"Hodge decomposition" meaning in All languages combined

{
  "etymology_text": "Named after W. V. D. Hodge.",
  "forms": [
    {
      "form": "Hodge decompositions",
      "tags": [
        "plural"
      ]
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  ],
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      "expansion": "Hodge decomposition (plural Hodge decompositions)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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      ],
      "glosses": [
        "A decomposition of a differential form according to the Hodge theorem."
      ],
      "id": "en-Hodge_decomposition-en-noun-B50oEkGx",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "decomposition",
          "decomposition"
        ],
        [
          "differential form",
          "differential form"
        ],
        [
          "Hodge theorem",
          "Hodge theorem"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A decomposition of a differential form according to the Hodge theorem."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "W. V. D. Hodge"
      ]
    }
  ],
  "word": "Hodge decomposition"
}

{
  "etymology_text": "Named after W. V. D. Hodge.",
  "forms": [
    {
      "form": "Hodge decompositions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "Hodge decomposition (plural Hodge decompositions)",
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "A decomposition of a differential form according to the Hodge theorem."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "decomposition",
          "decomposition"
        ],
        [
          "differential form",
          "differential form"
        ],
        [
          "Hodge theorem",
          "Hodge theorem"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A decomposition of a differential form according to the Hodge theorem."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "W. V. D. Hodge"
      ]
    }
  ],
  "word": "Hodge decomposition"
}