def test_reversed():
assert (x < y).reversed == (y > x)
assert (x <= y).reversed == (y >= x)
assert Eq(x, y, evaluate=False).reversed == Eq(y, x, evaluate=False)
assert Ne(x, y, evaluate=False).reversed == Ne(y, x, evaluate=False)
assert (x >= y).reversed == (y <= x)
assert (x > y).reversed == (y < x)
def test_canonical():
one = Integer(1)
def unchanged(v):
c = v.canonical
return v.is_Relational and c.is_Relational and v == c
def isreversed(v):
return v.canonical == v.reversed
assert unchanged(x < one)
assert unchanged(x <= one)
assert isreversed(Eq(one, x, evaluate=False))
assert unchanged(Eq(x, one, evaluate=False))
assert isreversed(Ne(one, x, evaluate=False))
assert unchanged(Ne(x, one, evaluate=False))
assert unchanged(x >= one)
assert unchanged(x > one)
assert unchanged(x < y)
assert unchanged(x <= y)
assert isreversed(Eq(y, x, evaluate=False))
assert unchanged(Eq(x, y, evaluate=False))
assert isreversed(Ne(y, x, evaluate=False))
assert unchanged(Ne(x, y, evaluate=False))
assert isreversed(x >= y)
assert isreversed(x > y)
assert (-x < 1).canonical == (x > -1)
assert isreversed(-x > y)
def test_evaluate():
assert str(Eq(x, x, evaluate=False)) == 'Eq(x, x)'
assert Eq(x, x, evaluate=False).doit() == S.true
assert str(Ne(x, x, evaluate=False)) == 'Ne(x, x)'
assert Ne(x, x, evaluate=False).doit() == S.false
assert str(Ge(x, x, evaluate=False)) == 'x >= x'
assert str(Le(x, x, evaluate=False)) == 'x <= x'
assert str(Gt(x, x, evaluate=False)) == 'x > x'
assert str(Lt(x, x, evaluate=False)) == 'x < x'
def test_relational_bool_output():
# https://github.com/sympy/sympy/issues/5931
pytest.raises(TypeError, lambda: bool(x > 3))
pytest.raises(TypeError, lambda: bool(x >= 3))
pytest.raises(TypeError, lambda: bool(x < 3))
pytest.raises(TypeError, lambda: bool(x <= 3))
pytest.raises(TypeError, lambda: bool(Eq(x, 3)))
pytest.raises(TypeError, lambda: bool(Ne(x, 3)))
def test_simplify():
assert simplify(x * (y + 1) - x * y - x + 1 < x) == (x > 1)
assert simplify(Integer(1) < -x) == (x < -1)
# issue sympy/sympy#10304
d = -(3 * 2**pi)**(1 / pi) + 2 * 3**(1 / pi)
assert d.is_real
assert simplify(Eq(1 + I * d, 0)) is False
assert simplify(Ne(1 + I * d, 0)) is True
def test_univariate_relational_as_set():
assert (x > 0).as_set() == Interval(0, oo, True, True)
assert (x >= 0).as_set() == Interval(0, oo, False, True)
assert (x < 0).as_set() == Interval(-oo, 0, True, True)
assert (x <= 0).as_set() == Interval(-oo, 0, True)
assert Eq(x, 0).as_set() == FiniteSet(0)
assert Ne(x, 0).as_set() == Interval(-oo, 0, True, True) + \
Interval(0, oo, True, True)
assert (x**2 >= 4).as_set() == (Interval(-oo, -2, True) +
Interval(2, oo, False, True))
def test_bool():
assert Eq(0, 0) is S.true
assert Eq(1, 0) is S.false
assert Ne(0, 0) is S.false
assert Ne(1, 0) is S.true
assert Lt(0, 1) is S.true
assert Lt(1, 0) is S.false
assert Le(0, 1) is S.true
assert Le(1, 0) is S.false
assert Le(0, 0) is S.true
assert Gt(1, 0) is S.true
assert Gt(0, 1) is S.false
assert Ge(1, 0) is S.true
assert Ge(0, 1) is S.false
assert Ge(1, 1) is S.true
assert Eq(I, 2) is S.false
assert Ne(I, 2) is S.true
pytest.raises(TypeError, lambda: Gt(I, 2))
pytest.raises(TypeError, lambda: Ge(I, 2))
pytest.raises(TypeError, lambda: Lt(I, 2))
pytest.raises(TypeError, lambda: Le(I, 2))
a = Float('.000000000000000000001', '')
b = Float('.0000000000000000000001', '')
assert Eq(pi + a, pi + b) is S.false
def test_wrappers():
e = x + x**2
res = Relational(y, e, '==')
assert Rel(y, x + x**2, '==') == res
assert Eq(y, x + x**2) == res
res = Relational(y, e, '<')
assert Lt(y, x + x**2) == res
res = Relational(y, e, '<=')
assert Le(y, x + x**2) == res
res = Relational(y, e, '>')
assert Gt(y, x + x**2) == res
res = Relational(y, e, '>=')
assert Ge(y, x + x**2) == res
res = Relational(y, e, '!=')
assert Ne(y, x + x**2) == res
def test_rel_ne():
assert Relational(x, y, '!=') == Ne(x, y)
def test_new_relational():
assert Eq(x) == Relational(x, 0) # None ==> Equality
assert Eq(x) == Relational(x, 0, '==')
assert Eq(x) == Relational(x, 0, 'eq')
assert Eq(x) == Equality(x, 0)
assert Eq(x, -1) == Relational(x, -1) # None ==> Equality
assert Eq(x, -1) == Relational(x, -1, '==')
assert Eq(x, -1) == Relational(x, -1, 'eq')
assert Eq(x, -1) == Equality(x, -1)
assert Eq(x) != Relational(x, 1) # None ==> Equality
assert Eq(x) != Relational(x, 1, '==')
assert Eq(x) != Relational(x, 1, 'eq')
assert Eq(x) != Equality(x, 1)
assert Eq(x, -1) != Relational(x, 1) # None ==> Equality
assert Eq(x, -1) != Relational(x, 1, '==')
assert Eq(x, -1) != Relational(x, 1, 'eq')
assert Eq(x, -1) != Equality(x, 1)
assert Ne(x, 0) == Relational(x, 0, '!=')
assert Ne(x, 0) == Relational(x, 0, '<>')
assert Ne(x, 0) == Relational(x, 0, 'ne')
assert Ne(x, 0) == Unequality(x, 0)
assert Ne(x, 0) != Relational(x, 1, '!=')
assert Ne(x, 0) != Relational(x, 1, '<>')
assert Ne(x, 0) != Relational(x, 1, 'ne')
assert Ne(x, 0) != Unequality(x, 1)
assert Ge(x, 0) == Relational(x, 0, '>=')
assert Ge(x, 0) == Relational(x, 0, 'ge')
assert Ge(x, 0) == GreaterThan(x, 0)
assert Ge(x, 1) != Relational(x, 0, '>=')
assert Ge(x, 1) != Relational(x, 0, 'ge')
assert Ge(x, 1) != GreaterThan(x, 0)
assert (x >= 1) == Relational(x, 1, '>=')
assert (x >= 1) == Relational(x, 1, 'ge')
assert (x >= 1) == GreaterThan(x, 1)
assert (x >= 0) != Relational(x, 1, '>=')
assert (x >= 0) != Relational(x, 1, 'ge')
assert (x >= 0) != GreaterThan(x, 1)
assert Le(x, 0) == Relational(x, 0, '<=')
assert Le(x, 0) == Relational(x, 0, 'le')
assert Le(x, 0) == LessThan(x, 0)
assert Le(x, 1) != Relational(x, 0, '<=')
assert Le(x, 1) != Relational(x, 0, 'le')
assert Le(x, 1) != LessThan(x, 0)
assert (x <= 1) == Relational(x, 1, '<=')
assert (x <= 1) == Relational(x, 1, 'le')
assert (x <= 1) == LessThan(x, 1)
assert (x <= 0) != Relational(x, 1, '<=')
assert (x <= 0) != Relational(x, 1, 'le')
assert (x <= 0) != LessThan(x, 1)
assert Gt(x, 0) == Relational(x, 0, '>')
assert Gt(x, 0) == Relational(x, 0, 'gt')
assert Gt(x, 0) == StrictGreaterThan(x, 0)
assert Gt(x, 1) != Relational(x, 0, '>')
assert Gt(x, 1) != Relational(x, 0, 'gt')
assert Gt(x, 1) != StrictGreaterThan(x, 0)
assert (x > 1) == Relational(x, 1, '>')
assert (x > 1) == Relational(x, 1, 'gt')
assert (x > 1) == StrictGreaterThan(x, 1)
assert (x > 0) != Relational(x, 1, '>')
assert (x > 0) != Relational(x, 1, 'gt')
assert (x > 0) != StrictGreaterThan(x, 1)
assert Lt(x, 0) == Relational(x, 0, '<')
assert Lt(x, 0) == Relational(x, 0, 'lt')
assert Lt(x, 0) == StrictLessThan(x, 0)
assert Lt(x, 1) != Relational(x, 0, '<')
assert Lt(x, 1) != Relational(x, 0, 'lt')
assert Lt(x, 1) != StrictLessThan(x, 0)
assert (x < 1) == Relational(x, 1, '<')
assert (x < 1) == Relational(x, 1, 'lt')
assert (x < 1) == StrictLessThan(x, 1)
assert (x < 0) != Relational(x, 1, '<')
assert (x < 0) != Relational(x, 1, 'lt')
assert (x < 0) != StrictLessThan(x, 1)
# finally, some fuzz testing
for i in range(100):
while 1:
strtype, length = (chr, 65535) if random.randint(0, 1) else (chr,
255)
relation_type = strtype(random.randint(0, length))
if random.randint(0, 1):
relation_type += strtype(random.randint(0, length))
if relation_type not in ('==', 'eq', '!=', '<>', 'ne', '>=', 'ge',
'<=', 'le', '>', 'gt', '<', 'lt'):
break
pytest.raises(ValueError, lambda: Relational(x, 1, relation_type))