NumberFieldSignature
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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Scope (4)
Applications (1)
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 
:
Use Exponent and MinimalPolynomial to verify the result:
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