sympy/core/tests/test_functions.py

   1 from sympy import *
   2 from sympy.utilities.pytest import XFAIL
   3
   4
   5 def test_log():
   6     assert log(2) > 0
   7     assert log(1).is_zero
   8     assert log(0.5).is_negative == True
   9
  10 def test_exp_log():
  11     x = Symbol("x", real=True)
  12     assert log(exp(x)) == x
  13     assert exp(log(x)) == x
  14
  15 def test_log_expansion():
  16     x = Symbol("x", real=True)
  17     y = Symbol("y", real=True)
  18     ##assert log(x*y) != log(x)+log(y)
  19     #assert log(x**2) != 2*log(x)
  20     assert log(x*y).expand() == log(x)+log(y)
  21     assert log(x**2).expand() == 2*log(x)
  22     assert (log(x**-5)**-1).expand() == -1/log(x)/5
  23
  24 def test_log_hashing_bug():
  25     x = Symbol("y")
  26     assert x != log(log(x))
  27     assert hash(x) != hash(log(log(x)))
  28     assert log(x) != log(log(log(x)))
  29
  30     e = 1/log(log(x)+log(log(x)))
  31     assert isinstance(e.base, Basic.log)
  32     e = 1/log(log(x)+log(log(log(x))))
  33     assert isinstance(e.base, Basic.log)
  34
  35     x = Symbol("x")
  36     e = log(log(x))
  37     assert isinstance(e, Basic.log)
  38     assert not isinstance(x, Basic.log)
  39     assert hash(log(log(x))) != hash(x)
  40     assert e != x
  41
  42 def test_sign():
  43     assert sign(log(2)) == 1
  44
  45 def test_exp_bug():
  46     x = Symbol("x")
  47     assert exp(1*log(x)) == x
  48
  49 def test_exp_expand():
  50     x = Symbol("x")
  51     y = Symbol("y")
  52
  53     e = exp(log(Rational(2))*(1+x)-log(Rational(2))*x)
  54     assert e.expand() == 2
  55     # XXX The RHS is automatically combined so that it equals the LHS
  56     #assert exp(x+y) != exp(x)*exp(y)
  57     assert exp(x+y).expand() == exp(x)*exp(y)
  58
  59 def test_pi():
  60     assert cos(pi)==-1
  61     assert cos(2*pi)==1
  62     assert sin(pi)==0
  63     assert sin(2*pi)==0
  64
  65 def test_bug1():
  66     x = Symbol("x")
  67     w = Symbol("w")
  68
  69     e = sqrt(-log(w))
  70     assert e.subs(log(w),-x) == sqrt(x)
  71
  72     e = sqrt(-5*log(w))
  73     assert e.subs(log(w),-x) == sqrt(5*x)
  74
  75 @XFAIL
  76 def test_invtrig(): # XXX No inverse trig yet
  77     x = Symbol("x")
  78     assert atan(0) == 0
  79     assert atan(x).diff(x) == 1/(1+x**2)
  80
  81 def test_general_function():
  82     nu = Function('nu', nofargs=1)
  83     x = Symbol("x")
  84     y = Symbol("y")
  85
  86     e = nu(x)
  87     edx = e.diff(x)
  88     edy = e.diff(y)
  89     edxdx = e.diff(x).diff(x)
  90     edxdy = e.diff(x).diff(y)
  91     assert e == nu(x)
  92     assert edx != nu(x)
  93     assert edx == Derivative(nu(x), x)
  94     assert edy == 0
  95     assert edxdx == Derivative(Derivative(nu(x), x), x)
  96     assert edxdy == 0
  97
  98 @XFAIL
  99 def test_derivative_subs_bug():
 100     x = Symbol("x")
 101     l = Function('l', nofargs=1)
 102     n = Function('n', nofargs=1)
 103
 104     e = Derivative(n(x), x)
 105     assert e.subs(n, l) != e
 106     assert e.subs(n, l) == Derivative(l(x), x)
 107     assert e.subs(n, -l) == Derivative(-l(x), x)
 108
 109 def test_derivative_linearity():
 110     x = Symbol("x")
 111     y = Symbol("y")
 112     n = Function('n', nofargs=1)
 113
 114     assert Derivative(-n(x), x) == -Derivative(n(x), x)
 115     assert Derivative(8*n(x), x) == 8*Derivative(n(x), x)
 116     assert Derivative(8*n(x), x) != 7*Derivative(n(x), x)
 117     assert Derivative(8*n(x)*x, x) == 8*n(x) + 8*x*Derivative(n(x), x)
 118     assert Derivative(8*n(x)*y*x, x) == 8*y*n(x) + 8*y*x*Derivative(n(x), x)
 119
 120 @XFAIL
 121 def test_combine():
 122     # XXX combine no longer exists
 123     x = Symbol("x")
 124     y = Symbol("y")
 125     assert exp(x)*exp(-x) != 1
 126     assert (exp(x)*exp(-x)).combine() == 1
 127
 128     assert exp(x)**2 != exp(2*x)
 129     assert (exp(x)**2).combine() == exp(2*x)
 130
 131     assert exp(x)*exp(-x/2)*exp(-x/2) != 1
 132     assert (exp(x)*exp(-x/2)*exp(-x/2)).combine() == 1
 133
 134     assert (2*log(x)).combine() == log(x**2)
 135     assert exp(2*log(x)) != x**2
 136     assert exp(2*log(x)).combine() == x**2
 137
 138     assert exp(x)*exp(-x)-1 !=0
 139     assert (exp(x)*exp(-x)-1).combine() == 0
 140
 141     assert (2*exp(x)*exp(-x)).combine() == 2
 142     assert (x/exp(x)*exp(-x)).combine() == x*exp(-2*x)