Full symbolic sum function

[rwst]

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

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 7e8d0d0

Reviewer: Nils Bruin

Issue created by migration from https://trac.sagemath.org/ticket/21645

[sagetrac-tmonteil]

comment:1

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.

[rwst]

Description changed:

--- 
+++ 
@@ -9,3 +9,5 @@
 ```
 
 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

[rwst]

Branch: u/rws/full_symbolic_sum_function

[rwst]

New commits:

65d3d44

21645: full symbolic sum function

[rwst]

Author: Ralf Stephan

[rwst]

Commit: 65d3d44

[sagetrac-git]

Changed commit from 65d3d44 to 29f7d1b

[sagetrac-git]

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

29f7d1b

21645: remove forgotten diagnostic

[nbruin]

comment:6

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?

[sagetrac-git]

Changed commit from 29f7d1b to 7e8d0d0