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Re: How to assume that a function is positive?

• To: mathgroup at smc.vnet.net
• Subject: [mg114359] Re: How to assume that a function is positive?
• From: Valeri Astanoff <astanoff at gmail.com>
• Date: Thu, 2 Dec 2010 05:38:38 -0500 (EST)
• References: <id2emr$d88$1@smc.vnet.net> <id4sff$cbo$1@smc.vnet.net>

On Dec 1, 8:11 am, "Kevin J. McCann" <Kevin.McC... at umbc.edu> wrote:
> How about
>
> (f[x + y]^2)^(1/2)//PowerExpand
>
> Kevin
>
> On 11/30/2010 4:04 AM, Sam Takoy 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- Hide quoted text -
>
> - Show quoted text -


Sometimes PowerExpand doesn't suffice :

In[1]:= pos[fun_, ex_] := And @@ (fun[#] > 0 & /@
 (Identity @@@ Extract[ex, Position[ex, fun[__]] ]) )

In[2]:= z = (Abs@f[x + y]^2)^(1/2) + (f[x]^2)^(1/2);

In[3]:= Assuming[pos[f, z], z // Simplify]

Out[3]= f[x] + f[x + y]


In[4]:= z // PowerExpand

Out[4]= Abs[f[x + y]] + f[x]

--
Valeri