Units in number fields.
I want to get the expression of a unit in a number field in terms of the base by means of
Here is my code:
K.<z> = CyclotomicField(21) U = UnitGroup(K) U.fundamental_units() a=(z^3+z^6+z^12)/2+1 # a is (3 + i sqrt)/4 so it is a unit in K U.log(a)
I get the error
ValueError: 1/2*z^11 - 1/2*z^9 + 1/2*z^8 + 1/2*z^4 + 1/2*z + 1/2 is not a unit
But it is a unit. It is true that
a = 1/2*z^11 - 1/2*z^9 + 1/2*z^8 + 1/2*z^4 + 1/2*z + 1/2.
What I'm doing wrong ?