BUILT-IN MATHEMATICA SYMBOL

# ToNumberField

ToNumberField[a, ]
expresses the algebraic number a in the number field generated by .

ToNumberField[{a1, a2, ...}, ]
expresses the in the field generated by .

ToNumberField[{a1, a2, ...}]
expresses the in a common extension field generated by a single algebraic number.

## DetailsDetails

• ToNumberField gives AlgebraicNumber objects corresponding to elements of the rational extension .
• ToNumberField[a, ] remains unevaluated if a does not exist in .
• 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[, list].
• ToNumberField[{a1, a2, ...}] gives a representation of the 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Express in the number field generated by :

 Out[1]=