I found the following:
{{{
sage: N.<s2,s3,s5> = NumberField([x^2-2, x^2-3, x^2-5],'s2,s3,s5')
sage: M = N.absolute_field('gamma')
sage: N_to_M = M.structure()[1]
sage: phi = N.hom([N_to_M(s2)])
sage: phi(s2) == N_to_M(s2)
True
sage: phi(s3) == N_to_M(s3)
True
sage: phi(s5) == N_to_M(s5)
False
sage: phi(s5) == -N_to_M(s5)
True
}}}
I would expect that phi(s5) == N_to_M(s5), but I am not sure if this
is a bug or a feature. Relative number fields seem hard to deal with.
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