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# Frank Luebeck’s tables of Conway polynomials over finite fields

class `sage.databases.conway.``ConwayPolynomials`

  Bases: `_abcoll.Mapping`

  Initialize the database.

  TESTS:

      sage: c = ConwayPolynomials()
      sage: c
      Frank Luebeck's database of Conway polynomials

  `degrees`(p)

    Return the list of integers `n` for which the database of Conway polynomials contains the polynomial of degree `n` over `GF(p)`.

    EXAMPLES:

        sage: c = ConwayPolynomials()
        sage: c.degrees(60821)
        [1, 2, 3, 4]
        sage: c.degrees(next_prime(10^7))
        []

  `has_polynomial`(p, n)

    Return True if the database of Conway polynomials contains the polynomial of degree `n` over `GF(p)`.

    INPUT:

    - `p` – prime number
    - `n` – positive integer

    EXAMPLES:

        sage: c = ConwayPolynomials()
        sage: c.has_polynomial(97, 12)
        True
        sage: c.has_polynomial(60821, 5)
        False

  `polynomial`(p, n)

    Return the Conway polynomial of degree `n` over `GF(p)`, or raise a RuntimeError if this polynomial is not in the database.

    Note

    See also the global function `conway_polynomial` for a more user-friendly way of accessing the polynomial.

    INPUT:

    - `p` – prime number
    - `n` – positive integer

    OUTPUT:

    List of Python int’s giving the coefficients of the corresponding Conway polynomial in ascending order of degree.

    EXAMPLES:

        sage: c = ConwayPolynomials()
        sage: c.polynomial(3, 21)
        (1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
        sage: c.polynomial(97, 128)
        Traceback (most recent call last):
        ...
        RuntimeError: Conway polynomial over F_97 of degree 128 not in database.

  `primes`()

    Return the list of prime numbers `p` for which the database of Conway polynomials contains polynomials over `GF(p)`.

    EXAMPLES:

        sage: c = ConwayPolynomials()
        sage: P = c.primes()
        sage: 2 in P
        True
        sage: next_prime(10^7) in P
        False

class `sage.databases.conway.``DictInMapping`(dict)

  Bases: `_abcoll.Mapping`

  Places dict into a non-mutable mapping.

  TESTS:

      sage: from sage.databases.conway import DictInMapping
      sage: d = {}
      sage: m = DictInMapping(d); m
      {}
      sage: d[0] = 1; m
      {0: 1}
      sage: m[2] = 3
      Traceback (most recent call last):
      ...
      TypeError: 'DictInMapping' object does not support item assignment

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