def test_count_ops_visual(): ADD, MUL, POW, SIN, COS, EXP, AND, D, G, M = symbols( 'Add Mul Pow sin cos exp And Derivative Integral Sum'.upper()) DIV, SUB, NEG = symbols('DIV SUB NEG') LT, LE, GT, GE, EQ, NE = symbols('LT LE GT GE EQ NE') NOT, OR, AND, XOR, IMPLIES, EQUIVALENT, _ITE, BASIC, TUPLE = symbols( 'Not Or And Xor Implies Equivalent ITE Basic Tuple'.upper()) def count(val): return count_ops(val, visual=True) assert count(7) is S.Zero assert count(S(7)) is S.Zero assert count(-1) == NEG assert count(-2) == NEG assert count(S(2) / 3) == DIV assert count(Rational(2, 3)) == DIV assert count(pi / 3) == DIV assert count(-pi / 3) == DIV + NEG assert count(I - 1) == SUB assert count(1 - I) == SUB assert count(1 - 2 * I) == SUB + MUL assert count(x) is S.Zero assert count(-x) == NEG assert count(-2 * x / 3) == NEG + DIV + MUL assert count(Rational(-2, 3) * x) == NEG + DIV + MUL assert count(1 / x) == DIV assert count(1 / (x * y)) == DIV + MUL assert count(-1 / x) == NEG + DIV assert count(-2 / x) == NEG + DIV assert count(x / y) == DIV assert count(-x / y) == NEG + DIV assert count(x**2) == POW assert count(-x**2) == POW + NEG assert count(-2 * x**2) == POW + MUL + NEG assert count(x + pi / 3) == ADD + DIV assert count(x + S.One / 3) == ADD + DIV assert count(x + Rational(1, 3)) == ADD + DIV assert count(x + y) == ADD assert count(x - y) == SUB assert count(y - x) == SUB assert count(-1 / (x - y)) == DIV + NEG + SUB assert count(-1 / (y - x)) == DIV + NEG + SUB assert count(1 + x**y) == ADD + POW assert count(1 + x + y) == 2 * ADD assert count(1 + x + y + z) == 3 * ADD assert count(1 + x**y + 2 * x * y + y**2) == 3 * ADD + 2 * POW + 2 * MUL assert count(2 * z + y + x + 1) == 3 * ADD + MUL assert count(2 * z + y**17 + x + 1) == 3 * ADD + MUL + POW assert count(2 * z + y**17 + x + sin(x)) == 3 * ADD + POW + MUL + SIN assert count(2 * z + y**17 + x + sin(x**2)) == 3 * ADD + MUL + 2 * POW + SIN assert count(2 * z + y**17 + x + sin(x**2) + exp(cos(x))) == 4 * ADD + MUL + 2 * POW + EXP + COS + SIN assert count(Derivative(x, x)) == D assert count(Integral(x, x) + 2 * x / (1 + x)) == G + DIV + MUL + 2 * ADD assert count(Sum(x, (x, 1, x + 1)) + 2 * x / (1 + x)) == M + DIV + MUL + 3 * ADD assert count(Basic()) is S.Zero assert count({x + 1: sin(x)}) == ADD + SIN assert count([x + 1, sin(x) + y, None]) == ADD + SIN + ADD assert count({x + 1: sin(x), y: cos(x) + 1}) == SIN + COS + 2 * ADD assert count({}) is S.Zero assert count([x + 1, sin(x) * y, None]) == SIN + ADD + MUL assert count([]) is S.Zero assert count(Basic()) == 0 assert count(Basic(Basic(), Basic(x, x + y))) == ADD + 2 * BASIC assert count(Basic(x, x + y)) == ADD + BASIC assert [count(Rel(x, y, op)) for op in '< <= > >= == <> !='.split() ] == [LT, LE, GT, GE, EQ, NE, NE] assert count(Or(x, y)) == OR assert count(And(x, y)) == AND assert count(Or(x, Or(y, And(z, a)))) == AND + OR assert count(Nor(x, y)) == NOT + OR assert count(Nand(x, y)) == NOT + AND assert count(Xor(x, y)) == XOR assert count(Implies(x, y)) == IMPLIES assert count(Equivalent(x, y)) == EQUIVALENT assert count(ITE(x, y, z)) == _ITE assert count([Or(x, y), And(x, y), Basic(x + y)]) == ADD + AND + BASIC + OR assert count(Basic(Tuple(x))) == BASIC + TUPLE #It checks that TUPLE is counted as an operation. assert count(Eq(x + y, S(2))) == ADD + EQ
def test_true_false(): assert true is S.true assert false is S.false assert true is not True assert false is not False assert true assert not false assert true == True assert false == False assert not (true == False) assert not (false == True) 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 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 assert all(i.simplify(1, 2) is i for i in (S.true, S.false))
def test_Nor(): assert Nor() is true assert Nor(A) == ~A assert Nor(True) is false assert Nor(False) is true assert Nor(True, True) is false assert Nor(True, False) is false assert Nor(False, False) is true assert Nor(True, A) is false assert Nor(False, A) == ~A assert Nor(True, True, True) is false assert Nor(True, True, A) is false assert Nor(True, False, A) is false
def test_Nor(): A, B, C = symbols('ABC') assert Nor() == False assert Nor(A) == ~A assert Nor(True) == False assert Nor(False) == True assert Nor(True, True ) == False assert Nor(True, False) == False assert Nor(False, False) == True assert Nor(True, A) == False assert Nor(False, A) == ~A assert Nor(True, True, True) == False assert Nor(True, True , A) == False assert Nor(True, False, A) == False
from sympy import symbols Xor(True, False) Xor(True, True) Xor(True, False, True) Xor(True, False, True, False) Xor(True, False, True, False, True) a, b = symbols('a b') a ^ b from sympy.logic.boolalg import Nand Nand(True, False) Nand(True, True) Nand(a, b) from sympy.logic.boolalg import Nor Nor(True, False) Nor(True, True) Nor(False, True) Nor(False, False) Nor(a, b) from sympy.logic.boolalg import Equivalent, And Equivalent(False, False, False) Equivalent(True, False, False) Equivalent(a, And(a, True)) from sympy.logic.boolalg import Implies Implies(False, True) Implies(True, False) Implies(False, False) Implies(True, True)
def test_sympy__logic__boolalg__Nor(): from sympy.logic.boolalg import Nor assert _test_args(Nor(x, y, 2))