integrals/tests/test_deltafunctions.py

1 from sympy import cos, DiracDelta, Heaviside, Function, pi, S, sin, symbols, Rational
11     assert change_mul(x*y*DiracDelta(x), x) == (DiracDelta(x), x*y)
12     assert change_mul(x*y*DiracDelta(x)*DiracDelta(y), x) == \
13         (DiracDelta(x), x*y*DiracDelta(y))
14     assert change_mul(DiracDelta(x)**2, x) == \
15         (DiracDelta(x), DiracDelta(x))
16     assert change_mul(y*DiracDelta(x)**2, x) == \
17         (DiracDelta(x), y*DiracDelta(x))
22     assert deltaintegrate(x + DiracDelta(x), x) is None
23     assert deltaintegrate(DiracDelta(x, 0), x) == Heaviside(x)
25         assert deltaintegrate(DiracDelta(x, n + 1), x) == DiracDelta(x, n)
26     assert deltaintegrate(DiracDelta(x), x) == Heaviside(x)
27     assert deltaintegrate(DiracDelta(-x), x) == Heaviside(x)
28     assert deltaintegrate(DiracDelta(x - y), x) == Heaviside(x - y)
29     assert deltaintegrate(DiracDelta(y - x), x) == Heaviside(x - y)
31     assert deltaintegrate(x*DiracDelta(x), x) == 0
32     assert deltaintegrate((x - y)*DiracDelta(x - y), x) == 0
34     assert deltaintegrate(DiracDelta(x)**2, x) == DiracDelta(0)*Heaviside(x)
35     assert deltaintegrate(y*DiracDelta(x)**2, x) == \
36         y*DiracDelta(0)*Heaviside(x)
37     assert deltaintegrate(DiracDelta(x, 1), x) == DiracDelta(x, 0)
38     assert deltaintegrate(y*DiracDelta(x, 1), x) == y*DiracDelta(x, 0)
39     assert deltaintegrate(DiracDelta(x, 1)**2, x) == -DiracDelta(0, 2)*Heaviside(x)
40     assert deltaintegrate(y*DiracDelta(x, 1)**2, x) == -y*DiracDelta(0, 2)*Heaviside(x)
43     assert deltaintegrate(DiracDelta(x) * f(x), x) == f(0) * Heaviside(x)
44     assert deltaintegrate(DiracDelta(-x) * f(x), x) == f(0) * Heaviside(x)
45     assert deltaintegrate(DiracDelta(x - 1) * f(x), x) == f(1) * Heaviside(x - 1)
46     assert deltaintegrate(DiracDelta(1 - x) * f(x), x) == f(1) * Heaviside(x - 1)
47     assert deltaintegrate(DiracDelta(x**2 + x - 2), x) == \
50     p = cos(x)*(DiracDelta(x) + DiracDelta(x**2 - 1))*sin(x)*(x - pi)
56     p = x_2*DiracDelta(x - x_2)*DiracDelta(x_2 - x_1)
57     assert deltaintegrate(p, x_2) == x*DiracDelta(x - x_1)*Heaviside(x_2 - x)
59     p = x*y**2*z*DiracDelta(y - x)*DiracDelta(y - z)*DiracDelta(x - z)
60     assert deltaintegrate(p, y) == x**3*z*DiracDelta(x - z)**2*Heaviside(y - x)
61     assert deltaintegrate((x + 1)*DiracDelta(2*x), x) == S.Half * Heaviside(x)
62     assert deltaintegrate((x + 1)*DiracDelta(x*Rational(2, 3) + Rational(4, 9)), x) == \
66     assert deltaintegrate(DiracDelta(x - y)*f(x - b)*f(x - a), x) == \
69     p = f(x - a)*DiracDelta(x - y)*f(x - c)*f(x - b)
72     p = DiracDelta(x - z)*f(x - b)*f(x - a)*DiracDelta(x - y)
73     assert deltaintegrate(p, x) == DiracDelta(y - z)*f(y - b)*f(y - a) * \