convert/RealRange - Maple Help

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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

 > $z::\left(\mathrm{ComplexRange}\left(-1-I,1+I\right)\right)$
 ${z}{::}\left({\mathrm{ComplexRange}}{}\left({-}{1}{-}{I}{,}{1}{+}{I}\right)\right)$ (1)
 > $\mathrm{convert}\left(,\mathrm{RealRange}\right)$
 $\left({\mathrm{ℜ}}{}\left({z}\right)\right){::}\left({\mathrm{RealRange}}{}\left({-}{1}{,}{1}\right)\right){,}\left({\mathrm{ℑ}}{}\left({z}\right)\right){::}\left({\mathrm{RealRange}}{}\left({-}{1}{,}{1}\right)\right)$ (2)
 > $z\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}∈\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{ComplexRange}\left(-\mathrm{∞}I,I\right)$
 ${z}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{ComplexRange}}{}\left({-}{\mathrm{∞}}{}{I}{,}{I}\right)$ (3)
 > $\mathrm{convert}\left(,\mathrm{RealRange}\right)$
 ${\mathrm{ℜ}}{}\left({z}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{0}{,}{\mathrm{ℑ}}{}\left({z}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({-}{\mathrm{∞}}{,}{1}\right)$ (4)

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

 > $\left[\right]=\mathrm{convert}\left(\left[\right],\mathrm{relation}\right)$
 $\left[{\mathrm{ℜ}}{}\left({z}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{0}{,}{\mathrm{ℑ}}{}\left({z}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({-}{\mathrm{∞}}{,}{1}\right)\right]{=}\left[{\mathrm{ℜ}}{}\left({z}\right){=}{0}{,}{\mathrm{And}}{}\left({-}{\mathrm{∞}}{\le }{\mathrm{ℑ}}{}\left({z}\right){,}{\mathrm{ℑ}}{}\left({z}\right){\le }{1}\right)\right]$ (5)
 > $\mathrm{FunctionAdvisor}\left(\mathrm{branch_cuts},\mathrm{arccot}\right)$
 $\left[{\mathrm{arccot}}{}\left({z}\right){,}{z}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{ComplexRange}}{}\left({-}{\mathrm{∞}}{}{I}{,}{-}{I}\right){,}{z}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{ComplexRange}}{}\left({I}{,}{\mathrm{∞}}{}{I}\right)\right]$ (6)
 > $\mathrm{convert}\left(,\mathrm{relation}\right)$
 $\left[{\mathrm{arccot}}{}\left({z}\right){,}{\mathrm{And}}{}\left({\mathrm{ℜ}}{}\left({z}\right){=}{0}{,}{-}{\mathrm{∞}}{\le }{\mathrm{ℑ}}{}\left({z}\right){,}{\mathrm{ℑ}}{}\left({z}\right){\le }{-}{1}\right){,}{\mathrm{And}}{}\left({\mathrm{ℜ}}{}\left({z}\right){=}{0}{,}{1}{\le }{\mathrm{ℑ}}{}\left({z}\right){,}{\mathrm{ℑ}}{}\left({z}\right){\le }{\mathrm{∞}}\right)\right]$ (7)

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

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