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RealBox

 SetTheory
 set-theoretic operations on RealBox objects
 Union
 compute the union of two RealBox objects
 Intersection
 compute the intersection of two RealBox objects
 NonNegativePart
 compute the intersection of a RealBox with the non-negative real axis

 Calling Sequence Union( a, b ) Intersection( a, b ) NonNegativePart( b )

Parameters

 a - RealBox object b - RealBox object precopt - (optional) equation of the form precision = n, where n is a positive integer

Description

 • There are two set-theoretic operations defined on RealBox objects.

 Union( a, b ) the union of the RealBox objects a and b Intersection( a, b ) the intersection of the RealBox objects a and b NonNegativePart( b ) the intersection of the RealBox b with the non-negative real axis

 • Note that there are also predicates Contains and Overlaps that are set-theoretic in nature which are documented in RealBox[Predicates].
 • Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.

Examples

 > $a≔\mathrm{RealBox}\left(1.0,0.5\right)$
 ${a}{≔}{⟨}{\text{RealBox:}}{1}{±}{0.5}{⟩}$ (1)
 > $b≔\mathrm{RealBox}\left(1.5,0.6\right)$
 ${b}{≔}{⟨}{\text{RealBox:}}{1.5}{±}{0.6}{⟩}$ (2)
 > $\mathrm{Union}\left(a,b\right)$
 ${⟨}{\text{RealBox:}}{1.3}{±}{0.8}{⟩}$ (3)
 > $\mathrm{Intersection}\left(a,b\right)$
 ${⟨}{\text{RealBox:}}{1.2}{±}{0.3}{⟩}$ (4)
 > $\mathrm{Union}\left(\mathrm{RealBox}\left(2,0.5\right),\mathrm{RealBox}\left(3,0.5\right)\right)$
 ${⟨}{\text{RealBox:}}{2.5}{±}{1}{⟩}$ (5)
 > $\mathrm{Intersection}\left(\mathrm{RealBox}\left(2,0.5\right),\mathrm{RealBox}\left(3,0.5\right)\right)$
 ${⟨}{\text{RealBox:}}{2.5}{±}{9.31323ⅇ-10}{⟩}$ (6)

Note that an intersection can only be formed for RealBox objects that have nonempty intersection.

 > $\mathrm{Intersection}\left(\mathrm{RealBox}\left(2,0.4\right),\mathrm{RealBox}\left(3,0.4\right)\right)$
 > $\mathrm{Overlaps}\left(\mathrm{RealBox}\left(2,0.4\right),\mathrm{RealBox}\left(3,0.4\right)\right)$
 ${\mathrm{false}}$ (7)

This is not necessary, however, for unions.

 > $\mathrm{Union}\left(\mathrm{RealBox}\left(2,0.4\right),\mathrm{RealBox}\left(3,0.4\right)\right)$
 ${⟨}{\text{RealBox:}}{2.5}{±}{0.9}{⟩}$ (8)

Compatibility

 • The RealBox[SetTheory], RealBox:-Union, RealBox:-Intersection and RealBox:-NonNegativePart commands were introduced in Maple 2022.