Hi,
On 17 jan, 16:51, Francois Maltey <fmal...@nerim.fr> wrote:
> Hello Jean-Pierre,> It would be nice to add an option to set Maxima simpsum
> option when
> > calling Sage symbolic_sum function, or to enable it by default.
> > Indeed, without it Maxima (and so Sage) does not evaluate symbolic
> > sums of sums, i.e. something as
> > sage: var('n')
> > n
> > sage: sum(2^x+2^-x,x,0,n)
> > sum((2^(2*x) + 1)/2^x, x, 0, n)
>
> It's a fine idea to improve the Maxima interface to Sage.
>
> I feel your purpose comes into simplify, combine, expand or rewrite rules.
>
Kind of, my main problem here is I thought that it is strange that
such a sum does get simplified.
> I use a rewrite function with many parameters for others rewrite rules.
> A global method rewrite over expression would be better but force to
> patch Sage code.
>
> http://wiki.sagemath.org/symbolics/rewrite
>
> Very few functions with an optional parameter seems better than a lot of
> functions simplify_by_way as maxima.
> Your awful maxima command seems be an expand rules :
Unfortunately my command is not so awful. The code for symbolic code
is just as horrible (look in sage/calculus/calculus.py):
sum = "'sum(%s, %s, %s, %s)" % tuple([repr(expr._maxima_())
for expr in (expression, v, a, b)])
try:
result = maxima.simplify_sum(sum)
result = result.ratsimp()
return expression.parent()(result)
so it also call atsimp().
My point was, even if I was not clear at all, that it could be a not
so bad idea to add 'simpsum' option because it allows Maxima to
simplify such sums and anyway we already call simplify_sum() and
ratsimp().
Maybe a better way to go, is not to call any of those ant let the user
decide, but here the job is kind of half done.
>
> sum (2^x, x, 0, n) and sum (2^-x, x, 0, n) are right.
> _add_ (sum (each term)) is right but sum (of_an_add...) fails.
>
> We can also see a simplify rule.
> But I dislike this simplify name because the word "simplify" doesn't
> describe a method.
>
> I vote to discover in a next version a generic method for this sum as :
>
> sum(2^x+2^-x, x, 0, n).expand(rules="sum") .
>
> There was also the #7334 patch for log.
> The rule log(x) + log(y) -> log(x*y) is a combine rule with less atomic
> terms.
> And the rue log(x*y) =maybe= log(x) + log(y) is an expand one, as your sum.
>
> Have a nice day !
>
> Francois
Anyway, Sage should do all this kind of things by itself at some
point, look at http://groups.google.com/group/sage-support/msg/7323dfc3db4883c8
and http://wiki.sagemath.org/symbolics.
Cheers,
JP
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