Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Nasser Abbasi Posts: 6,677 Registered: 2/7/05
Re: can your CAS help proving inequalities?
Posted: Mar 9, 2013 1:04 PM
 Plain Text Reply

On 3/9/2013 6:07 AM, A N Niel wrote:

>
> In Maple, the response
> {}
> means there is no solution, while the response
>
> (that is, no response) means no solution was found. A third
> possibility is where some solutions are shown, and then a disclaimer
> that some solutions may have been lost.
>
> What CAS did you use, and what does {} mean for it?
>

Mathematica. It has a special command called

"FindInstance[expr, vars]

finds an instance of vars that makes the statement expr be True.
gives results in the same form as Solve: if an instance exists,
and {} if it does not. "

http://reference.wolfram.com/mathematica/ref/FindInstance.html

So that is what I used:

-----------------------------
Remove["Global`*"]
r[a_, b_, c_, d_] := (a - c)*(a - d)*(b - c)*(b - d)
s[a_, b_, c_, d_] := (a + b)*(c + d) - 2*(a*b + c*d) -
Abs[(a - b)*(c - d)]
t[a_, b_, c_, d_] := (a + b)*(c + d) - 2*(a*b + c*d) +
Abs[(a - b)*(c - d)]
-----------------------------

and now

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

{}

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

{}

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

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

But I was not sure this qualifies as "proof" that is why I asked first.

--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

© The Math Forum at NCTM 1994-2018. All Rights Reserved.