def test_global(): """Test for global assumptions""" global_assumptions.add(Q.is_true(x > 0)) assert Q.is_true(x > 0) in global_assumptions global_assumptions.remove(Q.is_true(x > 0)) assert not Q.is_true(x > 0) in global_assumptions # same with multiple of assumptions global_assumptions.add(Q.is_true(x > 0), Q.is_true(y > 0)) assert Q.is_true(x > 0) in global_assumptions assert Q.is_true(y > 0) in global_assumptions global_assumptions.clear() assert not Q.is_true(x > 0) in global_assumptions assert not Q.is_true(y > 0) in global_assumptions
def test_binary_symbols(): assert ITE(x < 1, y, z).binary_symbols == set((y, z)) for f in (Eq, Ne): assert f(x, 1).binary_symbols == set() assert f(x, True).binary_symbols == set([x]) assert f(x, False).binary_symbols == set([x]) assert S.true.binary_symbols == set() assert S.false.binary_symbols == set() assert x.binary_symbols == set([x]) assert And(x, Eq(y, False), Eq(z, 1)).binary_symbols == set([x, y]) assert Q.prime(x).binary_symbols == set() assert Q.is_true(x < 1).binary_symbols == set() assert Q.is_true(x).binary_symbols == set([x]) assert Q.is_true(Eq(x, True)).binary_symbols == set([x]) assert Q.prime(x).binary_symbols == set()
def test_binary_symbols(): assert ITE(x < 1, y, z).binary_symbols == {y, z} for f in (Eq, Ne): assert f(x, 1).binary_symbols == set() assert f(x, True).binary_symbols == {x} assert f(x, False).binary_symbols == {x} assert S.true.binary_symbols == set() assert S.false.binary_symbols == set() assert x.binary_symbols == {x} assert And(x, Eq(y, False), Eq(z, 1)).binary_symbols == {x, y} assert Q.prime(x).binary_symbols == set() assert Q.lt(x, 1).binary_symbols == set() assert Q.is_true(x).binary_symbols == {x} assert Q.eq(x, True).binary_symbols == {x} assert Q.prime(x).binary_symbols == set()
def test_refine(): # relational assert not refine(x < 0, ~Q.is_true(x < 0)) assert refine(x < 0, Q.is_true(x < 0)) assert refine(x < 0, Q.is_true(0 > x)) == True assert refine(x < 0, Q.is_true(y < 0)) == (x < 0) assert not refine(x <= 0, ~Q.is_true(x <= 0)) assert refine(x <= 0, Q.is_true(x <= 0)) assert refine(x <= 0, Q.is_true(0 >= x)) == True assert refine(x <= 0, Q.is_true(y <= 0)) == (x <= 0) assert not refine(x > 0, ~Q.is_true(x > 0)) assert refine(x > 0, Q.is_true(x > 0)) assert refine(x > 0, Q.is_true(0 < x)) == True assert refine(x > 0, Q.is_true(y > 0)) == (x > 0) assert not refine(x >= 0, ~Q.is_true(x >= 0)) assert refine(x >= 0, Q.is_true(x >= 0)) assert refine(x >= 0, Q.is_true(0 <= x)) == True assert refine(x >= 0, Q.is_true(y >= 0)) == (x >= 0) assert not refine(Eq(x, 0), ~Q.is_true(Eq(x, 0))) assert refine(Eq(x, 0), Q.is_true(Eq(x, 0))) assert refine(Eq(x, 0), Q.is_true(Eq(0, x))) == True assert refine(Eq(x, 0), Q.is_true(Eq(y, 0))) == Eq(x, 0) assert not refine(Ne(x, 0), ~Q.is_true(Ne(x, 0))) assert refine(Ne(x, 0), Q.is_true(Ne(0, x))) == True assert refine(Ne(x, 0), Q.is_true(Ne(x, 0))) assert refine(Ne(x, 0), Q.is_true(Ne(y, 0))) == (Ne(x, 0)) # boolean functions assert refine(And(x > 0, y > 0), Q.is_true(x > 0)) == (y > 0) assert refine(And(x > 0, y > 0), Q.is_true(x > 0) & Q.is_true(y > 0)) == True # predicates assert refine(Q.positive(x), Q.positive(x)) == True assert refine(Q.positive(x), Q.negative(x)) == False assert refine(Q.positive(x), Q.real(x)) == Q.positive(x)