Stavros Macrakis <macrakis <at> alum.mit.edu> writes:
>
> >
>
> The simple solution is assume(%e > 2.718, %e < 2.719) (to appropriate
> precision, of course).
>
> The problem is that, though Compar is smart enough to make simple
> deductions from this like is(%e*100 < 300), it can't make more
> complicated ones like is(%e^2 < 10).
I think this is a great limitation.
Perhaps it would'nt be very difficult to assert %e^2 < 10 (or things like
that) from assume(%e > 2.718, %e < 2.719), a very usefull tool for this purpose
is an easy test (or a database) to proof that a function is increasing:
So that a/b < e < a'/b' and f(x) increasing then
f(a/b) < f(e) < f(a'/b').
There are a lot of cases in which is evident that f is increasing, so I think
this can paid the effort, a good ratio power/cost.
It looks like that there is a strong need of an easy test for a function to
be increasing, I think this can be a first a useful first step to avoid the
above limitations.
Miguel.