The call type(expr, ratpoly(K, v)) checks to see if expr is a rational function in the variables v with coefficients in the domain K.

A typical calling sequence would be type(a, ratpoly(integer, x)) which tests to see if a is a rational polynomial in x over the integers.

The variable(s) v can be a single indeterminate or a list or set of indeterminates.  If v is omitted, then it defaults to a list of all indeterminates of type name in expr.

The domain specification K is a type name such as integer or algnum (algebraic number). If the domain specification is omitted, then it defaults to type constant.

$\mathrm{type}\left(\frac{1+x}{1-y}\,\mathrm{ratpoly}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\frac{1+\sin \left(x\right)}{y}\,\mathrm{ratpoly}\right)$

$\mathrm{false}$

$\mathrm{type}\left(\frac{1+\sin \left(x\right)}{y}\,\mathrm{ratpoly}\left(\mathrm{anything}\,y\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(\frac{1}{f\left(1\right)}+\frac{1}{x}\,\mathrm{ratpoly}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\sin \left(z\right)-\frac{\cos \left(z\right)}{x}\,\mathrm{ratpoly}\left(\mathrm{anything}\,x\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(x+\mathrm{sqrt}\left(2\right)x^2\,\mathrm{ratpoly}\left(\mathrm{radnum}\right)\right)$

$\mathrm{true}$