From 42e00cf8026ec843754930d9318ef6e2fa3bb925 Mon Sep 17 00:00:00 2001 From: schillic Date: Wed, 6 Mar 2019 20:45:09 +0100 Subject: [PATCH] add isdisjoint for Complement --- docs/src/lib/binary_functions.md | 1 + docs/src/man/set_operations.md | 92 ++++++++++++++++---------------- src/is_intersection_empty.jl | 54 +++++++++++++++++++ test/unit_Complement.jl | 17 ++++-- 4 files changed, 115 insertions(+), 49 deletions(-) diff --git a/docs/src/lib/binary_functions.md b/docs/src/lib/binary_functions.md index a78300e0d1..e1f2f2d576 100644 --- a/docs/src/lib/binary_functions.md +++ b/docs/src/lib/binary_functions.md @@ -34,6 +34,7 @@ is_intersection_empty(::Union{HPolyhedron{N}, AbstractPolytope{N}}, ::Union{HPol is_intersection_empty(::UnionSet{N}, ::LazySet{N}, ::Bool=false) where {N<:Real} is_intersection_empty(::UnionSetArray{N}, ::LazySet{N}, ::Bool=false) where {N<:Real} is_intersection_empty(::Universe{N}, ::LazySet{N}, ::Bool=false) where {N<:Real} +is_intersection_empty(::Complement{N}, ::LazySet{N}, ::Bool=false) where {N<:Real} ``` ## Convex hull diff --git a/docs/src/man/set_operations.md b/docs/src/man/set_operations.md index c9821e3533..ec8256a879 100644 --- a/docs/src/man/set_operations.md +++ b/docs/src/man/set_operations.md @@ -228,56 +228,56 @@ The table entries consist of subsets of the following list of operations. | type ↓ \ type → |LazyS |APtop |ACSym |ACSPt |APgon |AHrec |AHPgn |ASing |Ball1 |Ball2 |BInf |Ballp |Ellip |Empty |HalfS |HPgon |HPhed |HPtop |Hplan |Hrect |Itrvl |Line |LineS |Singl |Universe |VPgon |VPtop |ZeroS |Zonot | CP | CPA | CH | CHA |EMap | EPM |Itsct |ItscA |LiMap | MS | MSA | CMS | ReMap | SIH | UnionSet | UnionSArr | Complem | |-------------------------------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------| | **Interfaces** | | | | | | | | | | | | | | | ⊎ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -| `LazySet` | ⊎ |⊆ ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i |⊆i ⊎ |⊆i ⊎ ∩ |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆ ⊎i |⊆i ⊎i |⊆ ⊎ |⊆i ⊎ |⊆i ⊎ |⊆i ⊎i |⊆i ⊎i | ⊎ |⊆i ⊎i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎ ∩ | ⊎ ∩ |⊆ | -| `APolytope` |⊆ ⊎i |⊆i ⊎i ∩ |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩ |⊆i ⊎i ∩ |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆ ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ACentrallySymmetric` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ACentrallySymmetricPolytope` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `APolygon` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `AHyperrectangle` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `AHPolygon` |⊆i ⊎ |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ASingleton` |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | +| `LazySet` | ⊎ |⊆ ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i |⊆i ⊎ |⊆i ⊎ ∩ |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆ ⊎i |⊆i ⊎i |⊆ ⊎ |⊆i ⊎ |⊆i ⊎ |⊆i ⊎i |⊆i ⊎i | ⊎ |⊆i ⊎i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎ ∩ | ⊎ ∩ |⊆ ⊎ | +| `APolytope` |⊆ ⊎i |⊆i ⊎i ∩ |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩ |⊆i ⊎i ∩ |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆ ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ACentrallySymmetric` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ACentrallySymmetricPolytope` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `APolygon` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `AHyperrectangle` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `AHPolygon` |⊆i ⊎ |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ASingleton` |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | | | | | | | | | | | | | | | | | ⊎ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | **Basic set types** | | | | | | | | | | | | | | | ⊎ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -| `Ball1` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Ball2` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i |⊆ ⊎ |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `BallInf` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Ballp` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Ellipsoid` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `EmptySet` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `HalfSpace` | ⊎ |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎ |⊆i ⊎i |⊆i ⊎i ∩ |⊆i ⊎i ∩ | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `HPolygon`/`HPolygonOpt` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i C |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i Ci|- |⊆i ⊎i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i | -| `HPolyhedron` | ⊎ |⊆i ⊎i ∩ C | ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci| ⊎i |⊆i ⊎i ∩i Ci| ⊎i | ⊎i | ⊎i |⊆i ⊎i ∩ |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ |⊆i ⊎i ∩ Ci| ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci| ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci| ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i | -| `HPolytope` |⊆i ⊎ |⊆i ⊎i ∩ C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i C |⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩ |⊆i ⊎i ∩i C |⊆i ⊎i ∩ |⊆i ⊎i ∩ Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i | -| `Hyperplane` | ⊎ |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Hyperrectangle` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Interval` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i ∩i |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |- |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Line` | ⊎ |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |- | ⊎i ∩ |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `LineSegment` |⊆ ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Singleton` |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Universe` |⊆ ⊎ ∩ |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `VPolygon` |⊆i ⊎i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|- |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i | -| `VPolytope` |⊆i ⊎i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ |⊆i ⊎i ∩ C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i | -| `ZeroSet` |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Zonotope` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎ |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i | +| `Ball1` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Ball2` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i |⊆ ⊎ |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `BallInf` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Ballp` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆ ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Ellipsoid` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `EmptySet` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `HalfSpace` | ⊎ |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎ |⊆i ⊎i |⊆i ⊎i ∩ |⊆i ⊎i ∩ | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `HPolygon`/`HPolygonOpt` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i C |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i Ci|- |⊆i ⊎i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `HPolyhedron` | ⊎ |⊆i ⊎i ∩ C | ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci| ⊎i |⊆i ⊎i ∩i Ci| ⊎i | ⊎i | ⊎i |⊆i ⊎i ∩ |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ |⊆i ⊎i ∩ Ci| ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci| ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci| ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `HPolytope` |⊆i ⊎ |⊆i ⊎i ∩ C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i C |⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩ |⊆i ⊎i ∩i C |⊆i ⊎i ∩ |⊆i ⊎i ∩ Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Hyperplane` | ⊎ |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Hyperrectangle` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Interval` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i ∩i |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |- |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |- |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Line` | ⊎ |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |- | ⊎i ∩ |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `LineSegment` |⊆ ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |- |⊆i ⊎i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Singleton` |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Universe` |⊆ ⊎ ∩ |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎ ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `VPolygon` |⊆i ⊎i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i C |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|- |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `VPolytope` |⊆i ⊎i |⊆i ⊎i ∩i C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ |⊆i ⊎i ∩ C |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩ Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ZeroSet` |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Zonotope` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i C |⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎ |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i Ci|⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i Ci|⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i Ci| ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | | | | | | | | | | | | | | | | | ⊎ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | **Lazy set operation types** | | | | | | | | | | | | | | | ⊎ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -| `CartesianProduct` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `CartesianProductArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ConvexHull` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ConvexHullArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ExponentialMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ExponentialProjectionMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `Intersection` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `IntersectionArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `LinearMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `MinkowskiSum` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `MinkowskiSumArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `CacheMinkowskiSum` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `ResetMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `SymmetricIntervalHull` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i | -| `UnionSet` |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎ | ⊎ |⊆i | -| `UnionSetArray` |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎ | ⊎ |⊆i | -| `Complement` | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | +| `CartesianProduct` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `CartesianProductArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ConvexHull` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ConvexHullArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ExponentialMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ExponentialProjectionMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `Intersection` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `IntersectionArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `LinearMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `MinkowskiSum` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `MinkowskiSumArray` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `CacheMinkowskiSum` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `ResetMap` | ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i |⊆i ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i | ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i |⊆i ⊎i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `SymmetricIntervalHull` |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i |⊆i ⊎i ∩i | ⊎i ∩i | ⊎i ∩i |⊆i ⊎i | +| `UnionSet` |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎ | ⊎ | | +| `UnionSetArray` |⊆ ⊎ ∩ |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i |⊆i ⊎i ∩i | ⊎ | ⊎ | | +| `Complement` | ⊎ | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | ⊎i | | | | ### `⊆` diff --git a/src/is_intersection_empty.jl b/src/is_intersection_empty.jl index 63568ff962..e105e12060 100644 --- a/src/is_intersection_empty.jl +++ b/src/is_intersection_empty.jl @@ -1087,6 +1087,10 @@ function is_intersection_empty(cup1::UnionSetArray{N}, return witness ? (result, w) : result end + +# --- Universe --- + + """ is_intersection_empty(U::Universe{N}, X::LazySet{N}, @@ -1225,6 +1229,56 @@ function is_intersection_empty(U::Universe{N}, U, hs, witness) end + +# --- Complement --- + + +""" + is_intersection_empty(C::Complement{N}, + X::LazySet{N}, + [witness]::Bool=false + )::Union{Bool, Tuple{Bool, Vector{N}}} where {N<:Real} + +Check whether a complement of a convex set and another set do not intersect. + +### Input + +- `C` -- complement of a convex set +- `X` -- convex set + +### Output + +* If `witness` option is deactivated: `true` iff ``X ∩ C = ∅`` +* If `witness` option is activated: + * `(true, [])` iff ``X ∩ C = ∅`` + * `(false, v)` iff ``X ∩ C ≠ ∅`` and ``v ∈ X ∩ C`` + +### Algorithm + +We fall back to `X ⊆ C.X`, which can be justified as follows. + +```math + X ∩ Y^C = ∅ ⟺ X ⊆ Y +``` +""" +function is_intersection_empty(C::Complement{N}, + X::LazySet{N}, + witness::Bool=false + )::Union{Bool, Tuple{Bool, Vector{N}}} where + {N<:Real} + return ⊆(X, C.X, witness) +end + +# symmetric method +function is_intersection_empty(X::LazySet{N}, + C::Complement{N}, + witness::Bool=false + )::Union{Bool, Tuple{Bool, Vector{N}}} where + {N<:Real} + return is_intersection_empty(C, X, witness) +end + + # --- alias --- diff --git a/test/unit_Complement.jl b/test/unit_Complement.jl index 51bbf9b371..d8b1d052fe 100644 --- a/test/unit_Complement.jl +++ b/test/unit_Complement.jl @@ -1,8 +1,7 @@ for N in [Float64, Rational{Int}, Float32] - B1 = BallInf(zeros(N, 2), N(1)) + B1 = BallInf(N[0, 0], N(1)) B2 = BallInf(N[4, -4], N(1)) B3 = BallInf(N[1, -1], N(1)) - B4 = BallInf(N[0, 0], N(1)) C = Complement(B1) # double-complement is the identity @@ -20,8 +19,20 @@ for N in [Float64, Rational{Int}, Float32] # inclusion subset, point = ⊆(B2, C, true) @test B2 ⊆ C && subset && point == N[] - for X in [B1, B3, B4] + for X in [B1, B3] subset, point = ⊆(X, C, true) @test !(X ⊆ C) && !subset && point ∈ X && point ∉ C end + + # isdisjoint + for X in [B2, B3] + res, w = isdisjoint(X, C, true) + @test !isdisjoint(X, C) && !res && w ∈ X && w ∈ C + res, w = isdisjoint(C, X, true) + @test !isdisjoint(C, X) && !res && w ∈ X && w ∈ C + end + res, w = isdisjoint(B1, C, true) + @test isdisjoint(B1, C) && res && w == N[] + res, w = isdisjoint(C, B1, true) + @test isdisjoint(C, B1) && res && w == N[] end