Dear Waldek, Waldek Hebisch <[EMAIL PROTECTED]> writes:
> I wonder what shall we do with issue 351. [...] > One possibility is to prevent creation of fake fields: when creating COMPLEX > F we may try to check if x^2 - 1 is irreducible over F. In general this may > be hard to check, but just looking at characteristic we can reject PF 5 > cheaply. I just tried to find out when x^2+1 factors in a finite field, but it seems that the characteristic is not enough to determine this. It seems that * For prime fields with characteristic p, x^2+1 factors if and only if p mod 4 = 1 * More generally, for finite fields with p^m elements and m odd, x^2+1 factors if p mod 4 = 1, if m is even, x^2+1 always factors. Maybe for infinite fields we just try to factor(x^2+1) and check the number of factors. However, there is a problem: currently, SPAD does not allow conditional exports being triggered by functions, but only by "has" and "is" statements, it seems. At least, I couldn't find an example, nor could I make up one. :-( Martin _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
