On 6 May 2014 16:11, <[email protected]> wrote: > 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.
The ring of integers is computed by the pari library. I don't know if pari checks to see if the field is cyclotomic and uses a short-cut if it is. We should check that, and of not then Sage could put in the shortcut instead; then you would not have to do what you were doing. > > 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. Agree, and that is a bug in the way that the syntax ZK.<x> = ... is interpreted. Try replacing that line with sage: ZK = ZZ[zeta] sage: x = ZK.gen(0) sage: x zeta0 but even more simply set sage: ZK = K.order(zeta) (but there may be a delay when Sage first decides that it needs to test sage: ZK.is_maximal() True though you could try to cheat like this sage: ZK=K.order(zeta) sage: ZK.is_maximal = lambda: True sage: ZK.is_maximal() True John > > 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, <[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. -- 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.
