def test_CondSet(): sin_sols_principal = ConditionSet(x, Eq(sin(x), 0), Interval(0, 2*pi, False, True)) assert pi in sin_sols_principal assert pi/2 not in sin_sols_principal assert 3*pi not in sin_sols_principal assert oo not in sin_sols_principal assert 5 in ConditionSet(x, x**2 > 4, S.Reals) assert 1 not in ConditionSet(x, x**2 > 4, S.Reals) # in this case, 0 is not part of the base set so # it can't be in any subset selected by the condition assert 0 not in ConditionSet(x, y > 5, Interval(1, 7)) # since 'in' requires a true/false, the following raises # an error because the given value provides no information # for the condition to evaluate (since the condition does # not depend on the dummy symbol): the result is `y > 5`. # In this case, ConditionSet is just acting like # Piecewise((Interval(1, 7), y > 5), (S.EmptySet, True)). raises(TypeError, lambda: 6 in ConditionSet(x, y > 5, Interval(1, 7))) X = MatrixSymbol('X', 2, 2) matrix_set = ConditionSet(X, Eq(X*Matrix([[1, 1], [1, 1]]), X)) Y = Matrix([[0, 0], [0, 0]]) assert matrix_set.contains(Y).doit() is S.true Z = Matrix([[1, 2], [3, 4]]) assert matrix_set.contains(Z).doit() is S.false assert isinstance(ConditionSet(x, x < 1, {x, y}).base_set, FiniteSet) raises(TypeError, lambda: ConditionSet(x, x + 1, {x, y})) raises(TypeError, lambda: ConditionSet(x, x, 1)) I = S.Integers U = S.UniversalSet C = ConditionSet assert C(x, False, I) is S.EmptySet assert C(x, True, I) is I assert C(x, x < 1, C(x, x < 2, I) ) == C(x, (x < 1) & (x < 2), I) assert C(y, y < 1, C(x, y < 2, I) ) == C(x, (x < 1) & (y < 2), I), C(y, y < 1, C(x, y < 2, I)) assert C(y, y < 1, C(x, x < 2, I) ) == C(y, (y < 1) & (y < 2), I) assert C(y, y < 1, C(x, y < x, I) ) == C(x, (x < 1) & (y < x), I) assert unchanged(C, y, x < 1, C(x, y < x, I)) assert ConditionSet(x, x < 1).base_set is U # arg checking is not done at instantiation but this # will raise an error when containment is tested assert ConditionSet((x,), x < 1).base_set is U c = ConditionSet((x, y), x < y, I**2) assert (1, 2) in c assert (1, pi) not in c raises(TypeError, lambda: C(x, x > 1, C((x, y), x > 1, I**2))) # signature mismatch since only 3 args are accepted raises(TypeError, lambda: C((x, y), x + y < 2, U, U))
def test_contains(): assert 6 in ConditionSet(x, x > 5, Interval(1, 7)) assert (8 in ConditionSet(x, y > 5, Interval(1, 7))) is False # `in` should give True or False; in this case there is not # enough information for that result raises(TypeError, lambda: 6 in ConditionSet(x, y > 5, Interval(1, 7))) # here, there is enough information but the comparison is # not defined raises(TypeError, lambda: 0 in ConditionSet(x, 1/x >= 0, S.Reals)) assert ConditionSet(x, y > 5, Interval(1, 7) ).contains(6) == (y > 5) assert ConditionSet(x, y > 5, Interval(1, 7) ).contains(8) is S.false assert ConditionSet(x, y > 5, Interval(1, 7) ).contains(w) == And(Contains(w, Interval(1, 7)), y > 5) # This returns an unevaluated Contains object # because 1/0 should not be defined for 1 and 0 in the context of # reals. assert ConditionSet(x, 1/x >= 0, S.Reals).contains(0) == \ Contains(0, ConditionSet(x, 1/x >= 0, S.Reals), evaluate=False) c = ConditionSet((x, y), x + y > 1, S.Integers**2) assert not c.contains(1) assert c.contains((2, 1)) assert not c.contains((0, 1)) c = ConditionSet((w, (x, y)), w + x + y > 1, S.Integers*S.Integers**2) assert not c.contains(1) assert not c.contains((1, 2)) assert not c.contains(((1, 2), 3)) assert not c.contains(((1, 2), (3, 4))) assert c.contains((1, (3, 4)))