"codifferential" meaning in English

See codifferential in All languages combined, or Wiktionary

Noun

Forms: codifferentials [plural]
Etymology: Etymology tree Proto-Indo-European *ḱe Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Latin co-der. English co- Proto-Indo-European *dwóh₁ Proto-Indo-European *d(w)is- Proto-Italic *dis- Latin dis- Proto-Indo-European *bʰer- Proto-Indo-European *bʰéreti Proto-Italic *ferō Latin ferō Latin differō Latin differēns Proto-Indo-European *-yós Proto-Italic *-ios Old Latin -ios Latin -ius Latin -ia Latin differentia Proto-Indo-European *h₂el-der.? Proto-Italic *-ālis Latin -ālis Latin differentiālislbor. English differential English codifferential From co- + differential. Etymology templates: {{etymon|en|:af|co-|differential|text=+|tree=1}} Etymology tree Proto-Indo-European *ḱe Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Latin co-der. English co- Proto-Indo-European *dwóh₁ Proto-Indo-European *d(w)is- Proto-Italic *dis- Latin dis- Proto-Indo-European *bʰer- Proto-Indo-European *bʰéreti Proto-Italic *ferō Latin ferō Latin differō Latin differēns Proto-Indo-European *-yós Proto-Italic *-ios Old Latin -ios Latin -ius Latin -ia Latin differentia Proto-Indo-European *h₂el-der.? Proto-Italic *-ālis Latin -ālis Latin differentiālislbor. English differential English codifferential [Appendix:Glossary#derived_terms|Derived]] from", "terms" : [ { "children" : [ { "terms" : [ { "id" : "bringing together", "children" : [ { "terms" : [ { "id" : "with", "children" : [ { "terms" : [ { "id" : "with", "children" : [ { "terms" : [ { "id" : "beside", "children" : [ { "terms" : [ { "id" : "here", "children" : [ ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*ḱe", "lang" : "ine-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*ḱóm", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Proto-Italic", "term" : "*kom", "lang" : "itc-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Proto-Italic", "term" : "*kom-", "lang" : "itc-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Latin", "term" : "con-", "lang" : "la" } ], "keyword_label" : "From", "keyword" : "from" } ], "lang_name" : "Latin", "term" : "co-", "status" : "ok", "lang" : "la" } ], "keyword" : "derived" } ], "lang_name" : "English", "term" : "co-", "status" : "ok", "lang" : "en" }, { "children" : [ { "keyword_abbrev" : "lbor.", "keyword_label" : "Learned borrowing from", "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "alt" : "*d(w)is-", "gloss" : "in two, apart", "children" : [ { "terms" : [ { "id" : "two", "children" : [ ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*dwóh₁", "lang" : "ine-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "lang_name" : "Proto-Indo-European", "term" : "*dwís", "status" : "ok", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Proto-Italic", "term" : "*dis-", "status" : "inline", "lang" : "itc-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Latin", "term" : "dis-", "status" : "ok", "lang" : "la" }, { "id" : "to carry", "children" : [ { "terms" : [ { "id" : "to carry", "children" : [ { "terms" : [ { "id" : "to be carrying", "children" : [ { "terms" : [ { "id" : "bear", "children" : [ ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*bʰer-", "lang" : "ine-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*bʰéreti", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Proto-Italic", "term" : "*ferō", "lang" : "itc-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Latin", "term" : "ferō", "lang" : "la" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "Latin", "term" : "differō", "status" : "ok", "lang" : "la" } ], "keyword_label" : "From", "keyword" : "from" } ], "lang_name" : "Latin", "term" : "differēns", "status" : "ok", "lang" : "la" }, { "id" : "abstract noun", "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "id" : "suffix forming adjectives", "children" : [ { "terms" : [ { "id" : "adjective suffix", "children" : [ { "terms" : [ { "children" : [ ], "lang_name" : "Proto-Indo-European", "term" : "*-yós", "status" : "ok", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Proto-Italic", "term" : "*-ios", "lang" : "itc-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Old Latin", "term" : "-ios", "lang" : "itc-ola" } ], "keyword_label" : "From", "keyword" : "from" } ], "lang_name" : "Latin", "term" : "-ius", "status" : "ok", "lang" : "la" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Latin", "term" : "-ia", "lang" : "la" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "Latin", "term" : "differentia", "status" : "ok", "lang" : "la" }, { "children" : [ { "terms" : [ { "children" : [ { "keyword_abbrev" : "der.", "is_uncertain" : true, "keyword_label" : "Derived from", "terms" : [ { "id" : "grow", "children" : [ ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*h₂el-", "lang" : "ine-pro" } ], "keyword" : "derived" } ], "lang_name" : "Proto-Italic", "term" : "*-ālis", "status" : "ok", "lang" : "itc-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Latin", "term" : "-ālis", "status" : "ok", "lang" : "la" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "Latin", "term" : "differentiālis", "status" : "ok", "lang" : "la" } ], "keyword" : "lbor" }, { "keyword_abbrev" : "surf.", "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "keyword_abbrev" : "bor.", "keyword_label" : "Borrowed from", "terms" : [ { "children" : [ { "keyword_abbrev" : "der.", "keyword_label" : "Derived from", "terms" : [ { "is_duplicate" : true, "children" : [ ], "status" : [ "la", "differō" ], "lang_name" : "Latin", "term" : "differēns", "lang" : "la" } ], "keyword" : "derived" } ], "lang_name" : "Old French", "term" : "different", "status" : "inline", "lang" : "fro" } ], "keyword" : "bor" } ], "lang_name" : "Middle English", "term" : "different", "status" : "ok", "lang" : "enm" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "English", "term" : "different", "status" : "ok", "lang" : "en" }, { "children" : [ { "terms" : [ { "children" : [ { "keyword_abbrev" : "der.", "keyword_label" : "Derived from", "terms" : [ { "children" : [ { "keyword_abbrev" : "der.", "keyword_label" : "Derived from", "terms" : [ { "is_duplicate" : true, "children" : [ ], "status" : { "1" : "la", "2" : ":inh", "3" : "itc-pro:*-ālis", "id" : "adjectivizing suffix", "title" : "-ālis", "pos" : "suffix" }, "lang_name" : "Latin", "term" : "-ālis", "lang" : "la" } ], "keyword" : "derived" } ], "lang_name" : "Old French", "term" : "-ial", "status" : "inline", "lang" : "fro" } ], "keyword" : "derived" } ], "lang_name" : "Middle English", "term" : "-ial", "status" : "inline", "lang" : "enm" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "English", "term" : "-ial", "status" : "ok", "lang" : "en" } ], "keyword_label" : "By surface analysis,", "is_group" : true, "keyword" : "surf", "is_invisible" : "tree" } ], "lang_name" : "English", "term" : "differential", "status" : "ok", "lang" : "en" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "English", "term" : "codifferential", "status" : "ok", "lang" : "en" }" data-lang="en" data-title="codifferential"> From co- + differential. Head templates: {{en-noun}} codifferential (plural codifferentials)
  1. (mathematics) The projected differential of an extensor field.
    Sense id: en-codifferential-en-noun-s9GGSNJj Categories (other): Mathematics Topics: mathematics, sciences
  2. (differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β).
    Sense id: en-codifferential-en-noun-kpnRXw7u Categories (other): Differential geometry, English entries with etymology texts, English entries with etymology trees, English entries with incorrect language header, English terms prefixed with co-, Pages using etymon with no ID, Pages with 1 entry, Pages with entries, Pages with etymology trees Disambiguation of English entries with etymology texts: 25 75 Disambiguation of English entries with etymology trees: 25 75 Disambiguation of English entries with incorrect language header: 22 78 Disambiguation of English terms prefixed with co-: 38 62 Disambiguation of Pages using etymon with no ID: 21 79 Disambiguation of Pages with 1 entry: 10 90 Disambiguation of Pages with entries: 20 80 Disambiguation of Pages with etymology trees: 23 77

Inflected forms

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  "etymology_text": "Etymology tree\nProto-Indo-European *ḱe\nProto-Indo-European *ḱóm\nProto-Italic *kom\nProto-Italic *kom-\nLatin con-\nLatin co-der.\nEnglish co-\nProto-Indo-European *dwóh₁\nProto-Indo-European *d(w)is-\nProto-Italic *dis-\nLatin dis-\nProto-Indo-European *bʰer-\nProto-Indo-European *bʰéreti\nProto-Italic *ferō\nLatin ferō\nLatin differō\nLatin differēns\nProto-Indo-European *-yós\nProto-Italic *-ios\nOld Latin -ios\nLatin -ius\nLatin -ia\nLatin differentia\nProto-Indo-European *h₂el-der.?\nProto-Italic *-ālis\nLatin -ālis\nLatin differentiālislbor.\nEnglish differential\nEnglish codifferential\nFrom co- + differential.",
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          "ref": "2016, Terence Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation”, in arXiv:",
          "text": "In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as #92;begin#123;matrix#125;#92;partial#95;t#92;omega#43;#123;#92;mathcalL#125;#95;u#92;omegaamp;#61;0#92;#92;uamp;#61;#92;delta#92;tilde#92;eta#123;-1#125;#92;Delta#123;-1#125;#92;omega#92;end#123;matrix#125; where #92;omega is the vorticity 2-form, #123;#92;mathcalL#125;#95;u denotes the Lie derivative with respect to the velocity field u, #92;Delta is the Hodge Laplacian, #92;delta is the codifferential (the negative of the divergence operator), and #92;tilde#92;eta#123;-1#125; is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric #92;eta.",
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          "text": "One important concept is the introduction of codifferential operator",
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      "glosses": [
        "the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
      ],
      "id": "en-codifferential-en-noun-kpnRXw7u",
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          "exterior derivative",
          "exterior derivative"
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          "divergence",
          "divergence"
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          "Hodge star",
          "Hodge star"
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          "Hermitian conjugate",
          "Hermitian conjugate"
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        "(differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
      ]
    }
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  "word": "codifferential"
}

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  "etymology_text": "Etymology tree\nProto-Indo-European *ḱe\nProto-Indo-European *ḱóm\nProto-Italic *kom\nProto-Italic *kom-\nLatin con-\nLatin co-der.\nEnglish co-\nProto-Indo-European *dwóh₁\nProto-Indo-European *d(w)is-\nProto-Italic *dis-\nLatin dis-\nProto-Indo-European *bʰer-\nProto-Indo-European *bʰéreti\nProto-Italic *ferō\nLatin ferō\nLatin differō\nLatin differēns\nProto-Indo-European *-yós\nProto-Italic *-ios\nOld Latin -ios\nLatin -ius\nLatin -ia\nLatin differentia\nProto-Indo-European *h₂el-der.?\nProto-Italic *-ālis\nLatin -ālis\nLatin differentiālislbor.\nEnglish differential\nEnglish codifferential\nFrom co- + differential.",
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          "ref": "2016, Terence Tao, “Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation”, in arXiv:",
          "text": "In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as #92;begin#123;matrix#125;#92;partial#95;t#92;omega#43;#123;#92;mathcalL#125;#95;u#92;omegaamp;#61;0#92;#92;uamp;#61;#92;delta#92;tilde#92;eta#123;-1#125;#92;Delta#123;-1#125;#92;omega#92;end#123;matrix#125; where #92;omega is the vorticity 2-form, #123;#92;mathcalL#125;#95;u denotes the Lie derivative with respect to the velocity field u, #92;Delta is the Hodge Laplacian, #92;delta is the codifferential (the negative of the divergence operator), and #92;tilde#92;eta#123;-1#125; is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric #92;eta.",
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        "The projected differential of an extensor field."
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        "(mathematics) The projected differential of an extensor field."
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        "the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
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        "(differential geometry) the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β)."
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  "word": "codifferential"
}

Download raw JSONL data for codifferential meaning in English (12.9kB)

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2026-05-23 from the enwiktionary dump dated 2026-05-01 using wiktextract (8336b26 and ae80fde). 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.

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