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isstrictsubset.jl
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/
isstrictsubset.jl
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"""
⊂(X::ConvexSet{N}, Y::ConvexSet, [witness]::Bool=false) where {N}
Strict inclusion check.
### Input
- `X` -- first set
- `Y` -- second set
- `witness` -- (optional, default: `false`) compute a witness if activated
### Output
* If `witness` option is deactivated: `true` iff ``X ⊂ Y``
* If `witness` option is activated:
* `(true, v)` iff ``X ⊂ Y`` and ``v ∈ Y \\setminus X``
* `(false, [])` iff not ``X ⊂ Y``
### Algorithm
We check inclusion of `X` in `Y` and then check inclusion of `Y` in `X`:
```math
X ⊂ Y \\Leftrightarrow X ⊆ Y \\land ¬ (Y ⊆ X)
```
"""
function ⊂(X::ConvexSet{N}, Y::ConvexSet, witness::Bool=false) where {N}
if witness
res, w = ⊆(X, Y, witness)
if res
res, w = ⊆(Y, X, witness)
if res
return (false, N[])
else
return (true, w)
end
else
return (res, N[])
end
end
return (X ⊆ Y) && !(Y ⊆ X)
end