Fortunately, Maxima *does* have a package that solves your equation.
load(to_poly_solve)$
%solve(abs((x-1)/(x-5))<=1/3,x)
=>
%union([-1<x,x<1],[1<x,x<2],[x=-1],[x=1],[x=2])
This is still not ideal -- the various cases come down do -1 <= x, x <=2 --
but still, better than what you had.
-s
On Fri, Jun 28, 2013 at 12:25 PM, Robert Pollak <robert.pollak at jku.at>wrote:
> Am 28.06.2013 15:35, schrieb Stavros Macrakis:
> > There seems to be a typo in your example -- it won't parse. I tried
> > ineq:... instead of ineq=..., and tried removing ineq=, but that yields
> > an error from solve_rat_ineq. Tested in Maxima 5.28.0 and 5.30.0 / SBCL
> > / OSX / wxMaxima. Also, "==" (in your output) is not a standard Maxima
> > operator (does a newer version of solve_rat_ineq define it?).
> >
> > * What is the exact input you used?
> > * What is the version of Maxima you used?
> > * Are you using the version of solve_rat_ineq that came with Maxima, or
> > some other version?
> >
> > Complete and reproducible problem reports help us help you.
>
> Sure. I am sorry for having posed my question in such a bad form. The
> reason is that I am not using Maxima directly, but via Sage 5.4 instead
> (which says maxima.version() = 5.26.0).
>
> In Sage, when I enter
>
> solve(abs((x-1)/(x-5)) <= 1/3, x)
>
> I get the output
>
> #0: solve_rat_ineq(ineq=abs(x-1)/abs(x-5) <= 1/3)
> [[x == -1, -6 != 0, -6 != 0], [x == -1, -6 != 0, -6 != 0, -6 != 0], [x
> == -1, -6 != 0, -6 != 0], [x == -1, -6 != 0, -6 != 0, -6 != 0], [x == 2,
> -3 != 0, -3 != 0], [x == 2, -3 != 0, -3 != 0, -3 != 0], [x == 2, -3 !=
> 0, -3 != 0], [x == 2, -3 != 0, -3 != 0, -3 != 0], [x == 1], [1 < x, x
> < 2], [-1 < x, x < 1]]
>
> Since I did not know Maxima, I naively assumed this to be the log of the
> Maxima call.
>
> I have now installed Maxima-5.28.0-2. Unfortunately, as Volker has
> explained in the meantime, solve_rat_ineq cannot deal with 'abs':
>
> (%i1) load("solve_rat_ineq");
> (%o1)
>
> "C:/PROGRA~2/MAXIMA~1.0-2/share/maxima/5.28.0-2/share/solve_rat_ineq/solve_rat_ineq.mac"
> (%i2) solve_rat_ineq(abs(x-1)/abs(x-5) <= 1/3);
> solve_rat_ineq: abs(x-1)/abs(x-5)<=1/3 is not rational.
> #0: solve_rat_ineq(ineq=abs(x-1)/abs(x-5) <= 1/3)(solve_rat_ineq.mac
> line 59)
> -- an error. To debug this try: debugmode(true);
>
> So I assume that Sage does the case distinction for the 'abs' function
> by itself and calls Maxima on each case separately, like
>
> (%i5) solve_rat_ineq((x-1)/(x-5) <= 1/3);
> (%o5) [[x>=-1,x<5]]
>
> Therefore I will move my question over to the Sage people, since there
> seems to be no way to solve "abs(x-1)/abs(x-5) <= 1/3" in Maxima.
>
> Sorry again, and best regards,
> Robert
>
>