Revision history [back]

You can have a lool at the embeddings method:

sage: K.embeddings?

Then you can gel all embeddings into the (complex) algebraic field QQbar of the real algrbraic field AA.

sage: K.<a>= NumberField(x^2-2)
sage: K
Number Field in a with defining polynomial x^2 - 2
sage: K.embeddings(QQbar)
[
Ring morphism:
  From: Number Field in a with defining polynomial x^2 - 2
  To:   Algebraic Field
  Defn: a |--> -1.414213562373095?,
Ring morphism:
  From: Number Field in a with defining polynomial x^2 - 2
  To:   Algebraic Field
  Defn: a |--> 1.414213562373095?
]
sage: K.embeddings(AA)
[
Ring morphism:
  From: Number Field in a with defining polynomial x^2 - 2
  To:   Algebraic Real Field
  Defn: a |--> -1.414213562373095?,
Ring morphism:
  From: Number Field in a with defining polynomial x^2 - 2
  To:   Algebraic Real Field
  Defn: a |--> 1.414213562373095?
]

Or,

sage: K.<a>= NumberField(x^2+1)
sage: K.embeddings(QQbar)
[
Ring morphism:
  From: Number Field in a with defining polynomial x^2 + 1
  To:   Algebraic Field
  Defn: a |--> -1*I,
Ring morphism:
  From: Number Field in a with defining polynomial x^2 + 1
  To:   Algebraic Field
  Defn: a |--> 1*I
]
sage: K.embeddings(AA)
[]