The call type(a, polynom(d, v)) checks to see if a is a polynomial in the variables v with coefficients in the domain d. A typical calling sequence is

which tests to see if a is a polynomial in x over the integers.

The parameter v can be a single indeterminate, or can be a list or set of indeterminates. The latter case tests for a multivariate polynomial.

If v is omitted, then it is taken to be a set of all the indeterminates of type name appearing in a.  Thus the function will check that a is a polynomial in all of its variables.

The domain specification d should be a type name, such as rational or algnum (algebraic number).  If the domain specification is given as anything then no restriction is placed on the coefficients.  If d is omitted, then it defaults to type constant.

$\mathrm{type}\left(x^2+y-z\,\mathrm{polynom}\right)$

$\mathrm{true}$

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

$\mathrm{false}$

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

$\mathrm{true}$

$\mathrm{type}\left(f\left(1\right)x+2^{\frac{1}{2}}\,\mathrm{polynom}\right)$

$\mathrm{true}$

$\mathrm{type}\left(x^2+\frac{y^3}{3}\,\mathrm{polynom}\left(\mathrm{anything}\,\left[x\,y\right]\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(x+\frac{1}{2}\,\mathrm{polynom}\left(\mathrm{integer}\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left(x+\frac{1}{2}\,\mathrm{polynom}\left(\mathrm{rational}\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left({\sin \left(x\right)}^2+\frac{1}{2}\sin \left(x\right)\,\mathrm{polynom}\left(\mathrm{rational}\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left({\sin \left(x\right)}^2+\frac{1}{2}\sin \left(x\right)\,\mathrm{polynom}\left(\mathrm{rational}\,\sin \left(x\right)\right)\right)$

$\mathrm{true}$