The normal way to get at the ring of integers would be to write ZK = K.ring_of_integers(). You have defined two separate algebraic objects, a ring and a field, and it is not clear what the relationship is beteween them.
You should have said what version of Sage you are running. In 6.2.rc2, at least, the word "fractional" is spelled correctly. What you posted cannot be a complete Sage sessions, since you do not define zeta0, and the ideal I you define is not the 20th power of anything. In future you should post exactly what you have in a complete session. John Cremona On 6 May 2014 14:52, <[email protected]> wrote: > > > Hi. > > I have some issue with ideals in number fields. I wanted to test something > about cyclotomic polynomials, so I had the following result : > > sage: N = 25 > sage: K.<zeta> = CyclotomicField(N) > sage: n = K.degree() > sage: ZK = ZZ[zeta] > sage: ZK > Order in Number Field in zeta0 with defining Polynomial > x^20+x^15+x^10+x^5+1 > > sage: I=ZK.ideal(5,zeta-1) > sage: I > Fractionnal ideal (5,zeta0-1) > > sage: I.factor() > (Fractionnal ideal (5,zeta0-1))^20 > > sage: I==I^20 > False > > sage: zeta0 > 1 > > sage: zeta > zeta > > I think there is a problem with the zeta0 (actually I tried to enforce the > name of the ZK variable by ZK.<zeta_int> = ZZ[zeta] or ZK.<zeta0> = > ZZ[zeta] or ZK.<zeta> = ZZ[zeta] but that doesn't work : it gives the same > result. > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
