"symmetric polynomial" meaning in English

{
  "forms": [
    {
      "form": "symmetric polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "symmetric polynomial (plural symmetric polynomials)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
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          "source": "w"
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
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            "Formal sciences",
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        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Polynomials",
          "orig": "en:Polynomials",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "x+y+z"
        },
        {
          "text": "xyz"
        },
        {
          "text": "2x²+2y²+2z², etc."
        },
        {
          "text": "An example of a non-symmetric polynomial is x+2y: if we interchange x and y, this polynomial changes to 2x+y."
        }
      ],
      "glosses": [
        "A polynomial which remains unchanged if its variables are permuted"
      ],
      "hyponyms": [
        {
          "word": "elementary symmetric polynomial"
        }
      ],
      "id": "en-symmetric_polynomial-en-noun-KNYrd43m",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "permute",
          "permute"
        ]
      ],
      "raw_glosses": [
        "(algebra) A polynomial which remains unchanged if its variables are permuted"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "symmetric polynomial"
      ]
    }
  ],
  "word": "symmetric polynomial"
}

{
  "forms": [
    {
      "form": "symmetric polynomials",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "symmetric polynomial (plural symmetric polynomials)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "elementary symmetric polynomial"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "English countable nouns",
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        "en:Polynomials"
      ],
      "examples": [
        {
          "text": "x+y+z"
        },
        {
          "text": "xyz"
        },
        {
          "text": "2x²+2y²+2z², etc."
        },
        {
          "text": "An example of a non-symmetric polynomial is x+2y: if we interchange x and y, this polynomial changes to 2x+y."
        }
      ],
      "glosses": [
        "A polynomial which remains unchanged if its variables are permuted"
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "permute",
          "permute"
        ]
      ],
      "raw_glosses": [
        "(algebra) A polynomial which remains unchanged if its variables are permuted"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "symmetric polynomial"
      ]
    }
  ],
  "word": "symmetric polynomial"
}