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Creating a polynomial with coefficients in a cyclotomic fields

Hi everyone

I am trying to create a polynomial from a list of its coefficients. In the past, I have done so when the coefficients are all integers (or they belong to a fixed number field). Typically, that would require me to declare the coefficient field at the beginning. The syntax would look like this

R.<x> = PolynomialRing(QQ)

def test(p):
    v = srange(1,p)
    v.reverse()
    F = R(v)
    return F

After that, I can create $F$ and do some calculations such as factoring $F$ over $\mathbb{Q}$.

My new problem is that I want to create a polynomial with coefficients in (varying) cyclotomic field. I tried the following code but it did not work (it will work if I use the coefficient field as $\overline{\mathbb{Q}}$. However, I won't be able to do factorization over the relevant cyclotomic field).

def test_2(p):
    K1.<x> = CyclotomicField(p**2)
    v = [E(p)**s for s in srange(0,p)]
    v.reverse()
    F = K1(v)
    return F

I appreciate any advice and suggestions.

Thank you for your help.

Best wishes, Tung