#1316 - Set difference between intervals

[mforets]

Closes #1316.

[schillic]

I have not looked at the code yet. First let us decide on the output type.

[schillic]

I am thinking about using - instead of \. The reason is that \ is already used for left division.

[schillic]

I do not see how your function computes the difference. At least give an explanation in the docs, but I have the feeling that it is just wrong.

[mforets]

I am thinking about using - instead of . The reason is that \ is already used for left division.

Thanks for raising the issue. Note that - is the difference between intervals in the arithmetic sense, so it would be a source of confusion if we use it in LazySets as alias for set diff (and it is already taken). Example:

julia> I1 = Interval(0, 1)
julia> I2 = Interval(2, 4)

julia> I1 - I2
Interval{Float64,IntervalArithmetic.Interval{Float64}}([-4, -1])

julia> I1.dat - I2.dat # the above implemented this rule
[-4, -1]

On the other hand, it is also true that backslash is used for division (although we don't offer this method in the Interval wrapper), example:

julia> I1.dat \ I2.dat
[2, ∞]

So i would suggest that we just keep difference for now. Unfortunately, set minus \ doesn't seem to be available as function name. Maybe there is another unicode alias?

[schillic]

Note that - is the difference between intervals in the arithmetic sense, so it would be a source of confusion if we use it in LazySets as alias for set diff (and it is already taken).

True! So let us keep \.

[mforets]

I do not see how your function computes the difference. At least give an explanation in the docs, but I have the feeling that it is just wrong.

I've added an Algorithm section. What do you think?

[mforets]

Alright, thanks for your review. I'm adding some docs and moving isflat to Interval.jl before merging (we could have isflat for AbstractHyperrectangle too! (It has to check the radius_hyperrectangle is flat in any dimension..)

Keeping \ as an alias for difference then and adding extra docs with the potential overlap with set \ from IntervalArithmetic.Interval.

[schillic]

Consider squashing.

[mforets]

Squashed and merged, thanks a lot for the review!