def test_simple_expression(self):
x1, x2 = symbols('x1, x2')
function = Or(x1, x2)
self.assertEquals(function.subs({'x1': False, 'x2': False}), False)
self.assertEquals(function.subs({'x1': True, 'x2': False}), True)
self.assertEquals(function.subs({'x1': False, 'x2': True}), True)
self.assertEquals(function.subs({'x1': True, 'x2': True}), True)
def test_complex_expression(self):
x1, x2, x3 = symbols('x1, x2, x3')
subfunction = And(x2, x3)
function = Or(x1, subfunction, And(x1, x2))
print(function.args[0])
print(function.args)
for combination in itertools.combinations((True, False), 3):
self.assertEquals(function.subs(dict(zip(('x1', 'x2', 'x3'), combination))),
combination[0] or (combination[1] and combination[2]))
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert not prntr.module_imports
assert prntr.doprint(pi) == 'math.pi'
assert prntr.module_imports == {'math': {'pi'}}
assert prntr.doprint(x**Rational(1, 2)) == 'math.sqrt(x)'
assert prntr.doprint(sqrt(x)) == 'math.sqrt(x)'
assert prntr.module_imports == {'math': {'pi', 'sqrt'}}
assert prntr.doprint(acos(x)) == 'math.acos(x)'
assert prntr.doprint(Assignment(x, 2)) == 'x = 2'
assert prntr.doprint(Piecewise(
(1, Eq(x, 0)),
(2, x > 6))) == '((1) if (x == 0) else (2) if (x > 6) else None)'
assert prntr.doprint(Piecewise((2, Le(x, 0)),
(3, Gt(x, 0)), evaluate=False)) == '((2) if (x <= 0) else'\
' (3) if (x > 0) else None)'
assert prntr.doprint(sign(x)) == '(0.0 if x == 0 else math.copysign(1, x))'
assert prntr.doprint(p[0, 1]) == 'p[0, 1]'
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == "x**y"
assert prntr.doprint(Mod(x, 2)) == "x % 2"
assert prntr.doprint(And(x, y)) == "x and y"
assert prntr.doprint(Or(x, y)) == "x or y"
assert not prntr.module_imports
assert prntr.doprint(pi) == "math.pi"
assert prntr.module_imports == {"math": {"pi"}}
assert prntr.doprint(x**Rational(1, 2)) == "math.sqrt(x)"
assert prntr.doprint(sqrt(x)) == "math.sqrt(x)"
assert prntr.module_imports == {"math": {"pi", "sqrt"}}
assert prntr.doprint(acos(x)) == "math.acos(x)"
assert prntr.doprint(Assignment(x, 2)) == "x = 2"
assert (prntr.doprint(Piecewise(
(1, Eq(x, 0)),
(2, x > 6))) == "((1) if (x == 0) else (2) if (x > 6) else None)")
assert (prntr.doprint(
Piecewise((2, Le(x, 0)), (3, Gt(x, 0)),
evaluate=False)) == "((2) if (x <= 0) else"
" (3) if (x > 0) else None)")
assert prntr.doprint(sign(x)) == "(0.0 if x == 0 else math.copysign(1, x))"
assert prntr.doprint(p[0, 1]) == "p[0, 1]"
def test_contains():
assert Interval(0, 2).contains(1) is S.true
assert Interval(0, 2).contains(3) is S.false
assert Interval(0, 2, True, False).contains(0) is S.false
assert Interval(0, 2, True, False).contains(2) is S.true
assert Interval(0, 2, False, True).contains(0) is S.true
assert Interval(0, 2, False, True).contains(2) is S.false
assert Interval(0, 2, True, True).contains(0) is S.false
assert Interval(0, 2, True, True).contains(2) is S.false
assert (Interval(0, 2) in Interval(0, 2)) is False
assert FiniteSet(1, 2, 3).contains(2) is S.true
assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x')) is S.true
assert FiniteSet(y)._contains(x) is None
raises(TypeError, lambda: x in FiniteSet(y))
assert FiniteSet({x, y})._contains({x}) is None
assert FiniteSet({x, y}).subs(y, x)._contains({x}) is True
assert FiniteSet({x, y}).subs(y, x + 1)._contains({x}) is False
# issue 8197
from sympy.abc import a, b
assert isinstance(FiniteSet(b).contains(-a), Contains)
assert isinstance(FiniteSet(b).contains(a), Contains)
assert isinstance(FiniteSet(a).contains(1), Contains)
raises(TypeError, lambda: 1 in FiniteSet(a))
# issue 8209
rad1 = Pow(Pow(2, S(1) / 3) - 1, S(1) / 3)
rad2 = Pow(S(1) / 9,
S(1) / 3) - Pow(S(2) / 9,
S(1) / 3) + Pow(S(4) / 9,
S(1) / 3)
s1 = FiniteSet(rad1)
s2 = FiniteSet(rad2)
assert s1 - s2 == S.EmptySet
items = [1, 2, S.Infinity, S('ham'), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is S.true for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false
assert S.EmptySet.contains(1) is S.false
assert FiniteSet(rootof(x**3 + x - 1, 0)).contains(S.Infinity) is S.false
assert rootof(x**5 + x**3 + 1, 0) in S.Reals
assert not rootof(x**5 + x**3 + 1, 1) in S.Reals
# non-bool results
assert Union(Interval(1, 2), Interval(3, 4)).contains(x) == \
Or(And(S(1) <= x, x <= 2), And(S(3) <= x, x <= 4))
assert Intersection(Interval(1, x), Interval(2, 3)).contains(y) == \
And(y <= 3, y <= x, S(1) <= y, S(2) <= y)
assert (S.Complexes).contains(S.ComplexInfinity) == S.false
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert not prntr.module_imports
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert not prntr.module_imports
assert prntr.doprint(pi) == 'math.pi'
assert prntr.module_imports == {'math': {'pi'}}
assert prntr.doprint(acos(x)) == 'math.acos(x)'
def convert_conjunction_try_flip(self, expr):
try:
return self.convert_conjunction(expr)
except CannotRepresentRule:
# try conversion to a disjunction with De Morgan
expr = Or(*(Not(a) for a in expr.args))
access_rules = self.convert_disjunction(expr)
# we must invert the resulting rule, cannot invert more than one
if len(access_rules) > 1:
raise CannotRepresentRule(
expr,
"tried to invert conjunction, but more than one access rule returned"
)
return ((access_rules[0][0], True), )
def test_PythonCodePrinter():
prntr = PythonCodePrinter()
assert prntr.doprint(x**y) == 'x**y'
assert prntr.doprint(Mod(x, 2)) == 'x % 2'
assert prntr.doprint(And(x, y)) == 'x and y'
assert prntr.doprint(Or(x, y)) == 'x or y'
assert prntr.doprint(Piecewise((x, x > 1), (y, True))) == ('if x > 1:\n'
' return x\n'
'else:\n'
' return y')
pw = Piecewise((x, x > 1), (y, x > 0))
assert prntr.doprint(pw) == (
'if x > 1:\n'
' return x\n'
'elif x > 0:\n'
' return y\n'
'else:\n'
' raise NotImplementedError("Unhandled condition in: %s")' % pw)
def generate_boolean_function(a, d=8, random_seed=0):
"""Generate a Boolean function in disjunctive normal form according to the
given parameters.
NOTE: This function implements the Boolean function generation algorithm as
given in "(2001) Sadohara - Learning of Boolean Functions using Support
Vector Machines - ALT".
Parameters
----------
a : int
The number of attributes/variables of the generated function.
d : int
The expected number of attributes/variables in a disjunct.
random_seed : int
The random seed with which to initialize a private Random object.
Returns
-------
attributes : list
The sympy's Symbol objects representing the attributes of the Boolean
function.
function : Boolean function comprised of Boolean operators from sympy.logic
The Boolean function.
"""
rand_obj = random.Random(random_seed)
attributes = symbols("x1:{}".format(a + 1))
function = []
for i in range(2**(d - 2)):
disjunct = []
for attr in attributes:
if rand_obj.random() < d / a:
if rand_obj.random() < 0.5:
disjunct.append(attr)
else:
disjunct.append(Not(attr))
# Note: Empty disjuncts are discarded since expression 'And(*disjunct)'
# would return value True for them and consequentially, the whole
# Boolean function would simplify to the value True.
if len(disjunct) > 0:
disjunct = And(*disjunct)
function.append(disjunct)
return attributes, Or(*function)
def test_union_contains():
x = Symbol('x')
i1 = Interval(0, 1)
i2 = Interval(2, 3)
i3 = Union(i1, i2)
assert i3.as_relational(x) == Or(And(S(0) <= x, x <= 1),
And(S(2) <= x, x <= 3))
raises(TypeError, lambda: x in i3)
e = i3.contains(x)
assert e == i3.as_relational(x)
assert e.subs(x, -0.5) is false
assert e.subs(x, 0.5) is true
assert e.subs(x, 1.5) is false
assert e.subs(x, 2.5) is true
assert e.subs(x, 3.5) is false
U = Interval(0, 2, True, True) + Interval(10, oo) + FiniteSet(-1, 2, 5, 6)
assert all(el not in U for el in [0, 4, -oo])
assert all(el in U for el in [2, 5, 10])
def test_Union_as_relational():
x = Symbol('x')
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_Finite_as_relational():
x = Symbol('x')
y = Symbol('y')
assert FiniteSet(1, 2).as_relational(x) == Or(Eq(x, 1), Eq(x, 2))
assert FiniteSet(y, -5).as_relational(x) == Or(Eq(x, y), Eq(x, -5))
def relationalize(gen):
return Or(*[i.as_relational(gen) for i in intervals])