Revision history [back]

I want to print the primitive root of unity $\zeta_m$ associated with the $m'th$ cyclotomic polynomial $\phi_m(x)$ where m is a power of two. I want to print the primitive root of this polynomial over $\mathbb{Z}_p$ with $p$ prime.

I tried the following as an example, with $p = 12206081$ and $m = 16384$. However this prints all the totient(16384) roots rather than just the primitive root.

x = PolynomialRing(GF(12206081), 'x').gen()

n = euler_phi(16384)

f = x^n + 1

print(f.roots())

I want to print the primitive root of unity $\zeta_m$ associated with the $m'th$ cyclotomic polynomial $\phi_m(x)$ where m is a power of two. I want to print the primitive root of this polynomial over $\mathbb{Z}_p$ with $p$ prime.

I tried the following as an example, with $p = 12206081$ and $m = 16384$. However this prints all the totient(16384) roots rather than just the primitive root.

x = PolynomialRing(GF(12206081), 'x').gen()
 
'x').gen()
n = euler_phi(16384)
 
euler_phi(16384)
f = x^n + 1
 
print(f.roots())1
print(f.roots())