It is a lack of coercion discovery

sage: K12.<zeta12> = CyclotomicField(12)
sage: K6.<zeta6> = CyclotomicField(6,embedding=zeta12**2)
sage: K3.<zeta3> = CyclotomicField(3,embedding=zeta6**2)

Then

sage: K6.has_coerce_map_from(K3)
True
sage: K12.has_coerce_map_from(K6)
True

But

sage: K12.has_coerce_map_from(K3)
!BOOM!

Could you test this on older Sage version? And even better find out the way coercion was discovered.

Vincent

On 26/04/16 08:57, John Cremona wrote:
In a publisged paper [1] I gave a reference to a Sage script which
could reproduce the results of the paper.  The output of this (using
sagetex) is also in the ArXiV version of the paper [2].

That was 3 years ago, and I just tried to see if that Sage script
would still work.  It didn't.  In the script I have several nested
cyclotomic fields, and I found that the easy way to be able to compute
with them all at once (as a mathematician would) was to first define
the largest one, Q(zeta_1092), and then define all the others as
subfields using the embedding= construction.  Here are the relevant
fields and assignments:

sage: Q1092.<zeta1092> = CyclotomicField(1092)
sage: Q84.<zeta84> = CyclotomicField(84, embedding=zeta1092^13)
sage: Q12.<zeta12> = CyclotomicField(12, embedding=zeta84^7)
sage: Q7.<zeta7> = CyclotomicField(7, embedding=zeta84^12)
sage: zeta7p=zeta7+1/zeta7
sage: Q7p.<zeta7p>=NumberField(zeta7p.minpoly(), embedding=zeta7+1/zeta7)
sage: a=1/zeta7p
sage: a*zeta12 # boom

Does anyone know how or why this happened, or how to do this
calculation now?  It used to be that one could do arithmetic between
elements of all these fields and Sage would magically find the
relavant embeddings.

John


[1] Cremona and Banwait, Tetrahedral Elliptic Curves and the
local-to-global principle for Isogenies, Algebra & Number Theory 8-5
(2014), 1201--1229. DOI 10.2140/ant.2014.8.1201
[2] http://arxiv.org/abs/1306.6818


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