Signature of a number field

Let be a number field of degree . Then has distinct field embeddings into , which are either real or unreal. Moreover, the unreal embeddings come in conjugate pairs. We label the embeddings such that are the real embeddings and are representatives of conjugate pairs of unreal embeddings. Then

and is called the signature of .

Sage

Given a number field K, we can get the signature using K.signature().

Signature of a number field

See also