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
2014-08-22
That is, should it include x=3?
Volker van Nek
2014-09-19
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.