Re: Mathematica Question

• To: mathgroup at smc.vnet.net
• Subject: [mg66373] Re: Mathematica Question
• From: Peter Pein <petsie at dordos.net>
• Date: Thu, 11 May 2006 02:14:36 -0400 (EDT)
• References: <e3shhl\$m39\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Bharat Bhole schrieb:
> Hello:
>
> Is there a way in Mathematica to check whether an algebraic expression is
> positive or negative, and a way to specify conditions on the variables in
> the expression? For example, is there a way to check whether x^2 is positive
> for any real x? I want to check this for a complicated
> expression...basically the sign of the second derivative of a function.
>
> Thank you very much for your help.
>
> Bharat.
>
>
Hi Bharat,

there are several ways:

Reduce[x^2 > 0, x \[Element] Reals]
--> x < 0 || x > 0

FullSimplify[%]
--> x != 0

FullSimplify[x^2 > 0, x \[Element] Reals]
--> x != 0

FullSimplify[ForAll[x, x \[Element] Reals, x^2 > 0]]
--> False

FullSimplify[ForAll[x, x \[Element] Reals, x^2 >= 0]]
--> True

hth,
Peter

```

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