Each ComplexBox object defines a number of predicates that can be used to query various properties of the box.

Predicates may be further sub-divided into unary predicates (of a single ComplexBox object) or binary (for comparing two ComplexBox objects).

The following table describes briefly the defined unary predicates.

The binary predicates (comparing two ComplexBox objects) that are defined are described briefly in the following table.

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

$\mathrm{IsZero}\left(\mathrm{ComplexBox}\left(0\right)\right)$

$\mathrm{true}$

$\mathrm{IsZero}\left(\mathrm{ComplexBox}\left(0.\right)\right)$

$\mathrm{true}$

$\mathrm{IsZero}\left(\mathrm{ComplexBox}\left(0.\mathrm{I}\right)\right)$

$\mathrm{true}$

$\mathrm{IsZero}\left(\mathrm{ComplexBox}\left(1.\times {10}^{\mathrm{-40}}\right)\right)$

$\mathrm{false}$

$\mathrm{IsZero}\left(\mathrm{ComplexBox}\left(1.\times {10}^{\mathrm{-40}}\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{HasZero}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\,1.\times {10}^{\mathrm{-20}}\right)\,\mathrm{RealBox}\left(0\right)\right)\right)$

$\mathrm{false}$

$\mathrm{HasZero}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(0.001\,0.002\right)\,\mathrm{RealBox}\left(0\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsOne}\left(\mathrm{ComplexBox}\left(1\right)\right)$

$\mathrm{true}$

$\mathrm{IsOne}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(1\,1.\times {10}^{\mathrm{-30}}\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsOne}\left(\mathrm{ComplexBox}\left(1.0+0.\mathrm{I}\right)\right)$

$\mathrm{true}$

$\mathrm{IsOne}\left(\mathrm{ComplexBox}\left(1.0-0.\mathrm{I}\right)\right)$

$\mathrm{true}$

$\mathrm{IsReal}\left(\mathrm{ComplexBox}\left(2.3\right)\right)$

$\mathrm{true}$

$\mathrm{IsReal}\left(\mathrm{ComplexBox}\left(2.3+1.\times {10}^{\mathrm{-40}}\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{IsReal}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\,1.\times {10}^{\mathrm{-20}}\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsReal}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\,1.\times {10}^{\mathrm{-20}}\right)\,\mathrm{RealBox}\left(0\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsReal}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\,1.\times {10}^{\mathrm{-20}}\right)\,\mathrm{RealBox}\left(0\,1.\times {10}^{\mathrm{-30}}\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsExact}\left(\mathrm{ComplexBox}\left(2.3+5.1\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{IsExact}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\,1.\times {10}^{\mathrm{-40}}\right)\,\mathrm{RealBox}\left(5.1\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsExact}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\right)\,\mathrm{RealBox}\left(5.1\,1.\times {10}^{\mathrm{-30}}\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsExact}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\,1.\times {10}^{\mathrm{-20}}\right)\,\mathrm{RealBox}\left(5.1\,1.\times {10}^{\mathrm{-30}}\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsExact}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(2.3\right)\,\mathrm{RealBox}\left(5.1\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsInteger}\left(\mathrm{ComplexBox}\left(4\right)\right)$

$\mathrm{true}$

$\mathrm{IsInteger}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(4\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsInteger}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(4\,1.\times {10}^{\mathrm{-20}}\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsInteger}\left(\mathrm{ComplexBox}\left(4\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{HasInteger}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(1.001\,0.002\right)\,\mathrm{RealBox}\left(0\right)\right)\right)$

$\mathrm{true}$

$\mathrm{HasInteger}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(0.5\right)\,\mathrm{RealBox}\left(1.001\,0.002\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsFinite}\left(\mathrm{ComplexBox}\left(2+3\mathrm{I}\right)\right)$

$\mathrm{true}$

$\mathrm{IsFinite}\left(\mathrm{ComplexBox}\left(2+\mathrm{\infty }\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{IsFinite}\left(\mathrm{ComplexBox}\left(-Float\left(\mathrm{\infty }\right)-3\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{IsUndefined}\left(\mathrm{ComplexBox}\left(Float\left(\mathrm{undefined}\right)-\mathrm{I}\left(Float\left(\mathrm{undefined}\right)\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsUndefined}\left(\mathrm{ComplexBox}\left(Float\left(\mathrm{\infty }\right)-\mathrm{I}\left(Float\left(\mathrm{undefined}\right)\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsUndefined}\left(\mathrm{ComplexBox}\left(Float\left(\mathrm{undefined}\right)+\mathrm{I}\left(Float\left(\mathrm{\infty }\right)\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsUndefined}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(0\,\mathrm{\infty }\right)\,\mathrm{RealBox}\left(2.3\right)\right)\right)$

$\mathrm{false}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(Float\left(\mathrm{\infty }\right)-3\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(-Float\left(\mathrm{\infty }\right)+3.2\mathrm{I}\right)\right)$

$\mathrm{false}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(Float\left(\mathrm{\infty }\right)+\mathrm{I}\left(Float\left(\mathrm{\infty }\right)\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(Float\left(\mathrm{\infty }\right)-\mathrm{I}\left(Float\left(\mathrm{\infty }\right)\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(-Float\left(\mathrm{\infty }\right)+\mathrm{I}\left(Float\left(\mathrm{\infty }\right)\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(-Float\left(\mathrm{\infty }\right)-\mathrm{I}\left(Float\left(\mathrm{\infty }\right)\right)\right)\right)$

$\mathrm{true}$

$\mathrm{IsInfinity}\left(\mathrm{ComplexBox}\left(\mathrm{RealBox}\left(0\,\mathrm{\infty }\right)\,\mathrm{RealBox}\left(0\,\mathrm{\infty }\right)\right)\right)$

$\mathrm{false}$

The ComplexBox[Predicates], ComplexBox:-IsZero, ComplexBox:-HasZero, ComplexBox:-IsOne, ComplexBox:-IsReal, ComplexBox:-IsExact, ComplexBox:-IsInteger, ComplexBox:-HasInteger, ComplexBox:-IsFinite, ComplexBox:-IsInfinity, ComplexBox:-IsUndefined, ComplexBox:-Equal, ComplexBox:-Eq, ComplexBox:-NotEq, ComplexBox:-Overlaps and ComplexBox:-Contains commands were introduced in Maple 2022.

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