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#178 Linear Agebra problem ←	↑	→ #18 Axiom domains and Aldor return types

#179 differentiating sums with respect to a bound is wrong

Edit detail for #179 differentiating sums with respect to a bound is wrong revision 1 of 1

	1
Editor: Time: 2007/11/17 22:03:19 GMT-8
Note: Continued in Bug #180

changed:
-
From BillPage Wed Jun 22 13:55:51 -0500 2005
From: Bill Page
Date: Wed, 22 Jun 2005 13:55:51 -0500
Subject: (new) differentiating sums with respect to a bound is wrong
Message-ID: <20050622-185531.sv12157.42107@savannah.nongnu.org>

Update of bug #9216 (project axiom):

Status:   None => transferred            

Example of code trigerring the bug:
\begin{axiom}
f:=operator 'f
D(sum(f(i),i=a..x),x)
\end{axiom}

is nonsense. The problem is in COMBF/dvdsum:

\begin{axiom}
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]
\end{axiom}

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



From kratt6 Thu Jun 23 02:18:19 -0500 2005
From: kratt6
Date: Thu, 23 Jun 2005 02:18:19 -0500
Subject: Continued in Bug #180
Message-ID: <20050623021819-0500@page.axiom-developer.org>

Category:  => Axiom Compiler 
Severity:  => critical 
Status:  => duplicate

(new) differentiating sums with respect to a bound is wrong --Bill Page, Wed, 22 Jun 2005 13:55:51 -0500 reply

Update of bug #9216 (project axiom):

Status: None => transferred

Example of code trigerring the bug:

fricas

(1) -> f:=operator 'f

$\label{eq1}f$

(1)

Type: BasicOperator?

fricas

D(sum(f(i),i=a..x),x)

$\label{eq2}{\%defsum_{, 5}}\left({{f \left({\%B}\right)}, \: \%B , \: i , \: a , \: x}\right)$

(2)

Type: Expression(Integer)

is nonsense. The problem is in COMBF/dvdsum:

fricas

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]

Type: Void

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

Continued in Bug #180 --kratt6, Thu, 23 Jun 2005 02:18:19 -0500 reply

Category: => Axiom Compiler Severity: => critical Status: => duplicate