# Axiom Computer Algebra System - Bugs: bug #9216, differentiating sums with respect...

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# bug #9216: differentiating sums with respect to a bound is wrong

 Submitter: Martin Rubey Submitted: Fri 04 Jun 2004 08:06:32 AM UTC Category: None Severity: 3 - Normal Item Group: code bug Status: transferred Privacy: Public Assigned to: None Originator Name: kratt6 Open/Closed: Open Release: tla from may 2004 Reproducibility: None Fixed Release: Error message: Example of code trigerring the bug: f:=operator 'f D(sum(f(i),i=a..x),x) Internal cause: dvdsum in COMBF is mathematically incorrect

## Discussion

Mon 21 Jun 2004 11:12:28 AM UTC, comment #1:
Martin Rubey <kratt6>
Fri 04 Jun 2004 08:06:32 AM UTC, original submission:

(1) f:=operator 'f
(1)  f
Type: BasicOperator
(2) -> D(sum(f(i),i=a..x),x)
(2)  f(x)                                                   Type: Expression Integer

is nonsense. The problem is in COMBF/dvdsum:

dvdsum(l, x) ==
x = retract(y := third l)@SE => 0
k := retract(d := second l)@K
differentiate(h := third rest rest l,x) * eval(f := first l, k, h)
- differentiate(g := third rest l, x) * eval(f, k, g)
+ opdsum [differentiate(f, x), d, y, g, h]

Although this -- d/dx sum_i^x f(i) = f(x) -- is a nice try, it is wrong. It seems that the order of magnitude is roughly correct, but that's about it.

Unfortunately, I do not know how to return the thing unevaluated, so I cannot fix the bug yet

Martin Rubey <kratt6>

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