Substitution of Indexed into Sum

[skyreflectedinmirrors]

Consider the following example:

from sympy import *

i, j, l = symbols('i j', cls=Idx)
a, b, c = symbols(a b c', cls=IndexedBase)

print Sum(a[i] * b[i], (i, 1, 10)).subs(a[i] * b[i], c[i])

Currently, this substitution is ignored, resulting in Sum(a[i]*b[i], (i, 1, 10)) due to the intersection of the old value's free symbols set([i, b, a]) with the summation variable i, however I think this is a legitimate substitution pattern.

I have found one way to fix this problem, by simply uncommenting Indexed.free_symbols

    @property
    def free_symbols(self):
        return {self}

However, doing so results in several test failures, and I am not sure that it is the best way to accomplish the above given that the ExprWithLimit's _eval_subs seems to be designed to not allow substitutions of variables that depend on the Summation index.

With that in mind:

1. Is this a change that would be supported for implementation? My use of Sympy relies quite a bit on it, but I could always derive my own Sum class and use that.

2. If so, what would be the best way of implementing this change? One thought I had (as opposed to the above) would be to modify the _eval_subs such that sub_into_function is allowed if the ExprWithLimit's function contains the old parameter exactly, e.g. on line 314 in r9ce7495:

if len(xab[0].free_symbols.intersection(old.free_symbols)) != 0:
    if not func.has(old):
        sub_into_func = False
        break

However, this again breaks many tests and the underlying architecture of the ExprWithLimit's _eval_subs. Perhaps in conjunction with a flag passed into the original subs call? Or with the stipulation that the summation variable must not be "directly" in old (e.g. c[i]) and the new must also indirectly contain the same summation variable?

Looking for feedback here,

Thanks,

arghdos

[oscarbenjamin]

You can use xreplace for this:

In [97]: Sum(a[i] * b[i], (i, 1, 10)).xreplace({a[i] * b[i]: c[i]})                                                                                           
Out[97]: 
  10      
 ___      
 ╲        
  ╲   c[i]
  ╱       
 ╱        
 ‾‾‾      
i = 1 

.