NumberFieldSignature
✖
NumberFieldSignature
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
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (4)Survey of the scope of standard use cases

https://wolfram.com/xid/0v53p071emzvm-ydvfoz

Root objects:

https://wolfram.com/xid/0v53p071emzvm-01ywyj

AlgebraicNumber objects:

https://wolfram.com/xid/0v53p071emzvm-brnh1z

NumberFieldSignature threads automatically over lists:

https://wolfram.com/xid/0v53p071emzvm-jbkv2b

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
:

https://wolfram.com/xid/0v53p071emzvm-670ub8


https://wolfram.com/xid/0v53p071emzvm-dfg7yx

The number field is not a Galois extension of
:

https://wolfram.com/xid/0v53p071emzvm-xtzoow

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:

https://wolfram.com/xid/0v53p071emzvm-bc7xla

https://wolfram.com/xid/0v53p071emzvm-hznbgx


https://wolfram.com/xid/0v53p071emzvm-6xohpa

The signature of the number field generated by :

https://wolfram.com/xid/0v53p071emzvm-yajuwv


https://wolfram.com/xid/0v53p071emzvm-yc7ex6


https://wolfram.com/xid/0v53p071emzvm-gmk401

Use Exponent and MinimalPolynomial to verify the result:

https://wolfram.com/xid/0v53p071emzvm-vzhsqm

Find the signature of the number field :

https://wolfram.com/xid/0v53p071emzvm-k5ye3p

https://wolfram.com/xid/0v53p071emzvm-3yjppr

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
]}
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
]}