From: SourceForge.net <no...@so...> - 2011-03-15 20:11:52
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Bugs item #3211975, was opened at 2011-03-14 16:38 Message generated for change (Settings changed) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3211975&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: https://www.google.com/accounts () Assigned to: Nobody/Anonymous (nobody) Summary: Integral shouldn't be zero, but Maxima says it is Initial Comment: The following behavior leads to some weird results. In particular, if one plots cos(w+T)/(1+e*cos(T))^2 for various 0<e<1 and various w, it becomes clear that the answer shouldn't be zero. This is also tracked at http://trac.sagemath.org/sage_trac/ticket/8728 Maxima 5.23.2 http://maxima.sourceforge.net using Lisp SBCL 1.0.24 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) assume(1-e^2>0); 2 (%o1) [e < 1] (%i3) integrate(cos(w+T)/(1+e*cos(T))^2,T,0,2*%pi); (%o3) 0 (%i4) integrate(cos(w+T)/(1+.5*cos(T))^2,T,0,2*%pi); rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.0625 by 1/16 = 0.0625 (%o4) 0 (%i5) integrate(cos(.5+T)/(1+.25*cos(T))^2,T,0,2*%pi); rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced -0.5 by -1/2 = -0.5 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.015625 by 1/64 = 0.015625 rat: replaced 0.5 by 1/2 = 0.5 (%o5) 0 (%i6) keepfloat:True; (%o6) True (%i7) integrate(cos(.5+T)/(1+.25*cos(T))^2,T,0,2*%pi); Maxima encountered a Lisp error: The value 0.0625 is not of type FIXNUM. Automatically continuing. To enable the Lisp debugger set *debugger-hook* to nil. ---------------------------------------------------------------------- >Comment By: Dan Gildea (dgildea) Date: 2011-03-15 16:11 Message: Fixed in defint.lisp rev 1.86. However, lisp error with keepfloat:true is still present. (%i5) integrate(cos(w+T)/(1+(1/2)*cos(T))^2,T,0,2*%pi); (%o5) -8*%pi*cos(w)/3^(3/2) (%i4) integrate(cos(w+T)/(1+.5*cos(T))^2,T,0,2*%pi); rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.0625 by 1/16 = 0.0625 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 1.0 by 1/1 = 1.0 rat: replaced 0.25 by 1/4 = 0.25 rat: replaced 0.5 by 1/2 = 0.5 rat: replaced 0.0625 by 1/16 = 0.0625 (%o4) -8*%pi*cos(w)/3^(3/2) (%i6) integrate(cos(w+T)/(1+.5*cos(T))^2,T,0,2*%pi),keepfloat:true; Maxima encountered a Lisp error: Type-error in KERNEL::OBJECT-NOT-FIXNUM-ERROR-HANDLER: 0.25 is not of type FIXNUM Automatically continuing. To enable the Lisp debugger set *debugger-hook* to nil. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3211975&group_id=4933 |