from sympy.sets import (ConditionSet, Intersection, FiniteSet, EmptySet, Union) from sympy import (Symbol, Eq, S, Abs, sin, pi, Interval, And, Mod, oo, Function) from sympy.utilities.pytest import raises w = Symbol('w') x = Symbol('x') y = Symbol('y') z = Symbol('z') L = Symbol('lambda') f = Function('f') 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 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))) 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 C = ConditionSet 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) 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 C(y, x < 1, C(x, y < x, I) ) == C(L, (x < 1) & (y < L), I) c = C(y, x < 1, C(x, L < y, I)) assert c == C(c.sym, (L < y) & (x < 1), I) assert c.sym not in (x, y, L) c = C(y, x < 1, C(x, y < x, FiniteSet(L))) assert c == C(L, And(x < 1, y < L), FiniteSet(L)) def test_CondSet_intersect(): input_conditionset = ConditionSet(x, x**2 > 4, Interval(1, 4, False, False)) other_domain = Interval(0, 3, False, False) output_conditionset = ConditionSet(x, x**2 > 4, Interval(1, 3, False, False)) assert Intersection(input_conditionset, other_domain) == output_conditionset def test_issue_9849(): assert ConditionSet(x, Eq(x, x), S.Naturals) == S.Naturals assert ConditionSet(x, Eq(Abs(sin(x)), -1), S.Naturals) == S.EmptySet def test_simplified_FiniteSet_in_CondSet(): assert ConditionSet(x, And(x < 1, x > -3), FiniteSet(0, 1, 2)) == FiniteSet(0) assert ConditionSet(x, x < 0, FiniteSet(0, 1, 2)) == EmptySet() assert ConditionSet(x, And(x < -3), EmptySet()) == EmptySet() y = Symbol('y') assert (ConditionSet(x, And(x > 0), FiniteSet(-1, 0, 1, y)) == Union(FiniteSet(1), ConditionSet(x, And(x > 0), FiniteSet(y)))) assert (ConditionSet(x, Eq(Mod(x, 3), 1), FiniteSet(1, 4, 2, y)) == Union(FiniteSet(1, 4), ConditionSet(x, Eq(Mod(x, 3), 1), FiniteSet(y)))) def test_free_symbols(): assert ConditionSet(x, Eq(y, 0), FiniteSet(z) ).free_symbols == {y, z} assert ConditionSet(x, Eq(x, 0), FiniteSet(z) ).free_symbols == {z} assert ConditionSet(x, Eq(x, 0), FiniteSet(x, z) ).free_symbols == {x, z} def test_subs_CondSet(): s = FiniteSet(z, y) c = ConditionSet(x, x < 2, s) # you can only replace sym with a symbol that is not in # the free symbols assert c.subs(x, 1) == c assert c.subs(x, y) == ConditionSet(y, y < 2, s) # double subs needed to change dummy if the base set # also contains the dummy orig = ConditionSet(y, y < 2, s) base = orig.subs(y, w) and_dummy = base.subs(y, w) assert base == ConditionSet(y, y < 2, {w, z}) assert and_dummy == ConditionSet(w, w < 2, {w, z}) assert c.subs(x, w) == ConditionSet(w, w < 2, s) assert ConditionSet(x, x < y, s ).subs(y, w) == ConditionSet(x, x < w, s.subs(y, w)) # if the user uses assumptions that cause the condition # to evaluate, that can't be helped from SymPy's end n = Symbol('n', negative=True) assert ConditionSet(n, 0 < n, S.Integers) is S.EmptySet p = Symbol('p', positive=True) assert ConditionSet(n, n < y, S.Integers ).subs(n, x) == ConditionSet(x, x < y, S.Integers) nc = Symbol('nc', commutative=False) raises(ValueError, lambda: ConditionSet( x, x < p, S.Integers).subs(x, nc)) raises(ValueError, lambda: ConditionSet( x, x < p, S.Integers).subs(x, n)) raises(ValueError, lambda: ConditionSet( x + 1, x < 1, S.Integers)) raises(ValueError, lambda: ConditionSet( x + 1, x < 1, s)) assert ConditionSet( n, n < x, Interval(0, oo)).subs(x, p) == Interval(0, oo) assert ConditionSet( n, n < x, Interval(-oo, 0)).subs(x, p) == S.EmptySet assert ConditionSet(f(x), f(x) < 1, {w, z} ).subs(f(x), y) == ConditionSet(y, y < 1, {w, z}) def test_subs_CondSet_tebr(): # to eventually be removed c = ConditionSet((x, y), {x + 1, x + y}, S.Reals) assert c.subs(x, z) == c def test_dummy_eq(): C = ConditionSet I = S.Integers c = C(x, x < 1, I) assert c.dummy_eq(C(y, y < 1, I)) assert c.dummy_eq(1) == False assert c.dummy_eq(C(x, x < 1, S.Reals)) == False raises(ValueError, lambda: c.dummy_eq(C(x, x < 1, S.Reals), z)) # to eventually be removed c1 = ConditionSet((x, y), {x + 1, x + y}, S.Reals) c2 = ConditionSet((x, y), {x + 1, x + y}, S.Reals) c3 = ConditionSet((x, y), {x + 1, x + y}, S.Complexes) assert c1.dummy_eq(c2) assert c1.dummy_eq(c3) is False assert c.dummy_eq(c1) is False assert c1.dummy_eq(c) is False 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))) 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(w >= 1, w <= 7, y > 5)