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ToNumberField

ToNumberField
expresses the algebraic number a in the number field generated by .
ToNumberField
expresses the in the field generated by .
ToNumberField
expresses the in a common extension field generated by a single algebraic number.
  • The and can be given in terms of Root or AlgebraicNumber objects, or ordinary rationals and radicals.
  • If is an algebraic integer the results will always be given in terms of AlgebraicNumber.
  • ToNumberField gives a representation of the in terms of a primitive element of the field .
  • ToNumberField[{a1, a2, ...}, All] always uses the smallest common field extension.
Express in the number field generated by :
Express in the number field generated by :
In[1]:=
Click for copyable input
Out[1]=
The generator of the number field will autoreduce to an algebraic integer:
Radical expressions:
Root objects:
Express and in a common extension field:
Express algebraic numbers in the smallest common extension field:
Find a primitive element for over :
Convert an algebraic number to an explicit AlgebraicNumber object:
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