1 | initial version |
Do you mean
sage: from itertools import product
sage: GF2x = GF(2)['x']
sage: for coeffs in product(GF(2), repeat=7):
....: p = GF2x(coeffs + (1,))
....: if p.is_irreducible():
....: print(p)
x^7 + x^6 + 1
x^7 + x^4 + 1
x^7 + x^6 + x^5 + x^4 + 1
x^7 + x^3 + 1
x^7 + x^5 + x^4 + x^3 + 1
x^7 + x^6 + x^5 + x^2 + 1
x^7 + x^6 + x^4 + x^2 + 1
x^7 + x^4 + x^3 + x^2 + 1
x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + 1
x^7 + x + 1
x^7 + x^6 + x^4 + x + 1
x^7 + x^6 + x^3 + x + 1
x^7 + x^5 + x^3 + x + 1
x^7 + x^5 + x^2 + x + 1
x^7 + x^6 + x^5 + x^4 + x^2 + x + 1
x^7 + x^3 + x^2 + x + 1
x^7 + x^6 + x^5 + x^3 + x^2 + x + 1
x^7 + x^5 + x^4 + x^3 + x^2 + x + 1
2 | No.2 Revision |
Do you mean
sage: from itertools import product
sage: GF2x = GF(2)['x']
sage: for coeffs in product(GF(2), repeat=7):
repeat=8):
....: p = GF2x(coeffs + (1,))
....: if p.is_irreducible():
....: print(p)
x^7 + x^6 + 1
x^7 + x^4 + 1
x^7 + x^6 + x^5 + x^4 + 1
x^7 + x^3 + 1
x^7 + x^5 + x^4 + x^3 + 1
x^7 + x^6 + x^5 + x^2 + 1
x^7 + x^6 + x^4 + x^2 + 1
x^7 + x^4 + x^3 + x^2 + 1
x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + 1
x^7 + x + 1
x^7 + x^6 + x^4 + x + 1
x^7 + x^6 + x^3 + x + 1
x^7 + x^5 + x^3 + x + 1
x^7 + x^5 + x^2 + x + 1
x^7 + x^6 + x^5 + x^4 + x^2 + x + 1
x^7 + x^3 + x^2 + x + 1
x^7 + x^6 + x^5 + x^3 + x^2 + x + 1
x^7 ....:
x^8 + x^7 + x^5 + x^4 + 1
x^8 + x^6 + x^5 + x^4 + 1
x^8 + x^7 + x^5 + x^3 + 1
x^8 + x^6 + x^5 + x^3 + 1
x^8 + x^5 + x^4 + x^3 + 1
x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
x^8 + x^6 + x^5 + x^2 + 1
x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1
x^8 + x^7 + x^3 + x^2 + 1
x^8 + x^6 + x^3 + x^2 + 1
x^8 + x^5 + x^3 + x^2 + 1
x^8 + x^4 + x^3 + x^2 + 1
x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1
x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 1
x^8 + x^7 + x^6 + x + 1
x^8 + x^7 + x^5 + x + 1
x^8 + x^6 + x^5 + x + 1
x^8 + x^7 + x^6 + x^5 + x^4 + x + 1
x^8 + x^7 + x^3 + x + 1
x^8 + x^5 + x^3 + x + 1
x^8 + x^4 + x^3 + x + 1
x^8 + x^6 + x^5 + x^4 + x^3 + x + 1
x^8 + x^7 + x^2 + x + 1
x^8 + x^7 + x^6 + x^5 + x^2 + x + 1
x^8 + x^7 + x^6 + x^4 + x^2 + x + 1
x^8 + x^6 + x^5 + x^4 + x^2 + x + 1
x^8 + x^7 + x^6 + x^3 + x^2 + x + 1
x^8 + x^7 + x^4 + x^3 + x^2 + x + 1
x^8 + x^6 + x^4 + x^3 + x^2 + x + 1
x^8 + x^5 + x^4 + x^3 + x^2 + x + 1
Some explanations:
GF(2^8)
if and only if it has degree 8 and is irreducibleGF(2)^8