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.
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 :
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
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