Python Q.positive方法代码示例

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_float_1():
    z = 1.0
    assert ask(Q.commutative(z))      == True
    assert ask(Q.integer(z))          == True
    assert ask(Q.rational(z))         == True
    assert ask(Q.real(z))             == True
    assert ask(Q.complex(z))          == True
    assert ask(Q.irrational(z))       == False
    assert ask(Q.imaginary(z))        == False
    assert ask(Q.positive(z))         == True
    assert ask(Q.negative(z))         == False
    assert ask(Q.even(z))             == False
    assert ask(Q.odd(z))              == True
    assert ask(Q.bounded(z))          == True
    assert ask(Q.infinitesimal(z))    == False
    assert ask(Q.prime(z))            == False
    assert ask(Q.composite(z))        == True

    z = 7.2123
    assert ask(Q.commutative(z))      == True
    assert ask(Q.integer(z))          == False
    assert ask(Q.rational(z))         == True
    assert ask(Q.real(z))             == True
    assert ask(Q.complex(z))          == True
    assert ask(Q.irrational(z))       == False
    assert ask(Q.imaginary(z))        == False
    assert ask(Q.positive(z))         == True
    assert ask(Q.negative(z))         == False
    assert ask(Q.even(z))             == False
    assert ask(Q.odd(z))              == False
    assert ask(Q.bounded(z))          == True
    assert ask(Q.infinitesimal(z))    == False
    assert ask(Q.prime(z))            == False
    assert ask(Q.composite(z))        == False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_extended_real():
    x = symbols('x')
    assert ask(Q.extended_real(x), Q.positive(x)) == True
    assert ask(Q.extended_real(-x), Q.positive(x)) == True
    assert ask(Q.extended_real(-x), Q.negative(x)) == True

    assert ask(Q.extended_real(x+S.Infinity), Q.real(x)) == True

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_functions_in_assumptions():
    from sympy.logic.boolalg import Equivalent, Xor

    x = symbols("x")
    assert ask(x, Q.negative, Q.real(x) >> Q.positive(x)) is False
    assert ask(x, Q.negative, Equivalent(Q.real(x), Q.positive(x))) is False
    assert ask(x, Q.negative, Xor(Q.real(x), Q.negative(x))) is False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
 def Pow(expr, assumptions):
     """
     Real**Integer         -> Real
     Positive**Real        -> Real
     Real**(Integer/Even)  -> Real if base is nonnegative
     Real**(Integer/Odd)   -> Real
     Real**Imaginary       -> ?
     Imaginary**Real       -> ?
     Real**Real            -> ?
     """
     if expr.is_number:
         return AskRealHandler._number(expr, assumptions)
     if ask(Q.imaginary(expr.base), assumptions):
         if ask(Q.real(expr.exp), assumptions):
             if ask(Q.odd(expr.exp), assumptions):
                 return False
             elif ask(Q.even(expr.exp), assumptions):
                 return True
     elif ask(Q.real(expr.base), assumptions):
         if ask(Q.real(expr.exp), assumptions):
             if expr.exp.is_Rational and \
                ask(Q.even(expr.exp.q), assumptions):
                 return ask(Q.positive(expr.base), assumptions)
             elif ask(Q.integer(expr.exp), assumptions):
                 return True
             elif ask(Q.positive(expr.base), assumptions):
                 return True
             elif ask(Q.negative(expr.base), assumptions):
                 return False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def refine_atan2(expr, assumptions):
    """
    Handler for the atan2 function

    Examples
    ========

    >>> from sympy import Symbol, Q, refine, atan2
    >>> from sympy.assumptions.refine import refine_atan2
    >>> from sympy.abc import x, y
    >>> refine_atan2(atan2(y,x), Q.real(y) & Q.positive(x))
    atan(y/x)
    >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.negative(x))
    atan(y/x) - pi
    >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.negative(x))
    atan(y/x) + pi
    """
    from sympy.functions.elementary.complexes import atan
    from sympy.core import S
    y, x = expr.args
    if ask(Q.real(y) & Q.positive(x), assumptions):
        return atan(y / x)
    elif ask(Q.negative(y) & Q.negative(x), assumptions):
        return atan(y / x) - S.Pi
    elif ask(Q.positive(y) & Q.negative(x), assumptions):
        return atan(y / x) + S.Pi
    else:
        return expr

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_refine():
    m0 = OperationsOnlyMatrix([[Abs(x)**2, sqrt(x**2)],
                 [sqrt(x**2)*Abs(y)**2, sqrt(y**2)*Abs(x)**2]])
    m1 = m0.refine(Q.real(x) & Q.real(y))
    assert m1 == Matrix([[x**2, Abs(x)], [y**2*Abs(x), x**2*Abs(y)]])

    m1 = m0.refine(Q.positive(x) & Q.positive(y))
    assert m1 == Matrix([[x**2, x], [x*y**2, x**2*y]])

    m1 = m0.refine(Q.negative(x) & Q.negative(y))
    assert m1 == Matrix([[x**2, -x], [-x*y**2, -x**2*y]])

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
    def Pow(expr, assumptions):
        """
        Real**Integer              -> Real
        Positive**Real             -> Real
        Real**(Integer/Even)       -> Real if base is nonnegative
        Real**(Integer/Odd)        -> Real
        Imaginary**(Integer/Even)  -> Real
        Imaginary**(Integer/Odd)   -> not Real
        Imaginary**Real            -> ? since Real could be 0 (giving real) or 1 (giving imaginary)
        b**Imaginary               -> Real if log(b) is imaginary and b != 0 and exponent != integer multiple of I*pi/log(b)
        Real**Real                 -> ? e.g. sqrt(-1) is imaginary and sqrt(2) is not
        """
        if expr.is_number:
            return AskRealHandler._number(expr, assumptions)

        if expr.base.func == exp:
            if ask(Q.imaginary(expr.base.args[0]), assumptions):
                if ask(Q.imaginary(expr.exp), assumptions):
                    return True
            # If the i = (exp's arg)/(I*pi) is an integer or half-integer
            # multiple of I*pi then 2*i will be an integer. In addition,
            # exp(i*I*pi) = (-1)**i so the overall realness of the expr
            # can be determined by replacing exp(i*I*pi) with (-1)**i.
            i = expr.base.args[0]/I/pi
            if ask(Q.integer(2*i), assumptions):
                return ask(Q.real(((-1)**i)**expr.exp), assumptions)
            return

        if ask(Q.imaginary(expr.base), assumptions):
            if ask(Q.integer(expr.exp), assumptions):
                odd = ask(Q.odd(expr.exp), assumptions)
                if odd is not None:
                    return not odd
                return

        if ask(Q.imaginary(expr.exp), assumptions):
            imlog = ask(Q.imaginary(log(expr.base)), assumptions)
            if imlog is not None:
                # I**i -> real, log(I) is imag;
                # (2*I)**i -> complex, log(2*I) is not imag
                return imlog

        if ask(Q.real(expr.base), assumptions):
            if ask(Q.real(expr.exp), assumptions):
                if expr.exp.is_Rational and \
                        ask(Q.even(expr.exp.q), assumptions):
                    return ask(Q.positive(expr.base), assumptions)
                elif ask(Q.integer(expr.exp), assumptions):
                    return True
                elif ask(Q.positive(expr.base), assumptions):
                    return True
                elif ask(Q.negative(expr.base), assumptions):
                    return False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_I():
    I = S.ImaginaryUnit
    z = I
    assert ask(Q.commutative(z))      == True
    assert ask(Q.integer(z))          == False
    assert ask(Q.rational(z))         == False
    assert ask(Q.real(z))             == False
    assert ask(Q.complex(z))          == True
    assert ask(Q.irrational(z))       == False
    assert ask(Q.imaginary(z))        == True
    assert ask(Q.positive(z))         == False
    assert ask(Q.negative(z))         == False
    assert ask(Q.even(z))             == False
    assert ask(Q.odd(z))              == False
    assert ask(Q.bounded(z))          == True
    assert ask(Q.infinitesimal(z))    == False
    assert ask(Q.prime(z))            == False
    assert ask(Q.composite(z))        == False

    z = 1 + I
    assert ask(Q.commutative(z))      == True
    assert ask(Q.integer(z))          == False
    assert ask(Q.rational(z))         == False
    assert ask(Q.real(z))             == False
    assert ask(Q.complex(z))          == True
    assert ask(Q.irrational(z))       == False
    assert ask(Q.imaginary(z))        == False
    assert ask(Q.positive(z))         == False
    assert ask(Q.negative(z))         == False
    assert ask(Q.even(z))             == False
    assert ask(Q.odd(z))              == False
    assert ask(Q.bounded(z))          == True
    assert ask(Q.infinitesimal(z))    == False
    assert ask(Q.prime(z))            == False
    assert ask(Q.composite(z))        == False

    z = I*(1+I)
    assert ask(Q.commutative(z))      == True
    assert ask(Q.integer(z))          == False
    assert ask(Q.rational(z))         == False
    assert ask(Q.real(z))             == False
    assert ask(Q.complex(z))          == True
    assert ask(Q.irrational(z))       == False
    assert ask(Q.imaginary(z))        == False
    assert ask(Q.positive(z))         == False
    assert ask(Q.negative(z))         == False
    assert ask(Q.even(z))             == False
    assert ask(Q.odd(z))              == False
    assert ask(Q.bounded(z))          == True
    assert ask(Q.infinitesimal(z))    == False
    assert ask(Q.prime(z))            == False
    assert ask(Q.composite(z))        == False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_negative():
    x, y = symbols('x,y')
    assert ask(Q.negative(x), Q.negative(x)) == True
    assert ask(Q.negative(x), Q.positive(x)) == False
    assert ask(Q.negative(x), ~Q.real(x)) == False
    assert ask(Q.negative(x), Q.prime(x)) == False
    assert ask(Q.negative(x), ~Q.prime(x)) == None

    assert ask(Q.negative(-x), Q.positive(x)) == True
    assert ask(Q.negative(-x), ~Q.positive(x)) == None
    assert ask(Q.negative(-x), Q.negative(x)) == False
    assert ask(Q.negative(-x), Q.positive(x)) == True

    assert ask(Q.negative(x-1), Q.negative(x)) == True
    assert ask(Q.negative(x+y)) == None
    assert ask(Q.negative(x+y), Q.negative(x)) == None
    assert ask(Q.negative(x+y), Q.negative(x) & Q.negative(y)) == True

    assert ask(Q.negative(x**2)) == None
    assert ask(Q.negative(x**2), Q.real(x)) == False
    assert ask(Q.negative(x**1.4), Q.real(x)) == None

    assert ask(Q.negative(x*y)) == None
    assert ask(Q.negative(x*y), Q.positive(x) & Q.positive(y)) == False
    assert ask(Q.negative(x*y), Q.positive(x) & Q.negative(y)) == True
    assert ask(Q.negative(x*y), Q.complex(x) & Q.complex(y)) == None

    assert ask(Q.negative(x**y)) == None
    assert ask(Q.negative(x**y), Q.negative(x) & Q.even(y)) == False
    assert ask(Q.negative(x**y), Q.negative(x) & Q.odd(y)) == True
    assert ask(Q.negative(x**y), Q.positive(x) & Q.integer(y)) == False

    assert ask(Q.negative(Abs(x))) == False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
 def log(expr, assumptions):
     r = ask(Q.real(expr.args[0]), assumptions)
     if r is not True:
         return r
     if ask(Q.positive(expr.args[0] - 1), assumptions):
         return True
     if ask(Q.negative(expr.args[0] - 1), assumptions):
         return False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
 def Add(expr, assumptions):
     if expr.is_number:
         return AskPositiveHandler._number(expr, assumptions)
     for arg in expr.args:
         if ask(Q.positive(arg), assumptions) is not True:
             break
     else:
         # if all argument's are positive
         return True

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
 def Pow(expr, assumptions):
     if expr.is_number: return expr.evalf() > 0
     if ask(Q.positive(expr.base), assumptions):
         return True
     if ask(Q.negative(expr.base), assumptions):
         if ask(Q.even(expr.exp), assumptions):
             return True
         if ask(Q.even(expr.exp), assumptions):
             return False

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
def test_real():
    x, y = symbols('x,y')
    assert ask(Q.real(x)) == None
    assert ask(Q.real(x), Q.real(x)) == True
    assert ask(Q.real(x), Q.nonzero(x)) == True
    assert ask(Q.real(x), Q.positive(x)) == True
    assert ask(Q.real(x), Q.negative(x)) == True
    assert ask(Q.real(x), Q.integer(x)) == True
    assert ask(Q.real(x), Q.even(x)) == True
    assert ask(Q.real(x), Q.prime(x)) == True

    assert ask(Q.real(x/sqrt(2)), Q.real(x)) == True
    assert ask(Q.real(x/sqrt(-2)), Q.real(x)) == False

    I = S.ImaginaryUnit
    assert ask(Q.real(x+1), Q.real(x)) == True
    assert ask(Q.real(x+I), Q.real(x)) == False
    assert ask(Q.real(x+I), Q.complex(x)) == None

    assert ask(Q.real(2*x), Q.real(x)) == True
    assert ask(Q.real(I*x), Q.real(x)) == False
    assert ask(Q.real(I*x), Q.imaginary(x)) == True
    assert ask(Q.real(I*x), Q.complex(x)) == None

    assert ask(Q.real(x**2), Q.real(x)) == True
    assert ask(Q.real(sqrt(x)), Q.negative(x)) == False
    assert ask(Q.real(x**y), Q.real(x) & Q.integer(y)) == True
    assert ask(Q.real(x**y), Q.real(x) & Q.real(y)) == None
    assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) == True

    # trigonometric functions
    assert ask(Q.real(sin(x))) == None
    assert ask(Q.real(cos(x))) == None
    assert ask(Q.real(sin(x)), Q.real(x)) == True
    assert ask(Q.real(cos(x)), Q.real(x)) == True

    # exponential function
    assert ask(Q.real(exp(x))) == None
    assert ask(Q.real(exp(x)), Q.real(x)) == True
    assert ask(Q.real(x + exp(x)), Q.real(x)) == True

    # Q.complexes
    assert ask(Q.real(re(x))) == True
    assert ask(Q.real(im(x))) == True

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
 def Mul(expr, assumptions):
     if expr.is_number:
         return AskPositiveHandler._number(expr, assumptions)
     result = True
     for arg in expr.args:
         if ask(Q.positive(arg), assumptions): continue
         elif ask(Q.negative(arg), assumptions):
             result = result ^ True
         else: return
     return result

# 需要导入模块: from sympy.assumptions import Q [as 别名]
# 或者: from sympy.assumptions.Q import positive [as 别名]
 def Pow(expr, assumptions):
     if expr.is_number:
         return AskEvenHandler._number(expr, assumptions)
     if ask(Q.integer(expr.exp), assumptions):
         if ask(Q.positive(expr.exp), assumptions):
             return ask(Q.even(expr.base), assumptions)
         elif ask(~Q.negative(expr.exp) & Q.odd(expr.base), assumptions):
             return False
         elif expr.base is S.NegativeOne:
             return False