Comment #3 on issue 2566 by [email protected]: Equating Sums shouldn't
depend on dummy variables
http://code.google.com/p/sympy/issues/detail?id=2566
IMO, since neither has any free_symbols, a test should be done by replacing
the symbols with equivalent symbols in both Sums and they should compare to
be the same:
def Integral_Sum_are_same(a, b):
"""Return True if Sum/Integral `a` is the same as Sum/Integral `b`.
The result depends only on the free symbols of `a` and `b`; order of
integration is also considered for simplicity reasons.
"""
ab = [a, b]
la, lb = [w.limits for w in ab]
if len(la) != len(lb) or any(lai[1:] != lbi[1:] for lai, lbi in
zip(la, lb)):
return False
ea, eb = [w.function for w in ab]
for i, vab in enumerate(zip(*[w.variables for w in ab])):
vai, vbi = vab
vi = Dummy(str(i))
ea = ea.subs(vai, vi)
eb = eb.subs(vbi, vi)
return ea == eb
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