Frank Luebeck’s tables of Conway polynomials over finite fields¶
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class
sage.databases.conway.
ConwayPolynomials
¶ Bases:
collections.abc.Mapping
Initialize the database.
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degrees
(p)¶ Return the list of integers
n
for which the database of Conway polynomials contains the polynomial of degreen
overGF(p)
.EXAMPLES:
sage: c = ConwayPolynomials() sage: c.degrees(60821) [1, 2, 3, 4] sage: c.degrees(next_prime(10^7)) []
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has_polynomial
(p, n)¶ Return True if the database of Conway polynomials contains the polynomial of degree
n
overGF(p)
.INPUT:
p
– prime numbern
– positive integer
EXAMPLES:
sage: c = ConwayPolynomials() sage: c.has_polynomial(97, 12) True sage: c.has_polynomial(60821, 5) False
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polynomial
(p, n)¶ Return the Conway polynomial of degree
n
overGF(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 numbern
– 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.
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primes
()¶ Return the list of prime numbers
p
for which the database of Conway polynomials contains polynomials overGF(p)
.EXAMPLES:
sage: c = ConwayPolynomials() sage: P = c.primes() sage: 2 in P True sage: next_prime(10^7) in P False
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class
sage.databases.conway.
DictInMapping
(dict)¶ Bases:
collections.abc.Mapping
Places dict into a non-mutable mapping.