I recognize that it is the empty set described in a different way. Is there
a reason why it can't always describe the empty set as [ ] ?
The question I am having is how do I tell if it is the empty set for more
complicated inputs? For example, consider setting t1 and t2 to large
polynomials computed somehow. Then the following can give an output that is
quite large and it is impossible to tell if it is the empty set. Here we
know it should be the empty set because of the trivial inequalities given
as inputs. But what if the inputs are something meaningful and realistic?
sage: g1,g2 = var('g1,g2')
sage: t1 = large polynomial
sage: t2 = large polynomial
sage: solve_ineq([t1 <= t2 , t1 > t2],[g1,g2])
# output that is large and impossible to tell visually that it is the empty
set
On Monday, December 3, 2012 9:05:57 PM UTC-8, P Purkayastha wrote:
>
> On 12/04/2012 08:51 AM, Cary Cherng wrote:
> > In the below why does solve_ineq called with the inequalities t1 <= t2 ,
> > t1 > t2 not return [ ], but the other invocations of solve_ineq return
> > the empty set as [ ] ?
> >
> > sage: g1,g2 = var('g1,g2')
> > sage: t1 = g1^2*g2^2
> > sage: t2 = g1^2*g2
> > sage: solve_ineq([t1 <= t2 , t1 > t2],[g1,g2])
> > [[g1 == 0, 1 < g2, 0 != 0], [g1 == 0, g2 < 0, 0 != 0]]
> > sage: solve_ineq([t1 < t2 , t1 > t2],[g1,g2])
> > []
> >
> > sage: s1 = g2^2
> > sage: s2 = g2
> > sage: solve_ineq([s1 <= s2 , s1 > s2],[g1,g2])
> > []
> >
>
> You have to consider what is in the output. Both the answers contain "0
> != 0", so essentially none of the answers are feasible since "0 != 0" is
> always false.
>
>
>
>
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