def test_diff():
x, y = symbols('x, y')
assert Rational(1, 3).diff(x) is S.Zero
assert I.diff(x) is S.Zero
assert pi.diff(x) is S.Zero
assert x.diff(x, 0) == x
assert (x**2).diff(x, 2, x) == 0
assert (x**2).diff(x, y, 0) == 2 * x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff(1, x))
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
p = Rational(5)
e = a * b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5 * b**4
assert e.diff(b).diff(a) == Rational(1)
e = a * (b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == Rational(1)
e = c**p
assert e.diff(c, 6) == Rational(0)
assert e.diff(c, 5) == Rational(120)
e = c**Rational(2)
assert e.diff(c) == 2 * c
e = a * b * c
assert e.diff(c) == a * b
def test_diff():
x, y = symbols('x, y')
assert Rational(1, 3).diff(x) is Integer(0)
assert I.diff(x) is Integer(0)
assert pi.diff(x) is Integer(0)
assert x.diff(x, 0) == x
assert (x**2).diff(x, 2, x) == 0
assert (x**2).diff(x, y, 0) == 2*x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff(1, x))
a = Symbol('a')
b = Symbol('b')
c = Symbol('c')
p = Integer(5)
e = a*b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5*b**4
assert e.diff(b).diff(a) == 1
e = a*(b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == 1
e = c**p
assert e.diff(c, 6) == 0
assert e.diff(c, 5) == 120
e = c**2
assert e.diff(c) == 2*c
e = a*b*c
assert e.diff(c) == a*b
f = Function('f')
assert f(x).diff(x, 2).diff(f(x).diff(x, 1)) == 0
def test_diff():
assert Rational(1, 3).diff(x) is Integer(0)
assert I.diff(x) is Integer(0)
assert pi.diff(x) is Integer(0)
assert x.diff((x, 0)) == x
assert (x**2).diff((x, 2), x) == 0
assert (x**2).diff(x, (y, 0)) == 2*x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff((1, x)))
p = Integer(5)
e = a*b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5*b**4
assert e.diff(b).diff(a) == 1
e = a*(b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == 1
e = c**p
assert e.diff((c, 6)) == 0
assert e.diff((c, 5)) == 120
e = c**2
assert e.diff(c) == 2*c
e = a*b*c
assert e.diff(c) == a*b
f = Function('f')
assert f(x).diff((x, 2)).diff(f(x).diff((x, 1))) == 0
def test_diff():
x, y = symbols('x, y')
assert Rational(1, 3).diff(x) is Integer(0)
assert I.diff(x) is Integer(0)
assert pi.diff(x) is Integer(0)
assert x.diff(x, 0) == x
assert (x**2).diff(x, 2, x) == 0
assert (x**2).diff(x, y, 0) == 2*x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff(1, x))
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
p = Integer(5)
e = a*b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5*b**4
assert e.diff(b).diff(a) == 1
e = a*(b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == 1
e = c**p
assert e.diff(c, 6) == 0
assert e.diff(c, 5) == 120
e = c**2
assert e.diff(c) == 2*c
e = a*b*c
assert e.diff(c) == a*b
f = Function('f')
assert f(x).diff(x, 2).diff(f(x).diff(x, 1)) == 0
def test_evalf_powers():
assert NS('pi**(10**20)', 10) == '1.339148777e+49714987269413385435'
assert NS(pi**(10**100), 10) == ('4.946362032e+4971498726941338543512682882'
'9089887365167832438044244613405349992494711208'
'95526746555473864642912223')
assert NS('2**(1/10**50)', 15) == '1.00000000000000'
assert NS('2**(1/10**50)-1', 15) == '6.93147180559945e-51'
assert Pow(2, 0, evaluate=False).evalf() == 1
assert Pow(I, 5, evaluate=False).evalf() == I.evalf()
def test_pow_as_base_exp():
assert (oo**(2 - x)).as_base_exp() == (oo, 2 - x)
assert (oo**(x - 2)).as_base_exp() == (oo, x - 2)
p = Rational(1, 2)**x
assert p.base, p.exp == p.as_base_exp() == (2, -x)
# issue sympy/sympy#8344:
assert Pow(1, 2, evaluate=False).as_base_exp() == (1, 2)
# issue sympy/sympy#21396
assert I.as_base_exp() == (-1, Rational(1, 2))
assert sqrt(I).as_base_exp() == (-1, Rational(1, 4))
def test_evalf_powers():
assert NS('pi**(10**20)', 10) == '1.339148777e+49714987269413385435'
assert NS(pi**(10**100), 10) == ('4.946362032e+4971498726941338543512682882'
'9089887365167832438044244613405349992494711208'
'95526746555473864642912223')
assert NS('2**(1/10**50)', 15) == '1.00000000000000'
assert NS('2**(1/10**50)-1', 15) == '6.93147180559945e-51'
assert Pow(2, 0, evaluate=False).evalf() == 1
assert Pow(I, 5, evaluate=False).evalf() == I.evalf()
def test_sympyissue_5486_bug():
assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15
pytest.raises(TypeError, lambda: Expr._from_mpmath(I, 15))
def test_issue_5486_bug():
from diofant import I, Expr
assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15
pytest.raises(TypeError, lambda: Expr._from_mpmath(I, 15))
def test_sympyissue_5486_bug():
assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15
pytest.raises(TypeError, lambda: Expr._from_mpmath(I, 15))
def test_sympyissue_5486():
assert not cos(sqrt(0.5 + I)).evalf(strict=False).is_Function
assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15
def test_sympyissue_5486_bug():
assert abs(Expr._from_mpmath(I._to_mpmath(15), 15) - I) < 1.0e-15