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[Axiomdeveloper] [#212 substituting for an operator in a sum does not a
From: 
billpage 
Subject: 
[Axiomdeveloper] [#212 substituting for an operator in a sum does not apply the summation algorithms] 
Date: 
Mon, 03 Oct 2005 01:21:10 0500 
Changes
http://wiki.axiomdeveloper.org/212SubstitutingForAnOperatorInASumDoesNotApplyTheSummationAlgorithms/diff

??changed:


From BillPage Mon Oct 3 01:08:57 0500 2005
From: Bill Page
Date: Mon, 03 Oct 2005 01:08:57 0500
Subject: (new) substituting for an operator in a sum does not apply the
 summation algorithms
MessageID: <address@hidden>


Update of bug #9217 (project axiom):

 Status: None => transferred
 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$InnerPolySum is never called, of course. A general
Original Savannah bug 9217
Summary:
Although axiom can evaluate this sum, it does not.
Example of code trigerring the bug:
\begin{axiom}
f := operator 'f
sum(f(i),i=a..b)
eval(%,f,x+>x)
\end{axiom}
Internal Cause
first the sum is evaluated. Since the argument 'f(x)' is not a polynomial
or rational function, using first iidsum, than idsum of COMBF. Afterwards
the substitution is performed. Now the sum has the internal format
'%defsum [%A, %A, i, a, b]', which is again evaluated with iidsum and idsum of
COMBF. The function 'sum$InnerPolySum' is never called, of course. A general
??changed:
the time to check) => 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)


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