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#211 Products are differentiated incorrectly ←	↑	→ #213 No equality of operators which use dummy variables

#212 substituting for an operator in a sum does not apply the summation algorithms

Edit detail for #212 substituting for an operator in a sum does not apply the summation algorithms revision 1 of 2

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Editor: Time: 2007/11/17 22:09:32 GMT-8
Note: property change

changed:
-
Original Savannah bug 9217

Submitted by: Martin Rubey <kratt6>	

Submitted on: Fri 06/04/04 at 08:18

Summary:

Although axiom can evaluate this sum, it does not.

Example of code trigerring the bug:

\begin{axiom}
f := operator 'f
sum(f(i),i=a..b)
eval(%,f,x+->x)
\end{axiom}

Internal Cause

  first the sum is evaluated. Since the argument 'f(x)' is not a polynomial
or rational function, using first iidsum, than idsum of COMBF. Afterwards
the substitution is performed. Now the sum has the internal format
'%defsum [%A, %A, i, a, b]', which is again evaluated with iidsum and idsum of
COMBF. The function 'sum$InnerPolySum' is never called, of course. A general
solution is to call sum from within idsum, but in this case, care has to be
taken that summation algorithms that can fail (such as Gosper's) do not
produce an infinite loop. (In fact I think this is OK, I only did not have
the time to check)


From kratt6 Tue Oct 4 05:47:07 -0500 2005
From: kratt6
Date: Tue, 04 Oct 2005 05:47:07 -0500
Subject: property change
Message-ID: <20051004054707-0500@wiki.axiom-developer.org>

Category:  => Axiom Library 
Severity:  => serious 
Status:  => open

Original Savannah bug 9217

Submitted by: Martin Rubey

Submitted on: Fri 06/04/04 at 08:18

Summary:

Although axiom can evaluate this sum, it does not.

Example of code trigerring the bug:

axiom

f := operator 'f

$\label{eq1}f$

(1)

Type: BasicOperator?

axiom

sum(f(i),i=a..b)

$\label{eq2}\sum_{ \displaystyle {i = a}}^{ \displaystyle b}{f \left({i}\right)}$

(2)

Type: Expression(Integer)

axiom

eval(%,f,x+->x)

$\label{eq3}\sum_{ \displaystyle {i = a}}^{ \displaystyle b}i$

(3)

Type: Expression(Integer)

Internal Cause

first the sum is evaluated. Since the argument f(x) is not a polynomial or rational function, using first iidsum, than idsum of COMBF. Afterwards the substitution is performed. Now the sum has the internal format '%defsum [%A, %A, i, a, b]?', which is again evaluated with iidsum and idsum of COMBF. The function sum$InnerPolySum is never called, of course. A general solution is to call sum from within idsum, but in this case, care has to be taken that summation algorithms that can fail (such as Gosper's) do not produce an infinite loop. (In fact I think this is OK, I only did not have the time to check)

property change --kratt6, Tue, 04 Oct 2005 05:47:07 -0500 reply

Category: => Axiom Library Severity: => serious Status: => open