The call type(m, monomial(K, v)) checks to see if m is a monomial in the variable(s) v over the coefficient domain K, where v is either an indeterminate or a list or set of indeterminates.

A monomial is defined to be a polynomial in v which syntactically is the product of powers of indeterminates in v with nonnegative exponents, times a coefficient $c$ free of the indeterminates in v, i.e., it is of the form $c\cdot x_1^{e_1}\cdots x_k^{e_k}$, where $v\=\left\{x_1\,\dots \,x_k\right\}$, $e_1\,\dots \,e_k\in \mathrm{\mathbb{N}}$, and $c$ does not contain any of the $x_i$. Note that the coefficient $c$ may be a sum. This function returns true if m is such a monomial, and false otherwise.

If v is omitted, it is taken to be the set of all indeterminates appearing in m, that is, it checks if m is a monomial in all of its variables.

The domain specification K should be a type name, such as rational or algebraic.  If K is specified, then this function will check that the coefficients of m come from the domain K.  If the coefficient domain K is omitted, then only coefficients of type constant are allowed.

$\mathrm{type}\left(\sin \left(1\right)x^2\,\mathrm{monomial}\right)$

$\mathrm{true}$

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

$\mathrm{false}$

$\mathrm{type}\left(\left(1+y\right)x^2\,\mathrm{monomial}\left(\mathrm{anything}\,y\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left(1+y\right)x^2\,\mathrm{monomial}\left(\mathrm{anything}\,x\right)\right)$

$\mathrm{true}$

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

$\mathrm{true}$

$f≔x+\mathrm{sqrt}\left(2\right)x$

$f≔x+\sqrt{2}x$

$\mathrm{type}\left(f\,\mathrm{monomial}\left(\mathrm{radalgnum}\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{collect}\left(f\,x\right)\,\mathrm{monomial}\left(\mathrm{radalgnum}\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{collect}\left(f\,x\right)\,\mathrm{monomial}\left(\mathrm{rational}\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left(1+\mathrm{sqrt}\left(2\right)\,\mathrm{monomial}\right)$

$\mathrm{true}$

The type/monomial command was updated in Maple 2020.