The call type(expr, algnum) checks whether expr is an algebraic number.

An algebraic number is defined as either a rational number, or a root of a univariate polynomial with algebraic number coefficients specified by a RootOf. A sum, product, or quotient of these is also an algebraic number.

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

$\mathrm{true}$

$\mathrm{type}\left(\ln \left(2\right)\,\mathrm{algnum}\right)$

$\mathrm{false}$

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

$\mathrm{true}$

$\mathrm{type}\left(2^{\frac{1}{2}}\,\mathrm{algnum}\right)$

$\mathrm{false}$

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

$\mathrm{true}$

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

$\mathrm{false}$