"elementary symmetric polynomial" meaning in English

{
  "forms": [
    {
      "form": "elementary symmetric polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {
        "head": "elementary symmetric polynomial"
      },
      "expansion": "elementary symmetric polynomial (plural elementary symmetric polynomials)",
      "name": "en-noun"
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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        {
          "kind": "other",
          "langcode": "en",
          "name": "Polynomials",
          "orig": "en:Polynomials",
          "parents": [],
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        }
      ],
      "glosses": [
        "a coefficient of some power of t in (t+x_1)(t+x_2)⋯(t+x_n), for some n∈ N"
      ],
      "hypernyms": [
        {
          "word": "symmetric polynomial"
        }
      ],
      "id": "en-elementary_symmetric_polynomial-en-noun-ZdtLHpwN",
      "links": [
        [
          "algebra",
          "algebra"
        ]
      ],
      "raw_glosses": [
        "(algebra) a coefficient of some power of t in (t+x_1)(t+x_2)⋯(t+x_n), for some n∈ N"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "algebra",
          "word": "symmetrinen alkeispolynomi"
        }
      ]
    }
  ],
  "word": "elementary symmetric polynomial"
}

{
  "forms": [
    {
      "form": "elementary symmetric polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
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        "head": "elementary symmetric polynomial"
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      "expansion": "elementary symmetric polynomial (plural elementary symmetric polynomials)",
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  ],
  "hypernyms": [
    {
      "word": "symmetric polynomial"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        "en:Algebra",
        "en:Polynomials"
      ],
      "glosses": [
        "a coefficient of some power of t in (t+x_1)(t+x_2)⋯(t+x_n), for some n∈ N"
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ]
      ],
      "raw_glosses": [
        "(algebra) a coefficient of some power of t in (t+x_1)(t+x_2)⋯(t+x_n), for some n∈ N"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
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  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "algebra",
      "word": "symmetrinen alkeispolynomi"
    }
  ],
  "word": "elementary symmetric polynomial"
}