Frank Lübeck’s tables of Conway polynomials over finite fields¶
- class sage.databases.conway.ConwayPolynomials[source]¶
- Bases: - Mapping- Initialize the database. - degrees(p)[source]¶
- Return the list of integers - nfor which the database of Conway polynomials contains the polynomial of degree- nover- GF(p).- EXAMPLES: - sage: c = ConwayPolynomials() sage: c.degrees(60821) [1, 2, 3, 4] sage: c.degrees(next_prime(10^7)) [] - >>> from sage.all import * >>> c = ConwayPolynomials() >>> c.degrees(Integer(60821)) [1, 2, 3, 4] >>> c.degrees(next_prime(Integer(10)**Integer(7))) [] 
 - has_polynomial(p, n)[source]¶
- Return - Trueif the database of Conway polynomials contains the polynomial of degree- nover- 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 - >>> from sage.all import * >>> c = ConwayPolynomials() >>> c.has_polynomial(Integer(97), Integer(12)) True >>> c.has_polynomial(Integer(60821), Integer(5)) False 
 - polynomial(p, n)[source]¶
- Return the Conway polynomial of degree - nover- GF(p), or raise a- RuntimeErrorif this polynomial is not in the database.- Note - See also the global function - conway_polynomialfor 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. - >>> from sage.all import * >>> c = ConwayPolynomials() >>> c.polynomial(Integer(3), Integer(21)) (1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) >>> c.polynomial(Integer(97), Integer(128)) Traceback (most recent call last): ... RuntimeError: Conway polynomial over F_97 of degree 128 not in database. 
 - primes()[source]¶
- Return the list of prime numbers - pfor 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 - >>> from sage.all import * >>> c = ConwayPolynomials() >>> P = c.primes() >>> Integer(2) in P True >>> next_prime(Integer(10)**Integer(7)) in P False