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

 Messages: [ Previous | Next ]
 Nasser Abbasi Posts: 6,677 Registered: 2/7/05
Re: can your CAS help proving inequalities?
Posted: Mar 10, 2013 3:27 PM

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
>
> 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

Date Subject Author
3/8/13 clicliclic@freenet.de
3/8/13 Mate
3/9/13 clicliclic@freenet.de
3/9/13 clicliclic@freenet.de
3/8/13 Nasser Abbasi
3/9/13 Mate
3/9/13 Nasser Abbasi
3/9/13 A N Niel
3/9/13 Mate
3/10/13 A N Niel
3/10/13 Mate
3/9/13 Nasser Abbasi
3/10/13 Mate
3/10/13 Nasser Abbasi
3/10/13 Mate
3/10/13 clicliclic@freenet.de
3/10/13 Nasser Abbasi
3/11/13 Peter Pein
3/11/13 clicliclic@freenet.de
3/11/13 Peter Pein