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BUILT-IN MATHEMATICA SYMBOL

NumberFieldSignature

NumberFieldSignature[a]
gives the signature of the field

generated by the algebraic number

NumberFieldSignature[a] gives a list of the number of real roots and the number of pairs of conjugate roots for the minimal polynomial of .

Find the signature of the number field

A number field with signature

Find the signature of the number field

Out[1]=

A number field with signature

Out[1]=

Radical expressions:

Root objects:

NumberFieldSignature threads automatically over lists:

Signatures of Galois extension fields of

are of the form

for some integer

The number field

is not a Galois extension of

The minimal polynomial of

has two real roots and a pair of complex roots:

The signature of the number field generated by

The degree of a number field:

Use Exponent and MinimalPolynomial to verify the result:

Find the signature of the number field