Interval arithmetic seems to be more powerful than either of the current
assumptions systems in the case of real variables. I've heard people
mention this topic on the listhost before. Is there any past
attempt/knowledge on this subject?
On Sat, Feb 18, 2012 at 9:51 AM, krastanov.ste...@gmail.com <
krastanov.ste...@gmail.com> wrote:
> It seems to me that the assumption system is a better place to put all
> this. I may be wrong but I was left with the impression that it is
> meant to replace all the is_something stuff.
>
> On 18 February 2012 07:37, Nathan Alison <nathan.f.ali...@gmail.com>
> wrote:
> > It would be nice if we could have variables take an interval as an input
> > argument, to replace or augment the current system of "is_something"
> flags.
> >
> > Say,
> >
> >>>> x = Symbol('x', domain=Interval(0, oo))
> >>>> x.is_positive
> > True
> >>>> x.is_real
> > True
> >>>> x.is_bounded
> > False
> >
> > The variable x would carry around its interval, and we could use interval
> > arithmetic on functions of variables to find the interval of an
> expression:
> >
> >>>> x = Symbol('x', domain=Interval(-1, 1))
> >>>> y = Symbol('y', domain=Interval(0, 2))
> >>>> (x+y).domain
> > Interval(-1, 3)
> >
> > Currently (I think), there's no way to specify a range that a symbol can
> > take to this extent. Hopefully, notation like this would simplify things
> > like solving equations within a bounded domain, perhaps.
> >
> > If we want to be really ambitious, since an Interval is simply a type of
> > set, we can extend this notation to support arbitrary sets, though
> > specifying a symbol to be in the set of Reals would not add any extra
> > functionality...
> >
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