NumberFieldDiscriminant
gives the discriminant of the field 
generated by the algebraic number 
.
Examples
open all close allBasic Examples (1)
Scope (4)
NumberFieldDiscriminant[Sqrt[3 + Sqrt[2]]]Root objects:
NumberFieldDiscriminant[Root[2# ^ 3 - # + 1&, 2]]AlgebraicNumber objects:
NumberFieldDiscriminant[AlgebraicNumber[Root[# ^ 3 + # + 1&, 3], {1, 2, 1}]]NumberFieldDiscriminant automatically threads over lists:
NumberFieldDiscriminant[{Sqrt[2], 2 ^ (1 / 3), 2 ^ (1 / 4)}]Applications (2)
Rational primes that ramify in 
:
Select[Divisors[NumberFieldDiscriminant[2 ^ (1 / 3)]], PrimeQ]Check that 
is the ring of integers of 
:
NumberFieldDiscriminant[Sqrt[5]] == Discriminant[MinimalPolynomial[(1 + Sqrt[5]) / 2, x], x]NumberFieldIntegralBasis[Sqrt[5]]Properties & Relations (2)
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