       Re: How to assume that a function is positive?

• To: mathgroup at smc.vnet.net
• Subject: [mg114333] Re: How to assume that a function is positive?
• From: ADL <alberto.dilullo at tiscali.it>
• Date: Wed, 1 Dec 2010 02:12:29 -0500 (EST)
• References: <id2emr\$d88\$1@smc.vnet.net>

```On 30 Nov, 10:04, Sam Takoy <sam.ta... at yahoo.com> wrote:
> Hi,
>
> Who do I let Mathematica know that a function f is positive for all
> arguments? For example, how do I make the following work (I think my
> intention is clear):
>
> Assuming[f[x] > 0, (f[x + y]^2)^(1/2) // Simplify]
>
>
> Sam

This fact is even more puzzling after observing the following results:

Clear[f];

Simplify[Sqrt[f[x]^2], f[x] > 0]
Out[]= f[x]

Simplify[Sqrt[f[x]^2],  !f[x] < 0]
Out[]= f[x]

f/:f[_]>0=True;

Simplify[Sqrt[f[x]^2], f[x]>0]
Out[]= Sqrt[f[x] ^2]

f/:f[_]<0=False;

Simplify[Sqrt[f[x]^2],  !f[x] < 0]
Out[]= Sqrt[f[x] ^2]

In other terms, not only any way to impose the positivity of f appears
to fail, but it also *breaks* Mathematica (8) capability to perform
the simplifications!

Can anyone explain this behavior?