Add some set operations (#154)

Author: eeshan9815

src/IntervalArithmetic.jl

@@ -40,7 +40,7 @@ export
     @interval, @biginterval, @floatinterval, @make_interval,
     diam, radius, mid, mag, mig, hull,
     emptyinterval, ∅, ∞, isempty, isinterior, isdisjoint, ⪽,
-    precedes, strictprecedes, ≺,
+    precedes, strictprecedes, ≺, ⊂, ⊃, ⊇,
     entireinterval, isentire, nai, isnai, isthin, iscommon, isatomic,
     widen, inf, sup,
     parameters, eps, dist,

src/intervals/set_operations.jl

@@ -26,6 +26,18 @@ function ⊆(a::Interval, b::Interval)
     b.lo ≤ a.lo && a.hi ≤ b.hi
 end
 
+function ⊂(a::Interval, b::Interval)
+    a == b && return false
+    a ⊆ b
+end
+
+function ⊇(a::Interval, b::Interval)
+    b ⊆ a
+end
+
+function ⊃(a::Interval, b::Interval)
+    b ⊂ a
+end
 
 # isinterior
 function isinterior(a::Interval, b::Interval)

test/interval_tests/consistency.jl

@@ -93,6 +93,18 @@ c = @interval(0.25, 4.0)
         @test !(b ⪽ emptyinterval(b))
         @test emptyinterval(c) ⪽ c
         @test emptyinterval(c) ⪽ emptyinterval(c)
+        @test b ⊂ c
+        @test !(b ⊂ b)
+        @test emptyinterval(c) ⊂ c
+        @test !(c ⊂ emptyinterval(c))
+        @test c ⊃ b
+        @test !(b ⊃ b)
+        @test !(emptyinterval(c) ⊃ c)
+        @test c ⊃ emptyinterval(c)
+        @test c ⊇ b
+        @test b ⊇ b
+        @test !(emptyinterval(c) ⊇ c)
+        @test c ⊇ emptyinterval(c)
         @test isdisjoint(a, @interval(2.1))
         @test !(isdisjoint(a, b))
         @test isdisjoint(emptyinterval(a), a)