NumberFieldNormRepresentatives

NumberFieldNormRepresentatives[a,m]

gives a list of representatives of classes of algebraic integers of norm +/-m in the field generated by the algebraic number a.

Details

  • 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 +/-m can be obtained from the representatives by multiplication by units in the field.

Examples

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Basic Examples  (1)

Find the representatives of classes of algebraic integers of norm in :

Scope  (4)

Radical expressions:

Root objects:

AlgebraicNumber objects:

NumberFieldNormRepresentatives automatically threads over lists:

Properties & Relations  (5)

Representatives of norm in :

The number has norm :

It can be represented in terms of the representative by multiplying by a unit:

Obtain all elements of norm in by multiplying representatives with units:

Elements generated by :

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 in :

Introduced in 2007
 (6.0)