The call type(x, constant) verifies whether x is a constant.

The global variable constants is an expression sequence of all names which are initially known as symbolic constants in Maple.  These are: false, gamma, infinity, true, Catalan, FAIL and Pi.

The values undefined and Float(undefined) do not appear on this list because neither is a constant.

The user can declare any symbol other than undefined to be a constant by appending it to constants. In order to make the evalf command evaluate such a constant to a floating-point number, define a procedure of the form `evalf/constant/y`, where y is the name of the constant. This process is described on the detailed evalf help page.

The numeric constants in Maple are integers, fractions, floating-point numbers, and complex numbers whose real and imaginary parts are any of these types of numbers.

The expression (-1)^(1/2) is implemented as Complex(1).

More generally, a Maple expression is of type constant if it is an unevaluated function with all arguments of type constant, or a sum, product, or power with all operands of type constant.

Additionally, the RootOf function can be a constant. This is determined by calling the indets command on it. Suppose r is of the form RootOf(...). If indets(r, name) only returns entries that occur in constants, then r is a constant, and otherwise it is not.

$\mathrm{type}\left(5\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(0.05\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\ln \left(-\mathrm{\pi }\right)\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{\infty }\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(g\left(1\right)\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{false}\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(x^2\,\mathrm{constant}\right)$

$\mathrm{false}$

$\mathrm{constants}$

$\mathrm{false},\mathrm{\gamma },\mathrm{\infty },\mathrm{true},\mathrm{Catalan},\mathrm{FAIL},\mathrm{\pi }$

$\mathrm{type}\left(f\left(\exp \left(\mathrm{\gamma }\right)+3\right)+\frac{1}{4}\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{type}\left(f\left(\exp \left(\mathrm{\gamma }\right)+x\right)+\frac{1}{4}\,\mathrm{constant}\right)$

$\mathrm{false}$

$\mathrm{constants}≔\mathrm{constants},x$

$\mathrm{constants}≔\mathrm{false},\mathrm{\gamma },\mathrm{\infty },\mathrm{true},\mathrm{Catalan},\mathrm{FAIL},\mathrm{\pi },x$

$\mathrm{type}\left(f\left(\exp \left(\mathrm{\gamma }\right)+x\right)+\frac{1}{4}\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{r1}≔\mathrm{RootOf}\left(\sin \left(z+\frac{\mathrm{\pi }}{6}\right)-z^2\,z\right)$

$\mathrm{r1}≔\mathrm{RootOf}\left(-\sin \left(\mathrm{\_Z}+\frac{\mathrm{\pi }}{6}\right)+{\mathrm{\_Z}}^2\right)$

$\mathrm{indets}\left(\mathrm{r1}\,\mathrm{name}\right)$

$\left\{\mathrm{\pi }\right\}$

$\mathrm{type}\left(\mathrm{r1}\,\mathrm{constant}\right)$

$\mathrm{true}$

$\mathrm{r2}≔\mathrm{RootOf}\left(\sin \left(z+y\right)-z^2\,z\right)$

$\mathrm{r2}≔\mathrm{RootOf}\left(-\sin \left(\mathrm{\_Z}+y\right)+{\mathrm{\_Z}}^2\right)$

$\mathrm{indets}\left(\mathrm{r2}\,\mathrm{name}\right)$

$\left\{y\right\}$

$\mathrm{type}\left(\mathrm{r2}\,\mathrm{constant}\right)$

$\mathrm{false}$