"vanishing ideal" meaning in English

{
  "forms": [
    {
      "form": "vanishing ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "vanishing ideal (plural vanishing ideals)",
      "name": "en-noun"
    }
  ],
  "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": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "glosses": [
        "An ideal consisting of all polynomials (belonging to a certain polynomial ring) which zero out within a given algebraic variety."
      ],
      "hypernyms": [
        {
          "word": "radical ideal"
        }
      ],
      "id": "en-vanishing_ideal-en-noun-QcjmesHy",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "ideal",
          "ideal#English"
        ],
        [
          "polynomial ring",
          "polynomial ring"
        ],
        [
          "zero out",
          "zero out"
        ],
        [
          "algebraic variety",
          "algebraic variety"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) An ideal consisting of all polynomials (belonging to a certain polynomial ring) which zero out within a given algebraic variety."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "vanishing ideal"
}

{
  "forms": [
    {
      "form": "vanishing ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "vanishing ideal (plural vanishing ideals)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "radical ideal"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English countable nouns",
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        "en:Algebraic geometry"
      ],
      "glosses": [
        "An ideal consisting of all polynomials (belonging to a certain polynomial ring) which zero out within a given algebraic variety."
      ],
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "ideal",
          "ideal#English"
        ],
        [
          "polynomial ring",
          "polynomial ring"
        ],
        [
          "zero out",
          "zero out"
        ],
        [
          "algebraic variety",
          "algebraic variety"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) An ideal consisting of all polynomials (belonging to a certain polynomial ring) which zero out within a given algebraic variety."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "vanishing ideal"
}