# Translating a list of polynomials using sage

I have a list of polynomials in Sage as follows:

```
n=5
W=[P.coxeter_polynomial() for P in posets(n)]
```

Now I want to have the list of all such polynomials as polynomials in `R.<x> = PolynomialRing(ComplexField(100))`

.

My question is:
Is there an easy way to translate the above list W so that Sage views every polynomial in that list as a polynomial in `R.<x> = PolynomialRing(ComplexField(100))`

?

Side remark :

`sage: P.is_cyclotomic_product()`

is useful to recognize polynomials with all their roots on the unit circle.