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Re: Inequality
On 10 Oct 2011, at 10:25, ff mm wrote:
>
> Thank a lot
> If I can use functions to judge the inequality ture directly
>
>
>
>
I assume that by "directly" you mean something like
Assuming[assumptions,FullSimplify[inequalities]] returning True. This is
what works in many simpler cases but not in the one you posted. At this
time this is too hard a problem for FullSimplify or any other function
in Mathematica (and I suspect other similar programs). Firstly, the
problem has to be reduced to one involving analytic functions of one
variable and this needs a small mathematical trick which I don't think a
computer program is likely to attempt without human help (though it
might be possible to implement this sort of heuristics). Secondly, the
ability to solve such inequalities depends on mathematical techniques
that are only used by Reduce (and, in version 8, by Solve) but not by
FullSimplify. I believe that the reason for this is that Reduce and
Solve are "solvers" and FullSimplify are simplifiers, and while their
areas of applicability overlap they do not coincide. In particular,
FullSimplify works by trying to reduce an expression to a "simpler form"
"step by step" but the methods needed to solve problems do not fit into
this sort of pattern.
Of course, it is quite possible that in the future FullSimplify will be
able to solve this problem and many others "directly" - but I am sure
there will always remain problems of this and other kinds that will
first require intelligent human intervention before Mathematica can be
usefully applied to them.
Andrzej
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