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| from sympy.core.expr import unchanged | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import Symbol | |
| from sympy.sets.contains import Contains | |
| from sympy.sets.fancysets import Interval | |
| from sympy.sets.powerset import PowerSet | |
| from sympy.sets.sets import FiniteSet | |
| from sympy.testing.pytest import raises, XFAIL | |
| def test_powerset_creation(): | |
| assert unchanged(PowerSet, FiniteSet(1, 2)) | |
| assert unchanged(PowerSet, S.EmptySet) | |
| raises(ValueError, lambda: PowerSet(123)) | |
| assert unchanged(PowerSet, S.Reals) | |
| assert unchanged(PowerSet, S.Integers) | |
| def test_powerset_rewrite_FiniteSet(): | |
| assert PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) == \ | |
| FiniteSet(S.EmptySet, FiniteSet(1), FiniteSet(2), FiniteSet(1, 2)) | |
| assert PowerSet(S.EmptySet).rewrite(FiniteSet) == FiniteSet(S.EmptySet) | |
| assert PowerSet(S.Naturals).rewrite(FiniteSet) == PowerSet(S.Naturals) | |
| def test_finiteset_rewrite_powerset(): | |
| assert FiniteSet(S.EmptySet).rewrite(PowerSet) == PowerSet(S.EmptySet) | |
| assert FiniteSet( | |
| S.EmptySet, FiniteSet(1), | |
| FiniteSet(2), FiniteSet(1, 2)).rewrite(PowerSet) == \ | |
| PowerSet(FiniteSet(1, 2)) | |
| assert FiniteSet(1, 2, 3).rewrite(PowerSet) == FiniteSet(1, 2, 3) | |
| def test_powerset__contains__(): | |
| subset_series = [ | |
| S.EmptySet, | |
| FiniteSet(1, 2), | |
| S.Naturals, | |
| S.Naturals0, | |
| S.Integers, | |
| S.Rationals, | |
| S.Reals, | |
| S.Complexes] | |
| l = len(subset_series) | |
| for i in range(l): | |
| for j in range(l): | |
| if i <= j: | |
| assert subset_series[i] in \ | |
| PowerSet(subset_series[j], evaluate=False) | |
| else: | |
| assert subset_series[i] not in \ | |
| PowerSet(subset_series[j], evaluate=False) | |
| def test_failing_powerset__contains__(): | |
| # XXX These are failing when evaluate=True, | |
| # but using unevaluated PowerSet works fine. | |
| assert FiniteSet(1, 2) not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Naturals not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Naturals not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) | |
| assert S.Naturals0 not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Naturals0 not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) | |
| assert S.Integers not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Integers not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) | |
| assert S.Rationals not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Rationals not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) | |
| assert S.Reals not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Reals not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) | |
| assert S.Complexes not in PowerSet(S.EmptySet).rewrite(FiniteSet) | |
| assert S.Complexes not in PowerSet(FiniteSet(1, 2)).rewrite(FiniteSet) | |
| def test_powerset__len__(): | |
| A = PowerSet(S.EmptySet, evaluate=False) | |
| assert len(A) == 1 | |
| A = PowerSet(A, evaluate=False) | |
| assert len(A) == 2 | |
| A = PowerSet(A, evaluate=False) | |
| assert len(A) == 4 | |
| A = PowerSet(A, evaluate=False) | |
| assert len(A) == 16 | |
| def test_powerset__iter__(): | |
| a = PowerSet(FiniteSet(1, 2)).__iter__() | |
| assert next(a) == S.EmptySet | |
| assert next(a) == FiniteSet(1) | |
| assert next(a) == FiniteSet(2) | |
| assert next(a) == FiniteSet(1, 2) | |
| a = PowerSet(S.Naturals).__iter__() | |
| assert next(a) == S.EmptySet | |
| assert next(a) == FiniteSet(1) | |
| assert next(a) == FiniteSet(2) | |
| assert next(a) == FiniteSet(1, 2) | |
| assert next(a) == FiniteSet(3) | |
| assert next(a) == FiniteSet(1, 3) | |
| assert next(a) == FiniteSet(2, 3) | |
| assert next(a) == FiniteSet(1, 2, 3) | |
| def test_powerset_contains(): | |
| A = PowerSet(FiniteSet(1), evaluate=False) | |
| assert A.contains(2) == Contains(2, A) | |
| x = Symbol('x') | |
| A = PowerSet(FiniteSet(x), evaluate=False) | |
| assert A.contains(FiniteSet(1)) == Contains(FiniteSet(1), A) | |
| def test_powerset_method(): | |
| # EmptySet | |
| A = FiniteSet() | |
| pset = A.powerset() | |
| assert len(pset) == 1 | |
| assert pset == FiniteSet(S.EmptySet) | |
| # FiniteSets | |
| A = FiniteSet(1, 2) | |
| pset = A.powerset() | |
| assert len(pset) == 2**len(A) | |
| assert pset == FiniteSet(FiniteSet(), FiniteSet(1), | |
| FiniteSet(2), A) | |
| # Not finite sets | |
| A = Interval(0, 1) | |
| assert A.powerset() == PowerSet(A) | |
| def test_is_subset(): | |
| # covers line 101-102 | |
| # initialize powerset(1), which is a subset of powerset(1,2) | |
| subset = PowerSet(FiniteSet(1)) | |
| pset = PowerSet(FiniteSet(1, 2)) | |
| bad_set = PowerSet(FiniteSet(2, 3)) | |
| # assert "subset" is subset of pset == True | |
| assert subset.is_subset(pset) | |
| # assert "bad_set" is subset of pset == False | |
| assert not pset.is_subset(bad_set) | |