Updates:
Status: Accepted
Comment #1 on issue 1964 by asmeurer: as_real_imag for Piecewise does not
give correct answer
http://code.google.com/p/sympy/issues/detail?id=1964
I get the following in master:
In [1]: x = Symbol('x', real=True)
In [2]: a = 2*I*(3*sin(4*x)-3*sin(4*x)*Piecewise((2.0, x<0), (1.0, 0 <= x)))
In [3]: a.as_real_imag()
Out[3]:
⎛-6⋅ⅈ⋅⎛ⅈ⋅im⎛⎧2.0 for x < 0⎞ + re⎛⎧2.0 for x < 0⎞⎞⋅sin(4⋅x), 6⋅sin(4⋅x)⎞
⎜ ⎜ ⎜⎨ ⎟ ⎜⎨ ⎟⎟ ⎟
⎝ ⎝ ⎝⎩1.0 for 0 ≤ x⎠ ⎝⎩1.0 for 0 ≤ x⎠⎠ ⎠
In [4]: re(a)
Out[4]:
-im⎛2⋅⎛3⋅sin(4⋅x) - 3⋅sin(4⋅x)⋅⎧2.0 for x < 0⎞⎞
⎜ ⎜ ⎨ ⎟⎟
⎝ ⎝ ⎩1.0 for 0 ≤ x⎠⎠
In [5]: im(a)
Out[5]:
re⎛2⋅⎛3⋅sin(4⋅x) - 3⋅sin(4⋅x)⋅⎧2.0 for x < 0⎞⎞
⎜ ⎜ ⎨ ⎟⎟
⎝ ⎝ ⎩1.0 for 0 ≤ x⎠⎠
In Maple (assuming x is real):
Re(a);
6 sin(4 x) / / 0. x < 0 \
|{ |
\ \ 0. 0 <= x/
Im(a);
6 sin(4 x) - 6 sin(4 x) / / 2.0 x < 0 \
|{ |
\ \ 1.0 0 <= x/
But not assuming x is real:
Re(a);
6 Im/-sin(4 x) + sin(4 x) / / 2.0 x < 0 \\
| |{ ||
\ \ \ 1.0 0 <= x//
Im(a);
-6 Re/-sin(4 x) + sin(4 x) / / 2.0 x < 0 \\
| |{ ||
\ \ \ 1.0 0 <= x//
So I think SymPy is just not doing enough assumptions simplification.
Someone else should do some closer debugging.
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