Merge pull request #1308 from skirpichev/1288-remove-UniversalSet

sets: removed S.UniversalSet

diofant/logic/boolalg.py

@@ -170,17 +170,8 @@ def __hash__(self):
         return hash(True)
 
     def as_set(self):
-        """
-        Rewrite logic operators and relationals in terms of real sets.
-
-        Examples
-        ========
-
-        >>> true.as_set()
-        UniversalSet()
-
-        """
-        return S.UniversalSet
+        """Rewrite logic operators and relationals in terms of real sets."""
+        return S.ExtendedReals
 
 
 class BooleanFalse(BooleanAtom, metaclass=Singleton):

diofant/sets/sets.py

@@ -37,7 +37,6 @@ class Set(Basic):
     is_Union = False
     is_Intersection: bool | None = None
     is_EmptySet: bool | None = None
-    is_UniversalSet: bool | None = None
     is_Complement: bool | None = None
     is_SymmetricDifference: bool | None = None
 
@@ -153,9 +152,6 @@ def complement(self, universe):
         >>> Interval(0, 1).complement(S.Reals)
         (-oo, 0) U (1, oo)
 
-        >>> Interval(0, 1).complement(S.UniversalSet)
-        UniversalSet() \ [0, 1]
-
         """
         return Complement(universe, self)
 
@@ -908,8 +904,6 @@ def _union(self, other):
         See Set._union for docstring
 
         """
-        if other.is_UniversalSet:
-            return S.UniversalSet
         if other.is_Interval and self._is_comparable(other):
             from ..functions import Max, Min
 
@@ -1356,10 +1350,6 @@ def flatten(arg):
                 return sum(map(flatten, arg), [])
             raise TypeError('Input must be Sets or iterables of Sets')
         args = flatten(args)
-
-        if len(args) == 0:
-            return S.UniversalSet
-
         args = list(ordered(args, Set._infimum_key))
 
         # Reduce sets using known rules
@@ -1522,11 +1512,6 @@ class EmptySet(Set, metaclass=Singleton):
     >>> Interval(1, 2).intersection(S.EmptySet)
     EmptySet()
 
-    See Also
-    ========
-
-    UniversalSet
-
     References
     ==========
 
@@ -1573,59 +1558,6 @@ def _symmetric_difference(self, other):
         return other
 
 
-class UniversalSet(Set, metaclass=Singleton):
-    """
-    Represents the set of all things.
-
-    The universal set is available as a singleton as S.UniversalSet
-
-    Examples
-    ========
-
-    >>> S.UniversalSet
-    UniversalSet()
-
-    >>> Interval(1, 2).intersection(S.UniversalSet)
-    [1, 2]
-
-    See Also
-    ========
-
-    EmptySet
-
-    References
-    ==========
-
-    * https://en.wikipedia.org/wiki/Universal_set
-
-    """
-
-    is_UniversalSet = True
-
-    def _intersection(self, other):
-        return other
-
-    def _complement(self, other):
-        return S.EmptySet
-
-    def _symmetric_difference(self, other):
-        return other
-
-    @property
-    def measure(self):
-        return oo
-
-    def _contains(self, other):
-        return true
-
-    def as_relational(self, symbol):
-        return true
-
-    @property
-    def boundary(self):
-        return EmptySet()
-
-
 class FiniteSet(Set, EvalfMixin):
     """
     Represents a set that has a finite number of elements.

diofant/tests/core/test_args.py

@@ -85,7 +85,7 @@
 from diofant.printing.codeprinter import Assignment
 from diofant.sets.fancysets import (ExtendedReals, Integers, Naturals,
                                     Naturals0, Rationals, Reals)
-from diofant.sets.sets import EmptySet, UniversalSet
+from diofant.sets.sets import EmptySet
 from diofant.simplify.hyperexpand import G_Function, Hyper_Function
 from diofant.tensor import ImmutableDenseNDimArray, ImmutableSparseNDimArray
 from diofant.tensor.tensor import (TensAdd, TensorHead, TensorIndex,
@@ -441,10 +441,6 @@ def test_diofant__sets__sets__EmptySet():
     assert _test_args(EmptySet())
 
 
-def test_diofant__sets__sets__UniversalSet():
-    assert _test_args(UniversalSet())
-
-
 def test_diofant__sets__sets__FiniteSet():
     assert _test_args(FiniteSet(x, y, z))
 

diofant/tests/logic/test_boolalg.py

@@ -560,7 +560,7 @@ def test_bool_as_set():
     assert ((x <= 2) & (x >= -2)).as_set() == Interval(-2, 2)
     assert ((x >= 2) | (x <= -2)).as_set() == (Interval(-oo, -2) + Interval(2, oo, False))
     assert Not(x > 2, evaluate=False).as_set() == Interval(-oo, 2, True)
-    assert true.as_set() == S.UniversalSet
+    assert true.as_set() == S.ExtendedReals
     assert false.as_set() == EmptySet()
 
 

diofant/tests/sets/test_sets.py

@@ -165,8 +165,8 @@ def test_Complement():
     assert -1 in Complement(S.Reals, S.Naturals, evaluate=False)
     assert 1 not in Complement(S.Reals, S.Naturals, evaluate=False)
 
-    assert Complement(S.Integers, S.UniversalSet) == EmptySet()
-    assert S.UniversalSet.complement(S.Integers) == EmptySet()
+    assert Complement(S.Integers, S.Reals) == EmptySet()
+    assert S.Reals.complement(S.Integers) == EmptySet()
 
     assert (0 not in S.Reals.intersection(S.Integers - FiniteSet(0)))
 
@@ -188,10 +188,8 @@ def test_complement():
     assert Interval(0, 1, True, True).complement(S.Reals) == \
         Union(Interval(-oo, 0, True, False), Interval(1, oo, False, True))
 
-    assert S.UniversalSet.complement(S.EmptySet) == S.EmptySet
-    assert S.UniversalSet.complement(S.Reals) == S.EmptySet
-    assert S.UniversalSet.complement(S.UniversalSet) == S.EmptySet
-
+    assert S.Reals.complement(S.EmptySet) == S.EmptySet
+    assert S.Reals.complement(S.Reals) == S.EmptySet
     assert S.EmptySet.complement(S.Reals) == S.Reals
 
     assert Union(Interval(0, 1), Interval(2, 3)).complement(S.Reals) == \
@@ -229,8 +227,6 @@ def test_complement():
 def test_intersection():
     pytest.raises(TypeError, lambda: Intersection(1))
 
-    assert Intersection() == S.UniversalSet
-
     assert Interval(0, 2).intersection(Interval(1, 2)) == Interval(1, 2)
     assert Interval(0, 2).intersection(Interval(1, 2, True)) == \
         Interval(1, 2, True)
@@ -589,7 +585,7 @@ def test_Intersection_as_relational():
 
 def test_EmptySet():
     assert S.EmptySet.as_relational(x) is false
-    assert S.EmptySet.intersection(S.UniversalSet) == S.EmptySet
+    assert S.EmptySet.intersection(S.Reals) == S.EmptySet
     assert S.EmptySet.boundary == S.EmptySet
     assert Interval(0, 1).symmetric_difference(S.EmptySet) == Interval(0, 1)
     assert Interval(1, 2).intersection(S.EmptySet) == S.EmptySet
@@ -741,19 +737,6 @@ def test_supinf():
     assert FiniteSet('Ham', 'Eggs').sup == Max('Ham', 'Eggs')
 
 
-def test_universalset():
-    U = S.UniversalSet
-    assert U.as_relational(x) is true
-    assert U.union(Interval(2, 4)) == U
-
-    assert U.intersection(Interval(2, 4)) == Interval(2, 4)
-    assert U.measure == oo
-    assert U.boundary == S.EmptySet
-    assert U.contains(0) is true
-    assert Interval(0, 1).symmetric_difference(U) == Interval(0, 1)
-    assert U.complement(U) == S.EmptySet
-
-
 def test_Union_of_ProductSets_shares():
     line = Interval(0, 2)
     points = FiniteSet(0, 1, 2)
@@ -1013,25 +996,18 @@ def test_sympyissue_9808():
             Complement(FiniteSet(1), FiniteSet(y), evaluate=False))
 
 
-def test_sympyissue_9447():
+def test_sympyissue_10305():
     a = Interval(0, 1) + Interval(2, 3)
-    assert (Complement(S.UniversalSet, a) ==
-            Complement(S.UniversalSet,
-                       Union(Interval(0, 1), Interval(2, 3)), evaluate=False))
-    # issue sympy/sympy#10305:
     assert (Complement(S.Naturals, a) ==
             Complement(S.Naturals,
                        Union(Interval(0, 1), Interval(2, 3)), evaluate=False))
 
 
 def test_sympyissue_2799():
-    U = S.UniversalSet
     a = Symbol('a', real=True)
     inf_interval = Interval(a, oo)
     R = S.Reals
 
-    assert U + inf_interval == inf_interval + U
-    assert U + R == R + U
     assert R + inf_interval == inf_interval + R
 
 

docs/modules/sets.rst

@@ -38,9 +38,6 @@ Singleton Sets
 .. autoclass:: EmptySet
    :members:
 
-.. autoclass:: UniversalSet
-   :members:
-
 Special Sets
 ^^^^^^^^^^^^