def find_primitive_roots(degree):
roots = []
n = pow(modulus, degree)
for i in range(2, n):
e = decimal_to_base_n(i, modulus)
p = PolynomialOnRing(e)
if(is_primitive_root(p)):
roots.append(p)
return roots
def find_minimal_polynomial(polynomial):
zero = PolynomialOnRing([0])
i = 1
while True:
minimal_polynomial = decimal_to_base_n(i, modulus)
p = PolynomialOnRing([0])
for degree, coefficient in enumerate(reversed(minimal_polynomial)):
c = PolynomialOnRing([coefficient])
p += c * pow(polynomial, degree)
if(p == zero):
return PolynomialOnRing(minimal_polynomial)
i += 1
