def test_inequality_no_auto_simplify():
# no simplify on creation but can be simplified
lhs = cos(x)**2 + sin(x)**2
rhs = 2
e = Lt(lhs, rhs)
assert e == Lt(lhs, rhs, evaluate=False)
assert simplify(e)
def test_solve_univariate_inequality():
assert isolve(x**2 >= 4, x, relational=False) == Union(Interval(-oo, -2, True),
Interval(2, oo, False, True))
assert isolve(x**2 >= 4, x) == Or(And(Le(2, x), Lt(x, oo)), And(Le(x, -2),
Lt(-oo, x)))
assert isolve((x - 1)*(x - 2)*(x - 3) >= 0, x, relational=False) == \
Union(Interval(1, 2), Interval(3, oo, False, True))
assert isolve((x - 1)*(x - 2)*(x - 3) >= 0, x) == \
Or(And(Le(1, x), Le(x, 2)), And(Le(3, x), Lt(x, oo)))
# issue sympy/sympy#2785:
assert isolve(x**3 - 2*x - 1 > 0, x, relational=False) == \
Union(Interval(-1, -sqrt(5)/2 + Rational(1, 2), True, True),
Interval(Rational(1, 2) + sqrt(5)/2, oo, True, True))
# issue sympy/sympy#2794:
assert isolve(x**3 - x**2 + x - 1 > 0, x, relational=False) == \
Interval(1, oo, True, True)
# XXX should be limited in domain, e.g. between 0 and 2*pi
assert isolve(sin(x) < S.Half, x) == \
Or(And(-oo < x, x < pi/6), And(5*pi/6 < x, x < oo))
assert isolve(sin(x) > S.Half, x) == And(pi/6 < x, x < 5*pi/6)
# numerical testing in valid() is needed
assert isolve(x**7 - x - 2 > 0, x) == \
And(RootOf(x**7 - x - 2, 0) < x, x < oo)
# handle numerator and denominator; although these would be handled as
# rational inequalities, these test confirm that the right thing is done
# when the domain is EX (e.g. when 2 is replaced with sqrt(2))
assert isolve(1/(x - 2) > 0, x) == And(Integer(2) < x, x < oo)
den = ((x - 1)*(x - 2)).expand()
assert isolve((x - 1)/den <= 0, x) == \
Or(And(-oo < x, x < 1), And(Integer(1) < x, x < 2))
assert isolve(x > oo, x) is S.false
def test_ineq_avoid_wild_symbol_flip():
p = Wild('p')
assert Gt(x, p) == Gt(x, p, evaluate=False)
assert (x < p) == Lt(x, p, evaluate=False) # issue sympy/sympy#7951
# Previously failed as 'p > x':
e = Lt(x, y).subs({y: p})
assert e == Lt(x, p, evaluate=False)
# Previously failed as 'p <= x':
e = Ge(x, p).doit()
assert e == Ge(x, p, evaluate=False)
def test_reduce_piecewise_inequalities():
e = abs(x - 5) < 3
ans = And(Lt(2, x), Lt(x, 8))
assert reduce_inequalities(e) == ans
assert reduce_inequalities(e, x) == ans
assert reduce_inequalities(abs(x - 5)) == Eq(x, 5)
assert reduce_inequalities(abs(2 * x + 3) >= 8) == Or(
And(Le(Rational(5, 2), x), Lt(x, oo)),
And(Le(x, -Rational(11, 2)), Lt(-oo, x)))
assert reduce_inequalities(abs(x - 4) + abs(3 * x - 5) < 7) == And(
Lt(Rational(1, 2), x), Lt(x, 4))
assert reduce_inequalities(abs(x - 4) + abs(3*abs(x) - 5) < 7) == \
Or(And(Integer(-2) < x, x < -1), And(Rational(1, 2) < x, x < 4))
nr = Symbol('nr', extended_real=False)
pytest.raises(TypeError, lambda: reduce_inequalities(abs(nr - 5) < 3))
# sympy/sympy#10198
assert reduce_inequalities(-1 + 1/abs(1/x - 1) < 0) == \
Or(And(Lt(0, x), x < Rational(1, 2)), And(-oo < x, x < 0))
# sympy/sympy#10255
assert reduce_inequalities(Piecewise((1, x < 1), (3, True)) > 1) == \
And(Le(1, x), x < oo)
assert reduce_inequalities(Piecewise((x**2, x < 0), (2*x, x >= 0)) < 1) == \
And(Lt(-1, x), x < Rational(1, 2))
def test_doit():
p = Symbol('p', positive=True)
n = Symbol('n', negative=True)
np = Symbol('np', nonpositive=True)
nn = Symbol('nn', nonnegative=True)
assert Gt(p, 0).doit() is true
assert Gt(p, 1).doit() == Gt(p, 1)
assert Ge(p, 0).doit() is true
assert Le(p, 0).doit() is false
assert Lt(n, 0).doit() is true
assert Le(np, 0).doit() is true
assert Gt(nn, 0).doit() == Gt(nn, 0)
assert Lt(nn, 0).doit() is false
assert Eq(x, 0).doit() == Eq(x, 0)
def test_mathml_relational():
mml_1 = mp._print(Eq(x, 1))
assert mml_1.nodeName == 'apply'
assert mml_1.childNodes[0].nodeName == 'eq'
assert mml_1.childNodes[1].nodeName == 'ci'
assert mml_1.childNodes[1].childNodes[0].nodeValue == 'x'
assert mml_1.childNodes[2].nodeName == 'cn'
assert mml_1.childNodes[2].childNodes[0].nodeValue == '1'
mml_2 = mp._print(Ne(1, x))
assert mml_2.nodeName == 'apply'
assert mml_2.childNodes[0].nodeName == 'neq'
assert mml_2.childNodes[1].nodeName == 'cn'
assert mml_2.childNodes[1].childNodes[0].nodeValue == '1'
assert mml_2.childNodes[2].nodeName == 'ci'
assert mml_2.childNodes[2].childNodes[0].nodeValue == 'x'
mml_3 = mp._print(Ge(1, x))
assert mml_3.nodeName == 'apply'
assert mml_3.childNodes[0].nodeName == 'geq'
assert mml_3.childNodes[1].nodeName == 'cn'
assert mml_3.childNodes[1].childNodes[0].nodeValue == '1'
assert mml_3.childNodes[2].nodeName == 'ci'
assert mml_3.childNodes[2].childNodes[0].nodeValue == 'x'
mml_4 = mp._print(Lt(1, x))
assert mml_4.nodeName == 'apply'
assert mml_4.childNodes[0].nodeName == 'lt'
assert mml_4.childNodes[1].nodeName == 'cn'
assert mml_4.childNodes[1].childNodes[0].nodeValue == '1'
assert mml_4.childNodes[2].nodeName == 'ci'
assert mml_4.childNodes[2].childNodes[0].nodeValue == 'x'
def test_infinity():
# issue sympy/sympy#8449
p = Symbol('p', nonnegative=True)
assert Lt(-oo, p)
assert Ge(-oo, p) is false
assert Gt(oo, -p)
assert Le(oo, -p) is false
def test_sympyissue_8444():
x = Symbol('x', extended_real=True)
assert (x <= oo) == (x >= -oo) == true
x = Symbol('x', real=True)
assert x >= floor(x)
assert (x < floor(x)) is false
assert Gt(x, floor(x)) == Gt(x, floor(x), evaluate=False)
assert Ge(x, floor(x)) == Ge(x, floor(x), evaluate=False)
assert x <= ceiling(x)
assert (x > ceiling(x)) is false
assert Lt(x, ceiling(x)) == Lt(x, ceiling(x), evaluate=False)
assert Le(x, ceiling(x)) == Le(x, ceiling(x), evaluate=False)
i = Symbol('i', integer=True)
assert (i > floor(i)) is false
assert (i < ceiling(i)) is false
def test_python_relational():
assert python(Eq(x, y)) == 'e = Eq(x, y)'
assert python(Ge(x, y)) == "x = Symbol('x')\ny = Symbol('y')\ne = x >= y"
assert python(Le(x, y)) == "x = Symbol('x')\ny = Symbol('y')\ne = x <= y"
assert python(Gt(x, y)) == "x = Symbol('x')\ny = Symbol('y')\ne = x > y"
assert python(Lt(x, y)) == "x = Symbol('x')\ny = Symbol('y')\ne = x < y"
assert python(
Ne(x / (y + 1),
y**2)) in ['e = Ne(x/(1 + y), y**2)', 'e = Ne(x/(y + 1), y**2)']
def test_evaluate():
assert str(Eq(x, x, evaluate=False)) == 'Eq(x, x)'
assert Eq(x, x, evaluate=False).doit() == true
assert str(Ne(x, x, evaluate=False)) == 'Ne(x, x)'
assert Ne(x, x, evaluate=False).doit() == 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_x_minus_y_not_same_as_x_lt_y():
"""
A consequence of pull request sympy/sympy#7792 is that `x - y < 0` and `x < y`
are not synonymous.
"""
x = I + 2
y = I + 3
pytest.raises(TypeError, lambda: x < y)
assert x - y < 0
ineq = Lt(x, y, evaluate=False)
pytest.raises(TypeError, lambda: ineq.doit())
assert ineq.lhs - ineq.rhs < 0
t = Symbol('t', imaginary=True, nonzero=True)
x = 2 + t
y = 3 + t
ineq = Lt(x, y, evaluate=False)
pytest.raises(TypeError, lambda: ineq.doit())
assert ineq.lhs - ineq.rhs < 0
# this one should give error either way
x = I + 2
y = 2 * I + 3
pytest.raises(TypeError, lambda: x < y)
pytest.raises(TypeError, lambda: x - y < 0)
def test_Interval_as_relational():
x = Symbol('x')
assert Interval(-1, 2, False, False).as_relational(x) == \
And(Le(-1, x), Le(x, 2))
assert Interval(-1, 2, True, False).as_relational(x) == \
And(Lt(-1, x), Le(x, 2))
assert Interval(-1, 2, False, True).as_relational(x) == \
And(Le(-1, x), Lt(x, 2))
assert Interval(-1, 2, True, True).as_relational(x) == \
And(Lt(-1, x), Lt(x, 2))
assert Interval(-oo, 2, right_open=False).as_relational(x) == And(
Le(-oo, x), Le(x, 2))
assert Interval(-oo, 2, right_open=True).as_relational(x) == And(
Le(-oo, x), Lt(x, 2))
assert Interval(-2, oo, left_open=False).as_relational(x) == And(
Le(-2, x), Le(x, oo))
assert Interval(-2, oo, left_open=True).as_relational(x) == And(
Lt(-2, x), Le(x, oo))
assert Interval(-oo, oo).as_relational(x) == And(Le(-oo, x), Le(x, oo))
x = Symbol('x', extended_real=True)
y = Symbol('y', extended_real=True)
assert Interval(x, y).as_relational(x) == (x <= y)
assert Interval(y, x).as_relational(x) == (y <= x)
def test_inequalities_symbol_name_same_complex():
"""Using the operator and functional forms should give same results.
With complex non-real numbers, both should raise errors.
"""
for a in (x, Integer(0), Rational(1, 3), pi, oo):
pytest.raises(TypeError, lambda: Gt(a, I))
pytest.raises(TypeError, lambda: a > I)
pytest.raises(TypeError, lambda: Lt(a, I))
pytest.raises(TypeError, lambda: a < I)
pytest.raises(TypeError, lambda: Ge(a, I))
pytest.raises(TypeError, lambda: a >= I)
pytest.raises(TypeError, lambda: Le(a, I))
pytest.raises(TypeError, lambda: a <= I)
def test_inequalities_symbol_name_same():
"""Using the operator and functional forms should give same results."""
# We test all combinations from a set
A = (x, y, Integer(0), Rational(1, 3), pi, oo, -oo)
for a in A:
for b in A:
assert Gt(a, b) == (a > b)
assert Lt(a, b) == (a < b)
assert Ge(a, b) == (a >= b)
assert Le(a, b) == (a <= b)
for b in (y, Integer(0), Rational(1, 3), pi, oo, -oo):
assert Gt(x, b, evaluate=False) == (x > b)
assert Lt(x, b, evaluate=False) == (x < b)
assert Ge(x, b, evaluate=False) == (x >= b)
assert Le(x, b, evaluate=False) == (x <= b)
for b in (y, Integer(0), Rational(1, 3), pi, oo, -oo):
assert Gt(b, x, evaluate=False) == (b > x)
assert Lt(b, x, evaluate=False) == (b < x)
assert Ge(b, x, evaluate=False) == (b >= x)
assert Le(b, x, evaluate=False) == (b <= x)
def test_bool():
assert Eq(0, 0) is true
assert Eq(1, 0) is false
assert Ne(0, 0) is false
assert Ne(1, 0) is true
assert Lt(0, 1) is true
assert Lt(1, 0) is false
assert Le(0, 1) is true
assert Le(1, 0) is false
assert Le(0, 0) is true
assert Gt(1, 0) is true
assert Gt(0, 1) is false
assert Ge(1, 0) is true
assert Ge(0, 1) is false
assert Ge(1, 1) is true
assert Eq(I, 2) is false
assert Ne(I, 2) is 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 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_sympyissue_8545():
eq = 1 - x - abs(1 - x)
ans = And(Lt(1, x), Lt(x, oo))
assert reduce_piecewise_inequality(eq, '<', x) == ans
eq = 1 - x - sqrt((1 - x)**2)
assert reduce_inequalities(eq < 0) == ans
def test_reduce_poly_inequalities_real_interval():
assert reduce_rational_inequalities(
[[Eq(x**2, 0)]], x, relational=False) == FiniteSet(0)
assert reduce_rational_inequalities(
[[Le(x**2, 0)]], x, relational=False) == FiniteSet(0)
assert reduce_rational_inequalities(
[[Lt(x**2, 0)]], x, relational=False) == S.EmptySet
assert reduce_rational_inequalities(
[[Ge(x**2, 0)]], x, relational=False) == \
S.Reals if x.is_extended_real else Interval(-oo, oo)
assert reduce_rational_inequalities(
[[Gt(x**2, 0)]], x, relational=False) == \
FiniteSet(0).complement(S.Reals)
assert reduce_rational_inequalities(
[[Ne(x**2, 0)]], x, relational=False) == \
FiniteSet(0).complement(S.Reals)
assert reduce_rational_inequalities(
[[Eq(x**2, 1)]], x, relational=False) == FiniteSet(-1, 1)
assert reduce_rational_inequalities(
[[Le(x**2, 1)]], x, relational=False) == Interval(-1, 1)
assert reduce_rational_inequalities(
[[Lt(x**2, 1)]], x, relational=False) == Interval(-1, 1, True, True)
assert reduce_rational_inequalities(
[[Ge(x**2, 1)]], x, relational=False) == \
Union(Interval(-oo, -1, True), Interval(1, oo, False, True))
assert reduce_rational_inequalities(
[[Gt(x**2, 1)]], x, relational=False) == \
Interval(-1, 1).complement(S.Reals)
assert reduce_rational_inequalities(
[[Ne(x**2, 1)]], x, relational=False) == \
FiniteSet(-1, 1).complement(S.Reals)
assert reduce_rational_inequalities([[Eq(
x**2, 1.0)]], x, relational=False) == FiniteSet(-1.0, 1.0).evalf()
assert reduce_rational_inequalities(
[[Le(x**2, 1.0)]], x, relational=False) == Interval(-1.0, 1.0)
assert reduce_rational_inequalities([[Lt(
x**2, 1.0)]], x, relational=False) == Interval(-1.0, 1.0, True, True)
assert reduce_rational_inequalities(
[[Ge(x**2, 1.0)]], x, relational=False) == \
Union(Interval(-inf, -1.0, True), Interval(1.0, inf, False, True))
assert reduce_rational_inequalities(
[[Gt(x**2, 1.0)]], x, relational=False) == \
Union(Interval(-inf, -1.0, True, True),
Interval(1.0, inf, True, True))
assert reduce_rational_inequalities([[Ne(
x**2, 1.0)]], x, relational=False) == \
FiniteSet(-1.0, 1.0).complement(S.Reals)
s = sqrt(2)
assert reduce_rational_inequalities([[Lt(
x**2 - 1, 0), Gt(x**2 - 1, 0)]], x, relational=False) == S.EmptySet
assert reduce_rational_inequalities([[Le(x**2 - 1, 0), Ge(
x**2 - 1, 0)]], x, relational=False) == FiniteSet(-1, 1)
assert reduce_rational_inequalities(
[[Le(x**2 - 2, 0), Ge(x**2 - 1, 0)]], x, relational=False
) == Union(Interval(-s, -1, False, False), Interval(1, s, False, False))
assert reduce_rational_inequalities(
[[Le(x**2 - 2, 0), Gt(x**2 - 1, 0)]], x, relational=False
) == Union(Interval(-s, -1, False, True), Interval(1, s, True, False))
assert reduce_rational_inequalities(
[[Lt(x**2 - 2, 0), Ge(x**2 - 1, 0)]], x, relational=False
) == Union(Interval(-s, -1, True, False), Interval(1, s, False, True))
assert reduce_rational_inequalities(
[[Lt(x**2 - 2, 0), Gt(x**2 - 1, 0)]], x, relational=False
) == Union(Interval(-s, -1, True, True), Interval(1, s, True, True))
assert reduce_rational_inequalities(
[[Lt(x**2 - 2, 0), Ne(x**2 - 1, 0)]], x, relational=False
) == Union(Interval(-s, -1, True, True), Interval(-1, 1, True, True),
Interval(1, s, True, True))
# issue sympy/sympy#10237
assert reduce_rational_inequalities(
[[x < oo, x >= 0, -oo < x]], x, relational=False) == Interval(0, oo, False, True)
assert reduce_rational_inequalities([[Eq((x + 1)/(x**2 - 1),
0)]], x) is S.false
def test_reduce_inequalities_multivariate():
assert reduce_inequalities([Ge(x**2, 1), Ge(y**2, 1)]) == And(
Or(And(Le(1, x), Lt(x, oo)), And(Le(x, -1), Lt(-oo, x))),
Or(And(Le(1, y), Lt(y, oo)), And(Le(y, -1), Lt(-oo, y))))
def test_reduce_poly_inequalities_complex_relational():
assert reduce_rational_inequalities(
[[Eq(x**2, 0)]], x, relational=True) == Eq(x, 0)
assert reduce_rational_inequalities(
[[Le(x**2, 0)]], x, relational=True) == Eq(x, 0)
assert reduce_rational_inequalities(
[[Lt(x**2, 0)]], x, relational=True) is S.false
assert reduce_rational_inequalities(
[[Ge(x**2, 0)]], x, relational=True) == And(Lt(-oo, x), Lt(x, oo))
assert reduce_rational_inequalities(
[[Gt(x**2, 0)]], x, relational=True) == \
And(Or(And(Lt(-oo, x), Lt(x, 0)), And(Lt(0, x), Lt(x, oo))))
assert reduce_rational_inequalities(
[[Ne(x**2, 0)]], x, relational=True) == \
And(Or(And(Lt(-oo, x), Lt(x, 0)), And(Lt(0, x), Lt(x, oo))))
for one in (Integer(1), Float(1.0)):
inf = one*oo
assert reduce_rational_inequalities(
[[Eq(x**2, one)]], x, relational=True) == \
Or(Eq(x, -one), Eq(x, one))
assert reduce_rational_inequalities(
[[Le(x**2, one)]], x, relational=True) == \
And(And(Le(-one, x), Le(x, one)))
assert reduce_rational_inequalities(
[[Lt(x**2, one)]], x, relational=True) == \
And(And(Lt(-one, x), Lt(x, one)))
assert reduce_rational_inequalities(
[[Ge(x**2, one)]], x, relational=True) == \
And(Or(And(Le(one, x), Lt(x, inf)), And(Le(x, -one), Lt(-inf, x))))
assert reduce_rational_inequalities(
[[Gt(x**2, one)]], x, relational=True) == \
And(Or(And(Lt(-inf, x), Lt(x, -one)), And(Lt(one, x), Lt(x, inf))))
assert reduce_rational_inequalities(
[[Ne(x**2, one)]], x, relational=True) == \
Or(And(Lt(-inf, x), Lt(x, -one)),
And(Lt(-one, x), Lt(x, one)),
And(Lt(one, x), Lt(x, inf)))
def test_Union_as_relational():
assert (Interval(0, 1) + FiniteSet(2)).as_relational(x) == \
Or(And(Le(0, x), Le(x, 1)), Eq(x, 2))
assert (Interval(0, 1, True, True) + FiniteSet(1)).as_relational(x) == \
And(Lt(0, x), Le(x, 1))
def test_rich_cmp():
assert (x < y) == Lt(x, y)
assert (x <= y) == Le(x, y)
assert (x > y) == Gt(x, y)
assert (x >= y) == Ge(x, y)
def test_new_relational():
assert Eq(x, 0) == Relational(x, 0) # None ==> Equality
assert Eq(x, 0) == Relational(x, 0, '==')
assert Eq(x, 0) == Relational(x, 0, 'eq')
assert Eq(x, 0) == 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, 0) != Relational(x, 1) # None ==> Equality
assert Eq(x, 0) != Relational(x, 1, '==')
assert Eq(x, 0) != Relational(x, 1, 'eq')
assert Eq(x, 0) != 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))
assert all(Relational(x, 0, op).rel_op == '==' for op in ('eq', '=='))
assert all(
Relational(x, 0, op).rel_op == '!=' for op in ('ne', '<>', '!='))
assert all(Relational(x, 0, op).rel_op == '>' for op in ('gt', '>'))
assert all(Relational(x, 0, op).rel_op == '<' for op in ('lt', '<'))
assert all(Relational(x, 0, op).rel_op == '>=' for op in ('ge', '>='))
assert all(Relational(x, 0, op).rel_op == '<=' for op in ('le', '<='))
def test_sympyissue_8449():
p = Symbol('p', nonnegative=True)
assert Lt(-oo, p)
assert Ge(-oo, p) is false
assert Gt(oo, -p)
assert Le(oo, -p) is false
