Returned type of arithmetic operations and functions for IntervalBoxes

[lbenet]

I just noticed the following behavior:

julia> using IntervalArithmetic

julia> b = (0..1) × (0..1)
IntervalBox(Interval(0.0, 1.0), Interval(0.0, 1.0))

julia> b+b
2-element StaticArrays.SArray{Tuple{2},IntervalArithmetic.Interval{Float64},1,2}:
 Interval(0.0, 2.0)
 Interval(0.0, 2.0)

julia> typeof(ans)
StaticArrays.SArray{Tuple{2},IntervalArithmetic.Interval{Float64},1,2}

Similar behavior is obtained for other arithmetic operations and functions:

julia> 2*b
2-element StaticArrays.SArray{Tuple{2},IntervalArithmetic.Interval{Float64},1,2}:
 Interval(0.0, 2.0)
 Interval(0.0, 2.0)

julia> exp(b)
2-element StaticArrays.SArray{Tuple{2},IntervalArithmetic.Interval{Float64},1,2}:
 Interval(1.0, 2.7182818284590455)
 Interval(1.0, 2.7182818284590455)

In order to use interval boxes in functions or types which require interval boxes, the returned type of such arithmetic operations should be an IntervalBox.

[lbenet]

Is there a reason not to have IntervalBoxes be the returned type in the above cases?

Tests actually check things like A + B == IntervalBox( A .+ B), which A and B IntervalBoxes. My suggestion is to that A + B returns directly IntervalBox( A .+ B).

[dpsanders]

Yes I think these opérations should return IntervalBoxes as you suggest.

[lbenet]

I just noticed i actually don't need this in TaylorModels, but still it would be nice to have it like that. I'll send a PR tomorrow; I haven't completed the tests...

[lbenet]

Closing in favor of #150