From: SourceForge.net <noreply@so...>  20070821 16:36:11

Bugs item #1778796, was opened at 20070821 09:36 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1778796&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: Open Resolution: None Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( (x^3+1)/(x^4 + 4*x + 1), 0, 1); Initial Comment: Maxima: 5.11.0 Lisp: SBCL 1.0.3 On the mailing list, I asked about a definite integral that seems to make Maxima hang. 8< (%i1) integrate( (x^3+1)/(x^4 + 4*x + 1), x); 4 log(x + 4 x + 1) (%o1)  4 (%i2) integrate( (x^3+1)/(x^4 + 4*x + 1), x, 0, 1); [... no output, sblc cpu usage at 87% ...]  Barton Willis replied and suggested to file a bug report. He said: > > To see in part what is going on, try this: > > (%i4) trace(?csign); > (%o4) [csign] > (%i5) integrate( (x^3+1)/(x^4 + 4*x + 1), x, 0, 1); > > > Yikes! all kinds of junk! > > Also try integrate((x^3+1)/(x^4 + 4*x + 1), x,a,b). > > I suppose that Maxima is struggling to show that the antiderivative > is continuous on [0,1]. But Maxima goes about it in just about the > worst of all possible ways. Maxima does know that x^4 + 4*x + 1 is > positive > for x in [0,1], so it should be able to determine that > log(x^4 + 4*x + 1) is continuous on [0,1]. > > (%i1) assume(x >= 0, x<=1); > (%o1) [x>=0,x<=1] > (%i2) sign(x^4 + 4*x + 1); > (%o2) pos  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1778796&group_id=4933 