I'm sorry but I use the notebook / worksheet working on virtual box so copy-paste the file is long and painful. So actually I wrote it manually, that's why there is a mistake on "Fractional". My version is 5.13. I know I could have use K.ring_of_integers(), but I don't want that : I don't want sage to compute the ring of integer when I know it.
I restarted the notebook, and tried once more to have a complete session. I admit I was unable to reproduce the factor problem, but there is still something odd : x should not be 1. sage: N=25 sage: K.<zeta> = CyclotomicField(N) sage: n = K.degree() sage: ZK.<x> = ZZ[zeta] sage: ZK Order in Number Field in zeta0 with defining polynomial x^20 + x^15 + x^10 + x^5 + 1 sage: x 1 sage: zeta0 Traceback (most recent call last): ... NameError: name 'zeta0' is not defined sage: x^2-1 0 On Tuesday, 6 May 2014 15:12:32 UTC+1, John Cremona wrote: > > 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, <ad1...@bristol.ac.uk <javascript:>> 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 sage-support...@googlegroups.com <javascript:>. > > To post to this group, send email to > > sage-s...@googlegroups.com<javascript:>. > > > 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 sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
