These are the standard basic elementary functions defined for ComplexBox objects.

They override the standard Maple procedures for ComplexBox objects.

Additionally, via "arblib", there are a number of variations that are not defined for standard numerics in Maple.

Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.

$b≔\mathrm{ComplexBox}\left(2.3+11.35\mathrm{I}\right)$

$b≔⟨\text{ComplexBox:}\text{[2.3 +/- 2.32831e-10]}+\text{[11.35 +/- 9.31323e-10]}\cdot \mathrm{I}⟩$

$\mathrm{\Re }\left(b\right)$

$⟨\text{RealBox:}2.3\pm \mathrm{2.32831\ⅇ-10}⟩$

$\mathrm{\Im }\left(b\right)$

$⟨\text{RealBox:}11.35\pm \mathrm{9.31323\ⅇ-10}⟩$

$\mathrm{abs}\left(b\right)$

$⟨\text{RealBox:}11.5807\pm \mathrm{1.97203\ⅇ-09}⟩$

$\mathrm{argument}\left(b\right)$

$⟨\text{RealBox:}1.37086\pm \mathrm{1.7137\ⅇ-10}⟩$

$\mathrm{signum}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.198606 +/- 8.5212e-11]}+\text{[0.980079 +/- 3.88106e-10]}\cdot \mathrm{I}⟩$

$\mathrm{csgn}\left(b\right)$

$⟨\text{RealBox:}1\pm 0⟩$

$\mathrm{csgn}\left(1\,b\right)$

$⟨\text{RealBox:}0\pm 0⟩$

$\mathrm{csgn}\left(1\,\mathrm{ComplexBox}\left(4.1\mathrm{I}\right)\right)$

Error, (in ComplexBox:-csgn) csgn is not differentiable on the imaginary axis

$\mathrm{csgn}\left(0\,\mathrm{ComplexBox}\left(0\right)\,1\right)$

$⟨\text{RealBox:}1\pm 0⟩$

$\mathrm{csgn}\left(0\,\mathrm{ComplexBox}\left(0\right)\,-1\right)$

$⟨\text{RealBox:}-1\pm 0⟩$

$b:-\mathrm{sqrt}\left(b\right)$

$⟨\text{ComplexBox:}\text{[2.63445 +/- 3.66495e-10]}+\text{[2.15415 +/- 5.18888e-10]}\cdot \mathrm{I}⟩$

$\mathrm{rsqrt}\left(b\right)$

$⟨\text{ComplexBox:}\text{[0.227487 +/- 6.46232e-11]}+\text{[-0.186012 +/- 5.43171e-11]}\cdot \mathrm{I}⟩$

$\exp \left(b\right)$

$⟨\text{ComplexBox:}\text{[3.46156 +/- 1.05079e-08]}+\text{[-9.35425 +/- 7.86248e-09]}\cdot \mathrm{I}⟩$

$\mathrm{expm1}\left(b\right)$

$⟨\text{ComplexBox:}\text{[2.46156 +/- 9.94183e-09]}+\text{[-9.35425 +/- 6.5501e-09]}\cdot \mathrm{I}⟩$

$\mathrm{expPiI}\left(b\right)$

$⟨\text{ComplexBox:}\text{[1.92109e-16 +/- 1.79641e-24]}+\text{[2.64415e-16 +/- 2.33121e-24]}\cdot \mathrm{I}⟩$

$\log \left(b\right)$

$⟨\text{ComplexBox:}\text{[2.44934 +/- 3.15894e-10]}+\text{[1.37086 +/- 1.7137e-10]}\cdot \mathrm{I}⟩$

$\mathrm{log1p}\left(b\right)$

$⟨\text{ComplexBox:}\text{[2.46979 +/- 3.14239e-10]}+\text{[1.28785 +/- 1.75505e-10]}\cdot \mathrm{I}⟩$

The ComplexBox[Elementary], ComplexBox:-Re, ComplexBox:-Im, ComplexBox:-abs, ComplexBox:-argument, ComplexBox:-sqrt, ComplexBox:-exp, ComplexBox:-log, ComplexBox:-rsqrt, ComplexBox:-expm1, ComplexBox:-expPiI, ComplexBox:-log1p, ComplexBox:-signum and ComplexBox:-csgn commands were introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.