fourier_elim does not always return empty set as emptyset

Does this mean that Maxima is unable to handle arbitrary sets of polynomial
inequations? Is there software that can handle that?


On Wed, Mar 6, 2013 at 10:26 AM, Barton Willis <willisb at unk.edu> wrote:

>  Fourier elimination is only defined on sets of * linear  *inequations.
> But Maxima's Fourier code has a preprocessor that is able to convert *some
> *
> nonlinear inequations to linear inequations (it doesn't try all that
> hard). The pre-processor is unable to convert [x^2 < y , x^2 > y] to
> a linear form--in this case it simply returns the inequations unchanged.
> If you view Fourier elimination as a simplification, this behavior is
> consistent
> with other Maxima simplification functions--when no simplification is
> found, the input is returned. Programatically, this means that a calling
> function may need to check if Fourier elimination returns a triangularized
> systems of inequations--and that's not all that convenient.
>
> If your code calls Fourier elimination inside some code, I would suggest
> that it checks that the inputs are all linear inequations. If the inputs
> aren't
> linear, it's unlikely that Fouier elimination will return a triangularized
> systems of inequations.
>
>  --Barton (author of fourier_elimination)
>
>   ------------------------------
> *From:* maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu]
> on behalf of Cary Cherng [ccherng at gmail.com]
> *Sent:* Tuesday, March 05, 2013 19:19
> *To:* maxima at math.utexas.edu
> *Subject:* [Maxima] fourier_elim does not always return empty set as
> emptyset
>
>   (%i1) load(fourier_elim);
> (%i2) fourier_elim([x^2 < y , x^2 > y],[x,y]);
>                                   2            2
> (%o2)                    [- (y - x ) > 0, y - x  > 0]
>
>  The empty set should be displayed as emptset not  [- (y - x ) > 0, y - x
>  > 0].
>
>  Is this a bug in fourier_elim or a limitation in the underlying
> algorithm?
>