An expression expr is of type algfun (algebraic function) if it is an expression in the variable(s) V over the domain K extended by (polynomial) RootOfs.

The domain specification K must be a type name, such as rational or anything.  If K is omitted, then it defaults to type constant.

The optional argument V is an indeterminate or a list or set of indeterminates.  If V is not specified, then all the indeterminates of expr, which are names, are used.  That is, expr must be an algebraic function in all of its variables.

$\mathrm{type}\left(\frac{x}{1-x}\,\mathrm{algfun}\left(\mathrm{rational}\,x\right)\right)$

$\mathrm{true}$

$f≔1+2\mathrm{RootOf}\left(x^3-y\,x\right)+yz$

$f≔1+2\mathrm{RootOf}\left({\mathrm{\_Z}}^3-y\right)+yz$

$\mathrm{type}\left(f\,\mathrm{algfun}\left(\mathrm{anything}\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(f\,\mathrm{algfun}\left(\mathrm{rational}\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(f\,\mathrm{algfun}\left(\mathrm{rational}\,y\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left(f\,\mathrm{algfun}\left(\mathrm{rational}\,\left[y\,z\right]\right)\right)$

$\mathrm{true}$