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[Maxima-bugs] [ maxima-Bugs-1582625 ] integrate(t^2*log(t)/((t^2-1)*(t^4+1)), t, 0, 1) wrong?
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From: SourceForge.net <no...@so...> - 2006-11-05 02:53:46
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Bugs item #1582625, was opened at 2006-10-23 00:22 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1582625&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core - Integration Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(t^2*log(t)/((t^2-1)*(t^4+1)), t, 0, 1) wrong? Initial Comment: Symbolic integration seems to return an incorrect result: (%i1) integrate(t^2*log(t)/((t^2-1)*(t^4+1)), t, 0, 1); (sqrt(2) + 1) %pi (%o1) ------------------ 16 sqrt(2) (%i2) float(%); (%o2) 1.053029287545515 (%i3) romberg(t^2*log(t)/((t^2-1)*(t^4+1)), t, 0.0000001, 0.9999999); (%o3) 0.1806718095951 (%i4) float(%pi^2/(16*(2+sqrt(2)))); (%o4) 0.18067126259065 ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-11-04 21:53 Message: Logged In: YES user_id=28849 Fixed in defint.lisp as suggested. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-11-03 16:40 Message: Logged In: YES user_id=28849 The issue appears to be in log-imag-0-2%pi. Some of the poles are of the form (-1)^(1/4) or sqrt(-%i). The call to simplify %plog(pole) doesn't actually simplify and the noun form is returned (I think). If we replace (defun log-imag-0-2%pi (x) (let ((plog (simplify ((%plog) ,x)))) with (defun log-imag-0-2%pi (x) (let ((plog (simplify ($rectform `((%plog) ,x))))) maxima returns -(sqrt(2)-2)*%pi^2/32 which is .1806712625906549, which corresponds pretty well with the numerical result from romberg and quad_qags. The test suite runs fine with this change. I think the real problem is in the simplifier for plog, but I'm not too motivated in fixing that. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-10-23 13:57 Message: Logged In: YES user_id=28849 Maxima uses the substitution t = exp(-y) to change the integral from 0 to 1 to 0 to inf. Then it uses its routine to handle this infinite integral by converting it to an integral from minf to inf, because the integrand is even. Finally, it uses rectzto%pi2 to integrate this final integrand. rectzto%pi2 needs to find the poles of the denominator. I'm guessing it's getting that wrong. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1582625&group_id=4933 |