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NumberFieldNormRepresentatives

NumberFieldNormRepresentatives
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 in :
Find the representatives of classes of algebraic integers of norm in :
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Out[1]=
In[2]:=
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Radical expressions:
Root objects:
NumberFieldNormRepresentatives automatically threads over lists:
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 :
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