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Mathematica > Mathematics and Algorithms > Number Theory > Algebraic Number Theory >

Built-in Mathematica Symbol

NumberFieldDiscriminant

NumberFieldDiscriminant[a]
gives the discriminant of the field

generated by the algebraic number

For a number field with integral basis ${a_1,...,a_n}$ the discriminant is the determinant of the matrix of traces of products in .

Find the discriminant of the number field

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:

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