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Comment #1 on issue 1499 by asmeurer: Sum function seems to fail
http://code.google.com/p/sympy/issues/detail?id=1499
The reason that this is happening is that the limits of Sum are not being
substituted with subs.
Putting them in directly works as expected:
>>> m = Symbol('m')
>>> I = Symbol('I')
>>> s = Sum(m*exp(m), (m, -2, 2))
>>> s
Sum(m*exp(m), (m, -2, 2))
>>> s.evalf() # I believe this is the right result
16.8578440186757
>>> s = Sum(m*exp(m), (m, -2, 2)).doit()
>>> print s # This looks right too
E - exp(-1) - 2*exp(-2) + 2*exp(2)
You can see that this is the case by looking at the source for
Sum._eval_subs():
from line 154 in sympy/concrete/summations.py:
def _eval_subs(self, old, new):
return Sum(self.args[0].subs(old, new), *self.args[1])
As you can see, self.args[1], which is the limits, is not substituted with
subs here.
I have attached a patch which fixes and adds a test.
Here is what your test case goes with my patch. I assume that this is the
behavior you were wanting:
>>> from sympy import *
>>> m = Symbol('m')
>>> I = Symbol('I')
>>> s = Sum(exp(m), (m, -I, I))
>>> # m should be -2 .. 2
... s = s.subs(I,2).doit()
>>> print(s)
1 + E + exp(-1) + exp(-2) + exp(2)
>>> # prints: (exp(-I) - exp(1 + I))/(1 - E)
... s.subs(I,2).evalf()
11.6105526517978
>>> # 11.61... the correct result
... # now just slightly different:
... s = Sum(m*exp(m), (m, -I, I))
>>> # m should be -2 .. 2
... s = s.subs(I,2).doit()
>>> print(s)
E - exp(-1) - 2*exp(-2) + 2*exp(2)
>>> # Sum(m*exp(m), (m, -I, I)), so it did not expand
... # infinite loop here:
... s.subs(I, 2).evalf()
16.8578440186757
My patch doesn't substitute the summation variable, because you could get
>>> Sum(m*exp(m), (m, -2, 2)).subs(m,2) # Try substituting for a number
<Traceback>
ValueError: Invalid summation variable or limits
>>> Sum(m*exp(m), (m, -2 2)).subs(x*y, 2) # Try substituting for a Mul
<Traceback>
ValueError: Invalid summation variable or limits
...
and so on.
That would only happen if you tried to substitute the summation variable
for anything that isn't a Symbol. What do you
think? Should subs substitute the summation variable too? It could be
useful if you want to change the name of the
summation variable in a Sum.
Attachments:
0001-Made-Sum._eval_subs-substitute-the-limits-of-a-sum.patch 1.9 KB
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