#2804 solve_rat_ineq includes non-solution

[kcrisman]

Should this solution include x = -3?

Maxima 5.33.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
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) load("solve_rat_ineq"); 
(%o1) /Users/.../sage/local/share/maxima/5.33.0/share/solve\
_rat_ineq/solve_rat_ineq.mac
(%i2) solve_rat_ineq((x^2-9)/(x-3) >= 0);
(%o2)                            [[x >= - 3]]

I understand that

(%i6) x^2/x;
(%o6)                                  x

so maybe this is intended behavior, but maybe solve_rat_ineq shouldn't do any simplifications like this - I hope I haven't asked this question before, years ago...

Downstream at http://ask.sagemath.org/question/23837/

[kcrisman]

That is, should it include x=3?

[Volker van Nek]

Actually, this is intended behaviour. Both solve and algsys behave the same:

(%i1) algsys([x^2/x],[x]);
(%o1) [[x = 0]]
(%i2) solve(x^2/x);
(%o2) [x = 0]

The inequality is fullratsimplified just right in the beginning. So if we could identify the discontinuities before simplifying them away, we could use a mechanism which is already inherent in solve_rat_ineq to clean out these discontinuities.

But I don't see a quick solution to that problem.