"polynomial form" meaning in All languages combined

{
  "forms": [
    {
      "form": "polynomial forms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "polynomial form (plural polynomial forms)",
      "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",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
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          "name": "Pages with entries",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
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            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Polynomials",
          "orig": "en:Polynomials",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)"
      ],
      "id": "en-polynomial_form-en-noun-xBDqI8W9",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "linear combination",
          "linear combination"
        ],
        [
          "power",
          "power"
        ],
        [
          "indeterminate",
          "indeterminate"
        ],
        [
          "integral domain",
          "integral domain"
        ],
        [
          "field",
          "field"
        ],
        [
          "variable",
          "variable"
        ],
        [
          "polynomial function",
          "polynomial function"
        ],
        [
          "Gaussian integer",
          "Gaussian integer"
        ],
        [
          "monoid",
          "monoid"
        ]
      ],
      "raw_glosses": [
        "(algebra) A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "polynomial form"
}

{
  "forms": [
    {
      "form": "polynomial forms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "polynomial form (plural polynomial forms)",
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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:Algebra",
        "en:Polynomials"
      ],
      "glosses": [
        "A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)"
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "linear combination",
          "linear combination"
        ],
        [
          "power",
          "power"
        ],
        [
          "indeterminate",
          "indeterminate"
        ],
        [
          "integral domain",
          "integral domain"
        ],
        [
          "field",
          "field"
        ],
        [
          "variable",
          "variable"
        ],
        [
          "polynomial function",
          "polynomial function"
        ],
        [
          "Gaussian integer",
          "Gaussian integer"
        ],
        [
          "monoid",
          "monoid"
        ]
      ],
      "raw_glosses": [
        "(algebra) A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "polynomial form"
}