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Topic: can your CAS help proving inequalities?
Replies: 19   Last Post: Mar 11, 2013 12:00 PM

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Nasser Abbasi

Posts: 5,688
Registered: 2/7/05
Re: can your CAS help proving inequalities?
Posted: Mar 10, 2013 3:27 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 3/10/2013 11:57 AM, clicliclic@freenet.de wrote:

>
> Since the Mathematica variables are complex by default, they must here
> perhaps be explicitly restricted to real.


Sure.

------------
FindInstance[
Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c,
d}, Reals]

FindInstance[
Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c,

d}, Reals]
FindInstance[
Min[t[a, b, c, d], t[a, c, b, d], t[a, d, c, b]] > 0, {a, b, c,
d}, Reals]
-------------------

{}
{}
{}
--------------------

> Judging form the "Notes On
> Internal Implementation" it looks like Mathematica's Reduce[] might be
> able to do reduce such inequalities: among other techniques, it fields
> cylindrical algebraic decomposition (CAD).
>
> Martin.
>


yes:

---------------------
Reduce[Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c,
d}, Reals]

Reduce[Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c,
d}, Reals]

Reduce[Min[t[a, b, c, d], t[a, c, b, d], t[a, d, c, b]] > 0, {a, b, c,
d}, Reals]
------------------------
False
False
False
-------------

--Nasser



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