> sage: > F.<x>=GF(2^8,name='x',modulus=z^8+z^4+z^3+z^2+1,check_irreducible=False) > sage: F > Finite Field in x of size 2^8 > sage: F.polynomial() > x^8 + x^4 + x^3 + x^2 + 1 > > Andrzej Chrzeszczyk
In this case sage does not complaint, but check_irreducible is not intended for this use, but to avoid the time of checking that your polynomial is irreducible whenever you are sure it is irreducible. If you put a reducible polynomial then the behaviour of GF is undefined and will probably be wrong. sage: K.<z>=GF(2)[] sage: F.<x>=GF(2^8,name='x',modulus=z^8 + z^7 + z^4 + z^3 + z + 1,check_irreducible=False) sage: F Finite Field in x of size 2^8 sage: F.polynomial() x^8 + x^4 sage: x+1 1 sage: x+ (1-1) x sage: (x+1)-1 0 sage: x^8 x^4 If you really want to work with this modulus, you do not have to use GF which is for finite fields. You are looking for quotient algebras sage: F.<x>=K.quotient(z^8 + z^7 + z^4 + z^3 + z + 1) sage: x+1 x + 1 sage: x^8 x^7 + x^4 + x^3 + x + 1 sage: 1/x x^7 + x^6 + x^3 + x^2 + 1 sage: 1/(x+1) ... ZeroDivisionError: element x + 1 of quotient polynomial ring not invertible -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
