Re: Very Strange Behaviour about something Very Simple

• To: mathgroup at smc.vnet.net
• Subject: [mg77138] Re: [mg77130] Very Strange Behaviour about something Very Simple
• From: "A. E. A. S. Evangelopoulos" <a.e.a.s.evangelopoulos at sms.ed.ac.uk>
• Date: Tue, 5 Jun 2007 06:23:20 -0400 (EDT)
• References: <10484442.1180954035728.JavaMail.root@eastrmwml15.mgt.cox.net>

```Thanks Andrzej and Bob, for getting back to me.

Bob:

Interestingly, the results with Version 5.2 for Windows are a bit different:

In:        eqn=8 R^3/(3 h)-h^2/3\[Equal](8 R^3+2 h^3-3 h^3)/(3 h)
Out:    -h^2/3 + (8*R^3)/(3*h) == (-h^3 + 8*R^3)/(3*h)

In:         Simplify[eqn]
Out:      True

In:         Together[eqn]
Out:      -h^2/3 + (8*R^3)/(3*h) == (-h^3 + 8*R^3)/(3*h)

In:         Expand[eqn]
Out:      -h^2/3 + (8*R^3)/(3*h) == (-h^3 + 8*R^3)/(3*h)

In:         Reduce[eqn, h]
Out:      True

In:         Eliminate[eqn, h]
Out:      True

Expand is especially strange, when the right hand side on its own,
expands perfectly well.

Thanks again,
Apostolos

Bob Hanlon wrote:
> Determining that it is an identity is easy enough
>
> \$Version
>
> 6.0 for Mac OS X x86 (32-bit) (April 20, 2007)
>
> eqn = 8 R^3/(3 h) - h^2/3 == (8 R^3 + 2 h^3 - 3 h^3)/(3 h);
>
> Simplify[eqn]
>
> True
>
> Together[eqn]
>
> True
>
> Expand[eqn]
>
> True
>
> Reduce[eqn, h]
>
> True
>
> Eliminate[eqn, h]
>
> True
>
>
> Bob Hanlon
>
> ---- "Apostolos E. A. S. Evangelopoulos" <a.e.a.evangelopoulos at sms.ed.ac.uk> wrote:
>
>> Hello all!
>>
>> The following results appear extremely weird and I shall definitely appreciate ideas about why this might be happening!
>>
>> I am asking for a solution of the following equation:
>> Solve[8R^3/(3h)-h^2/3\[Equal](8R^3+2h^3-3h^3)/(3h), h]
>> The result is {}, meaning -as far as I know- that there are no solutions.
>>
>> Equivalently, I ask for the following:
>> True &&8R^3/(3h)-h^2/3\[Equal](8R^3+2h^3-3h^3)/(3h),
>> and, instead of getting a `False' statement, which would be consistent with the previous output, I get the same line in equation form, i.e.
>> -h^2/3 + (8*R^3)/(3*h) == (-h^3 + 8*R^3)/(3*h),
>> meaning that -again as far as I know- there exists a finite number of particular vaules of R and h satisfying this equality.
>>
>> And here comes the incredible bit:
>>
>> Taking the right hand side of the above just one small step further and splitting the fraction into two, one easily observes that the above is an identity! Indeed, Mathematica will respond as follows (and correctly this time):
>>
>> Solve[8R^3/(3h)-h^2/3\[Equal]8R^3/(3h)-h^2/3, h]
>> Output: {{}}
>>
>> True && 8R^3/(3h) - h^2/3 == 8R^3/(3h) - h^2/3
>> Output: True
>>
>> Ultimately, in asking for a simplification of either of the two sides (even from much more complex but equivalent forms) Mathematica always gives the same output and verifies identity. But does this mean I always have to be so careful and simplify everything as much as I can before manipulating it at all!?
>>
>> What more can I say...
>>
>> I eagerly await your view on this!
>>
>> Cheers,
>> Apostolos
>>
>>
>
>

```

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