The convert(expr, relation) function converts Real ranges and Complex ranges found in $\mathrm{expr}$ into relations using $=,<=,<,>=,>$.

Note: in Maple, by convention, when you say, for instance, z <= 1, it is implicitly assumed that $\mathrm{\Im }$(z) = 0.

$z::\mathrm{ComplexRange}\left(-1-\mathrm{I}\&comma;1+\mathrm{I}\right)$

$z::\mathrm{ComplexRange}\left(\mathrm{-1}-\mathrm{I}\&comma;1+\mathrm{I}\right)$

$\mathrm{convert}\left(\&comma;\mathrm{relation}\right)$

$\mathrm{-1}\le \mathrm{\Re }\left(z\right)\wedge \mathrm{\Re }\left(z\right)\le 1\wedge \mathrm{-1}\le \mathrm{\Im }\left(z\right)\wedge \mathrm{\Im }\left(z\right)\le 1$

$z\mathbf{in}\mathrm{ComplexRange}\left(-\mathrm{\infty }\mathrm{I}\&comma;\mathrm{I}\right)$

$z\in \mathrm{ComplexRange}\left(-\mathrm{\infty }\mathrm{I}\&comma;\mathrm{I}\right)$

$\mathrm{convert}\left(\&comma;\mathrm{RealRange}\right)$

$\mathrm{\Re }\left(z\right)\in 0,\mathrm{\Im }\left(z\right)\in \left(-\mathrm{\infty }\&comma;1\right]$

$\mathrm{convert}\left(\left[\right]\&comma;\mathrm{relation}\right)$

$\left[\mathrm{\Re }\left(z\right)=0\&comma;-\mathrm{\infty }\le \mathrm{\Im }\left(z\right)\wedge \mathrm{\Im }\left(z\right)\le 1\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{branch\_cuts}\&comma;\arcsin \right)$

$\left[\arcsin \left(z\right)\&comma;z\le \mathrm{-1}\vee 1\le z\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{branch\_cuts}\&comma;\mathrm{arccot}\right)$

$\left[\mathrm{arccot}\left(z\right)\&comma;z\in \mathrm{ComplexRange}\left(-\mathrm{\infty }\mathrm{I}\&comma;\mathrm{-I}\right)\vee z\in \mathrm{ComplexRange}\left(\mathrm{I}\&comma;\mathrm{\infty }\mathrm{I}\right)\right]$

$\mathrm{convert}\left(\&comma;\mathrm{relation}\right)$

$\left[\mathrm{arccot}\left(z\right)\&comma;\left(\mathrm{\Re }\left(z\right)=0\wedge -\mathrm{\infty }\le \mathrm{\Im }\left(z\right)\wedge \mathrm{\Im }\left(z\right)\le \mathrm{-1}\right)\vee \left(\mathrm{\Re }\left(z\right)=0\wedge 1\le \mathrm{\Im }\left(z\right)\wedge \mathrm{\Im }\left(z\right)\le \mathrm{\infty }\right)\right]$