Kiran, Did this ever work?
When I have needed to work in several nested cyclotomic fields I have done this using the Lord of the Rings strategy "One ring to contain them all": define the largest one first and then define the subfields with explicit embeddings. Taken from code at https://arxiv.org/abs/1306.6818 I have The following lines which first define Q(zeta_1092) and then various subfields. All that worked. However I tried changing your second line to K1.<z1> = CyclotomicField(3, embedding=z^4) and it did not help. John Q1092.<zeta1092> = CyclotomicField(1092) conj1092 = Q1092.hom([zeta1092^(-1)]) # complex conjugation on Q1092 # Q13.<zeta13> = CyclotomicField(13, embedding=zeta1092^84) eQ13Q1092 = Q13.hom([Q1092(zeta13)]) # embedding Q13 into Q1092 Q13sigma = Q13.hom([zeta13^4]) # auto of order 3 of Q13 Q13aut = Q13.hom([zeta13^2]) # auto of order 6 of Q13 # Q91.<zeta91> = CyclotomicField(91,embedding=zeta1092^12) eQ91Q1092 = Q91.hom([zeta1092^12]) # embedding Q91 into Q1092 eQ13Q91 = Q13.hom([zeta91^7]) # embedding Q13 into Q91 Q91aut = Q91.hom([zeta91^53]) # auto of order 3 of Q91 fixing Q13 # Q84.<zeta84> = CyclotomicField(84, embedding=zeta1092^13) conj84 = Q84.hom([zeta84^(-1)]) # complex conjugation on Q84 Q12.<zeta12> = CyclotomicField(12, embedding=zeta84^7) Q7.<zeta7> = CyclotomicField(7, embedding=zeta84^12) Q1092._latex_ = lambda: "\mathbb{Q}(\zeta_{1092})" Q13._latex_ = lambda: "\mathbb{Q}(\zeta_{13})" Q91._latex_ = lambda: "\mathbb{Q}(\zeta_{91})" Q84._latex_ = lambda: "\mathbb{Q}(\zeta_{84})" Q12._latex_ = lambda: "\mathbb{Q}(\zeta_{12})" Q7._latex_ = lambda: "\mathbb{Q}(\zeta_{7})" zeta7p=zeta7+1/zeta7 Q7p.<zeta7p>=NumberField(zeta7p.minpoly(), embedding=zeta7+1/zeta7) # zeta13pp = zeta13+zeta13^5+zeta13^8+zeta13^12 # generates cubic subfield Q13pp.<zeta13pp> = NumberField(zeta13pp.minpoly(), embedding=zeta13pp) eQ13ppQ13 = Q13pp.hom([Q13(zeta13pp)]) # zeta13c = zeta13+zeta13^3+zeta13^9 # generates quartic subfield Q13c.<zeta13c> = NumberField(zeta13c.minpoly(), embedding=zeta13c) eQ13cQ13 = Q13c.hom([Q13(zeta13c)]) Q7p._latex_ = lambda: "\mathbb{Q}(\zeta_{7}^{+})" Q13pp._latex_ = lambda: "\mathbb{Q}(\zeta_{13}^{++})" Q13c._latex_ = lambda: "\mathbb{Q}(\zeta_{13}^{c})" On Sat, 18 Apr 2020 at 23:30, Kiran Kedlaya <[email protected]> wrote: > > I've already created ticket #29511 for this, but to advertise this more > broadly: there seems to be an issue with the canonical embedding of one > cyclotomic field into another, where elements that come from the subfield > cannot always be coerced back. > {{{ > > sage: K.<z> = CyclotomicField(12) > sage: K1.<z1> = CyclotomicField(3) > sage: K(z1) in K1 > True > sage: K1(K(z1)) > z1 > > sage: K(2) in K1 ## This is the source of the trouble > > False > > sage: K1(K(2)) ## Error! > > ... > > }}} > > > I am up for trying to fix this myself, but I probably need some help from > someone who understands coercion in Sage better than I do. > > > Kiran > > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/d4708760-19b2-4a5c-a0b4-756eb592b08c%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/CAD0p0K6OWMB5sb3ZwwOWWEwfop-dXqnb5%2BtdGr52f2A%2Bx8moZw%40mail.gmail.com.
