RealRange - Maple Help

convert/RealRange

convert ComplexRanges into RealRanges

 Calling Sequence convert( expr, RealRange )

Parameters

 expr - expression

Description

 • The convert(expr, RealRange) function converts Complex ranges (see assume[parametric]) in $\mathrm{expr}$ into Real ranges.
 Note: in Maple, by convention, when you say, for instance, $z\le 1$, it is implicitly assumed that $\mathrm{\Im }\left(z\right)$ = 0.

Examples

 > $z::\mathrm{ComplexRange}\left(-1-I,1+I\right)$
 ${z}{::}{\mathrm{ComplexRange}}{}\left({-1}{-}{I}{,}{1}{+}{I}\right)$ (1)
 > $\mathrm{convert}\left(,\mathrm{RealRange}\right)$
 ${\mathrm{\Re }}{}\left({z}\right){::}\left[{-1}{,}{1}\right]{,}{\mathrm{\Im }}{}\left({z}\right){::}\left[{-1}{,}{1}\right]$ (2)
 > $z\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{in}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{ComplexRange}\left(-\mathrm{\infty }I,I\right)$
 ${z}{\in }{\mathrm{ComplexRange}}{}\left({-}{\mathrm{\infty }}{}{I}{,}{I}\right)$ (3)
 > $\mathrm{convert}\left(,\mathrm{RealRange}\right)$
 ${\mathrm{\Re }}{}\left({z}\right){\in }{0}{,}{\mathrm{\Im }}{}\left({z}\right){\in }\left({-}{\mathrm{\infty }}{,}{1}\right]$ (4)

In turn, RealRanges as well as ComplexRanges can be converted into relations.

 > $\left[\right]=\mathrm{convert}\left(\left[\right],\mathrm{relation}\right)$
 $\left[{\mathrm{\Re }}{}\left({z}\right){\in }{0}{,}{\mathrm{\Im }}{}\left({z}\right){\in }\left({-}{\mathrm{\infty }}{,}{1}\right]\right]{=}\left[{\mathrm{\Re }}{}\left({z}\right){=}{0}{,}{-}{\mathrm{\infty }}{\le }{\mathrm{\Im }}{}\left({z}\right){\wedge }{\mathrm{\Im }}{}\left({z}\right){\le }{1}\right]$ (5)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{branch_cuts},\mathrm{arccot}\right)$
 $\left[{\mathrm{arccot}}{}\left({z}\right){,}{z}{\in }{\mathrm{ComplexRange}}{}\left({-}{\mathrm{\infty }}{}{I}{,}{-I}\right){\vee }{z}{\in }{\mathrm{ComplexRange}}{}\left({I}{,}{\mathrm{\infty }}{}{I}\right)\right]$ (6)
 > $\mathrm{convert}\left(,\mathrm{relation}\right)$
 $\left[{\mathrm{arccot}}{}\left({z}\right){,}\left({\mathrm{\Re }}{}\left({z}\right){=}{0}{\wedge }{-}{\mathrm{\infty }}{\le }{\mathrm{\Im }}{}\left({z}\right){\wedge }{\mathrm{\Im }}{}\left({z}\right){\le }{-1}\right){\vee }\left({\mathrm{\Re }}{}\left({z}\right){=}{0}{\wedge }{1}{\le }{\mathrm{\Im }}{}\left({z}\right){\wedge }{\mathrm{\Im }}{}\left({z}\right){\le }{\mathrm{\infty }}\right)\right]$ (7)

Note that when constructions such as $z or $z\le a$ are used, it is understood that $z$ is real

 > $\mathrm{FunctionAdvisor}\left(\mathrm{branch_cuts},\mathrm{arcsin}\right)$
 $\left[{\mathrm{arcsin}}{}\left({z}\right){,}{z}{\le }{-1}{\vee }{1}{\le }{z}\right]$ (8)