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