This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

NumberFieldDiscriminant

NumberFieldDiscriminant[a]
gives the discriminant of the field generated by the algebraic number .
  • 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.
Find the discriminant of the number field :
Find the discriminant of the number field :
In[1]:=
Click for copyable input
Out[1]=
Radical expressions:
Root objects:
NumberFieldDiscriminant automatically threads over lists:
Rational primes that ramify in :
Check that is the ring of integers of :
Find the discriminant of the number field :
The discriminant of a number field is always congruent to 0 or 1 modulo 4:
New in 6