The call type(expr, algnumext) checks to see if expr is an algebraic number extension.

An algebraic number extension is a root of a univariate polynomial with algebraic number coefficients, specified by a RootOf.

For example, the algebraic number $\sqrt{2}$ could be specified as RootOf(z^2-2, z).

The expression type(expr, algnumext) is equivalent to the expression:  type(expr, RootOf) and type(expr, algnum) .

$\mathrm{type}\left(\frac{2}{3}\,\mathrm{algnumext}\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{RootOf}\left(z^2+1\,z\right)\,\mathrm{algnumext}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{RootOf}\left(z^2+y\,z\right)\,\mathrm{algnumext}\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{RootOf}\left(z^2-\mathrm{RootOf}\left(x^2-5\right)\,z\right)\,\mathrm{algnumext}\right)$

$\mathrm{true}$