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I believe this is a problem with the Ubuntu package of maxima and/or gcl. There have been other reported issues with maxima and Ubuntu.
All of your examples work fine using other distributions of gcl. The examples also work fine with clisp and cmucl (the two that I tried).
And if you're worried about trusting maxima, don't. Check the results if you're not sure. :-)
Marking this as...
2009-11-20 00:52:27 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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It's not hung; it's just slow. With the adaptive plotter, maxima is trying very hard to refine the graph because every calculated point is not a number which makes maxima think some kind of discontinuity exists. I think this is a deficiency caused by gcl not quite supporting the needed feature to make it stop early.
Perhaps the level to which the adaptive plotter divides intervals should be...
2009-11-09 23:17:50 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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Isn't the limit 1? Let any x small enough, 1/x = n + e, where n is an integer and e < 1. Then floor(1/x) = n and x*floor(1/x) is n/(n+e) = 1 - e/(n+e). As n gets larger (and x gets smaller), this approaches 1.
Did I make a mistake?.
2009-11-09 17:17:50 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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Some simple tests show that just applying the rule tan(a)=sin(a)/cos(a) in same-sheet-subs is enough to fix this problem. I do not know why running trigsimp itself causes problems or why, as mitreude says, changing the order of the rules in trgsmp makes it work. Especially in this case since the expression is atan(tan(x+%pi/6)).
2009-11-09 15:19:08 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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Marking as pending/invalid.
2009-11-09 15:06:13 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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Please read the documentation of what realroots does:
Computes rational approximations of the real roots of the
polynomial or polynomial equation of one variable, to
within a tolerance of . Coefficients of or
If you want to know the exact roots, solve(x^3-2*x^2-x-1) will tell you. It appears there is no rational root.
2009-11-09 15:05:34 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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Just to note that trgsmp gets loaded because same-sheet-subs (in defint.lisp) calls trigsimp. The whole purpose (based on the comments) is to convert tan to sin/cos.
Also, on the first integrate, same-sheet-subs is called just once on atan(tan(x+%pi/6)) for x=0,%pi/3, and returns 4*%pi/3.
On the second integration, same-sheet-subs is called twice with the same arguments and same results.
2009-11-06 16:45:42 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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All of these work for me with 5.19post using gcl 2.6.8.
5.17.1 is pretty old.
Marking as pending/worksforme.
2009-11-06 16:35:19 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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This looks like a good solution. But is it too broad? Are there cases in trigint where triginverses set to $all would be wrong? Maybe a more careful solution that only sets it when we use the tan(x/2) substitution would be better?
I couldn't see any cases where it would produce incorrect results.
2009-11-05 17:55:28 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
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The issue is how maxima does plots. Basically, plots are done by uniformly sampling the x range. (Roughly). But when you want to do a log plot, the x range should be sampled logarithmically. When you specify logx, maxima knows to do the sampling correctly. That's why you get a nice smooth curve.
But with the preamble, maxima doesn't know you're producing a log plot, so it does the normal...
2009-11-05 01:31:25 UTC in Maxima -- GPL CAS based on DOE-MACSYMA
