This is true of many problems in algebraic manipulation, but (a) there are
many problems we *don't* handle which are easy to handle with cheap
algorithms; (b) even algorithms which are asymptotically slow in the
general case are often fast enough for small or special cases; (c)
sometimes the user may be willing to wait for the correct answer.
Michal's particular case, for example, is easily handled with basic
interval arithmetic. (case (a))
Even without breakthroughs in algorithmic complexity, there is a lot we can
do.
-s
On Fri, Oct 18, 2013 at 2:48 PM, Henry Baker <hbaker1 at pipeline.com> wrote:
> The problem with such a request is that the questions quickly become
> undecidable or exceedingly expensive [O(2^2^n) or worse] to compute.
>
> Even something as simple as the theory of linear order can be doubly
> exponential in complexity.
>
> I believe that there is now serious money in awards for someone who
> comes up with good solutions to problems like these.
>
> At 01:49 AM 10/18/2013, =?ISO-8859-2?Q?Michal_Kvasni=E8ka?= wrote:
> >Hallo.
> >
> >I'm sorry I'm asking such a simple question, but is there a better
> >proposition tester than is()? The function is() is really poor. Let us
> >assume this case:
> >
> >assume(x>0,x<1,y>0,y<1);
> >is(x>0);
> >is(x+y>0);
> >is(x*y>0);
> >is(x+y<2);
> >is(x*y<1);
> >
> >The first three questions are correctly answered true, but the last
> >two questions are unknown. Is there a (automatic) way around such
> >obvious problems?
> >
> >Many thanks,
> >Michal
>
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