gives the signature of the field generated by the algebraic number a.


  • NumberFieldSignature[a] gives a list {s,t} of the number of real roots and the number of pairs of conjugate roots for the minimal polynomial of a.


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Basic Examples  (2)

Find the signature of the number field :

A number field with signature :

Scope  (4)

Radical expressions:

Root objects:

AlgebraicNumber objects:

NumberFieldSignature threads automatically over lists:

Applications  (1)

Signatures of Galois extension fields of are of the form or for some integer :

The number field is not a Galois extension of :

Properties & Relations  (3)

The minimal polynomial of has two real roots and a pair of complex roots:

The signature of the number field generated by :

The degree of a number field:

Use Exponent and MinimalPolynomial to verify the result:

Find the signature of the number field :

Introduced in 2007