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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.
Details
- 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.
- ToNumberField[x] converts any form of algebraic number to an explicit AlgebraicNumber object.
Examplesopen all
Basic Examples (1)
Express 
in the number field generated by 
:
| In[1]:= |
| Out[1]= |  |
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