On Monday, July 1, 2013 5:37:02 AM UTC-4, Robert Pollak wrote:
>
> 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]]
>
>
>
> 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.
>
>
As you see in your examples below, to_poly_solve and fourier_elim in Maxima
simply don't return their information like that, they return them as a
union of open intervals and points. It would be possible to try to merge
those intervals, but likely at a large computational cost (since a generic
solution probably won't piece together so nicely). So I don't know whether
it would be worth it to try to do that.
> 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?
>
>
Presumably, yes.
> 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:
>
>
sage: F = abs((2*x-2)/(x-5)) <= 2/3
sage: F0 = [F._maxima_()]
sage: F0
[2*abs(x-1)/abs(x-5)<=2/3]
sage: F0[0]
2*abs(x-1)/abs(x-5)<=2/3
sage: F0[0].parent()
Maxima_lib
sage: F0[0].parent().fourier_elim(F0,[x])
[x=-1,-6#0,-6#0]or[x=-1,-6#0,-6#0,-6#0]or[x=-1,-6#0,-6#0]or[x=-1,-6#0,-6#0,-6#0]or[x=2,-3#0,-3#0]or[x=2,-3#0,-3#0,-3#0]or[x=2,-3#0,-3#0]or[x=2,-3#0,-3#0,-3#0]or[x=1]or[1<x,x<2]or[-1<x,x<1]
which is a Maxima object, and that is what generates it. But I have
trouble getting this to happen in the Maxima console.
(%i5) g:2*abs(x-1)/abs(x-5)<=2/3;
2 abs(x - 1) 2
(%o5) ------------ <= -
abs(x - 5) 3
(%i6) fourier_elim(g,[x]);
(%o6) [x = - 1] or [x = 2] or [x = 1] or [1 < x, x < 2] or [- 1 < x, x < 1]
(%i7) fourier_elim([g],[x]);
(%o7) [x = - 1] or [x = 2] or [x = 1] or [1 < x, x < 2] or [- 1 < x, x < 1]
I feel like this might have something to do with the fact we're using the
binary ECL interface, maybe?
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