simplify works on expression but not on its negative

[Greg Grunberg]

I'm new to SymPy and this group.  My apologies if I'm submitting this to the wrong group.  Please feel free to indicate a more appropriate alternate group, if there is such.

I ran into a behavior of the simplify function which strikes me as strange.  Notice that in[4] and in[5] below are identical, except that the expression to be simplified in the latter is the negative of the former.  out[4] is what I expected, but out[5] is not.  Shouldn't out[5] be the negative of out[4]?  Can anyone explain?  Note that out[5] is not mathematically incorrect but just not what one would expect.

Python 3.5.1 |Anaconda 2.5.0 (64-bit)| (default, Jan 29 2016, 15:01:46) [MSC v.1900 64 bit (AMD64)]

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In [1]: from sympy import *

In [2]: init_session()

IPython console for SymPy 1.0 (Python 3.5.1-64-bit) (ground types: python)

These commands were executed:

>>> from __future__ import division

>>> from sympy import *

>>> x, y, z, t = symbols('x y z t')

>>> k, m, n = symbols('k m n', integer=True)

>>> f, g, h = symbols('f g h', cls=Function)

>>> init_printing()

Documentation can be found at http://docs.sympy.org/1.0/

In [3]: theta = symbols('theta', real=True)

In [4]: simplify(+I/2*exp(I*theta) - I/2*exp(-I*theta))

Out[4]: -sin(theta)

In [5]: simplify(-I/2*exp(I*theta) + I/2*exp(-I*theta))

Out[5]:

  /   2*I*theta    \  -I*theta

I*\- e          + 1/*e

------------------------------

              2



[Francesco Bonazzi]

A related issue:

In [6]: m = Matrix([[0, theta], [-theta, 0]])

In [7]: exp(m)
Out[7]:
[   I*theta    -I*theta         I*theta      -I*theta]
[  e          e              I*e          I*e        ]
[  -------- + ---------    - ---------- + -----------]
[     2           2              2             2     ]
[                                                    ]
[   I*theta      -I*theta      I*theta    -I*theta   ]
[I*e          I*e             e          e           ]
[---------- - -----------     -------- + ---------   ]
[    2             2             2           2       ]

In [8]: simplify(exp(m))
Out[8]:
[               /   2*I*theta    \  -I*theta]
[             I*\- e          + 1/*e        ]
[cos(theta)   ------------------------------]
[                           2               ]
[                                           ]
[-sin(theta)            cos(theta)          ]

[Aaron Meurer]

Definitely a bug. A workaround is to use (-I/2*exp(I*theta) +
I/2*exp(-I*theta)).rewrite(sin), which will force the exponentials to
be rewritten in terms of sin and cos.

Aaron Meurer

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