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I wrote following program for finding out which ring of integers of cyclotomic fields are unique factorization domains:

max_limit=100
i=3
while i <= max_limit:
K=CyclotomicField(i)
O_K=K.ring_of_integers()
print(i , O_K in UniqueFactorizationDomains())
i=i+1

This gives me output as false for all numbers. But this wiki article https ://en.wikipedia.org/wiki/List_of_number_fields_with_class_number_one#Cyclotomic_fields suggests that there are bunch of them for which the class number is actually 1 i.e. the rings are unique factorization domains. I don't understand where I went wrong?

I wrote following program for finding out which ring of integers of cyclotomic fields are unique factorization domains:

max_limit=100
i=3
while i <= max_limit:
 K=CyclotomicField(i)
 O_K=K.ring_of_integers()
 print(i , O_K in UniqueFactorizationDomains())
 i=i+1

This gives me output as false for all numbers. But this wiki article https ://en.wikipedia.org/wiki/List_of_number_fields_with_class_number_one#Cyclotomic_fields suggests that there are bunch of them for which the class number is actually 1 i.e. the rings are unique factorization domains. I don't understand where I went wrong?

I wrote following program for finding out which ring of integers of cyclotomic fields are unique factorization domains:

max_limit=100
i=3
while i <= max_limit:
    K=CyclotomicField(i)
    O_K=K.ring_of_integers()
    print(i , O_K in UniqueFactorizationDomains())
    i=i+1

This gives me output as false for all numbers. But this wiki article https ://en.wikipedia.org/wiki/List_of_number_fields_with_class_number_one#Cyclotomic_fields article suggests that there are bunch of them for which the class number is actually 1 i.e. the rings are unique factorization domains. I don't understand where I went wrong?