[Maxima-bugs] [ maxima-Bugs-3006875 ] ldefint() integration seems to be not correct

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Bugs item #3006875, was opened at 2010-05-25 17:55
Message generated for change (Comment added) made by aleckalinin
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: akalinin (aleckalinin)
Assigned to: Nobody/Anonymous (nobody)
Summary: ldefint() integration seems to be not correct

Initial Comment:
The ldefint() integration seems to be not correct. I compared Maxima results with Maple results. I tried to integrate "Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);" function and I got three strange results in Maxima:
1. Too many terms in sum after integration.
2. Some terms have strange "false" factor in numerator.
3. Several terms have the singularity 1/epsilon, epsilon -> 0.

The Maple integration produces less terms and no 1/epsilon singularity. Please, see attachments for details. I put the Maxima "false" strange term and singular term in double bar.


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Comment By: akalinin (aleckalinin)
Date: 2010-05-26 14:42

Message:
Some additional information. I tried to use integrate(...) instead of
ldefint(...) and got the incorrect results. The coefficient a1 change the
behavior of the integral:

--- Maxima script ---
logexpand : all;
logarc : true;

assume(epsilon > 0);
assume(a1 > 0);
assume(a1 - 2.0 > 0);

kern1 : Lambda^4 / (Lambda^2 + epsilon * Lambda + epsilon^2 )^(5/2);
kern2 : Lambda^4 / (Lambda^2 + a1 * epsilon * Lambda + epsilon^2)^(5/2);

phi1 : integrate(kern1, Lambda);

phi2 : integrate(kern2, Lambda);
phi2 : subst(a1 = 1, phi2);

res : phi2 - phi1;
---

The res is not zero!

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Comment By: akalinin (aleckalinin)
Date: 2010-05-26 12:22

Message:
Thanks for comments.

Version of maxima:
Maxima version: 5.21.0
Maxima build date: 8:38 4/12/2010
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

About the divergence. It should be log(epsilon) but not 1/epsilon. And
after integration I manually separate this log(epsilon) term.

Without a1 coefficient Maxima works correct, see maxima-results2.pdf and
maxima-script2.mac in attachment. In this case both Maxima and Maple
produces the same results. But when the a1 term is present, Maxima produces
1/epsilon divergence. I think this is not right, because a1 term cannot
change the behavior of the integral. 

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Comment By: l_butler ()
Date: 2010-05-26 00:34

Message:
Hi, Thanks for the report. A few comments:

1. Rather than using expand, try ratsimp. This produces a relatively
compact expression. 

2. I can confirm there is a bug in Maxima's integral with v5.21.1: false
appears as a term. When a1=0, this term disappears.

3. If you look at your integrand, when epsilon=0 (a1 is irrelevant), you
are computing the integral of 1/x from 0 to QL, which diverges. From that,
one expects that the integral will have a singularity at epsilon=0. If
Maple doesn't produce such a result, this is a bug in Maple.

Please report your version of Maxima when filing a bug report. Just copy
the output of the 'build_info' command into your report.



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