The question is, do we want Sum to automatically combine like that?
If not, then I would add it as a different method than __sub__.
Aaron Meurer
On Thu, Aug 30, 2012 at 8:51 AM, Chris Smith <smi...@gmail.com> wrote:
> On Thu, Aug 30, 2012 at 8:02 PM, Saurabh Jha <saurabh.j...@gmail.com> wrote:
>> Hi,
>>
>> In the course of implementing kauers algorithm I wanted to implement a
>> function that can take as input a term like summation(f(x), (x, 1, k)) and
>> outputs the f(x+1) that is the difference between (f(x), (x, 1, k + 1)) and
>> (f(x), (x, 1, k)). Instead, it just returns "summation(f(x), (x, 1, k + 1) -
>> summation(f(x), (x, 1, k)" I thought of just returning f(x + 1) directly but
>> it will not work for nested sums. Is there any known way in sympy to deal
>> with this problem? With this difficulty resolved, the implementation of the
>> complete kauers algorithm will be done.
>>
>
> A __sub__ method needs to be defined for Sum. Something like this can
> get you started:
>
>
> ```
> def __sub__(self, other):
> if not isinstance(other, Sum):
> raise ValueError
> if self.variables == other.variables and \
> self.function == other.function and \
> self.limits[0][1] == other.limits[0][1]:
> x, _, s = self.limits[0]
> _, _, o = other.limits[0]
> dif = s - o
> if dif.is_Number:
> if dif is S.One:
> return self.function.subs(x, s)
> elif dif > 0:
> return Sum(self.function, (x, o + 1, o + dif))
> raise NotImplementedError
>
> ```
>
> ```
>>>> from sympy import *
>>>> var('x')
> x
>>>>
>>>> f=Function('f')
>>>> Sum(f(x),(x, 1, x + 1)) - Sum(f(x),(x, 1, x))
> f(x + 1)
>>>> Sum(f(x),(x, 1, x + 3)) - Sum(f(x),(x, 1, x))
> Sum(f(x), (x, x + 1, x + 3))
>>>> Sum(f(x),(x, 1, x + 3)) - Sum(f(x),(x, 1, x+1))
> Sum(f(x), (x, x + 2, x + 3))
>>>> Sum(f(x),(x, 1, x + 3)) - Sum(f(x),(x, 1, x+2))
> f(x + 3)
>>>>
> ```
> Then you think about what __add__ might be...whether Number or only
> Integer should be handled...what to do if the lower limits are not the
> same or if diff is negative, etc...
>
> /c
>
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