"algebraic analysis" meaning in English

{
  "etymology_text": "The area of study in algebraic geometry began as a research programme, instigated in 1959 by Japanese mathematician Mikio Sato.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "algebraic analysis (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "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",
      "links": [
        [
          "algebraic",
          "algebraic#English"
        ],
        [
          "analysis",
          "analysis#English"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "elementary algebra",
          "elementary algebra"
        ]
      ],
      "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",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "34 66",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        }
      ],
      "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 partial differential operators.",
          "type": "quotation"
        },
        {
          "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"
        ],
        [
          "microfunction",
          "microfunction"
        ]
      ],
      "raw_glosses": [
        "(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"
      ],
      "topics": [
        "algebraic-geometry",
        "algebraic-topology",
        "geometry",
        "mathematics",
        "sciences",
        "topology"
      ],
      "translations": [
        {
          "_dis1": "11 89",
          "code": "fr",
          "lang": "French",
          "sense": "study of systems of linear PDEs",
          "tags": [
            "feminine"
          ],
          "word": "analyse algébrique"
        },
        {
          "_dis1": "11 89",
          "code": "ja",
          "lang": "Japanese",
          "sense": "study of systems of linear PDEs",
          "word": "代数解析"
        },
        {
          "_dis1": "11 89",
          "code": "es",
          "lang": "Spanish",
          "sense": "study of systems of linear PDEs",
          "tags": [
            "masculine"
          ],
          "word": "análisis algebraico"
        }
      ]
    }
  ],
  "wikipedia": [
    "Mikio Sato",
    "algebraic analysis"
  ],
  "word": "algebraic analysis"
}

{
  "categories": [
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "English uncountable nouns"
  ],
  "etymology_text": "The area of study in algebraic geometry began as a research programme, instigated in 1959 by Japanese mathematician Mikio Sato.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "algebraic analysis (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "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."
      ],
      "links": [
        [
          "algebraic",
          "algebraic#English"
        ],
        [
          "analysis",
          "analysis#English"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "elementary algebra",
          "elementary algebra"
        ]
      ],
      "tags": [
        "uncountable"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "en:Algebraic geometry",
        "en:Algebraic topology"
      ],
      "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 partial differential operators.",
          "type": "quotation"
        },
        {
          "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)."
      ],
      "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"
        ],
        [
          "microfunction",
          "microfunction"
        ]
      ],
      "raw_glosses": [
        "(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"
      ],
      "topics": [
        "algebraic-geometry",
        "algebraic-topology",
        "geometry",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "study of systems of linear PDEs",
      "tags": [
        "feminine"
      ],
      "word": "analyse algébrique"
    },
    {
      "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"
}