On Wednesday, December 28, 2016 at 6:18:28 AM UTC-8, Emmanuel Charpentier
wrote:
>
> I d not understand what is possible and not possible about sums with Sage
> (and its minions).
>
> I am interested in the symbolic manipulation of a sum of (unspecified)
> data series X. Since Sage does nott (yet) admits indiced symbolic variable,
> it is reprsented by a function of an integer argument.
>
> Sage seems unable to show that
> $\sum_{i=1}^{p+1}X_i-\sum_{i=1}^pX_i==X_{p+1}$ :
>
> sage: var("p,j", domain="integer")
> ....: assume(p,"integer",j,"integer",p>0)
> ....: X=function("X")(j)
>
You can avoid the warning downstairs by simply setting X=function("X") or
(because of the side-effects of toplevel function, just function("X") .
> ....: foo(p)=sum(X(j),j,1,p)
>
This has the nasty sideeffect of clobbering "p" (which in your case doesn't
make any difference, I think). Calling
foo = sum(x(j),j,1,p).function(p)
has a cleaner result.
....: print foo
> ....: bool(foo(p+1)-foo(p)==X(p+1))
> ....:
> (p, j)
> /usr/local/sage-7/local/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2881:
>
> DeprecationWarning: Substitution using function-call syntax and unnamed
> arguments is deprecated and will be removed from a future release of Sage;
> you can use named arguments instead, like EXPR(x=..., y=...)
> See http://trac.sagemath.org/5930 for details.
> exec(code_obj, self.user_global_ns, self.user_ns)
> p |--> sum(X(j), j, 1, p)
> False
>
> I understand the warning, and think it's irrelevant. But I do not
> understand why the "obvious" expansion is not used. Similarly :
> sage: (foo(p+1)-foo(p)).maxima_methods().sumcontract()
> sum(X(j), j, 1, p + 1) - sum(X(j), j, 1, p)
>
> Am I missing something ?
>
It seems to me that this is an unnecessary limitation in the maxima
routines. It clearly knows something about sum manipulations. Perhaps it's
worth reporting to the Maxima tracker. I'm not so sure this will ever be
very powerful, though, but the following example shows that some
improvements should be within reach:
sage: T=foo(p+1)+foo(p)
sage: T.maxima_methods().sumcontract()
X(p + 1) + 2*sum(X(j), j, 1, p)
It does agree with the documentation of sumcontract, which deals with
addition of sums. Apparently, that does not include differences of sums ...
> --
> Emmanuel Charpentier
>
>
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