def test_equals():
assert Not(Or(A, B)).equals( And(Not(A), Not(B)) ) is True
assert Equivalent(A, B).equals((A >> B) & (B >> A)) is True
assert ((A | ~B) & (~A | B)).equals((~A & ~B) | (A & B)) is True
assert (A >> B).equals(~A >> ~B) is False
assert (A >> (B >> A)).equals(A >> (C >> A)) is False
pytest.raises(NotImplementedError, lambda: And(A, A < B).equals(And(A, B > A)))
def test_bool_as_set():
assert And(x <= 2, x >= -2).as_set() == Interval(-2, 2)
assert Or(x >= 2, x <= -2).as_set() == (Interval(-oo, -2, True) +
Interval(2, oo, False, True))
assert Not(x > 2, evaluate=False).as_set() == Interval(-oo, 2, True)
# issue sympy/sympy#10240
assert Not(And(x > 2, x < 3)).as_set() == \
Union(Interval(-oo, 2, True), Interval(3, oo, False, True))
assert true.as_set() == S.UniversalSet
assert false.as_set() == EmptySet()
def test_basic():
assert lambdarepr(x * y) == "x*y"
assert lambdarepr(x + y) in ["y + x", "x + y"]
assert lambdarepr(x**y) == "x**y"
assert lambdarepr(And(x, y)) == "((x) and (y))"
assert lambdarepr(Or(x, y)) == "((x) or (y))"
assert lambdarepr(Not(x)) == "(not (x))"
assert lambdarepr(false) == "False"
def test_to_cnf():
assert to_cnf(~(B | C)) == And(Not(B), Not(C))
assert to_cnf((A & B) | C) == And(Or(A, C), Or(B, C))
assert to_cnf(A >> B) == (~A) | B
assert to_cnf(A >> (B & C)) == (~A | B) & (~A | C)
assert to_cnf(A & (B | C) | ~A & (B | C), True) == B | C
assert to_cnf(Equivalent(A, B)) == And(Or(A, Not(B)), Or(B, Not(A)))
assert to_cnf(Equivalent(A, B & C)) == \
(~A | B) & (~A | C) & (~B | ~C | A)
assert to_cnf(Equivalent(A, B | C), True) == \
And(Or(Not(B), A), Or(Not(C), A), Or(B, C, Not(A)))
assert to_cnf(~(A | B) | C) == And(Or(Not(A), C), Or(Not(B), C))
def test_overloading():
"""Test that |, & are overloaded as expected."""
assert A & B == And(A, B)
assert A | B == Or(A, B)
assert (A & B) | C == Or(And(A, B), C)
assert A >> B == Implies(A, B)
assert A << B == Implies(B, A)
assert ~A == Not(A)
assert A ^ B == Xor(A, B)
def test_piecewise_fold_piecewise_in_cond():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (p1 / Abs(p1), True))
p3 = piecewise_fold(p2)
assert (p2.subs(x, -pi / 2) == 0.0)
assert (p2.subs(x, 1) == 0.0)
assert (p2.subs(x, -pi / 4) == 1.0)
p4 = Piecewise((0, Eq(p1, 0)), (1, True))
assert (piecewise_fold(p4) == Piecewise(
(0, Or(And(Eq(cos(x), 0), x < 0), Not(x < 0))), (1, True)))
r1 = 1 < Piecewise((1, x < 1), (3, True))
assert (piecewise_fold(r1) == Not(x < 1))
p5 = Piecewise((1, x < 0), (3, True))
p6 = Piecewise((1, x < 1), (3, True))
p7 = piecewise_fold(Piecewise((1, p5 < p6), (0, True)))
assert (Piecewise((1, And(Not(x < 1), x < 0)), (0, True)))
def test_numpy_logical_ops():
and_func = lambdify((x, y), And(x, y), modules="numpy")
or_func = lambdify((x, y), Or(x, y), modules="numpy")
not_func = lambdify((x), Not(x), modules="numpy")
arr1 = numpy.array([True, True])
arr2 = numpy.array([False, True])
numpy.testing.assert_array_equal(and_func(arr1, arr2), numpy.array([False, True]))
numpy.testing.assert_array_equal(or_func(arr1, arr2), numpy.array([True, True]))
numpy.testing.assert_array_equal(not_func(arr2), numpy.array([True, False]))
def test_basic():
assert lambdarepr(x * y) == 'x*y'
assert lambdarepr(x + y) in ['y + x', 'x + y']
assert lambdarepr(x**y) == 'x**y'
assert lambdarepr(And(x, y)) == '((x) and (y))'
assert lambdarepr(Or(x, y)) == '((x) or (y))'
assert lambdarepr(Not(x)) == '(not (x))'
assert lambdarepr(false) == 'False'
assert lambdarepr(Dummy('f(x)')) == '_f_lpar_x_rpar_'
def test_piecewise_fold_piecewise_in_cond():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (p1 / abs(p1), True))
assert p2.subs({x: -pi / 2}) == 0.0
assert p2.subs({x: 1}) == 0.0
assert p2.subs({x: -pi / 4}) == 1.0
p4 = Piecewise((0, Eq(p1, 0)), (1, True))
assert (piecewise_fold(p4) == Piecewise(
(0, Or(And(Eq(cos(x), 0), x < 0), Not(x < 0))), (1, True)))
r1 = 1 < Piecewise((1, x < 1), (3, True))
assert (piecewise_fold(r1) == Not(x < 1))
p5 = Piecewise((1, x < 0), (3, True))
p6 = Piecewise((1, x < 1), (3, True))
p7 = piecewise_fold(Piecewise((1, p5 < p6), (0, True)))
assert p7
assert Piecewise((1, And(Not(x < 1), x < 0)), (0, True))
def test_Not():
pytest.raises(TypeError, lambda: Not(True, False))
assert Not(True) is false
assert Not(False) is true
assert Not(0) is true
assert Not(1) is false
assert Not(2) is false
assert Not(Unequality(a, b)) == Equality(a, b)
def test_is_nnf():
assert is_nnf(true) is True
assert is_nnf(A) is True
assert is_nnf(~A) is True
assert is_nnf(A & B) is True
assert is_nnf((A & B) | (~A & A) | (~B & B) | (~A & ~B), False) is True
assert is_nnf((A | B) & (~A | ~B)) is True
assert is_nnf(Not(Or(A, B))) is False
assert is_nnf(A ^ B) is False
assert is_nnf((A & B) | (~A & A) | (~B & B) | (~A & ~B), True) is False
def test_to_dnf():
assert to_dnf(true) == true
assert to_dnf((~B) & (~C)) == (~B) & (~C)
assert to_dnf(~(B | C)) == And(Not(B), Not(C))
assert to_dnf(A & (B | C)) == Or(And(A, B), And(A, C))
assert to_dnf(A >> B) == (~A) | B
assert to_dnf(A >> (B & C)) == (~A) | (B & C)
assert to_dnf(Equivalent(A, B), True) == \
Or(And(A, B), And(Not(A), Not(B)))
assert to_dnf(Equivalent(A, B & C), True) == \
Or(And(A, B, C), And(Not(A), Not(B)), And(Not(A), Not(C)))
def test_Equivalent():
assert Equivalent(A, B) == Equivalent(B, A) == Equivalent(A, B, A)
assert Equivalent() is true
assert Equivalent(A, A) == Equivalent(A) is true
assert Equivalent(True, True) == Equivalent(False, False) is true
assert Equivalent(True, False) == Equivalent(False, True) is false
assert Equivalent(A, True) == A
assert Equivalent(A, False) == Not(A)
assert Equivalent(A, B, True) == A & B
assert Equivalent(A, B, False) == ~A & ~B
assert Equivalent(1, A) == A
assert Equivalent(0, A) == Not(A)
assert Equivalent(A, Equivalent(B, C)) != Equivalent(Equivalent(A, B), C)
assert Equivalent(A < 1, A >= 1) is false
assert Equivalent(A < 1, A >= 1, 0) is false
assert Equivalent(A < 1, A >= 1, 1) is false
assert Equivalent(A < 1, Integer(1) > A) == Equivalent(1, 1) == Equivalent(0, 0)
assert Equivalent(A < 1, B >= 1) == Equivalent(B >= 1, A < 1, evaluate=False)
def test_to_nnf():
assert to_nnf(true) is true
assert to_nnf(false) is false
assert to_nnf(A) == A
assert (~A).to_nnf() == ~A
class Boo(BooleanFunction):
pass
pytest.raises(ValueError, lambda: to_nnf(~Boo(A)))
assert to_nnf(A | ~A | B) is true
assert to_nnf(A & ~A & B) is false
assert to_nnf(A >> B) == ~A | B
assert to_nnf(Equivalent(A, B, C)) == (~A | B) & (~B | C) & (~C | A)
assert to_nnf(A ^ B ^ C) == \
(A | B | C) & (~A | ~B | C) & (A | ~B | ~C) & (~A | B | ~C)
assert to_nnf(ITE(A, B, C)) == (~A | B) & (A | C)
assert to_nnf(Not(A | B | C)) == ~A & ~B & ~C
assert to_nnf(Not(A & B & C)) == ~A | ~B | ~C
assert to_nnf(Not(A >> B)) == A & ~B
assert to_nnf(Not(Equivalent(A, B, C))) == And(Or(A, B, C), Or(~A, ~B, ~C))
assert to_nnf(Not(A ^ B ^ C)) == \
(~A | B | C) & (A | ~B | C) & (A | B | ~C) & (~A | ~B | ~C)
assert to_nnf(Not(ITE(A, B, C))) == (~A | ~B) & (A | ~C)
assert to_nnf((A >> B) ^ (B >> A)) == (A & ~B) | (~A & B)
assert to_nnf((A >> B) ^ (B >> A), False) == \
(~A | ~B | A | B) & ((A & ~B) | (~A & B))
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_relational_logic_symbols():
# See issue sympy/sympy#6204
assert (x < y) & (z < t) == And(x < y, z < t)
assert (x < y) | (z < t) == Or(x < y, z < t)
assert ~(x < y) == Not(x < y)
assert (x < y) >> (z < t) == Implies(x < y, z < t)
assert (x < y) << (z < t) == Implies(z < t, x < y)
assert (x < y) ^ (z < t) == Xor(x < y, z < t)
assert isinstance((x < y) & (z < t), And)
assert isinstance((x < y) | (z < t), Or)
assert isinstance(~(x < y), GreaterThan)
assert isinstance((x < y) >> (z < t), Implies)
assert isinstance((x < y) << (z < t), Implies)
assert isinstance((x < y) ^ (z < t), (Or, Xor))
def test_operators():
# Mostly test __and__, __rand__, and so on
assert True & A == (A & True) == A
assert False & A == (A & False) == false
assert A & B == And(A, B)
assert True | A == (A | True) == true
assert False | A == (A | False) == A
assert A | B == Or(A, B)
assert ~A == Not(A)
assert True >> A == (A << True) == A
assert False >> A == (A << False) == true
assert (A >> True) == (True << A) == true
assert (A >> False) == (False << A) == ~A
assert A >> B == B << A == Implies(A, B)
assert True ^ A == A ^ True == ~A
assert False ^ A == (A ^ False) == A
assert A ^ B == Xor(A, B)
def test_ITE():
A, B, C = map(Boolean, symbols('A,B,C'))
pytest.raises(ValueError, lambda: ITE(A, B))
assert ITE(True, False, True) is false
assert ITE(True, True, False) is true
assert ITE(False, True, False) is false
assert ITE(False, False, True) is true
assert isinstance(ITE(A, B, C), ITE)
assert ITE(True, B, C) == B
assert ITE(False, B, C) == C
assert ITE(A, B, B) == B
assert ITE(C, False, True) == Not(C)
assert ITE(C, True, False) == C
def test_Equivalent():
assert Equivalent(a, b) == Equivalent(b, a) == Equivalent(a, b, a)
assert Equivalent() is true
assert Equivalent(a, a) == Equivalent(a) is true
assert Equivalent(True, True) == Equivalent(False, False) is true
assert Equivalent(True, False) == Equivalent(False, True) is false
assert Equivalent(a, True) == a
assert Equivalent(a, False) == ~a
assert Equivalent(a, b, True) == a & b
assert Equivalent(a, b, False) == ~a & ~b
assert Equivalent(1, a) == a
assert Equivalent(0, a) == Not(a)
assert Equivalent(a, Equivalent(b, c)) != Equivalent(Equivalent(a, b), c)
assert Equivalent(a < 1, a >= 1) is false
assert Equivalent(a < 1, a >= 1, 0) is false
assert Equivalent(a < 1, a >= 1, 1) is false
assert Equivalent(a < 1, 1 > a) == Equivalent(1, 1) == Equivalent(0, 0)
assert Equivalent(a < 1, Integer(1) > a) == Equivalent(1, 1) == Equivalent(0, 0)
assert Equivalent(a < 1, b >= 1) == Equivalent(b >= 1, a < 1, evaluate=False)
def test_count_ops_non_visual():
def count(val):
return count_ops(val, visual=False)
assert count(x) == 0
assert count(x) is not Integer(0)
assert count(x + y) == 1
assert count(x + y) is not Integer(1)
assert count(x + y*x + 2*y) == 4
assert count({x + y: x}) == 1
assert count({x + y: 2 + x}) is not Integer(1)
assert count(Or(x, y)) == 1
assert count(And(x, y)) == 1
assert count(Not(x)) == 1
assert count(Nor(x, y)) == 2
assert count(Nand(x, y)) == 2
assert count(Xor(x, y)) == 1
assert count(Implies(x, y)) == 1
assert count(Equivalent(x, y)) == 1
assert count(ITE(x, y, z)) == 1
assert count(ITE(True, x, y)) == 0
def test_fcode_Xlogical():
# binary Xor
assert fcode(Xor(x, y, evaluate=False), source_format='free') == \
'x .neqv. y'
assert fcode(Xor(x, Not(y), evaluate=False), source_format='free') == \
'x .neqv. .not. y'
assert fcode(Xor(Not(x), y, evaluate=False), source_format='free') == \
'y .neqv. .not. x'
assert fcode(Xor(Not(x), Not(y), evaluate=False),
source_format='free') == '.not. x .neqv. .not. y'
assert fcode(Not(Xor(x, y, evaluate=False), evaluate=False),
source_format='free') == '.not. (x .neqv. y)'
# binary Equivalent
assert fcode(Equivalent(x, y), source_format='free') == 'x .eqv. y'
assert fcode(Equivalent(x, Not(y)), source_format='free') == \
'x .eqv. .not. y'
assert fcode(Equivalent(Not(x), y), source_format='free') == \
'y .eqv. .not. x'
assert fcode(Equivalent(Not(x), Not(y)), source_format='free') == \
'.not. x .eqv. .not. y'
assert fcode(Not(Equivalent(x, y), evaluate=False),
source_format='free') == '.not. (x .eqv. y)'
# mixed And/Equivalent
assert fcode(Equivalent(And(y, z), x), source_format='free') == \
'x .eqv. y .and. z'
assert fcode(Equivalent(And(z, x), y), source_format='free') == \
'y .eqv. x .and. z'
assert fcode(Equivalent(And(x, y), z), source_format='free') == \
'z .eqv. x .and. y'
assert fcode(And(Equivalent(y, z), x), source_format='free') == \
'x .and. (y .eqv. z)'
assert fcode(And(Equivalent(z, x), y), source_format='free') == \
'y .and. (x .eqv. z)'
assert fcode(And(Equivalent(x, y), z), source_format='free') == \
'z .and. (x .eqv. y)'
# mixed Or/Equivalent
assert fcode(Equivalent(Or(y, z), x), source_format='free') == \
'x .eqv. y .or. z'
assert fcode(Equivalent(Or(z, x), y), source_format='free') == \
'y .eqv. x .or. z'
assert fcode(Equivalent(Or(x, y), z), source_format='free') == \
'z .eqv. x .or. y'
assert fcode(Or(Equivalent(y, z), x), source_format='free') == \
'x .or. (y .eqv. z)'
assert fcode(Or(Equivalent(z, x), y), source_format='free') == \
'y .or. (x .eqv. z)'
assert fcode(Or(Equivalent(x, y), z), source_format='free') == \
'z .or. (x .eqv. y)'
# mixed Xor/Equivalent
assert fcode(Equivalent(Xor(y, z, evaluate=False), x),
source_format='free') == 'x .eqv. (y .neqv. z)'
assert fcode(Equivalent(Xor(z, x, evaluate=False), y),
source_format='free') == 'y .eqv. (x .neqv. z)'
assert fcode(Equivalent(Xor(x, y, evaluate=False), z),
source_format='free') == 'z .eqv. (x .neqv. y)'
assert fcode(Xor(Equivalent(y, z), x, evaluate=False),
source_format='free') == 'x .neqv. (y .eqv. z)'
assert fcode(Xor(Equivalent(z, x), y, evaluate=False),
source_format='free') == 'y .neqv. (x .eqv. z)'
assert fcode(Xor(Equivalent(x, y), z, evaluate=False),
source_format='free') == 'z .neqv. (x .eqv. y)'
# mixed And/Xor
assert fcode(Xor(And(y, z), x, evaluate=False), source_format='free') == \
'x .neqv. y .and. z'
assert fcode(Xor(And(z, x), y, evaluate=False), source_format='free') == \
'y .neqv. x .and. z'
assert fcode(Xor(And(x, y), z, evaluate=False), source_format='free') == \
'z .neqv. x .and. y'
assert fcode(And(Xor(y, z, evaluate=False), x), source_format='free') == \
'x .and. (y .neqv. z)'
assert fcode(And(Xor(z, x, evaluate=False), y), source_format='free') == \
'y .and. (x .neqv. z)'
assert fcode(And(Xor(x, y, evaluate=False), z), source_format='free') == \
'z .and. (x .neqv. y)'
# mixed Or/Xor
assert fcode(Xor(Or(y, z), x, evaluate=False), source_format='free') == \
'x .neqv. y .or. z'
assert fcode(Xor(Or(z, x), y, evaluate=False), source_format='free') == \
'y .neqv. x .or. z'
assert fcode(Xor(Or(x, y), z, evaluate=False), source_format='free') == \
'z .neqv. x .or. y'
assert fcode(Or(Xor(y, z, evaluate=False), x), source_format='free') == \
'x .or. (y .neqv. z)'
assert fcode(Or(Xor(z, x, evaluate=False), y), source_format='free') == \
'y .or. (x .neqv. z)'
assert fcode(Or(Xor(x, y, evaluate=False), z), source_format='free') == \
'z .or. (x .neqv. y)'
# trinary Xor
assert fcode(Xor(x, y, z, evaluate=False), source_format='free') == \
'x .neqv. y .neqv. z'
assert fcode(Xor(x, y, Not(z), evaluate=False), source_format='free') == \
'x .neqv. y .neqv. .not. z'
assert fcode(Xor(x, Not(y), z, evaluate=False), source_format='free') == \
'x .neqv. z .neqv. .not. y'
assert fcode(Xor(Not(x), y, z, evaluate=False), source_format='free') == \
'y .neqv. z .neqv. .not. x'
def test_fcode_Logical():
# unary Not
assert fcode(Not(x), source_format='free') == '.not. x'
# binary And
assert fcode(And(x, y), source_format='free') == 'x .and. y'
assert fcode(And(x, Not(y)), source_format='free') == 'x .and. .not. y'
assert fcode(And(Not(x), y), source_format='free') == 'y .and. .not. x'
assert fcode(And(Not(x), Not(y)), source_format='free') == \
'.not. x .and. .not. y'
assert fcode(Not(And(x, y), evaluate=False), source_format='free') == \
'.not. (x .and. y)'
# binary Or
assert fcode(Or(x, y), source_format='free') == 'x .or. y'
assert fcode(Or(x, Not(y)), source_format='free') == 'x .or. .not. y'
assert fcode(Or(Not(x), y), source_format='free') == 'y .or. .not. x'
assert fcode(Or(Not(x), Not(y)), source_format='free') == \
'.not. x .or. .not. y'
assert fcode(Not(Or(x, y), evaluate=False), source_format='free') == \
'.not. (x .or. y)'
# mixed And/Or
assert fcode(And(Or(y, z), x),
source_format='free') == 'x .and. (y .or. z)'
assert fcode(And(Or(z, x), y),
source_format='free') == 'y .and. (x .or. z)'
assert fcode(And(Or(x, y), z),
source_format='free') == 'z .and. (x .or. y)'
assert fcode(Or(And(y, z), x), source_format='free') == 'x .or. y .and. z'
assert fcode(Or(And(z, x), y), source_format='free') == 'y .or. x .and. z'
assert fcode(Or(And(x, y), z), source_format='free') == 'z .or. x .and. y'
# trinary And
assert fcode(And(x, y, z), source_format='free') == 'x .and. y .and. z'
assert fcode(And(x, y, Not(z)), source_format='free') == \
'x .and. y .and. .not. z'
assert fcode(And(x, Not(y), z), source_format='free') == \
'x .and. z .and. .not. y'
assert fcode(And(Not(x), y, z), source_format='free') == \
'y .and. z .and. .not. x'
assert fcode(Not(And(x, y, z), evaluate=False), source_format='free') == \
'.not. (x .and. y .and. z)'
# trinary Or
assert fcode(Or(x, y, z), source_format='free') == 'x .or. y .or. z'
assert fcode(Or(x, y, Not(z)), source_format='free') == \
'x .or. y .or. .not. z'
assert fcode(Or(x, Not(y), z), source_format='free') == \
'x .or. z .or. .not. y'
assert fcode(Or(Not(x), y, z), source_format='free') == \
'y .or. z .or. .not. x'
assert fcode(Not(Or(x, y, z), evaluate=False), source_format='free') == \
'.not. (x .or. y .or. z)'
def test_simplification():
"""Test working of simplification methods."""
set1 = [[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 1, 0]]
set2 = [[0, 0, 0], [0, 1, 0], [1, 0, 1], [1, 1, 1]]
assert SOPform([x, y, z], set1) == Or(And(Not(x), z), And(Not(z), x))
assert Not(SOPform([x, y, z],
set2)) == Not(Or(And(Not(x), Not(z)), And(x, z)))
assert POSform([x, y, z], set1 + set2) is true
assert SOPform([x, y, z], set1 + set2) is true
assert SOPform([Dummy(), Dummy(), Dummy()], set1 + set2) is true
minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], [1, 0, 1, 1],
[1, 1, 1, 1]]
dontcares = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]]
assert (SOPform([w, x, y, z], minterms,
dontcares) == Or(And(Not(w), z), And(y, z)))
assert POSform([w, x, y, z], minterms, dontcares) == And(Or(Not(w), y), z)
# test simplification
ans = And(A, Or(B, C))
assert simplify_logic(A & (B | C)) == ans
assert simplify_logic((A & B) | (A & C)) == ans
assert simplify_logic(Implies(A, B)) == Or(Not(A), B)
assert simplify_logic(Equivalent(A, B)) == \
Or(And(A, B), And(Not(A), Not(B)))
assert simplify_logic(And(Equality(A, 2), C)) == And(Equality(A, 2), C)
assert simplify_logic(And(Equality(A, 2), A)) == And(Equality(A, 2), A)
assert simplify_logic(And(Equality(A, B), C)) == And(Equality(A, B), C)
assert simplify_logic(Or(And(Equality(A, 3), B), And(Equality(A, 3), C))) \
== And(Equality(A, 3), Or(B, C))
e = And(A, x**2 - x)
assert simplify_logic(e) == And(A, x * (x - 1))
assert simplify_logic(e, deep=False) == e
pytest.raises(ValueError, lambda: simplify_logic(A & (B | C), form='spam'))
e = x & y ^ z | (z ^ x)
res = [(x & ~z) | (z & ~x) | (z & ~y), (x & ~y) | (x & ~z) | (z & ~x)]
assert simplify_logic(e) in res
assert SOPform(
[z, y, x],
[[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 0, 1], [1, 1, 0]]) == res[1]
# check input
ans = SOPform([x, y], [[1, 0]])
assert SOPform([x, y], [[1, 0]]) == ans
assert POSform([x, y], [[1, 0]]) == ans
pytest.raises(ValueError, lambda: SOPform([x], [[1]], [[1]]))
assert SOPform([x], [[1]], [[0]]) is true
assert SOPform([x], [[0]], [[1]]) is true
assert SOPform([x], [], []) is false
pytest.raises(ValueError, lambda: POSform([x], [[1]], [[1]]))
assert POSform([x], [[1]], [[0]]) is true
assert POSform([x], [[0]], [[1]]) is true
assert POSform([x], [], []) is false
# check working of simplify
assert simplify((A & B) | (A & C)) == And(A, Or(B, C))
assert simplify(And(x, Not(x))) is false
assert simplify(Or(x, Not(x))) is true
def test_bool_as_set():
assert ((x <= 2) & (x >= -2)).as_set() == Interval(-2, 2)
assert ((x >= 2) | (x <= -2)).as_set() == (Interval(-oo, -2) + Interval(2, oo, False))
assert Not(x > 2, evaluate=False).as_set() == Interval(-oo, 2, True)
assert true.as_set() == S.UniversalSet
assert false.as_set() == EmptySet()
def test_true_false():
# pylint: disable=singleton-comparison,comparison-with-itself
assert true is true
assert false is false
assert true is not True
assert false is not False
assert true
assert not false
assert true == True # noqa: E712
assert false == False # noqa: E712
assert not true == False # noqa: E712
assert not false == True # noqa: E712
assert not true == false
assert hash(true) == hash(True)
assert hash(false) == hash(False)
assert len({true, True}) == len({false, False}) == 1
assert int(true) == 1
assert int(false) == 0
assert isinstance(true, BooleanAtom)
assert isinstance(false, BooleanAtom)
assert not isinstance(true, bool)
assert not isinstance(false, bool)
assert ~true is false
assert Not(True) is false
assert ~false is true
assert Not(False) is true
for T, F in itertools.product([True, true], [False, false]):
assert And(T, F) is false
assert And(F, T) is false
assert And(F, F) is false
assert And(T, T) is true
assert And(T, x) == x
assert And(F, x) is false
if not (T is True and F is False):
assert T & F is false
assert F & T is false
if F is not False:
assert F & F is false
if T is not True:
assert T & T is true
assert Or(T, F) is true
assert Or(F, T) is true
assert Or(F, F) is false
assert Or(T, T) is true
assert Or(T, x) is true
assert Or(F, x) == x
if not (T is True and F is False):
assert T | F is true
assert F | T is true
if F is not False:
assert F | F is false
if T is not True:
assert T | T is true
assert Xor(T, F) is true
assert Xor(F, T) is true
assert Xor(F, F) is false
assert Xor(T, T) is false
assert Xor(T, x) == ~x
assert Xor(F, x) == x
if not (T is True and F is False):
assert T ^ F is true
assert F ^ T is true
if F is not False:
assert F ^ F is false
if T is not True:
assert T ^ T is false
assert Nand(T, F) is true
assert Nand(F, T) is true
assert Nand(F, F) is true
assert Nand(T, T) is false
assert Nand(T, x) == ~x
assert Nand(F, x) is true
assert Nor(T, F) is false
assert Nor(F, T) is false
assert Nor(F, F) is true
assert Nor(T, T) is false
assert Nor(T, x) is false
assert Nor(F, x) == ~x
assert Implies(T, F) is false
assert Implies(F, T) is true
assert Implies(F, F) is true
assert Implies(T, T) is true
assert Implies(T, x) == x
assert Implies(F, x) is true
assert Implies(x, T) is true
assert Implies(x, F) == ~x
if not (T is True and F is False):
assert T >> F is false
assert F << T is false
assert F >> T is true
assert T << F is true
if F is not False:
assert F >> F is true
assert F << F is true
if T is not True:
assert T >> T is true
assert T << T is true
assert Equivalent(T, F) is false
assert Equivalent(F, T) is false
assert Equivalent(F, F) is true
assert Equivalent(T, T) is true
assert Equivalent(T, x) == x
assert Equivalent(F, x) == ~x
assert Equivalent(x, T) == x
assert Equivalent(x, F) == ~x
assert ITE(T, T, T) is true
assert ITE(T, T, F) is true
assert ITE(T, F, T) is false
assert ITE(T, F, F) is false
assert ITE(F, T, T) is true
assert ITE(F, T, F) is false
assert ITE(F, F, T) is true
assert ITE(F, F, F) is false
def test_overloading():
assert a & b == And(a, b)
assert a | b == Or(a, b)
assert a >> b == Implies(a, b)
assert ~a == Not(a)
assert a ^ b == Xor(a, b)
def test_eliminate_implications():
assert eliminate_implications(Implies(A, B, evaluate=False)) == (~A) | B
assert eliminate_implications(A >> (C >> Not(B))) == Or(
Or(Not(B), Not(C)), Not(A))
assert eliminate_implications(Equivalent(A, B, C, D)) == \
(~A | B) & (~B | C) & (~C | D) & (~D | A)
def test_piecewise_fold_piecewise_in_cond_2():
p1 = Piecewise((cos(x), x < 0), (0, True))
p2 = Piecewise((0, Eq(p1, 0)), (1 / p1, True))
p3 = Piecewise((0, Or(And(Eq(cos(x), 0), x < 0), Not(x < 0))),
(1 / cos(x), True))
assert (piecewise_fold(p2) == p3)
def test_true_false():
assert true is true
assert false is false
assert true is not True
assert false is not False
assert true
assert not false
assert true == True # noqa: E712
assert false == False # noqa: E712
assert not (true == False) # noqa: E712
assert not (false == True) # noqa: E712
assert not (true == false)
assert hash(true) == hash(True)
assert hash(false) == hash(False)
assert len({true, True}) == len({false, False}) == 1
assert isinstance(true, BooleanAtom)
assert isinstance(false, BooleanAtom)
# We don't want to subclass from bool, because bool subclasses from
# int. But operators like &, |, ^, <<, >>, and ~ act differently on 0 and
# 1 then we want them to on true and false. See the docstrings of the
# various And, Or, etc. functions for examples.
assert not isinstance(true, bool)
assert not isinstance(false, bool)
# Note: using 'is' comparison is important here. We want these to return
# true and false, not True and False
assert Not(true) is false
assert Not(True) is false
assert Not(false) is true
assert Not(False) is true
assert ~true is false
assert ~false is true
for T, F in itertools.product([True, true], [False, false]):
assert And(T, F) is false
assert And(F, T) is false
assert And(F, F) is false
assert And(T, T) is true
assert And(T, x) == x
assert And(F, x) is false
if not (T is True and F is False):
assert T & F is false
assert F & T is false
if F is not False:
assert F & F is false
if T is not True:
assert T & T is true
assert Or(T, F) is true
assert Or(F, T) is true
assert Or(F, F) is false
assert Or(T, T) is true
assert Or(T, x) is true
assert Or(F, x) == x
if not (T is True and F is False):
assert T | F is true
assert F | T is true
if F is not False:
assert F | F is false
if T is not True:
assert T | T is true
assert Xor(T, F) is true
assert Xor(F, T) is true
assert Xor(F, F) is false
assert Xor(T, T) is false
assert Xor(T, x) == ~x
assert Xor(F, x) == x
if not (T is True and F is False):
assert T ^ F is true
assert F ^ T is true
if F is not False:
assert F ^ F is false
if T is not True:
assert T ^ T is false
assert Nand(T, F) is true
assert Nand(F, T) is true
assert Nand(F, F) is true
assert Nand(T, T) is false
assert Nand(T, x) == ~x
assert Nand(F, x) is true
assert Nor(T, F) is false
assert Nor(F, T) is false
assert Nor(F, F) is true
assert Nor(T, T) is false
assert Nor(T, x) is false
assert Nor(F, x) == ~x
assert Implies(T, F) is false
assert Implies(F, T) is true
assert Implies(F, F) is true
assert Implies(T, T) is true
assert Implies(T, x) == x
assert Implies(F, x) is true
assert Implies(x, T) is true
assert Implies(x, F) == ~x
if not (T is True and F is False):
assert T >> F is false
assert F << T is false
assert F >> T is true
assert T << F is true
if F is not False:
assert F >> F is true
assert F << F is true
if T is not True:
assert T >> T is true
assert T << T is true
assert Equivalent(T, F) is false
assert Equivalent(F, T) is false
assert Equivalent(F, F) is true
assert Equivalent(T, T) is true
assert Equivalent(T, x) == x
assert Equivalent(F, x) == ~x
assert Equivalent(x, T) == x
assert Equivalent(x, F) == ~x
assert ITE(T, T, T) is true
assert ITE(T, T, F) is true
assert ITE(T, F, T) is false
assert ITE(T, F, F) is false
assert ITE(F, T, T) is true
assert ITE(F, T, F) is false
assert ITE(F, F, T) is true
assert ITE(F, F, F) is false
def test_bool_map():
"""Test working of bool_map function."""
minterms = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 1, 1, 1], [1, 0, 1, 1],
[1, 1, 1, 1]]
assert bool_map(Not(Not(a)), a) == (a, {a: a})
assert bool_map(SOPform([w, x, y, z], minterms),
POSform([w, x, y, z], minterms)) == \
(And(Or(Not(w), y), Or(Not(x), y), z), {x: x, w: w, z: z, y: y})
assert bool_map(SOPform([x, z, y], [[1, 0, 1]]),
SOPform([a, b, c], [[1, 0, 1]])) is not False
function1 = SOPform([x, z, y], [[1, 0, 1], [0, 0, 1]])
function2 = SOPform([a, b, c], [[1, 0, 1], [1, 0, 0]])
assert bool_map(function1, function2) == \
(function1, {y: a, z: b})
assert bool_map(And(x, Not(y)), Or(y, Not(x))) is False
assert bool_map(And(x, Not(y)), And(y, Not(x), z)) is False
assert bool_map(And(x, Not(y)), And(Or(y, z), Not(x))) is False
assert bool_map(Or(And(Not(y), a), And(Not(y), b), And(x, y)), Or(
x, y, a)) is False