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NumberFieldDiscriminant[a]

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

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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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NumberFieldDiscriminant

NumberFieldDiscriminant[a]

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

Details

  • For a number field with integral basis the discriminant is the determinant of the matrix of traces of products in .
  • The discriminant of a number field is always an integer.

Examples

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Basic Examples  (1)

Find the discriminant of the number field :

Scope  (4)

Radical expressions:

Root objects:

AlgebraicNumber objects:

NumberFieldDiscriminant automatically threads over lists:

Applications  (2)

Rational primes that ramify in :

Check that is the ring of integers of :

Properties & Relations  (2)

Find the discriminant of the number field :

The discriminant of a number field is always congruent to 0 or 1 modulo 4:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_numberfielddiscriminant, author="Wolfram Research", title="{NumberFieldDiscriminant}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldDiscriminant.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_numberfielddiscriminant, organization={Wolfram Research}, title={NumberFieldDiscriminant}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldDiscriminant.html}, note=[Accessed: 08-August-2025]}