"algebraic analysis" meaning in English

See algebraic analysis in All languages combined, or Wiktionary

Noun

Etymology: The area of study in algebraic geometry began as a research programme, instigated in 1959 by Japanese mathematician Mikio Sato. Head templates: {{en-noun|-}} algebraic analysis (uncountable)
  1. Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems. Tags: uncountable
    Sense id: en-algebraic_analysis-en-noun-cWZsYwUW
  2. (algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions). Tags: uncountable Categories (topical): Algebraic geometry, Algebraic topology Translations (study of systems of linear PDEs): analyse algébrique [feminine] (French), 代数解析 (Japanese), análisis algebraico [masculine] (Spanish)
    Sense id: en-algebraic_analysis-en-noun-7sVjvn4x Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with French translations, Terms with Japanese translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 34 66 Disambiguation of Entries with translation boxes: 23 77 Disambiguation of Pages with 1 entry: 35 65 Disambiguation of Pages with entries: 33 67 Disambiguation of Terms with French translations: 27 73 Disambiguation of Terms with Japanese translations: 26 74 Disambiguation of Terms with Spanish translations: 29 71 Topics: algebraic-geometry, algebraic-topology, geometry, mathematics, sciences, topology Disambiguation of 'study of systems of linear PDEs': 14 86
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "glosses": [
        "Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems."
      ],
      "id": "en-algebraic_analysis-en-noun-cWZsYwUW",
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          "algebra",
          "algebra"
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        [
          "elementary algebra",
          "elementary algebra"
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      ],
      "tags": [
        "uncountable"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebraic topology",
          "orig": "en:Algebraic topology",
          "parents": [
            "Algebra",
            "Topology",
            "Mathematics",
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        },
        {
          "_dis": "35 65",
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          "_dis": "29 71",
          "kind": "other",
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      "examples": [
        {
          "text": "1986, Goro Kato (translator), Masaki Kashiwara, Takahiro Kawai, Tatsuo Kimura, Foundations of Algebraic Analysis, Princeton Universty Press, https://books.google.com.au/books?id=qYUrDgAAQBAJ&printsec=frontcover&dq=%22algebraic+analysis%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiK5MSlvsLsAhWXbn0KHbPuBPQQ6AEwAnoECAYQAg#v=onepage&q=%22algebraic%20analysis%22&f=false."
        },
        {
          "ref": "1999, Goro Kato, Daniele C. Struppa, Fundamentals of Algebraic Microlocal Analysis, Marcel Dekker, page v:",
          "text": "In their classical work [123], Kashiwara, Kawai, and Kimura pointedly observe that the Japanese algebraic analysis is really the algebraic analysis in the tradition of Euler; we may add that what we mean by algebraic microlocal analysis is the successful attempt to adapt the methods of abstract algebraic geometry to the non-commutative setting in which the base ring is now the ring of variable coefficients^([sic]) partial differential operators.",
          "type": "quote"
        },
        {
          "text": "2008, Yoshitsugu Takei, The work of T. Kawai on exact WKB analysis, T. Aoki, H. Majima, Y. Takei, N. Tose (editors), Algebraic Analysis of Differential Equations, Springer, page 19,\nThus Kawai has been engaged mainly in the research of exact WKB analysis or algebraic analysis of singular perturbation theory since 1989."
        }
      ],
      "glosses": [
        "The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions)."
      ],
      "id": "en-algebraic_analysis-en-noun-7sVjvn4x",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "algebraic topology",
          "algebraic topology"
        ],
        [
          "linear",
          "linear"
        ],
        [
          "partial differential equation",
          "partial differential equation"
        ],
        [
          "sheaf theory",
          "sheaf theory"
        ],
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "function",
          "function"
        ],
        [
          "hyperfunction",
          "hyperfunction"
        ],
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          "microfunction",
          "microfunction"
        ]
      ],
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        "(algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions)."
      ],
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      ],
      "topics": [
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        "geometry",
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        "topology"
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        {
          "_dis1": "14 86",
          "code": "fr",
          "lang": "French",
          "sense": "study of systems of linear PDEs",
          "tags": [
            "feminine"
          ],
          "word": "analyse algébrique"
        },
        {
          "_dis1": "14 86",
          "code": "ja",
          "lang": "Japanese",
          "sense": "study of systems of linear PDEs",
          "word": "代数解析"
        },
        {
          "_dis1": "14 86",
          "code": "es",
          "lang": "Spanish",
          "sense": "study of systems of linear PDEs",
          "tags": [
            "masculine"
          ],
          "word": "análisis algebraico"
        }
      ]
    }
  ],
  "wikipedia": [
    "Mikio Sato",
    "algebraic analysis"
  ],
  "word": "algebraic analysis"
}
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        "Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems."
      ],
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          "analysis",
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          "algebra",
          "algebra"
        ],
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          "elementary algebra"
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          "text": "1986, Goro Kato (translator), Masaki Kashiwara, Takahiro Kawai, Tatsuo Kimura, Foundations of Algebraic Analysis, Princeton Universty Press, https://books.google.com.au/books?id=qYUrDgAAQBAJ&printsec=frontcover&dq=%22algebraic+analysis%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiK5MSlvsLsAhWXbn0KHbPuBPQQ6AEwAnoECAYQAg#v=onepage&q=%22algebraic%20analysis%22&f=false."
        },
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          "ref": "1999, Goro Kato, Daniele C. Struppa, Fundamentals of Algebraic Microlocal Analysis, Marcel Dekker, page v:",
          "text": "In their classical work [123], Kashiwara, Kawai, and Kimura pointedly observe that the Japanese algebraic analysis is really the algebraic analysis in the tradition of Euler; we may add that what we mean by algebraic microlocal analysis is the successful attempt to adapt the methods of abstract algebraic geometry to the non-commutative setting in which the base ring is now the ring of variable coefficients^([sic]) partial differential operators.",
          "type": "quote"
        },
        {
          "text": "2008, Yoshitsugu Takei, The work of T. Kawai on exact WKB analysis, T. Aoki, H. Majima, Y. Takei, N. Tose (editors), Algebraic Analysis of Differential Equations, Springer, page 19,\nThus Kawai has been engaged mainly in the research of exact WKB analysis or algebraic analysis of singular perturbation theory since 1989."
        }
      ],
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        "The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions)."
      ],
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        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "algebraic topology",
          "algebraic topology"
        ],
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          "linear",
          "linear"
        ],
        [
          "partial differential equation",
          "partial differential equation"
        ],
        [
          "sheaf theory",
          "sheaf theory"
        ],
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          "complex analysis",
          "complex analysis"
        ],
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          "function",
          "function"
        ],
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          "hyperfunction",
          "hyperfunction"
        ],
        [
          "microfunction",
          "microfunction"
        ]
      ],
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        "(algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions)."
      ],
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        "uncountable"
      ],
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  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "study of systems of linear PDEs",
      "tags": [
        "feminine"
      ],
      "word": "analyse algébrique"
    },
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      "code": "ja",
      "lang": "Japanese",
      "sense": "study of systems of linear PDEs",
      "word": "代数解析"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "study of systems of linear PDEs",
      "tags": [
        "masculine"
      ],
      "word": "análisis algebraico"
    }
  ],
  "wikipedia": [
    "Mikio Sato",
    "algebraic analysis"
  ],
  "word": "algebraic analysis"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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