# NumberFieldSignature

NumberFieldSignature[a]

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

# Details

• NumberFieldSignature[a] gives a list of the number of real roots and the number of pairs of conjugate roots for the minimal polynomial of .

# Examples

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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 :

Wolfram Research (2007), NumberFieldSignature, Wolfram Language function, https://reference.wolfram.com/language/ref/NumberFieldSignature.html.

#### Text

Wolfram Research (2007), NumberFieldSignature, Wolfram Language function, https://reference.wolfram.com/language/ref/NumberFieldSignature.html.

#### CMS

Wolfram Language. 2007. "NumberFieldSignature." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NumberFieldSignature.html.

#### APA

Wolfram Language. (2007). NumberFieldSignature. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NumberFieldSignature.html

#### BibTeX

@misc{reference.wolfram_2024_numberfieldsignature, author="Wolfram Research", title="{NumberFieldSignature}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldSignature.html}", note=[Accessed: 22-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_numberfieldsignature, organization={Wolfram Research}, title={NumberFieldSignature}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldSignature.html}, note=[Accessed: 22-April-2024 ]}