[Maxima-bugs] [ maxima-Bugs-657382 ] defint/limit infinite loop

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Bugs item #657382, was opened at 2002-12-21 20:20
Message generated for change (Comment added) made by rtoy
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 4
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: defint/limit infinite loop

Initial Comment:
integrate(1/(x^5-1),x,1,inf) appears to get into an infinite 
loop inside $limit (over 4 hours CPU).

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>Comment By: Raymond Toy (rtoy)
Date: 2007-06-19 13:27

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If IN-INTERVAL in defint.lisp is slightly modified to use ASK-GREAT
instead of ASK-GREATEQ, where ASK-GREAT checks if x > y instead of x >= y,
then maxima quickly says the integral is divergent.  I think this is
correct since 1/(x^5-1) has a partial fraction expansion of 1/5/(x-1) +
<stuff>.

Do not know if this change is the correct change or not.

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Comment By: Raymond Toy (rtoy)
Date: 2007-06-13 14:31

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FWIW, this still happens in 5.12 cvs.  

What's happening is that maxima has computed the antiderivative correctly
and is now trying to carefully substitute in the limits of integration to
make sure everything is on the right sheet.  This is basically done in
take-principal and intsubs.

I don't understand why maxima does the limit essentially twice like
limit(anti,x,1+eps,plus) - limit(anti,x,1-eps,minus).  This seems to be
where maxima is getting stuck.  If it were to finish, maxima would then go
and take the limit as eps goes to zero from above.

Perhaps if the pole is at one of the limits of integration as it is here,
maxima should do something else?  I think the current code assumes the pole
is within the integration interval.

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Comment By: Stavros Macrakis (macrakis)
Date: 2002-12-21 20:21

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Sorry,. I forgot to mention that this is under 5.5 
GCL/Windows 2000.

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