Full symbolic sum function

[rws]

sum(ex,...) always gets sent to calculus.symbolic_sum() where Maxima is called. If unevaluated an anonymous function sum is returned.

sage: ex=sum(gamma(n), n,1,a)
sage: ex.operator()
sum
sage: type(_)
<class 'sage.symbolic.function_factory.NewSymbolicFunction'>

This is unsatisfactory in many regards. Calls always go through Maxima, even if one wants just a sum expression held unevaluated. Also the anonymous function cannot be evaluated or substituted. For these reasons making a full symbolic sum function is a natural decision.

See also #17505

[tmonteil]

Indeed ! This issue is known for a while, see ​this ask question for a dirty workaround. Funnily, i recently got a similar request privately, and was about to open a ticket to add a hold parameter to symbolic sum, i guess this ticket will take care of that too.

[rws]

New commits:

​65d3d44

21645: full symbolic sum function

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​29f7d1b

21645: remove forgotten diagnostic

[nbruin]

Looking at the patch, I see presently special work happens on maxima's return values, which replaces maxima's "inert" sum with sage's newly grown symbolic sum function. I think that's problematic (for instance, we could have nested sums, and the nested sums would escape this treatment). Also, the test used (isinstance(op,SymbolicFunction)) is a little suspicious: I think it would get the result from

sum(f(x),n,0,0)

wrong.

It should be possible to use the standard SR-to-maxima and maxima-to-SR translation dictionaries for this, just as functions like sin etc. get properly translated. Isn't the line

+        BuiltinFunction.__init__(self, "sum", nargs=4,
+                               conversions=dict(maxima='sum'))

already enough to get the required automatic translations? If not, perhaps there is a manual override somewhere else that needs to be *removed* to let the normal translation take its course?

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​7e8d0d0

21645: remove unnecessary code

[rws]

You're right!

[nbruin]

Looks good and patchbot is happy (coverage plugin failure seems to be on code that this actual branch doesn't touch)