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Re: Mathematica Question


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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