Hello list! I have already posted the following question to the Maxima mailing list [1], but I am not sure whether corresponding improvements should go into Sage or Maxima.
In Sage 5.4, when I enter solve(abs((x-1)/(x-5)) <= 1/3, x) I get the following DNF as 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]] This has two issues: The minor one is that as a Sage newbie, I was confused by the line containing 'solve_rat_ineq'. I the meantime I learned that this just seems to be a byproduct of a failed try to use this function (because solve_rat_ineq cannot deal with 'abs'). Maybe Sage should give something more explicit like "Failed to use solve_rat_ineq" instead, or not print the line at all? The main issue is that the result should be [[-1 <= x, x <= 2]] , where terms like '-6 != 0' are evaluated and the intervals are merged. I am a Sage newbie, just having browsed its code the first time, and I see that solve_rat_ineq is called by solve_ineq_univar in sage/symbolic/relation.py, which itself is called by solve_ineq. (Therefore I am CCing the relevant author Robert Marik.) If we had a function that eliminates the constant inequalities and (for the univariate case) merges the intervals, this function could be applied to the result of solve_ineq before returning. Would this be the correct way to fix this issue? By the way, I do not really understand which Maxima function generates the current result. According to the Maxima list thread, both 'to_poly_solve' and 'fourier_elim' do not generate the '-6 != 0' terms: Stavros Macrakis proposed: 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]) and Volker van Nek gave: load(fourier_elim); fourier_elim([abs((x-1)/(x-5))<=1/3],[x]); => [x = - 1] or [x = 2] or [x = 1] or [1 < x, x < 2] or [- 1 < x, x < 1] Best regards, Robert [1] http://thread.gmane.org/gmane.comp.mathematics.maxima.general/42727/ -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
