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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]
>
> Many thanks in advance,
>
> 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?

ADL


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