneous number"
},
{
"_dis1": "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",
"word": "homogeneous radiation"
},
{
"_dis1": "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",
"word": "homogeneous space"
},
{
"_dis1": "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",
"word": "homogeneous width"
},
{
"_dis1": "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",
"word": "nonhomogeneous"
},
{
"_dis1": "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",
"word": "quasihomogeneous"
},
{
"_dis1": "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",
"word": "superhomogeneous"
},
{
"_dis1": "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",
"word": "ultrahomogeneous"
},
{
"_dis1": "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",
"source": "Thesaurus:homogeneous",
"word": "connatural"
},
{
"_dis1": "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",
"source": "Thesaurus:homogeneous",
"word": "monotone"
},
{
"_dis1": "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",
"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",
"word": "homogeneity"
},
{
"_dis1": "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",
"word": "homogenise"
},
{
"_dis1": "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",
"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": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "af",
"lang": "Afrikaans",
"sense": "of the same kind; alike, similar",
"word": "homogeen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "sq",
"lang": "Albanian",
"sense": "of the same kind; alike, similar",
"word": "homogjen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "hy",
"lang": "Armenian",
"roman": "miatarr",
"sense": "of the same kind; alike, similar",
"word": "միատարր"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "hy",
"lang": "Armenian",
"roman": "hamaseṙ",
"sense": "of the same kind; alike, similar",
"word": "համասեռ"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "bg",
"lang": "Bulgarian",
"roman": "ednoroden",
"sense": "of the same kind; alike, similar",
"word": "еднороден"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ca",
"lang": "Catalan",
"sense": "of the same kind; alike, similar",
"word": "homogeni"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tóngzhí, tóngzhì",
"sense": "of the same kind; alike, similar",
"word": "同質 /同质"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "cs",
"lang": "Czech",
"sense": "of the same kind; alike, similar",
"word": "stejnorodý"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "cs",
"lang": "Czech",
"sense": "of the same kind; alike, similar",
"word": "homogenní"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "nl",
"lang": "Dutch",
"sense": "of the same kind; alike, similar",
"word": "homogeen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fi",
"lang": "Finnish",
"sense": "of the same kind; alike, similar",
"word": "samanlainen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fi",
"lang": "Finnish",
"sense": "of the same kind; alike, similar",
"word": "homogeeninen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fr",
"lang": "French",
"sense": "of the same kind; alike, similar",
"word": "homogène"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "gl",
"lang": "Galician",
"sense": "of the same kind; alike, similar",
"word": "homoxéneo"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "de",
"lang": "German",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "de",
"lang": "German",
"sense": "of the same kind; alike, similar",
"word": "gleichartig"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "el",
"lang": "Greek",
"roman": "omogenís",
"sense": "of the same kind; alike, similar",
"word": "ομογενής"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "el",
"lang": "Greek",
"roman": "omoiogenís",
"sense": "of the same kind; alike, similar",
"word": "ομοιογενής"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "hu",
"lang": "Hungarian",
"sense": "of the same kind; alike, similar",
"word": "homogén"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "einsleitur"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "einleitur"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "eingerður"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "samkynja"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "is",
"lang": "Icelandic",
"sense": "of the same kind; alike, similar",
"word": "samleitur"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ga",
"lang": "Irish",
"sense": "of the same kind; alike, similar",
"word": "aonchineálach"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "it",
"lang": "Italian",
"sense": "of the same kind; alike, similar",
"word": "omogeneo"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"alt": "きんしつ",
"code": "ja",
"lang": "Japanese",
"roman": "kinshitsu",
"sense": "of the same kind; alike, similar",
"word": "均質"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"alt": "どうしつ",
"code": "ja",
"lang": "Japanese",
"roman": "dōshitsu",
"sense": "of the same kind; alike, similar",
"word": "同質"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "kk",
"lang": "Kazakh",
"roman": "gomogendık",
"sense": "of the same kind; alike, similar",
"word": "гомогендік"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "kk",
"lang": "Kazakh",
"roman": "bırtektı",
"sense": "of the same kind; alike, similar",
"word": "біртекті"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoobrazen",
"sense": "of the same kind; alike, similar",
"word": "еднообразен"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoroden",
"sense": "of the same kind; alike, similar",
"word": "еднороден"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mk",
"lang": "Macedonian",
"roman": "homogen",
"sense": "of the same kind; alike, similar",
"word": "хомоген"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "gv",
"lang": "Manx",
"sense": "of the same kind; alike, similar",
"word": "cocheintagh"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "nb",
"lang": "Norwegian Bokmål",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "nn",
"lang": "Norwegian Nynorsk",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "pl",
"lang": "Polish",
"sense": "of the same kind; alike, similar",
"word": "jednorodny"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "pl",
"lang": "Polish",
"sense": "of the same kind; alike, similar",
"word": "jednolity"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "pt",
"lang": "Portuguese",
"sense": "of the same kind; alike, similar",
"word": "homogêneo"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "pt",
"lang": "Portuguese",
"sense": "of the same kind; alike, similar",
"word": "homogéneo"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ro",
"lang": "Romanian",
"sense": "of the same kind; alike, similar",
"word": "omogen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ru",
"lang": "Russian",
"roman": "odnoródnyj",
"sense": "of the same kind; alike, similar",
"word": "одноро́дный"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ru",
"lang": "Russian",
"roman": "gomogénnyj",
"sense": "of the same kind; alike, similar",
"word": "гомоге́нный"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ru",
"lang": "Russian",
"roman": "jedinoobráznyj",
"sense": "of the same kind; alike, similar",
"word": "единообра́зный"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "es",
"lang": "Spanish",
"sense": "of the same kind; alike, similar",
"word": "homogéneo"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "sv",
"lang": "Swedish",
"sense": "of the same kind; alike, similar",
"word": "homogen"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "sv",
"lang": "Swedish",
"sense": "of the same kind; alike, similar",
"word": "enhetlig"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "tl",
"lang": "Tagalog",
"sense": "of the same kind; alike, similar",
"word": "tulad-uriin"
},
{
"_dis1": "28 6 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "te",
"lang": "Telugu",
"roman": "sajāti",
"sense": "of the same kind; alike, similar",
"word": "సజాతి"
}
]
},
{
"categories": [],
"examples": [
{
"bold_text_offsets": [
[
27,
38
]
],
"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"
},
{
"bold_text_offsets": [
[
34,
45
]
],
"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",
"links": [
[
"composition",
"composition"
],
[
"uniform",
"uniform"
]
],
"tags": [
"not-comparable"
],
"translations": [
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "hy",
"lang": "Armenian",
"roman": "hamaseṙ",
"sense": "having the same composition throughout",
"word": "համասեռ"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "bg",
"lang": "Bulgarian",
"roman": "ednoroden",
"sense": "having the same composition throughout",
"word": "еднороден"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "bg",
"lang": "Bulgarian",
"roman": "homogenen",
"sense": "having the same composition throughout",
"word": "хомогенен"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "ca",
"lang": "Catalan",
"sense": "having the same composition throughout",
"word": "homogeni"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fi",
"lang": "Finnish",
"sense": "having the same composition throughout",
"word": "tasa-aineinen"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fi",
"lang": "Finnish",
"sense": "having the same composition throughout",
"word": "homogeeninen"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fr",
"lang": "French",
"sense": "having the same composition throughout",
"word": "homogène"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "it",
"lang": "Italian",
"sense": "having the same composition throughout",
"word": "omogeneo"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoroden",
"sense": "having the same composition throughout",
"word": "еднороден"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mk",
"lang": "Macedonian",
"roman": "ednoobrazen",
"sense": "having the same composition throughout",
"word": "еднообразен"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mk",
"lang": "Macedonian",
"roman": "homogen",
"sense": "having the same composition throughout",
"word": "хомоген"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "mi",
"lang": "Maori",
"sense": "having the same composition throughout",
"word": "kanorite"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "fa",
"lang": "Persian",
"sense": "having the same composition throughout",
"word": "هملوناء"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "pt",
"lang": "Portuguese",
"sense": "having the same composition throughout",
"word": "homogêneo"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "es",
"lang": "Spanish",
"sense": "having the same composition throughout",
"word": "homogéneo"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "sv",
"lang": "Swedish",
"sense": "having the same composition throughout",
"word": "homogen"
},
{
"_dis1": "6 19 7 5 5 5 5 5 5 5 5 8 5 5 5",
"code": "tl",
"lang": "Tagalog",
"sense": "having the same composition throughout",
"word": "tulad-uriin"
}
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Chemistry",
"orig": "en:Chemistry",
"parents": [],
"source": "w"
}
],
"glosses": [
"In the same state of matter."
],
"id": "en-homogeneous-en-adj-1v2Brlrf",
"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": [
{
"kind": "other",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "2 4 5 12 12 6 7 9 6 7 5 6 7 8 5",
"kind": "other",
"name": "English terms prefixed with homo-",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 1 1 12 12 12 13 13 13 3 2 3 6 6 3",
"kind": "other",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [],
"source": "w+disamb"
}
],
"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."
],
"id": "en-homogeneous-en-adj-6x8KOypq",
"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"
],
[
"polynomial",
"polynomial"
],
[
"terms",
"terms"
],
[
"degree",
"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": [
{
"kind": "other",
"langcode": "en",
"name": "Linear algebra",
"orig": "en:Linear algebra",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "2 4 5 12 12 6 7 9 6 7 5 6 7 8 5",
"kind": "other",
"name": "English terms prefixed with homo-",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 1 1 12 12 12 13 13 13 3 2 3 6 6 3",
"kind": "other",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [],
"source": "w+disamb"
}
],
"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."
],
"id": "en-homogeneous-en-adj--KhrxETj",
"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"
],
[
"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": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "1 1 1 12 12 12 13 13 13 3 2 3 6 6 3",
"kind": "other",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"bold_text_offsets": [
[
46,
57
],
[
159,
170
]
],
"text": "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;.",
"type": "example"
}
],
"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( mathbf x) for some integer k and for all mathbf x in the domain and s scalars."
],
"id": "en-homogeneous-en-adj-9Pdked44",
"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( mathbf x) for some integer k and for all mathbf x in the domain and s scalars."
],
"raw_tags": [
"of a function f"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "1 2 3 9 9 9 11 11 11 4 3 4 11 10 3",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 12 12 12 3 2 3 12 10 4",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 9 9 9 11 11 11 3 3 3 11 10 4",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 11 11 11 4 2 3 11 13 4",
"kind": "other",
"name": "Terms with Norwegian Nynorsk translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 1 1 12 12 12 13 13 13 3 2 3 6 6 3",
"kind": "other",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [],
"source": "w+disamb"
}
],
"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:",
"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."
],
"id": "en-homogeneous-en-adj-WzaaG0IG",
"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"
],
[
"ordinary differential equation",
"ordinary differential equation#English"
],
[
"first-order",
"first-order"
],
[
"differential equation",
"differential equation"
]
],
"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:",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "1 2 3 9 9 9 11 11 11 4 3 4 11 10 3",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 12 12 12 3 2 3 12 10 4",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 9 9 9 11 11 11 3 3 3 11 10 4",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 11 11 11 4 2 3 11 13 4",
"kind": "other",
"name": "Terms with Norwegian Nynorsk translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 1 1 12 12 12 13 13 13 3 2 3 6 6 3",
"kind": "other",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [],
"source": "w+disamb"
}
],
"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:",
"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."
],
"id": "en-homogeneous-en-adj-ABwYTQRA",
"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"
],
[
"ordinary differential equation",
"ordinary differential equation#English"
],
[
"linear",
"linear"
],
[
"trivial",
"trivial"
]
],
"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:",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "1 2 3 9 9 9 11 11 11 4 3 4 11 10 3",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 12 12 12 3 2 3 12 10 4",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 9 9 9 11 11 11 3 3 3 11 10 4",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 11 11 11 4 2 3 11 13 4",
"kind": "other",
"name": "Terms with Norwegian Nynorsk translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 1 1 12 12 12 13 13 13 3 2 3 6 6 3",
"kind": "other",
"langcode": "en",
"name": "Systems theory",
"orig": "en:Systems theory",
"parents": [],
"source": "w+disamb"
}
],
"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:",
"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."
],
"id": "en-homogeneous-en-adj-8qY3rbC1",
"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"
],
[
"ordinary differential equation",
"ordinary differential equation#English"
]
],
"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:",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
}
],
"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.).",
"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)"
],
"id": "en-homogeneous-en-adj-YVVQHh0Y",
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"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": [
"(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.).",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
}
],
"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.).",
"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."
],
"id": "en-homogeneous-en-adj-LZthcufV",
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"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": [
"(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.).",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
}
],
"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.).",
"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)."
],
"id": "en-homogeneous-en-adj-gBV8zXhi",
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"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": [
"(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.).",
"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": [
{
"kind": "other",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"_dis": "1 2 3 9 9 9 11 11 11 4 3 4 11 10 3",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 12 12 12 3 2 3 12 10 4",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 9 9 9 11 11 11 3 3 3 11 10 4",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 11 11 11 4 2 3 11 13 4",
"kind": "other",
"name": "Terms with Norwegian Nynorsk translations",
"parents": [],
"source": "w+disamb"
}
],
"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.).",
"In abstract algebra and geometry:",
"Of or relating to homogeneous coordinates."
],
"id": "en-homogeneous-en-adj-LimbMW6c",
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"abstract algebra",
"abstract algebra#English"
],
[
"geometry",
"geometry#English"
],
[
"geometry",
"geometry"
],
[
"homogeneous coordinate",
"homogeneous coordinate"
]
],
"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.).",
"In abstract algebra and geometry:",
"(geometry) Of or relating to homogeneous coordinates."
],
"tags": [
"not-comparable"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "other",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Probability theory",
"orig": "en:Probability theory",
"parents": [],
"source": "w"
},
{
"_dis": "1 2 3 9 9 9 11 11 11 4 3 4 11 10 3",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 7 7 11 9 9 9 6 2 6 9 20 3",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 12 12 12 3 2 3 12 10 4",
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 9 9 9 11 11 11 3 3 3 11 10 4",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Afrikaans translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Albanian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 2 4 8 8 10 9 9 9 6 4 5 9 13 5",
"kind": "other",
"name": "Terms with Arabic translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Armenian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 10 9 9 9 6 3 5 9 14 4",
"kind": "other",
"name": "Terms with Bulgarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 7 8 9 9 9 9 6 3 6 9 14 6",
"kind": "other",
"name": "Terms with Catalan translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 7 8 10 9 9 9 7 3 5 9 13 5",
"kind": "other",
"name": "Terms with Czech translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 3 8 8 10 9 9 9 6 3 6 9 15 4",
"kind": "other",
"name": "Terms with Dutch translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 7 8 10 9 9 9 7 3 5 9 14 4",
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 3 3 8 8 9 9 9 9 6 3 6 9 15 4",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 6 9 15 4",
"kind": "other",
"name": "Terms with Galician translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 2 3 7 8 8 9 9 9 7 3 5 9 17 4",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 6 7 7 7 8 8 8 8 6 6 8 12 6",
"kind": "other",
"name": "Terms with Greek translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 6 7 7 8 8 8 8 8 6 6 7 12 6",
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 10 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Icelandic translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 6",
"kind": "other",
"name": "Terms with Irish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 7 7 9 9 9 9 5 4 6 9 15 5",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 10 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Kazakh translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 4",
"kind": "other",
"name": "Terms with Macedonian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 5 7 7 8 9 9 9 7 4 6 8 13 4",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Manx translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Maori translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 4 5 9 14 4",
"kind": "other",
"name": "Terms with Norwegian Bokmål translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 1 2 9 9 9 11 11 11 4 2 3 11 13 4",
"kind": "other",
"name": "Terms with Norwegian Nynorsk translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Persian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 10 9 9 9 7 4 5 9 14 4",
"kind": "other",
"name": "Terms with Polish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 2 3 7 7 8 9 9 9 5 4 6 9 15 6",
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 10 9 9 9 6 3 5 9 14 4",
"kind": "other",
"name": "Terms with Romanian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 2 2 8 8 10 9 9 9 7 3 5 9 15 4",
"kind": "other",
"name": "Terms with Russian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 3 2 8 8 9 10 10 10 5 3 5 10 16 3",
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Tagalog translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 2 2 8 8 9 9 9 9 6 3 5 10 15 5",
"kind": "other",
"name": "Terms with Telugu translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 3 3 8 8 9 9 9 9 6 3 5 9 14 5",
"kind": "other",
"name": "Terms with Urdu translations",
"parents": [],
"source": "w+disamb"
}
],
"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.).",
"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-jXduGPG-",
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"probability theory",
"probability theory"
],
[
"Fourier analysis",
"Fourier analysis"
],
[
"distribution",
"distribution"
],
[
"Euclidean",
"Euclidean"
],
[
"test function",
"test function"
]
],
"qualifier": "Fourier analysis",
"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.).",
"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": "Mathematics",
"orig": "en:Mathematics",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
"parents": [],
"source": "w"
}
],
"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.).",
"In miscellaneous other senses:",
"Holding between a set and itself; being an endorelation."
],
"id": "en-homogeneous-en-adj-NuXcSHKY",
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"set theory",
"set theory"
],
[
"order theory",
"order theory"
],
[
"relation",
"relation"
],
[
"set",
"set"
],
[
"endorelation",
"endorelation"
]
],
"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.).",
"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",
"source": "Thesaurus:homogeneous",
"word": "homogeneous"
},
{
"_dis1": "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",
"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",
"source": "Thesaurus:homogeneous",
"word": "onefold"
},
{
"_dis1": "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",
"source": "Thesaurus:homogeneous",
"word": "uniform"
},
{
"_dis1": "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",
"source": "Thesaurus:homogeneous",
"word": "unmixed"
},
{
"_dis1": "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",
"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": [
[
27,
38
]
],
"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"
},
{
"bold_text_offsets": [
[
34,
45
]
],
"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: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"
],
[
"polynomial",
"polynomial"
],
[
"terms",
"terms"
],
[
"degree",
"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"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"polynomial",
"polynomial#English"
],
[
"function",
"function#English"
],
[
"equation",
"equation#English"
],
[
"system",
"system#English"
],
[
"linear",
"linear#English"
],
[
"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": [
"English terms with usage examples",
"en:Mathematical analysis",
"en:Mathematics"
],
"examples": [
{
"bold_text_offsets": [
[
46,
57
],
[
159,
170
]
],
"text": "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;.",
"type": "example"
}
],
"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( mathbf x) for some integer k and for all mathbf x in the domain and s scalars."
],
"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( mathbf x) for some integer k and for all mathbf x in the domain and s scalars."
],
"raw_tags": [
"of a function f"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematical-analysis",
"mathematics",
"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.).",
"Of polynomials, functions, equations, systems of equations, or linear maps:",
"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": [
[
"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"
],
[
"ordinary differential equation",
"ordinary differential equation#English"
],
[
"first-order",
"first-order"
],
[
"differential equation",
"differential equation"
]
],
"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:",
"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"
],
"topics": [
"mathematics",
"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.).",
"Of polynomials, functions, equations, systems of equations, or linear maps:",
"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": [
[
"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"
],
[
"ordinary differential equation",
"ordinary differential equation#English"
],
[
"linear",
"linear"
],
[
"trivial",
"trivial"
]
],
"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:",
"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"
],
"topics": [
"mathematics",
"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.).",
"Of polynomials, functions, equations, systems of equations, or linear maps:",
"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": [
[
"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"
],
[
"ordinary differential equation",
"ordinary differential equation#English"
]
],
"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:",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en: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.).",
"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": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"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": [
"(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.).",
"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"
],
"topics": [
"mathematics",
"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.).",
"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": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"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": [
"(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.).",
"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"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Geometry",
"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.).",
"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": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"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": [
"(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.).",
"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",
"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.).",
"In abstract algebra and geometry:",
"Of or relating to homogeneous coordinates."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"abstract algebra",
"abstract algebra#English"
],
[
"geometry",
"geometry#English"
],
[
"geometry",
"geometry"
],
[
"homogeneous coordinate",
"homogeneous coordinate"
]
],
"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.).",
"In abstract algebra and geometry:",
"(geometry) Of or relating to homogeneous coordinates."
],
"tags": [
"not-comparable"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Mathematics",
"en:Probability theory"
],
"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.).",
"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": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"probability theory",
"probability theory"
],
[
"Fourier analysis",
"Fourier analysis"
],
[
"distribution",
"distribution"
],
[
"Euclidean",
"Euclidean"
],
[
"test function",
"test function"
]
],
"qualifier": "Fourier analysis",
"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.).",
"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:Mathematics",
"en:Set theory"
],
"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.).",
"In miscellaneous other senses:",
"Holding between a set and itself; being an endorelation."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"uniform",
"uniform"
],
[
"scalable",
"scalable"
],
[
"determined",
"determined"
],
[
"set theory",
"set theory"
],
[
"order theory",
"order theory"
],
[
"relation",
"relation"
],
[
"set",
"set"
],
[
"endorelation",
"endorelation"
]
],
"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.).",
"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 (33.6kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-29 from the enwiktionary dump dated 2025-05-20 using wiktextract (e937b02 and f1c2b61). 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.