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