On Wednesday, April 26, 2017 at 8:35:30 AM UTC+2, Emmanuel Charpentier
wrote:
>
> Sage can (awkwardly) do some simplifications of symbolic sums. For example
>
> sage: var("j,p", domain="integer")
> (j, p)
> sage: X,Y=function("X,Y")
> sage: (sum(X(j),j,1,p)+sum(Y(j),j,1,p)).maxima_methods().sumcontract()
> sum(X(j) + Y(j), j, 1, p)
>
> but, to the best of my (limited) knowledge, the reverse operation, useful
> in sime situations (trivial example : derive maximum likelihood estimators
> of the parameters of some distributions) is not possible (in other words,
> sum does not distribute over +).
> ...
> (the Maxima version also works (not shown)). Hence a few questions :
>
> 1. Did I oversee an existing way to do this ?
>
> Nearly. SymPy can do these things via simplify and expand. However, Sage
cannot translate your sums into SymPy via sympify because 1. there is no
conversion atm for Function_sum (trivial to fix), and 2. anonymous
functions like X here cannot be translated either (not so trivial). I
didn't check the backwards route but expect similar problems.
>
> 1. Is that a worthwile addition to Sage ?
>
> Of course.
>
> 1. Should it be implemented in Sage (probably as a method for SR), or
> via Maxima (like other sum functions) ?
>
> I would do like SymPy and put it as subfunction into expand() (check for
existence of Function_sum then call).
>
> 1. Should this be a special case of the expand() method ?
>
> Not a special case, a default service.
>
> 1. Are there possible improvements (I think so : for example, I have
> been unable to find the "right" designation of the operators : op_sum
> might be sage.functions.other.symbolic_sum, but I found nothing usable
> for op_add, hence the ridiculous re-computation of these constants at
> each call...).
>
> Yes, and sage.symbolic.operators.add_vararg.
Best,
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