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:

Introduced in 2007
 (6.0)