# [Maxima] Issue with solve_rat_ineq

Volker van Nek volkervannek at googlemail.com
Sun Nov 1 13:13:17 CST 2009

```Hello Sergio and Robert,

please excuse my late answer. I was out of office for a couple of days.

Thank you for finding bugs and especially Robert for proposing a fix.
Your proposed fix compared to the actual version helped me to see where
the errors come from. The 3 lines you want to change I already changed
in the past and marked the changes as a bug fix. Obviously I made it
worse than better.

As you described below problems arise when the inequality is checked in
the intervals (minf, x_1) and (x_last, inf). In case that algsys finds
floating point solutions for the corresponding equation the point of
checking must be far enough away from x_1 resp. x_last. A distance of
1.0 might be too close. It might happen that the left and right hand
side of the inequality do not vary within the floating point accuracy.
As this can also happen in "inner" intervals I would like to revise the
process of checking for all intervals in a way that always an
appropriate accuracy is used. I will do that next week.

Thank you and best regards
Volker van Nek
(the author of solve_rat_ineq)

Am Dienstag, den 20.10.2009, 15:36 +0000 schrieb Robert Marik:
> sergio rossi <arianefour <at> gmail.com> writes:
>
> >
> >
> > Hi,
> >
> > I tried the following in Maxima 5.19.2 and it doesn't seem to work:
> >
> >
> > (%o1)
> >     C:/PROGRA~1/MAXIMA~1.2/share/maxima/5.19.2/share/contrib/solve_rat_ineq.mac
> > (%i2) solve_rat_ineq((2*x-1)/(2*x*(x^2+1))>0);
> > Division by 0
> > #0: solve_rat_ineq(ineq=(2*x-1)/(2*x*(x^2+1)) > 0)(solve_rat_ineq.mac line 87)
> >  -- an error.  To debug this try debugmode(true);
> >
> > Maybe a bug? Thanks,
> >
>
>
> Hello, I found another bug in solve_rat_ineq. See the bug report
> http://sourceforge.net/tracker/?func=detail&aid=2882408&group_id=4933&atid=104933
> for description what happens and try to use attached fixed solve_rat_ineq.mac
> file. I cannot test it now against your inequality, but I hope that it will
> work. Maxima is trying to test if the ineqauality is valid on the interval
> (-infinity, 0) and because of minor bug in the definition, x=0 is used for this
> testing. It fails, of course ....
>
> This fix solves also bug  2636628 "solve_rat_ineq doesnt find all soloutions"
> https://sourceforge.net/tracker/index.php?
> func=detail&aid=2636628&group_id=4933&atid=104933
>
> If any of the developers is interested, please confirm this bug and that the
> fixed file solve_rat_ineq.mac attached to bugreport to bug "solve_rat_ineq
> returns false answers"  No 2882408
> http://sourceforge.net/tracker/?
> func=detail&aid=2882408&group_id=4933&atid=104933
>
> Works and could be accepted for future versions of Maxima. Many thanks.
> Robert Marik
>
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```