bugAxiom 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 <kratt6>
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

Internal cause: 

dvdsum in COMBF is mathematically incorrect

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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Follow 2 latest changes.

Date Changed by Updated Field Previous Value => Replaced by
2005-06-22 billpage1 StatusNone transferred
    Example of code trigerring the bugf:=operator 'f D(sum(f(i),i=a..x),x) f:=operator 'f D(sum(f(i),i=a..x),x)

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