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