Another question I just thought about was: Do we want:
1. every element in the universal cyclotomic field living in exactly
one cyclotomic field QQ( \zeta_n ) generated by ZumbroichBasis(n,1)
for some n, or
2. can an element have several monomials living in different
cyclotomic fields.
In gap, it is the first (as there is no universal cyclotomic field but
only smart back and forth going within several CFs: e.g.,
gap> E(8)^2;
E(4)
gap> E(8)+E(8)^2:
E(8)+E(8)^2
whereas in a not redundant basis expression in the universal
cyclotomic field, the second would answer E(8) + E(4). I personally
would prefer the first, as I think is quite annoying if one has longer
expressions with different E(n)'s involved. What do you think?
Best, Christian
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