WOLFRAM

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

Details

  • 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.

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Find the signature of the number field :

Out[1]=1

A number field with signature :

Out[1]=1

Scope  (4)Survey of the scope of standard use cases

Radical expressions:

Out[1]=1

Root objects:

Out[1]=1

AlgebraicNumber objects:

Out[1]=1

NumberFieldSignature threads automatically over lists:

Out[1]=1

Applications  (1)Sample problems that can be solved with this function

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

Out[1]=1
Out[2]=2

The number field is not a Galois extension of :

Out[3]=3

Properties & Relations  (3)Properties of the function, and connections to other functions

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

Out[2]=2
Out[3]=3

The signature of the number field generated by :

Out[4]=4

The degree of a number field:

Out[1]=1
Out[2]=2

Use Exponent and MinimalPolynomial to verify the result:

Out[3]=3

Find the signature of the number field :

Out[2]=2
Wolfram Research (2007), NumberFieldSignature, Wolfram Language function, https://reference.wolfram.com/language/ref/NumberFieldSignature.html.
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.

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.

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

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

BibTeX

@misc{reference.wolfram_2025_numberfieldsignature, author="Wolfram Research", title="{NumberFieldSignature}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldSignature.html}", note=[Accessed: 09-July-2025 ]}

@misc{reference.wolfram_2025_numberfieldsignature, author="Wolfram Research", title="{NumberFieldSignature}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldSignature.html}", note=[Accessed: 09-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_numberfieldsignature, organization={Wolfram Research}, title={NumberFieldSignature}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldSignature.html}, note=[Accessed: 09-July-2025 ]}

@online{reference.wolfram_2025_numberfieldsignature, organization={Wolfram Research}, title={NumberFieldSignature}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldSignature.html}, note=[Accessed: 09-July-2025 ]}