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

Built-in Mathematica Symbol

NumberFieldNormRepresentatives

NumberFieldNormRepresentatives[a, m]
gives a list of representatives of classes of algebraic integers of norm

in the field

generated by the algebraic number

Algebraic integers are considered to be in the same class if their quotient is a unit in the field .

All elements of the number field with norm can be obtained from the representatives by multiplication by units in the field.

Find the representatives of classes of algebraic integers of norm

Radical expressions:

Root objects:

NumberFieldNormRepresentatives automatically threads over lists:

Representatives of norm

The number

has norm

It can be represented in terms of the representative

by multiplying by a unit:

Obtain all elements of norm

by multiplying representatives with units:

Elements generated by

FindInstance gives all Gaussian integers of norm

Check the result:

Find an instance of a quadratic equation

Find the representatives of classes of algebraic integers of norm