#2783 fourier_elim and "domain : complex"

[Robert Pollak]

See the following commands:

(%i1) load(fourier_elim);
(%i2) fourier_elim((x-1)/(x-5) <= 1/3,[x]);
(%o2) [x=-1] or [-1<x,x<5]
(%i3) domain : complex;
(%i4) fourier_elim((x-1)/(x-5) <= 1/3,[x]);
(%o4) [x=-1,-6#0] or [-1<x,x<5]

In the complex case, should fourier_elim compute this interval solution or should it give some kind of error when dealing with inequalities?

Also, the inequality "-6#0" is redundant and should not be generated.

(Context: https://groups.google.com/forum/#!topic/sage-devel/QLEFLgkuXRg)

[Rupert Swarbrick]

My thoughts:

• Setting domain to complex doesn't affect all the calculations that Maxima does (that's an empirical fact, not something about which I have strong opinions either way).

• Fourier elimination doesn't really make sense with complex numbers. Indeed, you write (x-1)/(x-5) <= 1/3. What does that mean if x is not real?

• There aren't any functions (I don't think) that call fourier_elim "behind the scenes". So I don't think the user should be surprised if, after he or she types "fourier_elim" and some inequalities, Maxima does Fourier elimination based on those inequalities.

[Barton Willis]

A simple fix is to set domain to true at the top level of fourier_elim.

[Barton Willis]

This was fixed by Commit [a0e80d]

(%i1) load(fourier_elim);
(%o1)
    C:/Users/Barton/maxima-git/code/src/../share/fourier_elim/fourier_elim.lisp
(%i2) block([domain : complex], fourier_elim((x-1)/(x-5) <= 1/3,[x]));
(%o2)                    [x = - 1] or [- 1 < x, x < 5]
(%i3) build_info();
(%o3)
Maxima version: "5.45post"
Maxima build date: "2021-06-11 05:57:06"
Host type: "unknown"
Lisp implementation type: "SBCL"
Lisp implementation version: "2.0.0"
User dir: "C:/Users/Barton/maxima"
Temp dir: "C:/Users/Barton/AppData/Local/Temp"
Object dir: "C:/Users/Barton/maxima/binary/5_45post/sbcl/2_0_0"
Frontend: false