Are you perhaps looking for [`AlgebraicNumberPolynomial`](http://reference.wolfram.com/mathematica/ref/AlgebraicNumberPolynomial.html)?

    AlgebraicNumberPolynomial[AlgebraicNumber[1/2 (1 + Sqrt[5]), {-3, 2}], HoldForm[q]]

>     -3 + 2 q

The question states: "... *show* algebraic numbers" and "I would like to *view* ..."  If you would like to display the `AlgebraicNumber` expression this way but retain its full syntax you can use a formatting function.  You typically have several choices including [`Format`](http://reference.wolfram.com/mathematica/ref/Format.html), [`MakeBoxes`](http://reference.wolfram.com/mathematica/ref/MakeBoxes.html), and [`$PrePrint`](http://reference.wolfram.com/mathematica/ref/$PrePrint.html).  `MakeBoxes` is usually [preferred][1] for robustness and performance.  For example:

    MakeBoxes[p : AlgebraicNumber[_, {__}], fmt_] :=
      ToBoxes[Interpretation[AlgebraicNumberPolynomial[p, HoldForm @ q], p], fmt]

Now:

    AlgebraicNumber[1/2 (1 + Sqrt[5]), {-3, 2}]

>     -3 + 2 q

    % // InputForm

>     AlgebraicNumber[(1 + Sqrt[5])/2, {-3, 2}]


  [1]: http://stackoverflow.com/a/4119830/618728