def test_Not():
assert Not(Equality(x, y)) == Unequality(x, y)
assert Not(Unequality(x, y)) == Equality(x, y)
assert Not(StrictGreaterThan(x, y)) == LessThan(x, y)
assert Not(StrictLessThan(x, y)) == GreaterThan(x, y)
assert Not(GreaterThan(x, y)) == StrictLessThan(x, y)
assert Not(LessThan(x, y)) == StrictGreaterThan(x, y)
def test_interval_symbolic_end_points():
a = Symbol('a', extended_real=True)
assert Union(Interval(0, a), Interval(0, 3)).sup == Max(a, 3)
assert Union(Interval(a, 0), Interval(-3, 0)).inf == Min(-3, a)
assert Interval(0, a).contains(1) == LessThan(1, a)
def test_core_relational():
for c in (Equality, Equality(x, y), GreaterThan, GreaterThan(x,
y), LessThan,
LessThan(x, y), Relational, Relational(x, y), StrictGreaterThan,
StrictGreaterThan(x, y), StrictLessThan, StrictLessThan(x, y),
Unequality, Unequality(x, y)):
check(c)
def eval(cls, arg):
from diofant import (Equality, GreaterThan, LessThan,
StrictGreaterThan, StrictLessThan, Unequality)
if isinstance(arg, Number) or arg in (True, False):
return false if arg else true
if arg.is_Not:
return arg.args[0]
# Simplify Relational objects.
if isinstance(arg, Equality):
return Unequality(*arg.args)
if isinstance(arg, Unequality):
return Equality(*arg.args)
if isinstance(arg, StrictLessThan):
return GreaterThan(*arg.args)
if isinstance(arg, StrictGreaterThan):
return LessThan(*arg.args)
if isinstance(arg, LessThan):
return StrictGreaterThan(*arg.args)
if isinstance(arg, GreaterThan):
return StrictLessThan(*arg.args)
def test_lt_gt():
x, y = Symbol('x'), Symbol('y')
assert (x >= y) == GreaterThan(x, y)
assert (x >= 0) == GreaterThan(x, 0)
assert (x <= y) == LessThan(x, y)
assert (x <= 0) == LessThan(x, 0)
assert (0 <= x) == GreaterThan(x, 0)
assert (0 >= x) == LessThan(x, 0)
assert (Integer(0) >= x) == GreaterThan(0, x)
assert (Integer(0) <= x) == LessThan(0, x)
assert (x > y) == StrictGreaterThan(x, y)
assert (x > 0) == StrictGreaterThan(x, 0)
assert (x < y) == StrictLessThan(x, y)
assert (x < 0) == StrictLessThan(x, 0)
assert (0 < x) == StrictGreaterThan(x, 0)
assert (0 > x) == StrictLessThan(x, 0)
assert (Integer(0) > x) == StrictGreaterThan(0, x)
assert (Integer(0) < x) == StrictLessThan(0, x)
e = x**2 + 4 * x + 1
assert (e >= 0) == GreaterThan(e, 0)
assert (0 <= e) == GreaterThan(e, 0)
assert (e > 0) == StrictGreaterThan(e, 0)
assert (0 < e) == StrictGreaterThan(e, 0)
assert (e <= 0) == LessThan(e, 0)
assert (0 >= e) == LessThan(e, 0)
assert (e < 0) == StrictLessThan(e, 0)
assert (0 > e) == StrictLessThan(e, 0)
assert (Integer(0) >= e) == GreaterThan(0, e)
assert (Integer(0) <= e) == LessThan(0, e)
assert (Integer(0) < e) == StrictLessThan(0, e)
assert (Integer(0) > e) == StrictGreaterThan(0, e)
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', '<='))