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2015-03-03 22:04:35 +0200 commented answer Interpreting an element of CyclotomicField as an element of polynomial ring

Thank you for your prompt reply. This is useful to know, but I had in mind something else. Specifically, what I was trying to do was to recast Z3 as the generator of Z4. I am trying to compute a certain semiclassical approximation, i.e., I try to successively recast a given expression in z as expressions in various cyclotomic fields.

2015-03-03 15:12:21 +0200 asked a question Interpreting an element of CyclotomicField as an element of polynomial ring

I am trying to write a function that sums up numbers in different cyclotomic field formally, i.e., as expressions in $z$ where $z$ is the corresponding primitive root of unity. I run into a type error, however, as sage wouldn't let me sum elements of two different cyclotomic fields. Is there a way to typecast an expression in one cyclotomic field into the other, or, better yet, to a polynomial ring?