Bases: sage.databases.db.Database
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))
[]
Return True if the database of Conway polynomials contains the polynomial of degree n over GF(p).
INPUT:
EXAMPLES:
sage: c = ConwayPolynomials()
sage: c.has_polynomial(97, 12)
True
sage: c.has_polynomial(60821, 5)
False
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:
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.
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