# ToNumberField

ToNumberField[a,θ]

expresses the algebraic number a in the number field generated by θ.

ToNumberField[{a1,a2,},θ]

expresses the ai in the field generated by θ.

ToNumberField[{a1,a2,}]

expresses the ai in a common extension field generated by a single algebraic number.

# Details

• ToNumberField gives AlgebraicNumber objects corresponding to elements of the rational extension .
• ToNumberField[a,θ] remains unevaluated if a does not exist in .
• The ai and θ can be given in terms of Root or AlgebraicNumber objects, or ordinary rationals and radicals.
• If θ is an algebraic integer the results will always be given in terms of AlgebraicNumber[θ,list].
• ToNumberField[{a1,a2,}] gives a representation of the ai in terms of a primitive element of the field .
• ToNumberField[{a1,a2,}] is equivalent to ToNumberField[{a1,a2,},Automatic], and does not necessarily use the smallest common field extension.
• ToNumberField[{a1,a2,},All] always uses the smallest common field extension.
• converts any form of algebraic number to an explicit AlgebraicNumber object.

# Examples

open allclose all

## Basic Examples(1)

Express in the number field generated by :

 In[1]:=
 Out[1]=