"computational number theory" meaning in English

See computational number theory in All languages combined, or Wiktionary

Proper name

Head templates: {{en-proper noun}} computational number theory
  1. (mathematics, number theory) The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry. Wikipedia link: computational number theory Categories (topical): Mathematics, Number theory Synonyms (field of study dealing with computational methods in number theory): algorithmic number theory Translations (field of study dealing with computational methods in number theory): théorie algorithmique des nombres [feminine] (French), théorie calculatoire des nombres [feminine] (French), algorithmische Zahlentheorie [feminine] (German), teoria computazionale dei numeri [feminine] (Italian), teoria algoritmica dei numeri [feminine] (Italian), teoria computacional dos números [feminine] (Portuguese), teoria algorítmica dos números [feminine] (Portuguese)
    Sense id: en-computational_number_theory-en-name-XAwCOB1v Categories (other): English entries with incorrect language header Topics: mathematics, number-theory, sciences

Download JSON data for computational number theory meaning in English (4.1kB)

{
  "head_templates": [
    {
      "args": {},
      "expansion": "computational number theory",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "Topics studied in computational number theory include algorithms for primality testing and integer factorisation, finding solutions to Diophantine equations and explicit methods in arithmetic geometry.",
          "type": "example"
        },
        {
          "text": "Computational number theory has applications in cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis.",
          "type": "example"
        },
        {
          "text": "1990, Carl Pomerance, editor, Proceedings of Symposia in Applied Mathematics, Volume 42: Cryptology and Computational Number Theory, American Mathematical Society:",
          "type": "quotation"
        },
        {
          "text": "1994, Hari Krishna, Bal Krishna, Kuo-Yu Lin, Jenn-Dong Sun, Computational Number Theory and Digital Signal Processing: Fast Algorithms and Error Control Techniques, CRC Press, https://books.google.com.au/books?id=8u1kx3peO6AC&printsec=frontcover&dq=%22computational+number+theory%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiy0c_SnvjuAhUCyjgGHUIkBnUQ6AEwB3oECCUQAg#v=onepage&q=%22computational%20number%20theory%22&f=false."
        },
        {
          "text": "2001, Kazimierz Alster, Jerzy Urbanowicz, Hugh C. Williams, editors, Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference, Walter de Gruyter:",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry."
      ],
      "id": "en-computational_number_theory-en-name-XAwCOB1v",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "arithmetic geometry",
          "arithmetic geometry"
        ]
      ],
      "raw_glosses": [
        "(mathematics, number theory) The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry."
      ],
      "synonyms": [
        {
          "sense": "field of study dealing with computational methods in number theory",
          "word": "algorithmic number theory"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "fr",
          "lang": "French",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "théorie algorithmique des nombres"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "théorie calculatoire des nombres"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "algorithmische Zahlentheorie"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "teoria computazionale dei numeri"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "teoria algoritmica dei numeri"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "teoria computacional dos números"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "field of study dealing with computational methods in number theory",
          "tags": [
            "feminine"
          ],
          "word": "teoria algorítmica dos números"
        }
      ],
      "wikipedia": [
        "computational number theory"
      ]
    }
  ],
  "word": "computational number theory"
}
{
  "head_templates": [
    {
      "args": {},
      "expansion": "computational number theory",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English terms with usage examples",
        "English uncountable nouns",
        "Quotation templates to be cleaned",
        "en:Mathematics",
        "en:Number theory"
      ],
      "examples": [
        {
          "text": "Topics studied in computational number theory include algorithms for primality testing and integer factorisation, finding solutions to Diophantine equations and explicit methods in arithmetic geometry.",
          "type": "example"
        },
        {
          "text": "Computational number theory has applications in cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis.",
          "type": "example"
        },
        {
          "text": "1990, Carl Pomerance, editor, Proceedings of Symposia in Applied Mathematics, Volume 42: Cryptology and Computational Number Theory, American Mathematical Society:",
          "type": "quotation"
        },
        {
          "text": "1994, Hari Krishna, Bal Krishna, Kuo-Yu Lin, Jenn-Dong Sun, Computational Number Theory and Digital Signal Processing: Fast Algorithms and Error Control Techniques, CRC Press, https://books.google.com.au/books?id=8u1kx3peO6AC&printsec=frontcover&dq=%22computational+number+theory%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiy0c_SnvjuAhUCyjgGHUIkBnUQ6AEwB3oECCUQAg#v=onepage&q=%22computational%20number%20theory%22&f=false."
        },
        {
          "text": "2001, Kazimierz Alster, Jerzy Urbanowicz, Hugh C. Williams, editors, Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference, Walter de Gruyter:",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "arithmetic geometry",
          "arithmetic geometry"
        ]
      ],
      "raw_glosses": [
        "(mathematics, number theory) The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "computational number theory"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "field of study dealing with computational methods in number theory",
      "word": "algorithmic number theory"
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "théorie algorithmique des nombres"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "théorie calculatoire des nombres"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "algorithmische Zahlentheorie"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "teoria computazionale dei numeri"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "teoria algoritmica dei numeri"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "teoria computacional dos números"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "field of study dealing with computational methods in number theory",
      "tags": [
        "feminine"
      ],
      "word": "teoria algorítmica dos números"
    }
  ],
  "word": "computational number theory"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.