Given algebraic numbers 
, ..., 
it is always possible to find a single algebraic
number 
such that each of 
,
..., 
can be expressed as a polynomial in 
with rational coefficients. The number 
is then called a primitive element of the extension
field 
.
Stated differently, an algebraic number 
is a primitive element of 
iff 
. Primitive elements were implemented in
version of the Wolfram Language prior
to 6 as PrimitiveElement[z, 
a1, ..., an
] (after loading the package NumberTheory`PrimitiveElement`.
For example, a primitive element of 
is given by 
, with
 |  |  |
(1)
|
 |  |  |
(2)
|
