The charfcn function is the characteristic function of the "set" A.  It is defined to be

The set specification A can be a set, a real numeric, a complex numeric, a real numeric range, a complex numeric range, an arbitrary range, or an expression sequence of any of the previous.  The meaning of each one of these is as follows

When the specification is a set, the maple function member is used to test set membership, and thus charfcn will always return one of 0 or 1 in this case.  In the other cases, charfcn is symbolic, in that it will return unevaluated if the "in" conditions cannot be verified or the specification is not exactly as described above.

Ranges $a..b$ where $b<a$ are treated as empty, and so charfcn will return 0 for all input.

$\mathrm{charfcn}\left[3,5,9\right]\left(0\right)$

$0$

$\mathrm{charfcn}\left[3,5,9\right]\left(3\right)$

$1$

$\mathrm{charfcn}\left[3,5,9\right]\left(x\right)$

${\mathrm{charfcn}}_{3,5,9}\left(x\right)$

$\mathrm{charfcn}\left[3.13..3.16\right]\left(\mathrm{\pi }\right)$

$1$

$\mathrm{charfcn}\left[0..3,5..7\right]\left(6\right)$

$1$

$\mathrm{charfcn}\left[\left\{\mathrm{one}\&comma;\mathrm{three}\&comma;\mathrm{two}\right\}\right]\left(\mathrm{four}\right)$

$0$

$\mathrm{charfcn}\left[\left\{\mathrm{one}\&comma;\mathrm{three}\&comma;\mathrm{two}\right\}\right]\left(\mathrm{two}\right)$

$1$

$\mathrm{charfcn}\left[1+\mathrm{I}..3+2\mathrm{I}\right]\left(2+\mathrm{I}\right)$

$1$

$\mathrm{charfcn}\left[3+\mathrm{I}..3+2\mathrm{I},7,\mathrm{\pi }..{\mathrm{\pi }}^2\right]\left(\exp \left(y^3\right)\right)$

${\mathrm{charfcn}}_{3+\mathrm{I}..3+2\mathrm{I},7,\mathrm{\pi }..{\mathrm{\pi }}^2}\left({\&ExponentialE;}^{y^3}\right)$

$\mathrm{assume}\left(1.1<y\&comma;y<1.3\right)$

$\mathrm{charfcn}\left[3+\mathrm{I}..3+2\mathrm{I},7,\mathrm{\pi }..{\mathrm{\pi }}^2\right]\left(\exp \left(y^3\right)\right)$

$1$

$\mathrm{charfcn}\left[3+\mathrm{I}..-1+2\mathrm{I}\right]\left(x\right)$

$0$